Pioneer Affiliate Network for CTV/OTT/Advanced TV & DOOH

Affise

affise

As more and more brands have been launching their affiliate marketing programs, dozens of various tools and platforms have emerged to ease the task and boost the efficiency of marketing efforts. Such solutions are capable of solving most affiliate-related tasks, including searching for webmasters, providing them with materials, adding integrations, making payments, performing analytics, and more. is an affiliate marketing platform for the tourism industry with GMV over $1 billion and a multinational team. The platform connects over 100 trusted travel brands with clear statistics with 300k+ of inspired travel content creators and solo entrepreneurs from all over the world. Travelpayouts I've asked Ivan Baidin, Head of Travelpayouts, to elaborate on some important issues businesses face when launching an affiliate marketing program. What emerging trends do you see in the affiliate marketing market? How has it changed over the past couple of years? What were the main factors (like COVID, etc.)? Just a few years ago, it was really difficult and expensive to implement a fully functional affiliate program, but today affiliate marketing is no longer limited to big brands that can afford to invest $100k for the development of the program and a team. The market is now ready to offer software even for small brands—ranging from SaaS solutions, like Affise for about $1,000 a month, to advanced marketing platforms, like Travelpayouts, with payment only for actual results achieved. In terms of trends, affiliate marketing trends are not as important as global trends. Businesses either support them or become outsiders. One of the trends today is toward local travel and local service providers. Because of the accessibility of entry into affiliate marketing, even small local companies can effectively operate an affiliate program. The second trend has to do with the long-term changes on the market. Online shopping significantly and continues to grow. Consumers of goods and services make more purchases online than ever before. There are still people who buy airline tickets at an offline agency, but the potential reach of the audience that is willing to buy travel services online is now a lot wider than before. The number of online purchases has grown and is continuing to grow. Even with the easing of restrictions and the post-covid market recovery, people are staying online—it's convenient, fast and safe. Affiliate marketing is therefore a viable income source for content creators and businesses alike. has grown In my opinion, the most important global trend is More Focus on People, Make Brands Human. 84% of consumers prefer to be treated as a person and not a number. By creating memories, brands strengthen the personal connection between product and emotion which increases brand buy-in and conversions. Through partner marketing, brands can reach their target audiences without aggressive PPC advertising, but through influencers that they already trust. Since the business relies on trust between all participants in the process, I prefer to refer to it as partner marketing rather than affiliate marketing. Influencer marketing is on the rise these days. Can this tool be bundled with affiliate marketing, is this something common or unique now? Influencer marketing is getting extremely popular these days, whereas affiliate marketing is a way for businesses to reach thousands of influencers at once. Affiliates are influencers interested in offering your products and services to their audience. Unlike classic influencer marketing, where the brand pays for placement and coverage, with affiliate marketing you get placement, coverage and sales. Managing influencers isn't a walk in the park too as it takes a lot of time and paperwork. In affiliate marketing, partners promote your brand on their own—their motivation is to get a percentage of revenue from sales and a recommendation of a brand that they really love. For example, GetYourGuide—one of the most popular excursion search engines in the world—pays affiliates 9% of the cost of a tour. There are influencers of all scales, from local bloggers with an audience of a few thousand, to celebrities and opinion leaders. Through Travelpayouts, a travel brand can reach out to influencers with a combined reach of over 5,000,000 people. In your opinion, what types of businesses benefit from using affiliate marketing the most today, and how has that changed over time? The short answer is: virtually anyone who sells goods or services online. Obviously, these include services selling airline tickets, hotels, tours or car rentals, but there are also other types of businesses both outside and within travel. Here are just a few examples: E-commerce—the share of online purchases has increased significantly, to the UN; according Online education—also increased due to the COVID-19, to the World Economic Forum; according Legal services helping to get compensation for flight delays; SIM cards for travelers; Bank cards for travelers; and so on. There is also one common misconception, which is that if the structure of a business implies different margins for different goods and services (for example, one service generates income of 10%, and another just 1%), there is a fear that it is impossible to offer partners a solution. But there is a way out, if you don’t pay a % of the cost but share a portion of the income. EconomyBookings, for example, do this by sharing with partners 60% of their income rather than the cost of the service. What are the main issues that brands are facing when they deal with affiliate marketing? The first one is partners. Even having solved the technical problem, businesses face the issue of attracting partners. In this matter, the decision to connect to a network that already has a large pool of partners wins a lot. The second challenge is a transparent record of actions. The basic model is that the brand should account for all actions taken by the affiliate's audience, so correct and stable accounting is the cornerstone of affiliate marketing. No matter which technical solution you choose, the stability and transparency of accounting are important factors in developing the trust of bloggers. Third, there are violations by affiliates. Although the affiliate channel involves low risks—you only pay for results—affiliates can unintentionally or deliberately violate the rules. For example, buying PPC ads with brand requests, if this is prohibited. It is important to prescribe complete rules that take into account all the specifics and to monitor the execution of the rules. Or trust a service with an anti-fraud solution like Travelpayouts. Can you name some key mistakes brands make when they start working with the affiliate channel and scaling it? One of the common mistakes is setting too strict rules for traffic. A brand chooses its own types of traffic sources, and it can significantly reduce potential reach by setting excessively strict traffic rules. Everything that fits within the company's traffic policy should be allowed, and if something is controversial, it can always be handled by using prior approval. Another trivial but not uncommon mistake is starting an affiliate program and not investing in developing it further. Like any marketing channel, an affiliate program requires attention. Even though affiliates work with their own audiences and develop their own projects, your job is to help affiliates with their work, such as conducting training webinars, providing advanced tools, unique solutions for large affiliates, etc. Are there any new technology solutions that can solve these problems? Certainly. There are SaaS solutions like Affise, and platforms like Travelpayouts. The latter are solving all the issues with launching, developing, and operating. That doesn't mean a brand won't need to work with the channel at all, but of all the options available, it's probably the most efficient and easiest solution. For example, the Travelpayouts platform solves every basic point: Launch: no development required; Partners: no need to look for them on your own, there is an existing base; Growth: 10+ years of team expertise; Anti-fraud protection: artificial intelligence + automatic notifications of any anomalies. What is the main idea behind your First Digital Partnership Platform for Travel Brands? How does this work? Travelpayouts Digital Partnership Platform gives travel brands access to 300,000 travel influencers worldwide. You can reach new customers, pay in a single transaction. Our mission is simple—we help people travel more, show the world and earn money from it. We unite travel, experience, freedom, honesty, technology and money driven people and brands to benefit. The platform connects those who have an audience with those who have a product or service for that audience. This is the ultimate win-win story, where a brand gets sales and a creator of travel content earns money by offering relevant brand products or services to their audience. More than 300,000 travel content creators around the globe share their favorite travel brands and inspire travelers to get to know the world in a profitable and qualitative way. It benefits all: people get high-quality content and travel a lot; brands get a new channel to reach new audiences; and bloggers get a way to monetize their passion. What is your advice to those travel and non-travel brands that are starting their efforts in affiliate marketing? Launching an affiliate program is just the beginning of a long journey. And in order to get through it as efficiently as possible, you need to think about how you’re going to develop the program at the very beginning. There is also competition in affiliate marketing—big brands or older solutions are already on the market. And even if you have the resources to develop your own affiliate program, it's worth connecting to one or more platforms. These are not mutually exclusive options. Walking the path with a market expert is what will allow you to jumpstart in affiliate marketing.

"Affiliate Marketing is NO Longer Limited to Big Brands with Budgets over $100k" - Ivan Baidin 

Authors:
(1) Luyuan Peng, Acoustic Research Laboratory, National University of Singapore;
(2) Hari Vishnu, Acoustic Research Laboratory, National University of Singapore;
(3) Mandar Chitre, Acoustic Research Laboratory, National University of Singapore;
(4) Yuen Min Too, Acoustic Research Laboratory, National University of Singapore;
(5) Bharath Kalyan, Acoustic Research Laboratory, National University of Singapore;
(6) Rajat Mishra, Acoustic Research Laboratory, National University of Singapore. Table of Links I Introduction II Method III Datasets IV Experiments, Acknowledgment, and References II. METHOD We implement two different architectures. The first uses pretrained deep convolutional neural networks (DCNN) to extract features from the input images. The resulting feature map is then passed to an affine regressor consisting of dense neural layers to output a 7-dimensional pose vector estimates. The second architecture adds an additional LSTM layer between the DCNN and affine regressor to perform dimensionality reduction by assessing the spatial structure of the image. This is done by four LSTMs which parse the DCNN-output feature map in different directions starting at each of the four image corners to process the spatial trends, and compress it into lower-dimensional information which is easier processed by the affine regressor. The input images used in the training are rescaled to 256×256 pixels before cropping into a 224×224 feature input using centre cropping. To speed up training, the images are normalized by the mean and standard deviation of the images. The poses are also normalized to lie within [-1, 1]. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Luyuan Peng, Acoustic Research Laboratory, National University of Singapore; (2) Hari Vishnu, Acoustic Research Laboratory, National University of Singapore; (3) Mandar Chitre, Acoustic Research Laboratory, National University of Singapore; (4) Yuen Min Too, Acoustic Research Laboratory, National University of Singapore; (5) Bharath Kalyan, Acoustic Research Laboratory, National University of Singapore; (6) Rajat Mishra, Acoustic Research Laboratory, National University of Singapore. Authors: Authors: (1) Luyuan Peng, Acoustic Research Laboratory, National University of Singapore; (2) Hari Vishnu, Acoustic Research Laboratory, National University of Singapore; (3) Mandar Chitre, Acoustic Research Laboratory, National University of Singapore; (4) Yuen Min Too, Acoustic Research Laboratory, National University of Singapore; (5) Bharath Kalyan, Acoustic Research Laboratory, National University of Singapore; (6) Rajat Mishra, Acoustic Research Laboratory, National University of Singapore. Table of Links I Introduction I Introduction II Method II Method III Datasets III Datasets IV Experiments, Acknowledgment, and References IV Experiments, Acknowledgment, and References II. METHOD We implement two different architectures. The first uses pretrained deep convolutional neural networks (DCNN) to extract features from the input images. The resulting feature map is then passed to an affine regressor consisting of dense neural layers to output a 7-dimensional pose vector estimates. The second architecture adds an additional LSTM layer between the DCNN and affine regressor to perform dimensionality reduction by assessing the spatial structure of the image. This is done by four LSTMs which parse the DCNN-output feature map in different directions starting at each of the four image corners to process the spatial trends, and compress it into lower-dimensional information which is easier processed by the affine regressor. The input images used in the training are rescaled to 256×256 pixels before cropping into a 224×224 feature input using centre cropping. To speed up training, the images are normalized by the mean and standard deviation of the images. The poses are also normalized to lie within [-1, 1]. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Underwater Visual Localization Using Machine Learning and LSTM: Method

By Amanda Kavanagh While tech sectors like healthcare, climate tech and cybersecurity are urgently focused on retraining in AI, it’s not quite as important for other programmers. That’s according to Christian Rebernik, co-chief executive and co-founder of Tomorrow University of Applied Sciences, who reckons you don’t need to throw the baby out of the bath water, and ditch your expertise for AI. In an interview with the Financial Times, he makes this recommendation: “You can secure yourself, if you are a top-tier expert who can help teach AI in your field . . . [you can] earn from training models on data set created by you.” 3 high-paying roles to apply for today DevOps Engineer, Accenture Federal Services, Chantilly ($76,000 - $144,000)
Principal DevOps Engineer, Autodesk, TX ($141,400 - $228,800)
Staff/Sr. Staff DevOps Engineer, SciTec, Boulder ($93,000 - $137,000) The key is deep knowledge. As subject matter expertise really matters when it comes to creating the best prompts, once you’ve an understanding of prompt engineering, and experiment with AI tools in your day-to-day life, that may be enough for now. This frees programmers up to focus on the languages making waves in the coding community; here we’ll look at three of the newest and well-paid languages of the moment. Zig Created by Andrew Kelley in 2015, Zig is pitched as a general purpose language and as a modern alternative to C, but it’s still relatively obscure. In a Stack Overflow survey of 89,184 software developers across 185 countries, just 0.83% reported proficiency in Zig. However, the same survey also found that Zig developers command the highest median salaries on average. Median earnings of $103,000 may be pocket change to some in highly-paid AI roles, and it won’t put you in the top 10% of earners in the U.S. – you’ll need to be on $167,639 for that – but it’s the only programming language that hits six figures in the Stack Overflow survey. The next closest is Erlang ($99,492), F# ($99,492), Ruby ($98,522), and in fourth place, the former 2022 leader, Clojure ($96,381). Comparatively, the bottom four are: Visual Basic (.Net) with $65,000 median pay, MATLAB with $61,735, PHP at $58,899, and Dart, which commands the least at $55,862. Because Zig is compatible with C codebases, it may be readily incorporated with current projects, making it a solid option for systems development, embedded systems, game design, and scripting. Non-profit Zig boasts a vibrant contributor community where developers are invited to utilize it for personal open-source projects, allowing real-world problems to surface and be resolved in real-time. Its rarity makes it something of a risk, as you may have to plug and play, figuring out mistakes as you go. Depending on the pace in your current role, this may or may not be possible. But clearly, there can be salary gains if you can find a company that utilizes and values Zig. Finch Finch is the latest programming language from MIT, which was announced earlier this year. It aims to resolve the challenges associated with computing over-structured arrays. Finch does this by providing a programming model that unifies control flow and diverse data structures into a single representation that allows for co-optimization. Specifically, it automates the control flow to the data, freeing up performance engineers to experiment with many algorithms. MIT says that Finch is, to the best of its knowledge, the first programming language to support affine indexing or scatter/gather of sparse or structured operands, as well as if-conditions, early breaks, and multiple left hand sides over structured data. Early-adopters are praising the time-saving automatic specialization and smooth control flow, particularly in fields like image processing and scientific computing, where structured data is essential. Being a complete newbie, Finch doesn’t have a vast library of tools and frameworks to refer to, meaning it’s not really suitable for large-scale projects just yet. But if you’re a keen early-adopter, Finch is one to watch, and as the community expands, it may become a very valuable tool in the near future. Swift Apple’s Swift has been knocking around for a decade, but its next iteration – Swift 6 – is slated for release later this year. This is the first major update since Swift 5, five long years ago. This release expands upon the async/await, existentials, and macros capabilities that were first included in the Swift 5.x series. Apple director of languages and runtimes, Ted Kremenek says, “Swift’s safety, speed, and approachability, combined with built-in C and C++ interoperability, mean Swift is the best choice to succeed C++.” Meanwhile, forums and blogs are already advising programmers on how to migrate projects across, which is expected to be tricky for legacy codebases. 3 great tech jobs hiring now DevOps Engineer - Sports Technology, Electronic Arts, Orlando
Sr. DevOps Engineer - Store Frontend, hims & hers, San Francisco ($155,000 - $175,000)
Senior Engineer Fullstack (Java), GTT LLC, Chevy Chase The good news is there is clear demand for Swift programmers. According to jobs site Indeed, iOS developers and senior mobile developers are sought after in major companies all over the world, including Accenture, DataAnnotation, and Netflix. It’s widely-accepted that for a long, productive, and well-paid career in programming, developers must always move with the times. Ideally, your existing role will allow time for experimentation and upskilling, enabling you to explore these languages and integrate them into your projects. But if upskilling isn’t a priority in your workplace, it could be time to look for something new. Ready to find your next role in tech? Whether you want to pivot to AI or put your coding expertise to good use, visit the Hackernoon Job Board today By Amanda Kavanagh While tech sectors like healthcare, climate tech and cybersecurity are urgently focused on retraining in AI, it’s not quite as important for other programmers. That’s according to Christian Rebernik, co-chief executive and co-founder of Tomorrow University of Applied Sciences, who reckons you don’t need to throw the baby out of the bath water, and ditch your expertise for AI. In an interview with the Financial Times , he makes this recommendation: “You can secure yourself, if you are a top-tier expert who can help teach AI in your field . . . [you can] earn from training models on data set created by you.” Financial Times Financial Times 3 high-paying roles to apply for today 3 high-paying roles to apply for today DevOps Engineer, Accenture Federal Services, Chantilly ($76,000 - $144,000) Principal DevOps Engineer, Autodesk, TX ($141,400 - $228,800) Staff/Sr. Staff DevOps Engineer, SciTec, Boulder ($93,000 - $137,000) DevOps Engineer, Accenture Federal Services, Chantilly ($76,000 - $144,000) DevOps Engineer, Accenture Federal Services, Chantilly ($76,000 - $144,000) DevOps Engineer, Accenture Federal Services, Chantilly ($76,000 - $144,000) Principal DevOps Engineer, Autodesk, TX ($141,400 - $228,800) Principal DevOps Engineer, Autodesk, TX ($141,400 - $228,800) Principal DevOps Engineer, Autodesk, TX ($141,400 - $228,800) Staff/Sr. Staff DevOps Engineer, SciTec, Boulder ($93,000 - $137,000) Staff/Sr. Staff DevOps Engineer, SciTec, Boulder ($93,000 - $137,000) Staff/Sr. Staff DevOps Engineer, SciTec, Boulder ($93,000 - $137,000) The key is deep knowledge. As subject matter expertise really matters when it comes to creating the best prompts, once you’ve an understanding of prompt engineering, and experiment with AI tools in your day-to-day life, that may be enough for now. This frees programmers up to focus on the languages making waves in the coding community; here we’ll look at three of the newest and well-paid languages of the moment. Zig Zig Created by Andrew Kelley in 2015, Zig is pitched as a general purpose language and as a modern alternative to C, but it’s still relatively obscure. In a Stack Overflow survey of 89,184 software developers across 185 countries, just 0.83% reported proficiency in Zig. Stack Overflow survey Stack Overflow survey However, the same survey also found that Zig developers command the highest median salaries on average. Median earnings of $103,000 may be pocket change to some in highly-paid AI roles , and it won’t put you in the top 10% of earners in the U.S. – you’ll need to be on $167,639 for that – but it’s the only programming language that hits six figures in the Stack Overflow survey. highly-paid AI roles highly-paid AI roles The next closest is Erlang ($99,492), F# ($99,492), Ruby ($98,522), and in fourth place, the former 2022 leader, Clojure ($96,381). Comparatively, the bottom four are: Visual Basic (.Net) with $65,000 median pay, MATLAB with $61,735, PHP at $58,899, and Dart, which commands the least at $55,862. Because Zig is compatible with C codebases, it may be readily incorporated with current projects, making it a solid option for systems development, embedded systems, game design, and scripting. Non-profit Zig boasts a vibrant contributor community where developers are invited to utilize it for personal open-source projects, allowing real-world problems to surface and be resolved in real-time. vibrant contributor community vibrant contributor community Its rarity makes it something of a risk, as you may have to plug and play, figuring out mistakes as you go. Depending on the pace in your current role, this may or may not be possible. But clearly, there can be salary gains if you can find a company that utilizes and values Zig. company company Finch Finch Finch is the latest programming language from MIT, which was announced earlier this year. It aims to resolve the challenges associated with computing over-structured arrays. Finch Finch Finch does this by providing a programming model that unifies control flow and diverse data structures into a single representation that allows for co-optimization. Specifically, it automates the control flow to the data, freeing up performance engineers to experiment with many algorithms. MIT says that Finch is, to the best of its knowledge, the first programming language to support affine indexing or scatter/gather of sparse or structured operands, as well as if-conditions, early breaks, and multiple left hand sides over structured data. Early-adopters are praising the time-saving automatic specialization and smooth control flow, particularly in fields like image processing and scientific computing, where structured data is essential. Being a complete newbie, Finch doesn’t have a vast library of tools and frameworks to refer to, meaning it’s not really suitable for large-scale projects just yet. But if you’re a keen early-adopter, Finch is one to watch, and as the community expands, it may become a very valuable tool in the near future. Swift Apple’s Swift has been knocking around for a decade, but its next iteration – Swift 6 – is slated for release later this year. This is the first major update since Swift 5, five long years ago. This release expands upon the async/await, existentials, and macros capabilities that were first included in the Swift 5.x series. Apple director of languages and runtimes, Ted Kremenek says, “Swift’s safety, speed, and approachability, combined with built-in C and C++ interoperability, mean Swift is the best choice to succeed C++.” Meanwhile, forums and blogs are already advising programmers on how to migrate projects across, which is expected to be tricky for legacy codebases. 3 great tech jobs hiring now DevOps Engineer - Sports Technology, Electronic Arts, Orlando Sr. DevOps Engineer - Store Frontend, hims & hers, San Francisco ($155,000 - $175,000) Senior Engineer Fullstack (Java), GTT LLC, Chevy Chase DevOps Engineer - Sports Technology, Electronic Arts, Orlando DevOps Engineer - Sports Technology, Electronic Arts, Orlando DevOps Engineer - Sports Technology, Electronic Arts, Orlando Sr. DevOps Engineer - Store Frontend, hims & hers, San Francisco ($155,000 - $175,000) Sr. DevOps Engineer - Store Frontend, hims & hers, San Francisco ($155,000 - $175,000) Sr. DevOps Engineer - Store Frontend, hims & hers, San Francisco ($155,000 - $175,000) Senior Engineer Fullstack (Java), GTT LLC, Chevy Chase Senior Engineer Fullstack (Java), GTT LLC, Chevy Chase Senior Engineer Fullstack (Java), GTT LLC, Chevy Chase The good news is there is clear demand for Swift programmers. According to jobs site Indeed, iOS developers and senior mobile developers are sought after in major companies all over the world, including Accenture, DataAnnotation, and Netflix. It’s widely-accepted that for a long, productive, and well-paid career in programming, developers must always move with the times. Ideally, your existing role will allow time for experimentation and upskilling, enabling you to explore these languages and integrate them into your projects. But if upskilling isn’t a priority in your workplace, it could be time to look for something new. Ready to find your next role in tech? Whether you want to pivot to AI or put your coding expertise to good use, visit the Hackernoon Job Board today Ready to find your next role in tech? Whether you want to pivot to AI or put your coding expertise to good use, visit the Hackernoon Job Board today Ready to find your next role in tech? Whether you want to pivot to AI or put your coding expertise to good use, visit the Hackernoon Job Board today Ready to find your next role in tech? Whether you want to pivot to AI or put your coding expertise to good use, visit the Hackernoon Job Board today Ready to find your next role in tech? Whether you want to pivot to AI or put your coding expertise to good use, visit the Hackernoon Job Board today

3 High Paying Programming Languages Jobs On Developers’ Watchlists

ডেভেলপারদের ওয়াচলিস্টে 3টি উচ্চ অর্থপ্রদানকারী প্রোগ্রামিং ভাষার চাকরি

3 gut bezahlte Jobs im Bereich Programmiersprachen auf den Beobachtungslisten der Entwickler

3 trabajos de lenguajes de programación bien remunerados en las listas de vigilancia de desarrolladores

3 emplois bien rémunérés dans les langages de programmation sur les listes de surveillance des développeurs

डेवलपर्स की वॉचलिस्ट पर 3 उच्च भुगतान वाली प्रोग्रामिंग भाषा नौकरियां

開発者の注目リストに載っている高収入のプログラミング言語の仕事 3 つ

개발자 관심 목록에 있는 고임금 프로그래밍 언어 직업 3가지

3 empregos em linguagens de programação com altos salários nas listas de observação dos desenvolvedores

3 высокооплачиваемые вакансии в области языков программирования в списках разработчиков

Geliştiricilerin İzleme Listelerindeki Yüksek Ücretli 3 Programlama Dili İşi

3 công việc về ngôn ngữ lập trình được trả lương cao trong danh sách theo dõi của các nhà phát triển

开发人员关注的 3 个高薪编程语言职位

Authors:
(1) Kedan Li, University of Illinois at Urbana-Champaign;
(2) Min Jin Chong, University of Illinois at Urbana-Champaign;
(3) Jingen Liu, JD AI Research;
(4) David Forsyth, University of Illinois at Urbana-Champaign. Table of Links Abstract and Intro
Related Work
Proposed Method
Experiments
Conclusions and References 2. Related Work Image synthesis: Spatial transformer networks estimate geometric transformations using neural networks [23]. Subsequent work [28,39] shows how to warp one object to another. Warping can be used to produce images of rigid objects [26,30] and non-rigid objects (e.g., clothing) [17,12,45]. In contrast to prior work, we use multiple spatial warpers. Our warps must be combined into a single image, and our U-Net for producing this image follows trends in inpainting (methods that fill in missing portions of an image, see [48,31,50,49]). Han et al. [16,52] show inpainting methods can complete missing clothing items on people. In our work, we use FID∞ to quantitatively evaluate our method. This is based on the Frchet Inception Distance (FID) [18], a common metric in generative image modelling [5,54,29]. Chong et al. [9] recently showed that FID is biased; extrapolation removes the bias, to an unbiased score (FID∞). Generating clothed people: Zhu et al. [57] used a conditional GAN to generate images based on pose skeleton and text descriptions of garment. SwapNet [38] learns to transfer clothes from person A to person B by disentangling clothing and pose features. Hsiao et al. [20] learned a fashion model synthesis network using per-garment encodings to enable convenient minimal edit to specific items. In contrast, we warp products onto real model images. Shape matching underlies our method to match product to model. Tsiao et al. [19] built a shape embedding to enable matching between human body and well-fitting clothing items. Prior work estimated the shape of human body [4,27], clothing items [10,25] and both [35,40], through 2D images. The DensePose [1] descriptor helps modeling the deformation and shading of cloth and, therefore, has been adopted by recent work [36,13,47,51,7,52]. Virtual try-on (VTO) maps a product to a model image. VITON [17] uses a U-Net to generate a coarse synthesis and a mask on the model where the product is presented. A mapping from the product mask to the on-model mask is learned through Thin plate spline (TPS) transformation [3]. The learned mapping is applied on the product image to create a warp. Following their work, Wang et al. [45] improved the architecture using a Geometric Matching Module [39] to estimate the TPS transformations parameters directly from pairs of product image and target person. They train a separate refinement network to combine the warp and the target image. VTNFP [53] extends the work by incorporatiing body segments prediction and later works follow similar procedure [37,24,42,22,2]. However, TPS transformation fails to produce reasonable warps, due to the noisiness of generated masks in our dataset, as shown in Figure 6 right. Instead, we adopt affine transformations which we have found to be more robust to imperfections instead of TPS transformation. A group of following work extended the task to multi-pose. Warping-GAN [11] combined adversarial training with GMM, and generate post and texture separately using a two stage network. MG-VTON [12] further refine the generation method using a three-stage generation network. Other work [21,55,51,7,46] followed similar procedure. Han et al. [15] argued that TPS transformation has low degree of freedom and proposed a flow-based method to create the warp. Much existing virtual try-on work [17,12,21,47,55,53,24,37] is evaluated on datasets that only have tops (t-shirt, shirt, etc.). Having only tops largely reduces the likelihood of shape mismatch as tops have simple and similar shapes. In our work, we extend the problem to include clothing items of all categories(tshirt, shirt, pants, shorts, dress, skirt, robe, jacket, coat, etc.), and propose a method for matching the shape between the source product and the target model. Evaluation shows that using pairs that match in shape significantly increases the generation quality for both our and prior work (table 4.3). In addition, real studio outfits are often covered by an unzipped/unbuttoned outerwear, which is also not presented in prior work [17,12,21,47,55,53,37]. This can cause partition or severe occlusion to the garment, and is not addressed by prior work as shown in Figure 6. We show that our multi-warp generation module ameliorates these difficulties. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Kedan Li, University of Illinois at Urbana-Champaign; (2) Min Jin Chong, University of Illinois at Urbana-Champaign; (3) Jingen Liu, JD AI Research; (4) David Forsyth, University of Illinois at Urbana-Champaign. Authors: Authors: (1) Kedan Li, University of Illinois at Urbana-Champaign; (2) Min Jin Chong, University of Illinois at Urbana-Champaign; (3) Jingen Liu, JD AI Research; (4) David Forsyth, University of Illinois at Urbana-Champaign. Table of Links Abstract and Intro Related Work Proposed Method Experiments Conclusions and References Abstract and Intro Abstract and Intro Related Work Related Work Proposed Method Proposed Method Experiments Experiments Conclusions and References Conclusions and References 2. Related Work Image synthesis : Spatial transformer networks estimate geometric transformations using neural networks [23]. Subsequent work [28,39] shows how to warp one object to another. Warping can be used to produce images of rigid objects [26,30] and non-rigid objects (e.g., clothing) [17,12,45]. In contrast to prior work, we use multiple spatial warpers. Image synthesis Our warps must be combined into a single image, and our U-Net for producing this image follows trends in inpainting (methods that fill in missing portions of an image, see [48,31,50,49]). Han et al. [16,52] show inpainting methods can complete missing clothing items on people. In our work, we use FID∞ to quantitatively evaluate our method. This is based on the Frchet Inception Distance (FID) [18], a common metric in generative image modelling [5,54,29]. Chong et al. [9] recently showed that FID is biased; extrapolation removes the bias, to an unbiased score (FID∞). Generating clothed people: Zhu et al. [57] used a conditional GAN to generate images based on pose skeleton and text descriptions of garment. SwapNet [38] learns to transfer clothes from person A to person B by disentangling clothing and pose features. Hsiao et al. [20] learned a fashion model synthesis network using per-garment encodings to enable convenient minimal edit to specific items. In contrast, we warp products onto real model images. Generating clothed people: Shape matching underlies our method to match product to model. Tsiao et al. [19] built a shape embedding to enable matching between human body and well-fitting clothing items. Prior work estimated the shape of human body [4,27], clothing items [10,25] and both [35,40], through 2D images. The DensePose [1] descriptor helps modeling the deformation and shading of cloth and, therefore, has been adopted by recent work [36,13,47,51,7,52]. Shape matching Virtual try-on (VTO) maps a product to a model image. VITON [17] uses a U-Net to generate a coarse synthesis and a mask on the model where the product is presented. A mapping from the product mask to the on-model mask is learned through Thin plate spline (TPS) transformation [3]. The learned mapping is applied on the product image to create a warp. Following their work, Wang et al. [45] improved the architecture using a Geometric Matching Module [39] to estimate the TPS transformations parameters directly from pairs of product image and target person. They train a separate refinement network to combine the warp and the target image. VTNFP [53] extends the work by incorporatiing body segments prediction and later works follow similar procedure [37,24,42,22,2]. However, TPS transformation fails to produce reasonable warps, due to the noisiness of generated masks in our dataset, as shown in Figure 6 right. Instead, we adopt affine transformations which we have found to be more robust to imperfections instead of TPS transformation. A group of following work extended the task to multi-pose. Warping-GAN [11] combined adversarial training with GMM, and generate post and texture separately using a two stage network. MG-VTON [12] further refine the generation method using a three-stage generation network. Other work [21,55,51,7,46] followed similar procedure. Han et al. [15] argued that TPS transformation has low degree of freedom and proposed a flow-based method to create the warp. Virtual try-on Much existing virtual try-on work [17,12,21,47,55,53,24,37] is evaluated on datasets that only have tops (t-shirt, shirt, etc.). Having only tops largely reduces the likelihood of shape mismatch as tops have simple and similar shapes. In our work, we extend the problem to include clothing items of all categories(tshirt, shirt, pants, shorts, dress, skirt, robe, jacket, coat, etc.), and propose a method for matching the shape between the source product and the target model. Evaluation shows that using pairs that match in shape significantly increases the generation quality for both our and prior work (table 4.3). In addition, real studio outfits are often covered by an unzipped/unbuttoned outerwear, which is also not presented in prior work [17,12,21,47,55,53,37]. This can cause partition or severe occlusion to the garment, and is not addressed by prior work as shown in Figure 6. We show that our multi-warp generation module ameliorates these difficulties. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv

Toward Accurate, Realistic Virtual Try-on Through Shape Matching: Related Work

শেপ ম্যাচিং এর মাধ্যমে সঠিক, বাস্তবসম্মত ভার্চুয়াল ট্রাই-অন: সম্পর্কিত কাজ

Auf dem Weg zu präzisem, realistischem virtuellem Anprobieren durch Formabgleich: Verwandte Arbeiten

Hacia una prueba virtual precisa y realista mediante la combinación de formas: trabajo relacionado

Vers un essai virtuel précis et réaliste grâce à la correspondance de formes : travaux connexes

आकार मिलान के माध्यम से सटीक, यथार्थवादी आभासी ट्राई-ऑन की ओर: संबंधित कार्य

形状マッチングによる正確でリアルな仮想試着に向けて：関連研究

형태 매칭을 통한 정확하고 실감나는 가상 시착을 향하여: 관련 연구

Rumo a um teste virtual preciso e realista por meio da correspondência de formas: trabalho relacionado

На пути к точной и реалистичной виртуальной примерке посредством сопоставления форм: сопутствующие работы

Şekil Eşleştirme Yoluyla Doğru, Gerçekçi Sanal Denemeye Doğru: İlgili Çalışma

Hướng tới việc thử nghiệm ảo thực tế, chính xác thông qua việc khớp hình dạng: Công việc liên quan

通过形状匹配实现准确、逼真的虚拟试穿：相关工作

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Zheyu Oliver Wang, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA and olivrw@mit.edu;
(2)  Ricardo Baptista, Computing + Mathematical Sciences, California Institute of Technology, Pasadena, CA and rsb@caltech.edu;
(3) Youssef Marzouk, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA and ymarz@mit.edu;
(4) Lars Ruthotto, Department of Mathematics, Emory University, Atlanta, GA and lruthotto@emory.edu;
(5) Deepanshu Verma, Department of Mathematics, Emory University, Atlanta, GA and deepanshu.verma@emory.edu. Table of Links Abstract & Introduction
Background and Related Work
Partially Convex Potential Maps (PCP-Map) for Conditional OT
Conditional OT flow (COT-Flow)
Implementation and Experimental Setup
Numerical Experiments
Discussion and Reference 3. Partially Convex Potential Maps (PCP-Map) for Conditional OT. Our first approach, PCP-Map, approximately solves the static COT problem through maximum likelihood training over a set of partially monotone maps. Motivated by the structure of transport maps that are optimal with respect to the quadratic cost function, we parameterize these maps as the gradients of scalar-valued neural networks that are strictly convex in x for any choice of the weights. Training problem. Given samples from the joint distribution, our algorithm seeks a conditional generator g by solving the maximum likelihood problem The objective JNLL is the expected negative log-likelihood functional which agrees up to an additive constant with the negative logarithm of (2.1), and M is the set of maps that are monotonically increasing in their first argument, i.e., We note that JNLL also agrees (up to an additive constant) with the Kullback-Leibler (KL) divergence from the push forward of ρz through the generator g to the conditional distribution in expectation over the conditioning variable. Since the learning problem in (3.2) only involves the inverse generator g −1, we seek this map directly in the same space of monotone functions M in (3.3). This avoids inverting the generator during training. The drawback is that sampling the target conditional requires inverting the learned map. In this work, we will find the conditional generator g −1 (·, y) that pushes forward the conditional distribution π(x|y) to the reference distribution for each y. Limiting the search to monotone maps is motivated by the celebrated Brenier’s theorem, which ensures there exists a unique monotone map g −1 such that g −1 (·, y)♯π(x|y) = g(·, y) ♯π(x|y) = ρz among all maps written as the gradient of a convex potential; see [8] for the original result and [10] for conditional transport maps. Theorem 2.3 in [10] also shows that g −1 is optimal in the sense that among all maps that match the distributions, it minimizes the integrated L2 transport costs Neural Network Representation. In this work, we leverage the structural form of the conditional Brenier map by using partially input convex neural networks (PICNNs) [2] to express the inverse generator directly. In particular, we parameterize g −1 as the gradient of a PICNN G˜ θ : R n×R m → R that depends on weights θ. A PICNN is a feed-forward neural network that is specifically designed to ensure convexity in some of its inputs; see the original work that introduced this neural network architecture in [2] and its use for generative modeling in [20]. To the best of our knowledge, investigating if PICNNs are universal approximators of partially input convex functions is still an open issue, also see [23, Section IV], that is beyond the scope of our paper; a perhaps related result for fully input convex neural networks is given in [20, Appendix C]. To ensure the monotonicity of g −1, we construct G˜ to be strictly convex as a linear combination of a PICNN and a positive definite quadratic term. That is, where γ1, γ2, and γ3 are scalar parameters that are re-parameterized via the soft-plus function ψ(x) = log(1 + exp(x)) and the ReLU function σReLU(x) = max{0, x} to ensure strict convexity of G˜ θ. Here, wK is the output of an K-layer PICNN and is computed through forward propagation through the layers k = 0, . . . , K − 1 starting with the inputs v0 = y and w0 = x Using properties for the composition of convex functions [18], it can be verified that the forward propagation in (3.6) defines a function that is convex in x, but not necessarily in y (which is not needed), as long as σ (w) is convex and non-decreasing. To compute the log determinant of g −1, we use vectorized automatic differentiation to obtain the Hessian of G˜ θ with respect to its first input and then compute its eigenvalues. This is feasible when the Hessian is moderate; e.g., in our experiments, it is less than one hundred. We use efficient implementations of these methods that parallelize the computations over all the samples in a batch. Our algorithm enforces the non-negativity constraint by projecting the parameters into the non-negative orthant after each optimization step using ReLU. Thereby, we alleviate the need for re- parameterization, for example, using the softplus function in [2]. Another novelty introduced in PICNN is that we utilize trainable affine layer parameters L (v) k and a context feature width u as a hyperparameter to increase the expressiveness of the conditioning variables, which are pivotal to characterizing conditional distributions; existing works such as [20] set L (v) 1:K−2 = I. Sample generation. Due to our neural network parameterization, there is generally no closedform relation between g and g −1 = G˜ θ. As in [20], we approximate the inverse of G˜ θ during sampling as the Legendre-Fenchel dual. That is, we solve the convex optimization problem Due to the strict convexity of G˜ θ in its first argument, the first-order optimality conditions gives Hyperparameters. In our numerical experiments, we vary only three hyperparameters to adjust the complexity of the architecture. As described in section 5 we randomly sample the depth, K, the feature width, w, and the context width, u, from the values in Table 2. This paper is available on arxiv under CC 4.0 license. Authors: (1) Zheyu Oliver Wang, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA and olivrw@mit.edu; (2)  Ricardo Baptista, Computing + Mathematical Sciences, California Institute of Technology, Pasadena, CA and rsb@caltech.edu; (3) Youssef Marzouk, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA and ymarz@mit.edu; (4) Lars Ruthotto, Department of Mathematics, Emory University, Atlanta, GA and lruthotto@emory.edu; (5) Deepanshu Verma, Department of Mathematics, Emory University, Atlanta, GA and deepanshu.verma@emory.edu. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Zheyu Oliver Wang, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA and olivrw@mit.edu; (2)  Ricardo Baptista, Computing + Mathematical Sciences, California Institute of Technology, Pasadena, CA and rsb@caltech.edu; (3) Youssef Marzouk, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA and ymarz@mit.edu; (4) Lars Ruthotto, Department of Mathematics, Emory University, Atlanta, GA and lruthotto@emory.edu; (5) Deepanshu Verma, Department of Mathematics, Emory University, Atlanta, GA and deepanshu.verma@emory.edu. Table of Links Abstract & Introduction Background and Related Work Partially Convex Potential Maps (PCP-Map) for Conditional OT Conditional OT flow (COT-Flow) Implementation and Experimental Setup Numerical Experiments Discussion and Reference Abstract & Introduction Abstract & Introduction Background and Related Work Background and Related Work Partially Convex Potential Maps (PCP-Map) for Conditional OT Partially Convex Potential Maps (PCP-Map) for Conditional OT Conditional OT flow (COT-Flow) Conditional OT flow (COT-Flow) Implementation and Experimental Setup Implementation and Experimental Setup Numerical Experiments Numerical Experiments Discussion and Reference Discussion and Reference 3. Partially Convex Potential Maps (PCP-Map) for Conditional OT. Our first approach, PCP-Map, approximately solves the static COT problem through maximum likelihood training over a set of partially monotone maps. Motivated by the structure of transport maps that are optimal with respect to the quadratic cost function, we parameterize these maps as the gradients of scalar-valued neural networks that are strictly convex in x for any choice of the weights. Training problem. Given samples from the joint distribution, our algorithm seeks a conditional generator g by solving the maximum likelihood problem The objective JNLL is the expected negative log-likelihood functional which agrees up to an additive constant with the negative logarithm of (2.1), and M is the set of maps that are monotonically increasing in their first argument, i.e., We note that JNLL also agrees (up to an additive constant) with the Kullback-Leibler (KL) divergence from the push forward of ρz through the generator g to the conditional distribution in expectation over the conditioning variable. Since the learning problem in (3.2) only involves the inverse generator g −1, we seek this map directly in the same space of monotone functions M in (3.3). This avoids inverting the generator during training. The drawback is that sampling the target conditional requires inverting the learned map. In this work, we will find the conditional generator g −1 (·, y) that pushes forward the conditional distribution π(x|y) to the reference distribution for each y. Limiting the search to monotone maps is motivated by the celebrated Brenier’s theorem, which ensures there exists a unique monotone map g −1 such that g −1 (·, y)♯π(x|y) = g(·, y) ♯π(x|y) = ρz among all maps written as the gradient of a convex potential; see [8] for the original result and [10] for conditional transport maps. Theorem 2.3 in [10] also shows that g −1 is optimal in the sense that among all maps that match the distributions, it minimizes the integrated L2 transport costs Neural Network Representation. In this work, we leverage the structural form of the conditional Brenier map by using partially input convex neural networks (PICNNs) [2] to express the inverse generator directly. In particular, we parameterize g −1 as the gradient of a PICNN G˜ θ : R n×R m → R that depends on weights θ. A PICNN is a feed-forward neural network that is specifically designed to ensure convexity in some of its inputs; see the original work that introduced this neural network architecture in [2] and its use for generative modeling in [20]. To the best of our knowledge, investigating if PICNNs are universal approximators of partially input convex functions is still an open issue, also see [23, Section IV], that is beyond the scope of our paper; a perhaps related result for fully input convex neural networks is given in [20, Appendix C]. To ensure the monotonicity of g −1, we construct G˜ to be strictly convex as a linear combination of a PICNN and a positive definite quadratic term. That is, where γ1, γ2, and γ3 are scalar parameters that are re-parameterized via the soft-plus function ψ(x) = log(1 + exp(x)) and the ReLU function σReLU(x) = max{0, x} to ensure strict convexity of G˜ θ. Here, wK is the output of an K-layer PICNN and is computed through forward propagation through the layers k = 0, . . . , K − 1 starting with the inputs v0 = y and w0 = x v0 = y w0 = x Using properties for the composition of convex functions [18], it can be verified that the forward propagation in (3.6) defines a function that is convex in x, but not necessarily in y (which is not needed), as long as σ (w) is convex and non-decreasing. To compute the log determinant of g −1, we use vectorized automatic differentiation to obtain the Hessian of G˜ θ with respect to its first input and then compute its eigenvalues. This is feasible when the Hessian is moderate; e.g., in our experiments, it is less than one hundred. We use efficient implementations of these methods that parallelize the computations over all the samples in a batch. Our algorithm enforces the non-negativity constraint by projecting the parameters into the non-negative orthant after each optimization step using ReLU. Thereby, we alleviate the need for re- parameterization, for example, using the softplus function in [2]. Another novelty introduced in PICNN is that we utilize trainable affine layer parameters L (v) k and a context feature width u as a hyperparameter to increase the expressiveness of the conditioning variables, which are pivotal to characterizing conditional distributions; existing works such as [20] set L (v) 1:K−2 = I. Sample generation. Due to our neural network parameterization, there is generally no closedform relation between g and g −1 = G˜ θ. As in [20], we approximate the inverse of G˜ θ during sampling as the Legendre-Fenchel dual. That is, we solve the convex optimization problem Due to the strict convexity of G˜ θ in its first argument, the first-order optimality conditions gives Hyperparameters. In our numerical experiments, we vary only three hyperparameters to adjust the complexity of the architecture. As described in section 5 we randomly sample the depth, K, the feature width, w, and the context width, u, from the values in Table 2.

Efficient Neural Network Approaches: Partially Convex Potential Maps (PCP-Map) for Conditional OT

By utilizing simple mathematics and parallel computing, we can efficiently overcome performance constraints when manipulating large images. This article will explore how the geometric distortion features of can be used to transform color spaces, as demonstrated in the following example: ImageMetalling To comprehend the code discussed in this article, it would be beneficial to have knowledge of the Color Lookup Table, geometric distortion, and how to work with pixels using the GPU. Main idea Up until now, to alter the color ratio in an image's pixels, we've employed a variety of intuitive and familiar tools such as curves, levels, and , among others. Essentially, these tools manipulate the image's color space. Hue/Saturation What if we could replace all these tools with a single, definitive method? This method is unique because it can replace all other tools simultaneously. A method that's accurate due to its perceptual impact, aligning with the nature of human perception, rather than a literal or simplistic approach, like how Photoshop operates. This is the method we will explore in this article. Let's see how we can manipulate not just the image itself but also its color representation. This will be done in a simple, mechanical way that is accessible to all. Deformation of objects using the MLS method There are various methods of image deformation, such as or . These are indeed fundamental and excellent tools. However, they often suffer from limitations such as the restricted number of control points that can be manipulated, or the excessively smooth extrapolation of the target distortions. affine transformation nonlinear transformation on the B-Spline When dealing with color spaces, we may want to tightly associate a control point and its surroundings with their deformation. Furthermore, the set of points can be arbitrary. This issue has been effectively addressed for animation tasks in computer graphics, but it is still not widely used as a color correction tool in major photo editing software. is a method for reconstructing (approximating) an objective function on a set of known values using the values of the weighted mean square sum. This remarkable technique has many applications in regression analysis, statistics, Big Data, and deep learning. MLS Solving the problem So, imagine we have N control points on a plane. To visualize this, think of a rubber surface scattered with balls that lay flat on a hard table. Each of these balls can be moved and fixed to a target point. Now, envision this surface colored with a slice of color space, for instance, RGB, HSV, or, for the sake of clarity and smoothness, Lab. L=80 Then, with respect to affine transformation, we need to find a solution for the equation: - root mean square weight, - desired transformation function of point , X - initial position of control points, - target position of control points Let's minimize this: in our case, we need to find such a function: in which the sum of all differences between points (where we arrived) and the value of the function from the starting point (where we started) — would be minimal, or in mathematical terms, tend to zero. On the other hand, any affine transformation can be written through the equation: where is the transformation matrix (like ), and is the . M CCM T translation matrix We can assume that for each variable in equation , we can find the minimum value for equation . (1) (2) Because the derivatives with respect to each of the variables in are zero for equation , we can directly solve for through the matrix in equation . The partial derivatives with respect to the free variables in form a linear system of equations. (2) T M (2) T Now, as you can see, we are able to express as a function of : T M Where and — are : weighted centroids This enables us to express equation as a function of : (2) M As you can see, it makes no difference to us which points we look for in the minimum of equation . Whether to search for points (1) or distances between weighted centroids and control points. Therefore, we will not be solving equation for the original control points but instead for new ones: and Considering equation , the solution to the problem is simplified to finding M from: (1) (3) Next, the problem is simplified by differentiating equation and determining as a solution to a system of linear equations using inverse matrices. To find the inverse matrix, we must reduce the system to a solution that includes square matrices on both sides of the equation. And so from we first obtain: (4) M (4), Boom! That’s it, the required function has been found, use to substitute into : (5) (3) The only remaining task is to code the solution , as exemplified in the . Given that there is no necessity for a system of equations solver, and that the matrices involved are merely 2x2, the entire mechanism should, in theory, operate fairly rapidly. (6) ImageMetalling-16 example Expansion of optimization conditions Upon closer examination of , we can observe certain characteristics associated with it, as we have solved the problem by considering it as an affine transformation task, i.e., the task of scaling and shifting. It's clear that in reality, deformations are not confined to just these two parameters. Therefore, can be expressed in a more complex form. For instance, consider transformation which permits uneven translations of the original field. Therefore, let's envision M as: At the same time M M similarity where and are connected through the similarity coefficient M’ M’’ with other vectors and Since all are similar to each other as plane vectors, we can write the similarity equality as an equation for the two-dimensional case: Or rewrite it as: From which it follows that we can now write as: (1) Since we expressed M through and and both of them were found, then we can rewrite by solving , as we did in the previous step: (5) (7) Where In conclusion, the presents a method to link similarity transformation with the covariance matrix and to identify for what's termed the rigid transformation. This approach allows for maximum deformation of spatial properties. At first glance, this method appears quite intuitive, and we anticipate it will be effective in deforming certain color spaces for our intended purposes. original publication M However, this hypothesis still needs to be empirically tested, which you can do yourself. This can be accomplished by downloading and experimenting with the deformations in various spaces, and with different settings for finding . the example M Implementation We will write the main code of the solver in , taking into account the fact that the code will be executed both on the in Metal cores and on the ; for this, it will have to be wrapped in an extension. Obviously, running the solver code on the GPU will be beneficial if the size of the array of control points and the space that we will be modifying are large. C++ GPU CPU Objective-C++ Code of kernels using the solver
kernel void kernel_mlsSolver(
                             constant float2  *input_points  [[buffer(0)]],
                             device float2    *output_points [[buffer(1)]],
                             constant float2  *p      [[buffer(2)]],
                             constant float2  *q      [[buffer(3)]],
                             constant int    &count   [[buffer(4)]],
                             constant MLSSolverKind  &kind [[buffer(5)]],
                             constant float    &alpha [[buffer(6)]],
                             uint gid [[thread_position_in_grid]]
                             ){
    ///
    /// The core of the solver calculates new coordinates for each point 
    ///
    float2 point = input_points[gid];
    IMPMLSSolver solver = IMPMLSSolver(point,p,q,count,kind,alpha);
    output_points[gid] = solver.value(point);
} General MLS solver code

class IMPMLSSolver{
     
public:
         
    /**
     Create a solver for MNC
      
     @param point the current point relative to which we calculate the deformation 
     @param p array of initial control points
     @param q array of control target points
     @param count number of control points
     @param kind solver type: affine transformation, similarity transformation, transformation with maximum possible rigidity
     @param alpha - degree of deformation
     */
    IMPMLSSolver(const float2 point, 
#ifndef __METAL_VERSION__              
              const float2 *p, 
              const float2 *q,
#else
//
// It's important to understand that this is not just a different data type, but a different layout mechanism
// data in memory. In a specific solution for Metal Java, we pass arrays to
// GPU constant memory.                 
//                 
              constant float2 *p, 
              constant float2 *q,
#endif
              const int count, 
              const MLSSolverKind kind = MLSSolverKindAffine, 
              const float alpha = 1.0): 
    point_(point),
    kind_(kind), 
    alpha_(alpha), 
    count_(count),
    weight_(0),
    p_(p), q_(q)
    {
         
#ifndef __METAL_VERSION__
        //
        // For the assembly CPU, allocate temporary buffers for calculating intermediate values
        // solver
        //
        w_ = new float[count_];   
        pHat_ = new float2[count_];   
        qHat_ = new float2[count_];   
#endif
         
        // Finding the weights  
        solveW();
         
        // Finding a vector with a "header"
        solveHat();
         
        // Solving the main optimization equation
        solveM();  
         
#ifndef __METAL_VERSION__
        delete pHat_;
        delete qHat_;
        pHat_=qHat_=0;
#endif
         
    }    
         
    /**
     Returns the deformation point by coordinate
 
     @param point starting position
     @return new position 
     */
    float2 value(float2 point) {
        if (count_ <= 0) return point;   
        return (point - pStar_) * M + qStar_;
    }
     
    ~IMPMLSSolver() {
#ifndef __METAL_VERSION__
        delete w_;
        if (pHat_) delete pHat_;
        if (qHat_) delete qHat_;
#endif
    }
     
private:
     
    MLSSolverKind kind_;
    float   alpha_;
    int     count_;
    float2  point_;
#ifndef __METAL_VERSION__              
    const float2 *p_;
    const float2 *q_;
    float *w_;
    float2 *pHat_;
    float2 *qHat_;    
#else
    constant float2 *p_;
    constant float2 *q_;
    thread float w_[MLS_MAXIMUM_POINTS];
    thread float2 pHat_[MLS_MAXIMUM_POINTS];
    thread float2 qHat_[MLS_MAXIMUM_POINTS];
#endif
     
    float weight_;
    float2 pStar_;
    float2 qStar_;
    float mu_;
     
    float2x2 M;
     
    void solveW() {
         
        weight_ = 0;
        pStar_ = float2(0);
        qStar_ = float2(0);
 
        for (int i=0; i<count_ && i<MLS_MAXIMUM_POINTS; i++) {
             
            float d =  pow(distance(p_[i], point_), 2*alpha_);
             
            if (d < FLT_EPSILON)  d = FLT_EPSILON; 
             
            w_[i] = 1.0 / d;
            weight_ = weight_ + w_[i];
             
            pStar_ += w_[i] * p_[i];
            qStar_ += w_[i] * q_[i];
 
        }
         
        if (weight_ < FLT_EPSILON)  weight_ = FLT_EPSILON;
         
        pStar_ = pStar_ / weight_;                
        qStar_ = qStar_ / weight_;
    }  
     
    void solveHat(){        
         
        mu_ = 0;
         
        float _rmu1 = 0;
        float _rmu2 = 0;
         
        for (int i=0; i<count_ && i<MLS_MAXIMUM_POINTS; i++) {
             
            pHat_[i] = p_[i] - pStar_;                        
            qHat_[i] = q_[i] - qStar_;
             
            switch (kind_) {            
                case MLSSolverKindSimilarity:
                    mu_ += similarityMu(i);
                    break;                
                case MLSSolverKindRigid:
                    _rmu1 += rigidMu1(i); 
                    _rmu2 += rigidMu2(i);
                    break;
                default:
                    break;
            }
        }
         
        switch (kind_) {            
            case MLSSolverKindRigid:
                mu_ = sqrt(_rmu1*_rmu1 + _rmu2*_rmu2);
                break;
            default:
                break;
        }
         
        if (mu_ < FLT_EPSILON)  mu_ = FLT_EPSILON; 
         
        mu_ = 1/mu_;
    }
     
    void solveM() {
        switch (kind_) {
            case MLSSolverKindAffine:
                M = affineM();
                break;
            case MLSSolverKindSimilarity:
            case MLSSolverKindRigid:
                M = similarityM(point_);
                break;
        }
    }  
                    
    float2x2 affineM() {
        float2x2 mi = (float2x2){(float2){0,0},(float2){0,0}};
        float2x2 mj = (float2x2){(float2){0,0},(float2){0,0}};
 
        for (int i=0; i<count_ && i<MLS_MAXIMUM_POINTS; i++) {
             
            float2x2 pti({
                pHat_[i], 
                float2(0)                
            });
             
            float2x2 ppi({
                (float2){w_[i] * pHat_[i].x, 0.0}, 
                (float2){w_[i] * pHat_[i].y, 0.0}                
            });
             
            mi = mi + (float2x2)(pti * ppi);
             
             
            float2x2 ptj({
                w_[i] * pHat_[i], 
                float2(0)                
            });
             
            float2x2 qpj({
                (float2){qHat_[i].x, 0.0}, 
                (float2){qHat_[i].y, 0.0}                
            });
             
            mj = mj + (float2x2)(ptj * qpj);
        }        
        return inverse(mi) * mj;
    }
     
     
    float similarityMu(int i)  {
        return w_[i]*dot(pHat_[i], pHat_[i]);
    }
     
    float2x2 similarityM(float2 value) {
         
        float2x2 m = (float2x2){(float2){0,0},(float2){0,0}};
         
        for (int i=0; i<count_ && i<MLS_MAXIMUM_POINTS; i++) {
             
            float2 sp = -1 * __slashReflect(pHat_[i]);
            float2 sq = -1 * __slashReflect(qHat_[i]);
             
            float2x2 _p({
                (float2){w_[i] * pHat_[i].x, w_[i] * sp.x}, 
                (float2){w_[i] * pHat_[i].y, w_[i] * sp.y}                
            });
             
            float2x2 _q({qHat_[i], sq});
                         
            m = m + (float2x2)(_p * _q);
        }
        return  mu_ * m; 
    }
     
    float rigidMu1(int i) {
        return w_[i]*dot(qHat_[i], pHat_[i]);        
    }
     
    float rigidMu2(int i) {
        return w_[i]*dot(qHat_[i],  __slashReflect(pHat_[i]));        
    }
}; Examples In the application, you can interact with the colors of the picture; the colors will be marked on the Lab color space plane: a-b (in the code, you can replace it with any other). Colors that you want to fix and not change are also worth noting. Then, pull the color dot that you want to change to another. In this example, I highlighted the color of the bottle and chaotically marked a few more. As you can see, by significantly changing one color, the rest are practically unaffected, which can be very convenient for, for example, commercial photographers engaged in digital subject photography or for enthusiasts who dream of matching the color of a digital image to a film one. And this is what the RGB cube looks like after our Lab space settings. For reference, the application also draws a hald-LUT and an HV plane from HSV space. In this example, light color correction has been made: the cold tint of the original slide has been removed. This is how the LUT of the original RGB cube is approximately transformed. It is obvious that the presented framework for working with color spaces can become a universal color correction tool for future generations of digital photographers, when film finally leaves the scene, and color and sound design become a common practice. Also published . here

Understanding Color Space Transform Using The Moving Least Squares Method

This paper is available on arxiv under CC 4.0 license. Authors: (1) Terence Blésin, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (2) Wil Kao, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (3) Anat Siddharth, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (4) Alaina Attanasio, OxideMEMS lab, Purdue University; (5) Hao Tian, OxideMEMS lab, Purdue University; (6) Sunil A. Bhave, OxideMEMS lab, Purdue University; (7) Tobias J. Kippenberg, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL). Table of Links Introduction Results A. Physics and design B. Device characterization C. Bidirectional microwave-optical transduction D. Pulsed transduction Discussion Acknowledgments Appendix A: Theory Appendix B: Fabrication process flow Appendix C: Optical characterization Appendix D: Characterization of acoustic resonances Appendix E: Characterization of bidirectional transduction Appendix F: Optimization of optical extraction efficiency III. DISCUSSION Non-classically correlated microwave-optical photon pairs can be generated through spontaneous parametric down-conversion in our transducer. These correlated photon pairs constitute a key ingredient toward entangling distant quantum processors via the Duan-LukinCirac-Zoller protocol [4, 45]. With the current device parameters, the pair generation rate on chip amounts to 190 Hz, which is well above the thermal decoherence rate for 3.5 GHz at 10 mK as explained in Appendix A 4. However, losses in the measurement setup specific to such an experiment, as well as the gating of the optical pump required to alleviate the effective heat load, are expected to limit further the final heralding rate. Quasi-free-standing structures, such as 1D OMCs, do not readily thermalize and are thus more susceptible to heating effects. Even though our transducer also utilizes a suspended acoustic resonator, it may be feasible to operate at a higher duty cycle than what is presented in Fig. 4. It has been shown that a buffer gas environment can facilitate thermalization of a 1D OMC, at the cost of increased damping of the mechanical breathing mode [46]. On the contrary, the HBAR mode of interest here should be relatively insensitive to such viscous damping, as the acoustic wave propagates predominantly along the longitudinal direction inside the cladding. Therefore, a sample cell affixed to the mixing chamber flange and filled with buffer superfluid helium—an inviscid fluid that is both an excellent thermal conductor and electrical insulator—could potentially improve the heralding rate without hampering the conversion efficiency [47]. The present design is also suited for tasks beyond quantum state transfer. The transducer can be a key component of photonic interconnects for superconducting qubits [7, 8], where laser lights routed through optical fibers are used to encode microwave signals directly inside the dilution refrigerator during qubit readout. It may be challenging for traveling-wave EOMs to attain the requisite half-wave voltage to be competitive in noise performance against conventional all-electrical readout scheme utilizing high-electron-mobility transistor amplifiers [8]. Our triply resonant approach affords a path towards a scalable optically controlled cryogenic waveform generator for both qubit readout and control. The multimode nature of the transducer is particularly suited for frequency-multiplexed dispersive readout. Transduction leveraging multiple HBAR modes is already demonstrated in Fig. 3e. One can additionally utilize line-type instead of point-type dimer coupling for the photonic molecule, which gives rise to a dispersion in the supermode splitting [48]. In combination with the multitude of acoustic overtones, a single transducer can therefore support several spectrally distinguishable triply resonant systems that serve as qubit multiplex channels. Finally, since the transducer requires no superconducting element to function, it may be pertinent for applications in classical microwave photonics. Optimization of design and fabrication should engender further improvement on device performance. The conversion efficiency, proportional to microwave extraction efficiency (Eq. 2), can be improved by replacing AlN with scandium-doped AlN [49], which features a piezoelectric coefficient d33 about five times larger than AlN [50, 51] while preserving CMOS compatibility. There is likewise additional upside on the photonics (Appendix C 1). Bending radiation loss can be significantly reduced by increasing the micro-ring radius r. In particular, intrinsic quality factor exceeding 107 has been demonstrated with an r approximately ten times larger using the same fabrication process [52]. It may be anticipated that the efficiency gain here may be chiefly compensated by the reduction in optomechanical coupling rate g0 ∼ 1/ √ r. Nevertheless, by thinning the waveguide to 200 nm that approaches half of the acoustic wavelength, g0 is expected to remain unchanged. As in the thick-core waveguide fabricated using the photonic Damascene process, such a thin-core waveguide on a subtractive manufacturing platform is expected to exhibit negligible bending loss [53]. Assuming critical coupling conditions (Appendix F), we therefore expect another 1.5- time gain in η tot. Finally, optical insertion loss can be nearly eliminated by employing a spot-size converter to facilitate mode-matching with lensed fiber [54–56]. Combining these improvements, our transducer could achieve a total efficiency η tot = 6 × 10−3 . In conclusion, we have designed, fabricated, and characterized a compact piezo-optomechanical microwaveoptical transducer that integrates wafer-scale, CMOScompatible HBAR and Si3N4 photonic technologies. Free of any superconducting components, this triply resonant transducer attains a bidirectional off-chip photon number conversion efficiency of 1.6 × 10−5 and a bandwidth of 25 MHz, with an input pump power of 21 dBm at room temperature. Multimode transduction leveraging distinct HBAR modes have been demonstrated, suggesting prospects for designing frequency-multiplexed photonic interconnects for superconducting qubits. Realistic design and fabrication improvements may even allow access to experiments in the quantum regime.

Bidirectional Microwave-optical Transduction Based on Integration: Discussion

Authors: (1) Eugene Y. S. Chua, Division of the Humanities and Social Sciences, California Institute of Technology; (2) Eddy Keming Chen, ‡Department of Philosophy, University of California. Table of Links Abstract & Introduction Decoherence and Branching The Born Rule Discussion Conclusion and References 3 The Born Rule 3.1 The Sebens-Carroll Program Sebens and Carroll (2018) proposes a strategy for justifying the Born rule for Alice above: the probabilities ascribed to each branch by the Born rule are to be interpreted as Alice’s self-locating uncertainty as to which branch they’re located in, postmeasurement but before they observe the measurement outcome. In their words: If we assume that the experimenter knows the relevant information about the wave function, it’s unclear what the agent might be uncertain of before a measurement is made. They know that every outcome will occur and that they will have a successor who sees each possible result. […] We must answer the question: What can one assign probabilities to? Our answer will be that agents performing measurements pass through a period of self-locating uncertainty, in which they can assign probabilities to being one of several identical copies, each on a different branch of the wave function. (ibid., 33) To elaborate, their strategy relies on (i) the fact that Alice knows the universal wave function, (ii) has undergone branching due to some measurement having been performed, but (iii) may not be able to discern which branch they’re on prior to observing the measurement outcome due to each copy of Alice, post-branching, having qualitatively identical internal states as each other. For Sebens and Carroll, “two agents are in the same internal qualitative state if they have identical current evidence: the paerns of colors in their visual fields are identical, they recall the same apparent memories, they both feel equally hungry, etc.” (2018, 36) In this ‘post-measurement pre-observation’ period, as they call it, the universal wave function is: Sebens and Carroll (2018) then proposes an intuitive epistemic principle with which they justify Alice’s use of the Born rule, where the probabilities are now interpreted in terms of subjective credences: Epistemic Separability Principle (ESP): Suppose that universe U contains within it a set of subsystems S such that every agent in an internally qualitatively identical state to agent A is located in some subsystem which is an element of S. The probability that A ought to assign to being located in a particular subsystem S given that they’re in U is identical in any possible universe which also contains subsystems S in the same exact states (and does not contain any copies of the agent in an internally qualitatively identical state that are not located in S). Case 1: Pure states 3.2 The McQueen-Vaidman Program Similar to the Sebens-Carroll program, Mceen and Vaidman (2018) also proposes an interpretation of the Born rule in terms of self-locating uncertainty. is follows earlier aempts initiated by e.g. Vaidman (1998) and Tappenden (2011). Mceen and Vaidman’s setup depends on the fiction of a sleeping pill, which induces the same post-measurement pre-observation uncertainty as the Sebens-Carroll program: The experimenter performs the experiment without looking at the result; she instead arranges to be put to sleep with a sleeping pill and taken to room A if the result was a, and room B if the result was b. e rooms are identical from the inside. So when each of the experimenter’s descendants [post-branching copies] wakes up, they will be uncertain as to which room they’re in, and therefore uncertain as to which result, a or b, obtains in their own world. The question: What is the probability for result a? makes sense for them. It’s not a question about what happened, it’s a question about their self-location. The descendants might know everything relevant regarding the wavefunction of the universe, but still be ignorant about who they are. The descendants are in states of self-location uncertainty. (2018, 2) However, instead of relying on ESP, they rely on three physical principles: • Symmetry: Symmetric situations should be assigned equal probabilities. • No-FTL: Faster-than-light signaling is impossible; the probability of finding a particle in some location with some state cannot be influenced by actions occurring remotely. • Locality: The probability of finding a particle somewhere in some state depends only on that particle’s quantum state. Given this situation, each agent – well aware of the symmetry of the situation – is put in a sleeping pill situation: they’re put to sleep before measurement in a ‘ready’ room, and then moved to a ‘found’ room – stipulated to be internally identical as the ‘ready’ room – if the particle is found by the measurement apparatus in their space-station. e measurement then takes place. 3.3 The Deutsch-Wallace Program Finally, we turn to the Deutsch-Wallace program. In contrast to the previous two, this program provides a justification of the Born rule in WFRE by appealing not to self-locating uncertainty, but to rational choice theory. A rational agent betting on outcomes of measurements for some wave function ought to bet in such a way that the credences they have over these outcomes are governed by the squared-amplitudes of the wave function. Deutsch (1999) provided one of the earliest proofs for this result. However, the most refined result is due to Wallace (2012), who proves a representation theorem to this effect given certain axioms of rational choice and assumptions about the structure of quantum bets. The decision problem can be summarized schematically as such: a system’s state space – its Hilbert space – can be decomposed into various macrostates π, with their fineness (i.e. size) determined by decoherence and the environment. Any system in a macrostate π is compatible with a set of unitary transformations, which are understood as acts on the system by an agent (for instance, measurement). These acts lead to outcomes in the form of the system ending up in different macrostates on different branches as a result of the unitary transformations. Agents are then asked how they would place monetary bets on these outcomes, on which they will collect rewards after the act is performed; that is, agents are asked to state their preferences for bets on these outcomes. Now, the question is this: what credences should agents rationally assign to these outcomes? Wallace assumes a set of four ‘richness’ axioms on the structure of the set of possible bets,[2] as well as a set of six ‘rationality’ axioms on the structure of the agent’s rational preferences on pairs of bets.[3] Thee first two are general axioms of rationality, while the latter four are ‘Everettian’ rationality axioms proposed by Wallace. We won’t go into detail stating the axioms, except for one (which we’ll discuss in the following section). e interested reader is invited to read Wallace (2012, §5). Wallace (2012, 172) proves the following theorem with the above set-up: There is a utility function on the set of rewards, unique up to positive affine transformations, such that one act is preferred to another if and only if its expected utility, calculated with respect to this utility function and to the quantum-mechanical weights of each reward, is higher. Born Rule Theorem: [1] We could also have made a measurement for z-spin, in which case completely analogous results follow: the density matrix gives rise to a different branching structure. [2] They are called Reward Availability, Branching Availability, Erasure, and Problem Continuity respectively. [3] They are called Ordering, Diachronic Consistency, Macrostate Indifference, Branching Indifference, State Supervenience, Solution-Continuity, respectively. [4] Many thanks to David Wallace for discussions about this point. This paper is under CC 4.0 license. available on arxiv

The Born Rule in a Mixed-State Everettian Multiverse

Authors: (1) JunJie Wee, Department of Mathematics, Michigan State University; (2) Jiahui Chen, Department of Mathematical Sciences, University of Arkansas; (3) Kelin Xia, Division of Mathematical Sciences, School of Physical and Mathematical Sciences Nanyang Technological University & xiakelin@ntu.edu.sg; (4)Guo-Wei Wei, 1Department of Mathematics, Michigan State University, Department of Biochemistry and Molecular Biology, Michigan State University, Department of Electrical and Computer Engineering, Michigan State University & xiakelin@ntu.edu.sg. Table of Links Abstract & Introduction Results Discussion Conclusion Materials and Methods Software and resources, Code and Data Availability Supporting Information, Acknowledgments & References 5 Materials and Methods In this section, we endeavor to elucidate key mathematical and computational foundations that are instrumental for the work presented in this study. Specifically, we delve into spectral graph theory, simplicial complex, and persistent Laplacian methods, highlighting their significance in capturing topological and spectral properties essential for the characterization of proteins. Additionally, we discuss machine learning and deep learning paradigms, focusing on their role in processing, analyzing, and interpreting these complex features, especially within the confines of test datasets and validation settings. 5.1 Persistent Laplacian characterization of proteins A simplicial complex is made up of a set of simplices and generalises beyond graph networks at higher dimensions [44, 45, 46, 47]. Every simplex is a finite set of vertices which can be interpreted as the atoms in a protein structure. Essentially, simplices can be a point (0-simplex), an edge (1-simplex), a triangle (2-simplex), a tetrahedron (3-simplex), or in higher dimensions, a p-simplex. In other words, a k-simplex σ k = {v0, v1, · · · , vk} is the convex hull formed by k + 1 affinely independent points v0, v1, · · · , vk as follows, Simplicial complex A geometric simplicial complex K is a finite set of geometric simplexes that satisfy two essential conditions. First, any face of a simplex from K is also in K. Second, the intersection of any two simplexes in K is either empty or shares faces. Commonly used methods to construct simplicial complexes are Cech complex, Vietoris-Rips complex, Alpha complex, Clique ˇ complex, Cubic complex, and Morse complex [44, 45, 46, 47]. In the case k = 0, then L0 = B1B⊤ 1 since ∂0 is a zero map Persistent Laplacian (PL) were first introduced by integrating graph Laplacian and multiscale filtration [25]. Analyzing the spectra of k-combinatorial Laplacian matrix allows both topological and geometric information (i.e. connectivity and robustness of simple graphs) to be obtained. However, this method is genuinely free of metrics or coordinates, which induced too little topological and geometric information that can be used to describe a single configuration. Persistent Laplacian Therefore, PL was extended to simplicial complexes. This allows a sequence of simplicial complexes from a filtration process to generate persistent Laplacian which is largely inspired by persistent homology and in earlier works in multiscale graphs. For the rest of this section, we introduce mainly on the construction of PL. First, a k-combinatorial Laplacian matrix is symmetric and positive semi-definite. Therefore, its eigenvalues are all real and non-negative. The multiplicity of zero spectra (also called harmonic spectra) reveals the topological information, and the geometric information will be preserved in the non-harmonic spectra. This nested sequence of simplicial complexes induces a family of chain complexes In order to illustrate the difference between PL and PH, Figure 5 describes a point cloud, basic simplices, a filtration process and the comparison between persistent Laplacian and persistent homology barcodes of 13 points. The filtration process in Figure 5(c) shows the different stages of a Rips filtration process for the 13 points. Figure 5(d) shows the persistent homology barcodes (in blue) and persistent non-harmonic spectra (in red). It can be seen that the nonharmonic spectra provides the additional homotopic shape evolution that is missing in persistent homology in the later part of the filtration process. 5.2 Persistent Laplacian descriptors where DE(·, ·) is the Euclidean distance between the two atoms and Loc(·) refers to the atom’s location which is either in the mutation site or in the rest of the protein. Here, we construct two types of simplicial complexes in our PL computation, such as Vietoris-Rips complex (VC) and Alpha complex (AC). Both complexes are used to characterize the first order interactions and higher order patterns respectively. To capture and characterize different types of atomatom interactions, we generate the PL based on different atom subsets by selecting one type of atom in the mutation site and one other atom type in the rest of the protein. Different types of atom-atom interactions characterize the different interactions in proteins. For example, interactions generated from carbon atoms are associated with hydrophobic interactions. Similarly, interactions between nitrogen and oxygen atoms correlate to hydrophilic interactions and/or hydrogen bonds. Both types of interactions are illustrated in Figure 6. Interactive PLs have the capability to unveil additional details about bonding interactions and offer a fresh and distinct representation of molecular interactions in proteins. For zero dimensions, we consider both the harmonic spectra and non-harmonic spectra information for each persistent Laplacian. Filtration using Rips complex with DI distance is used. The 0-dimensional PL features are generated from 0A to 6 ˚ A with 0.5 ˚ A gridsize. For the ˚ non-harmonic spectra information, we count the number of non-harmonic spectra and calculate seven statistical values of non-harmonic spectra such as sum, minimum, maximum, mean, standard deviation, variance and the sum of eigenvalues squared. This generates eight statistical values for each of the nine atomic pairs. Therefore, the dimension of 0-dimensional PL features for a protein is 72. In total, the 0-dimensional PL-based feature size after concatenating features at different dimensions for wild type and mutant is 1872. For one or two dimensions, we perform the filtration using Alpha complex with the DE distance. The limited number of atoms in the local protein structure can create only a few high-dimensional simplexes, resulting in minimal alterations in shape. As a result, it suffice to consider features from only harmonic spectra of persistent Laplacians by coding the topological invariants for the high-dimensional interactions. Using GUDHI[51], the persistence of the harmonic spectra can be represented by persistent barcodes. The topological feature vectors are generated by computing the statistics of bar lengths, births and deaths. Bars shorter than 0.1A are excluded as they do not exhibit any clear physical meaning. The remaining bars are ˚ then used for computing the statistics: (1) sum, maximum and mean for lengths of bars; (2) minimum and maximum for the birth values of bars; (3) minimum and maximum for the death values of bars. Each set of point clouds leads to a seven-dimensional vector. These features are calculated on nine single atomic pairs and one heavy atom pair. The dimension of oneand two-dimensional PL feature vectors for a protein is 140. In total, the higher-dimensional PL-based feature size after concatenating features at different dimensions for wild type, mutant and their difference is 420. 5.3 Persistent Homology Persistent homology is part of the harmonic spectra of PL. The homology groups in PH illustrate the persistence of topological invariants, hence providing the harmonic spectral information in PL. The site- and element-specific PH features are generated in a similar way as compared to PL. Similar to PL, filtration construction is also employed to PH. For the zero dimension, the filtration parameter can be discretized into several equally spaced bins, namely [0, 0.5], (0.5, 1], · · · , (5.5, 6]A. The death value of the bars are summed in each bin resulting in 12 ˚ ×18 features. For each bin, we count the numbers of persistent bars, resulting in a nine-dimensional vector for each point cloud. Similarly, this is performed for each of the nine single atomic pairs. Hence, the dimension of PH features for a protein is 216. For one or two dimensions, the identical featurization from the statistics of persistent bars in PH is used. The PH embedding combines features at different dimensions as described above and concatenated for wild type, mutant and their difference, resulting in a 648-dimensional vector 5.4 Transformer Features Recently, we have seen significant advancements in modelling protein properties using largescale protein transformer models trained on hundreds of millions of sequences. These models, like ESM [33] (evolutionary scale modeling) and ProtTrans[34, 35], have demonstrated impressive performance. Moreover, hybrid fine-tuning approaches that leverage both local and global evolutionary data have proven to enhance these models even further. For instance, eUniRep is an improved LSTM-based UniRep model achieved through fine-tuning with knowledge extracted from local multiple sequence alignments (MSAs). Additionally, the ESM model can be fine-tuned using either downstream task data or local MSAs. In our research, we employed the ESM-1b transformer, a model that falls under the transformer architecture. This particular variant was trained on a dataset of 250 million sequences using a masked filling procedure and boasts an architecture comprising 34 layers with a whopping 650 million parameters. The ESM transformer’s primary role in our work was to generate sequence embeddings. At each layer of the ESM model, it encoded a sequence of length L into a matrix sized at 1,280×L, excluding the start and terminal tokens. For our study, we utilized the sequence representation derived from the final (34th) layer and computed the average along the sequence length axis, resulting in a 1,280-component vector. 5.5 Performance Metrics PPV and NPV assesses the true positive and true negative proportion of the predicted results for each solubility class. PPV and NPV are computed based on TP, TN, FP and FN which represents the true positive, true negative, false positive and false negative values for each solubility class. For each solubility class, PPV and NPV can be computed by: This paper is under CC 4.0 license. available on arxiv

Interrogating TopLabGBT's Computational Framework

Authors: (1) Ruohan Zhang, Department of Computer Science, Stanford University, Institute for Human-Centered AI (HAI), Stanford University & Equally contributed; zharu@stanford.edu; (2) Sharon Lee, Department of Computer Science, Stanford University & Equally contributed; zharu@stanford.edu; (3) Minjune Hwang, Department of Computer Science, Stanford University & Equally contributed; zharu@stanford.edu; (4) Ayano Hiranaka, Department of Mechanical Engineering, Stanford University & Equally contributed; zharu@stanford.edu; (5) Chen Wang, Department of Computer Science, Stanford University; (6) Wensi Ai, Department of Computer Science, Stanford University; (7) Jin Jie Ryan Tan, Department of Computer Science, Stanford University; (8) Shreya Gupta, Department of Computer Science, Stanford University; (9) Yilun Hao, Department of Computer Science, Stanford University; (10) Ruohan Gao, Department of Computer Science, Stanford University; (11) Anthony Norcia, Department of Psychology, Stanford University (12) Li Fei-Fei, 1Department of Computer Science, Stanford University & Institute for Human-Centered AI (HAI), Stanford University; (13) Jiajun Wu, Department of Computer Science, Stanford University & Institute for Human-Centered AI (HAI), Stanford University. Table of Links Abstract & Introduction Brain-Robot Interface (BRI): Background The NOIR System Experiments Results Conclusion, Limitations, and Ethical Concerns Acknowledgments & References Appendix 1: Questions and Answers about NOIR Appendix 2: Comparison between Different Brain Recording Devices Appendix 3: System Setup Appendix 4: Task Definitions Appendix 5: Experimental Procedure Appendix 6: Decoding Algorithms Details Appendix 7: Robot Learning Algorithm Details 2 Brain-Robot Interface (BRI): Background Since Hans Berger’s discovery of EEG in 1924, several types of devices have been developed to record human brain signals. We chose non-invasive, saline-based EEG due to its cost and accessibility to the general population, signal-to-noise ratio, temporal and spatial resolutions, and types of signals that can be decoded (see Appendix 2). EEG captures the spontaneous electrical activity of the brain using electrodes placed on the scalp. EEG-based BRI has been applied to prosthetics, wheelchairs, as well as navigation and manipulation robots. For comprehensive reviews, see [22– 25]. We utilize two types of EEG signals that are frequently employed in BRI, namely, steady-state visually evoked potential (SSVEP) and motor imagery (MI). SSVEP is the brain’s exogenous response to periodic external visual stimulus [26], wherein the brain generates periodic electrical activity at the same frequency as flickering visual stimulus. The application of SSVEP in assistive robotics often involves the usage of flickering LED lights physically affixed to different objects [27, 28]. Attending to an object (and its attached LED light) will increase the EEG response at that stimulus frequency, allowing the object’s identity to be inferred. Inspired by prior work [15], our system utilizes computer vision techniques to detect and segment objects, attach virtual flickering masks to each object, and display them to the participants for selection. Motor Imagery (MI) differs from SSVEP due to its endogenous nature, requiring individuals to mentally simulate specific actions, such as imagining oneself manipulating an object. The decoded signals can be used to indicate a human’s intended way of interacting with the object. This approach is widely used for rehabilitation, and for navigation tasks [29] in BRI systems. This approach often suffers from low decoding accuracy [22]. Much existing BRI research focuses on the fundamental problem of brain signal decoding, while several existing studies focus on how to make robots more intelligent and adaptive [13–17, 30]. Inspired by this line of work, we leverage few-shot policy learning algorithms to enable robots to learn human preferences and goals. This minimizes the necessity for extensive brain signal decoding, thereby streamlining the interaction process and enhancing overall efficiency. Our study is grounded in substantial advancements in both the field of brain signal decoding and robot learning. Currently, many existing BRI systems target only one or a few specific tasks. To the best of our knowledge, no previous work has presented an intelligent, versatile system capable of successfully executing a wide range of complex tasks, as demonstrated in our study. This paper is under CC 4.0 license. available on arxiv

Understanding Brain-Robot Interfaces (BRIs)

Authors: (1) Chenhao Shi, Shanghai Jiao Tong University; (2) Ruibang Liu, Shanghai Jiao Tong University; (3) Guoqiang Li†, Shanghai Jiao Tong University. Table of Links Abstract & Introduction Preliminaries Normalization Algorithm Evaluation Conclusion & References II. PRELIMINARIES This section introduces the basic concepts and principles of zero-knowledge proof and discusses the role of R1CS and Circom in zero-knowledge-proof systems. It also explores the limitations of existing normalization techniques for R1CS and presents the proposed data-flow-based normalization generation algorithm, which is motivated by these limitations. A. ZK-SNARKS Zk-SNARK, which stands for Zero-Knowledge Succinct Non-interactive Argument of Knowledge, is a type of zeroknowledge proof introduced in a 2014 paper [12]. The objective of zk-SNARK is to enable one party to prove to another that they possess specific knowledge without revealing the knowledge itself, and to do so concisely and efficiently. The working principle of Zk-SNARK can be simplified into several steps. First, users convert the information they wish to verify into a mathematical problem called a computation. This computation can be implemented using any high-level programming language, such as OCaml, C++, Rust, or hardware description languages like Circom. Next, the computation result is usually transformed into an arithmetic circuit, a computational model for computing polynomials. An arithmetic circuit consists of inputs and multiple gates, performing an essential arithmetic operation such as addition or multiplication. The entire arithmetic circuit can be used to generate a specific format (R1CS), which takes the form of a constraint-based formula system (rank-1 constraint system) expressing the constraints of the arithmetic circuit. A verifiable arithmetic circuit is one of the inputs of the zk-SNARKs algorithm. The Quadratic Arithmetic Program (QAP) is a variant of linear pcp and plays a crucial role in the verifiable arithmetic circuit’s conversion into the QAP format. QAP is a formula system that employs polynomials to represent the behavior of the arithmetic circuit. By utilizing QAP, the security of the zkSNARKs algorithm is enhanced, along with the improvement of its implementation efficiency [13]. Finally, there is the zk-SNARK stage, where the verifiable arithmetic circuit and QAP are used to generate a proof. ZkSNARKs are powerful privacy protection protocols that can be utilized in digital payments, blockchain technology, and other fields. They can verify the authenticity of information while protecting the user’s privacy. Despite its relatively complex working principle, zk-SNARK technology has found widespread application, bringing higher security and privacy protection to the digital world. B. Circuit Language ZKP technology can address several fundamental issues in the modern digital world, including identity user’s verification without compromising their private information and safeguarding privacy data from unauthorized exploitation. Within ZKP, arithmetic circuits play a vital role in describing and computing complex operations. These circuits consist of a series of logic gates that can perform various arithmetic operations, such as addition, multiplication, and division. By combining these basic operations, the complex arithmetic circuits can be constructed to execute diverse computational tasks. The circuit referred to here is a theoretical computational model, not an actual electronic circuit. This is the formal arithmetic circuit definition in theoretical computer science [14]. **Definition II.**1. A finite field field F is a field that contains a finite number of integer elements. F = {0, . . . , p − 1} for some prime p > 2 The operations +, ×, = on F should (mod p) after calculation. A circuit is a triple (M, L, G), where Definition II.2. · M is a set of values, · L is a set of gate labels, each of which is a function from Mi to M for some non-negative integer i (where i represents the number of inputs to the gate), and · G is a labelled directed acyclic graph with labels from L. A arithmetic circuit is a map C : F n → F, where F is a finite field. Definition II.3. It is a directed acyclic graph (DAG) where internal nodes are labeled +, −, or × and inputs are labeled 1, x1, . . . , xn, the edges are wires or connections. 2) It defines an n-variable polynomial with an evaluation recipe. 3) Where |C| = # gates in C. This chapter mainly focuses on the Circom language, employed at the core step of zk-SNARK protocols for describing arithmetic circuits. Within the framework of ZKP systems, several commonly used arithmetic circuit description languages exist, including Arithmetica, libsnark DSL, and Circom. These languages are typically employed for building and verifying ZKP systems and can be used to describe various arithmetic circuits, such as linear constraint systems (LCS), bilinear pairings, and quadratic circuits. By representing an arithmetic circuit as a constraint system, Circom’s core idea involves describing inputs, outputs, and computation processes as linear equations and inequalities. This approach allows developers to define complex computation processes and generate the corresponding R1CS constraint system. Circom provides a set of high-level abstract concepts, enabling developers to focus more on the algorithm without being overwhelmed by low-level implementation details. C. Rank-1 Constraint Systems (R1CS) R1CS, a common Arithmetic Circuit format that underlies real-world systems [2] and an important part of the zkSNARKS algorithm groth16[15], represents computations as a set of constraint conditions, namely linear equations and inequalities. Each equation has its own set of coefficients, while each variable represents an input or output value. These equations and inequalities describe the limiting conditions of the computation, implying that satisfying these conditions correctly calculates the corresponding output result for the given input sequence. R1CS includes a formal definition of constraint-based computation rules, which can be verified using a set of public parameters and a private input sequence. For a more detailed understanding of the formal definition of R1CS, refer to Vitalik’s blog [13]. R1CS is a format for ZKP ACs. An R1CS is a conjunction of constraints, each of the form: Definition II.4. For example, a satisfied R1CS is shown in Fig.2: This constitutes a first-order constraint corresponding to a circuit multiplication gate. If we combine all constraints, we obtain a first-order constraint system. R1CS is widely used in practical applications as a powerful computational model. It serves as an integral component of the groth16 algorithm, which is a popular version of zk-SNARK algorithms. R1CS plays a crucial role in improving developers’ understanding of computer science and cryptography. Additionally, it offers crucial support for various privacy protection measures.54 In this paper, we propose the R1CS paradigm for constraint groups. It imposes constraints on the form and ordering of variable constraints. . R1CS paradigm is an R1CS satisfies the following requirements: Definition II.5 If a constraint in the R1CS paradigm contains multiplication between variables, it cannot have any other operators. 2) If a constraint in the R1CS paradigm does not contain multiplication between variables, it cannot contain intermediate variables generated by other linear constraints. 3) The ordering of constraints and variables (defined in ) in the R1CS paradigm must be consistent with the ordering method (× is in front of +) in this paper. Definition II.4 The specific adjustments required for converting a general constraint system into an R1CS paradigm will be explained through examples with concrete constraints. Requirement 1 suggests that complex quadratic constraints in the R1CS should be split into simpler forms. For instance. a × b + c + d = f =⇒ a × b = r, r + c + d = f 5 × a × b = c =⇒ 5 × a = r, r × b = c Requirement 2 indicates that linear constraints in the R1CS system must be eliminated by removing intermediate variables defined by other linear constraints. For example, a + b = c, c + d = e =⇒ a + b + d = e The specific sorting methods in requirement three will be discussed in later sections outlining the algorithm’s steps. D. Data Flow Graph In a bipartite-directed graph, known as a data flow graph, there are two types of nodes: links and actors. Actors are utilized to represent various operations, while links serve as the means by which data is received by actors. Additionally, arcs allow links to transmit values to actors. The formal definition of this concept can be found in Dennis’ paper [16]. . A data flow graph is a bipartite labeled graph where the two types of nodes are called actors and links. Definition II.6 G = ⟨A ∪ L, E⟩        (1) where A more detailed description can be found in [17]. E. Weighted Pagerank Algorithm In this paper, we adopt the weighted PageRank algorithm to compute the weight of each node in the data flow graph [18]. Pagerank algorithm is a method used for computing the ranking of web pages in search engine results. It was initially proposed by Larry Page and Sergey Brin, co-founders of Google, in 1998 and has since become one of the most essential algorithms in the field of search engines.[19] The algorithm assesses online web pages to determine their weight values, which it then utilizes to rank search results. PageRank is based on the notion that the weight of a web page is influenced by both the quantity and quality of the other web pages that link to it. The main steps of the Pagerank algorithm are as follows: Building the graph structure: First, the web pages and links on the internet must be converted into a graph structure. In this structure, each web page corresponds to a node and each link to a directed edge that points to the linked web page. 2) Computing the initial scores of each page: In Pagerank, the initial score of each page is set to 1. This means that initially, each node has an equal score. 3) Iteratively computing the scores of each page: Each node’s score is iteratively calculated based on its incoming links and averaged onto its outgoing links at each iteration. 4) Considering the number and quality of links: In addition to the relationships between nodes, Pagerank considers the number and quality of links pointing to a web page. Links from high-quality websites may carry more value than those from low-quality sites. Therefore, when computing scores, the algorithm weights links according to their number and quality. 5) Iterating until convergence: When the score of a node stabilizes, the algorithm stops iterating. This indicates that the final scores of all nodes have been determined and can be used to rank search results. The Weighted PageRank algorithm differs from the standard PageRank algorithm in that it incorporates the weight of each link as a factor, resulting in a more precise evaluation of a webpage’s importance. Considering the importance of pages, the original PageRank formula is modified as In this paper, we aim to use this algorithm to obtain more accurate weight values for each node in the data flow graph. sectionOverview In this section, we will introduce the procedure of normalization through the process of converting R1CS introduced in Vitalik’s blog [13] in the algorithm: Constraint Set: Firstly, the arithmetic tree generation process involves creating an arithmetic tree for each constraint within the input R1CS constraint group, which is subsequently merged. The resulting arithmetic tree comprises common subformulas stored in a DAG. The constructed data flow graph’s structure is shown in figure 5, which illustrates how the arithmetic trees are combined to form the data flow graph. Subsequently, a tile selection algorithm is implemented based on the data flow graph, which divides the graph into tiles. The division of the entire graph into tiles is illustrated in figure 6, depicting the overall procedure of the tile selection algorithm. The specifics of the tile selection process, including the form and selection logic, will be elaborated upon in subsequent chapters. Next, the data flow graph is abstracted further with the selection of tiles as a reference. A new abstracted node in the data flow graph replaces linear constraints represented by tiles. The abstracted node can be represented as an affine mapping, which preserves the linear relationship between the variables, enabling faster computation of the intermediate values during the proof generation process. This abstraction procedure streamlines the proof generation process and reduces the computational cost of generating the proof. We calculate the weight of each node with coefficients of the constraint. Then we calculate the weights of the selected individual tiles using the improved Weighted PageRank algorithm. The convergence process of the PageRank values of four nodes in the abstract graph is depicted in figure 8. Finally, constraints in the paradigm of R1CS are generated separately for each tile. And the constraints and variables are ranked by the node weights computed in the previous steps. Now we convert the input R1CS to its paradigm: This paper is under CC BY 4.0 DEED license. available on arxiv

How Zero-Knowledge Proofs and Rank-1 Constraint Systems Transform Blockchain Scalability

Introduction is a foundational class in UIKit and . Everything we see on the screen is constructed from `s and their subclasses. UIView iOS development UIView One topic often considered basic is the geometry of . It's easy to grasp initially, but complete understanding is often elusive, even for very experienced iOS engineers. In this article, we will dive deeply into the world of geometry. We will explain the main concepts, such as , , , , , how they relate to each other, and answer more advanced questions about computing the and Autolayout specifics. UIView UIView frame bounds center anchorPoint transform frame Playground To better understand the geometry, I've also developed a small iOS app: . https://github.com/psharanda/UIViewGeometry In the app, you can experiment with different properties in real time by adjusting sliders. Such an interactive approach is really helpful for grasping the nuances. UIView frame The definition of in Apple documentation is: UIView.frame The frame rectangle, which describes the view’s location and size in its superview’s coordinate system. Most of the time, we operate just with frames, either during manual layout or when printing the view's debug description. The designated initializer for also uses the frame as the only param. UIView This seems simple and straightforward. However, the reality is more complex. The frame is actually a computed property of . It is not the definitive source of the view's geometry. So, what is it exactly? UIView bounds Apparently, has many more properties related to geometry, and we’re now going to check the real, non-computed ones. Let’s examine the first of them: . UIView bounds The definition of is: UIView.bounds The bounds rectangle, which describes the view’s location and size in its own coordinate system. Usually, both and are simply equal to , and is the same as (however, it is not always true). bounds.origin.x bounds.origin.y 0.0 bounds.size frame.size What happens if is not equal to ? In that case, bounds basically act as a viewport, defining which part of the view coordinate system is visible to the outside world (superview). can also be seen as an additional translation (with a minus sign) for all subviews and view’s content rendered using . bounds.origin .zero bounds.origin drawRect This might remind you of . It is for a reason: the property of a is directly linked to its . UIScrollView contentOffset UIScrollView bounds.origin It's important to note that border, background, and shadow are rendered without considering . bounds.origin Previously, we mentioned that sometimes cannot be equal to . It may happen if transform is not equal to . frame.size bounds.size .identity According to the documentation, setting to any value when is not is considered undefined behavior (getting is still fine). However, setting when is not is valid.  In that case, describes the rectangle that fits the view after all transformations in its superview’s coordinate system. frame transform .identity bounds transform .identity frame center The definition of : UIView.center The center point of the view's frame rectangle in its superview’s coordinate system. However, the term "center" can be a bit misleading. It only represents the actual center of the view if the (more on this in the next section) is positioned at the center, specifically at ( , ). A more accurate definition for would be: view.anchorPoint 0.5 0.5 center The coordinates of the view’s anchor point in its superview’s coordinate system. UIView’s is exactly the same as . center CALayer.position The combination of and can fully replace the use of bounds center frame transform The transform property in iOS development is a fundamental concept that enables developers to apply geometric transformations to views. UIView The transform property of is of the type , which represents a matrix used for affine transformations. Affine transformations include: UIView CGAffineTransform Translation To move a view, you set the transform property with . For instance, moves the view 50 points to the right and 75 points down. CGAffineTransform(translationX:y:) view.transform = CGAffineTransform(translationX: 50, y: 75) Scaling To scale a view, use . For example, halves the size of the view in both width and height. CGAffineTransform(scaleX:y:) view.transform = CGAffineTransform(scaleX: 0.5, y: 0.5) Rotation To rotate a view, apply . The angle is in radians, so to rotate 30 degrees, you would use . CGAffineTransform(rotationAngle:) view.transform = CGAffineTransform(rotationAngle: .pi / 6) Combining Transforms One of the powerful aspects of the transform property is the ability to combine transformations. You can combine scaling, rotation, and translation into a single transform using concatenation, for example: var t = CGAffineTransform.identity // 0
t = t.concatenating(CGAffineTransform(scaleX: 0.5, y: 0.5)) //1
t = t.concatenating(CGAffineTransform(rotationAngle: .pi / 6)) //2
t = t.concatenating(CGAffineTransform(translationX: 50, y: 150)) //3
view.transform = t To reset a transformation, set the property to , which is also the default for a newly created . transform CGAffineTransform.identity UIView Perspective ’s transform is baked by which has the type and can be used for even more advanced transformations like changing the perspective UIView CALayer.transform CATransform3D var transform = CATransform3DIdentity;
transform.m34 = 1.0 / 500.0;
view.layer.transform = CATransform3DRotate(transform, .pi / 4, 0, 1, 0) anchorPoint The anchor point defines how a view behaves during transformations. It's specified using the unit coordinate space, where ( , ) is the top-left corner of the view's bounds rectangle, and ( , ) is the bottom-right corner. By default, the anchor point of a is set to ( , ), which is the center of the view’s bounds rectangle. 0 0 1 1 UIView 0.5 0.5 Interestingly, the property was only added to in iOS 16, but it has always been accessible through . anchorPoint UIView view.layer.anchorPoint Geometric manipulations, like rotation or scaling, occur around the anchor point. For example, if you apply a rotation transform to a view with the default anchor point, the view will rotate around its center. If you change the anchor point to a different location, the view will rotate around this new point. How to calculate the frame? We mentioned in the beginning that is a computed property. Now, with enough knowledge, let’s compile all the observations into actual code that computes the frame. frame First, let’s follow the positioning logic that is used during the render process. We start with a rectangle, with set to and set to . is not involved in calculations since it only affects subviews and the output. origin .zero size bounds.size bounds.origin drawRect Before applying the transform, we must translate the view according to its . We apply the transform only when the view, with its , is aligned with the starting point coordinates ( , ). anchorPoint anchorPoint 0 0 Now, we can apply the transform. The last step is to translate the view by its value, positioning it correctly. center These transformations can be concatenated into a single transform (i.e., absolute one), which is then applied to zero-origin bounds by using function. CGRectApplyAffineTransform Here is the final function which computes the frame: func computeFrame(bounds: CGRect,
                  center: CGPoint,
                  anchorPoint: CGPoint,
                  tranform: CGAffineTransform) -> CGRect {

    // set the initial rectangle to bounds with origin set to (0, 0)
    let zeroOriginBounds = CGRect(origin: .zero, size: bounds.size) // 1

    // combine transformations
    let absoluteTransform = CGAffineTransform(
            translationX: -anchorPoint.x * bounds.width,
            y: -anchorPoint.y * bounds.height
        ) // 2
        .concatenating(tranform) // 3
        .concatenating(CGAffineTransform(translationX: center.x, y: center.y)) // 4

    // apply transform to the initial rectangle
    return CGRectApplyAffineTransform(zeroOriginBounds, absoluteTransform)
} How can this knowledge be useful for us? Apart from just satisfying curiosity and gaining a better understanding of the internals, this algorithm has some real-world applications. A classic example is an image editor. Imagine you are building an application that creates custom stories. You want to place stickers on top of a photo, move, scale, and rotate them with your finger. For the editing mode, you use the actual and layout it by modifying its properties like center, bounds, and transform. Eventually, you’d like to render your story project into a bitmap and share it in high resolution, and that’s where understanding how geometry works becomes really useful. The image rendering code can look like the following: UIImageView UIView let renderer = UIGraphicsImageRenderer(size: imageSize)
let image = renderer.image { context in
    let cgContext = context.cgContext
    // render photo…
    // render other things…
    
    // render our sticker
    let absoluteTransform = CGAffineTransform(
        translationX: -sticker.anchorPoint.x * sticker.bounds.width,
        y: -sticker.anchorPoint.y * sticker.bounds.height
    )
        .concatenating(sticker.transform)
        .concatenating(
            CGAffineTransform(translationX: sticker.center.x, y: sticker.center.y)
        )
    
    cgContext.saveGState()
    cgContext.concatenate(absoluteTransform)
    sticker.image.draw(in: CGRect(origin: .zero, size: sticker.bounds.size))
    cgContext.restoreGState()
} What about Autolayout? Autolayout doesn't work with . It also ignores the and properties during its calculations. For each view, Autolayout calculates and sets only the and . The and are still used, but only for the final render on screen, and are applied afterward. frame transform anchorPoint bounds center transform anchorPoint To reiterate, in the Autolayout world, , , and don't exist. The Autolayout process is: constraints in, and out. frame transform anchorPoint bounds center Additional Resources UIView Documentation – https://developer.apple.com/documentation/uikit/uiview View Programming Guide – https://developer.apple.com/library/archive/documentation/WindowsViews/Conceptual/ViewPG_iPhoneOS/WindowsandViews/WindowsandViews.html#//apple_ref/doc/uid/TP40009503-CH2-SW5 Core Animation Basics – https://developer.apple.com/library/archive/documentation/Cocoa/Conceptual/CoreAnimation_guide/CoreAnimationBasics/CoreAnimationBasics.html#//apple_ref/doc/uid/TP40004514-CH2-SW3 Understanding UIKit Rendering – https://www.wwdcnotes.com/notes/wwdc11/121/ Understanding UIKit: CALayer Anchor Point – https://ikyle.me/blog/2022/understanding-uikit-calayer-anchor-point Understanding UIScrollView – https://oleb.net/blog/2014/04/understanding-uiscrollview/

Mastering UIView Geometry: A Dive into UIKit's Foundational Class and Geometry Concepts for iOS

PARAG AGRAWAL VIJAYA GADDE, and NED SEGAL v. Twitter Court Filing, retrieved on April 10, 2023, is part of . You can jump to any part in this filing . This is part 23 of 37. HackerNoon’s Legal PDF Series here ARTICLE X - GENERAL MATTERS 10.1 EXECUTION OF CORPORATE CONTRACTS AND INSTRUMENTS Except as otherwise provided by law, the certificate of incorporation or these bylaws, the board of directors may authorize any officer or officers, or agent or agents, to enter into any contract or execute any document or instrument in the name of and on behalf of the corporation; such authority may be general or confined to specific instances. Unless so authorized or ratified by the board of directors or within the agency power of an officer, no officer, agent or employee shall have any power or authority to bind the corporation by any contract or engagement or to pledge its credit or to render it liable for any purpose or for any amount. 10.2 FISCAL YEAR The fiscal year of the corporation shall be fixed by resolution of the board of directors and may be changed by the board of directors. 10.3 SEAL The corporation may adopt a corporate seal, which shall be adopted and which may be altered by the board of directors. The corporation may use the corporate seal by causing it or a facsimile thereof to be impressed or affixed or in any other manner reproduced. 10.4 CONSTRUCTION; DEFINITIONS Unless the context requires otherwise, the general provisions, rules of construction, and definitions in the DGCL shall govern the construction of these bylaws. Without limiting the generality of this provision, the singular number includes the plural, the plural number includes the singular, and the term person includes a corporation, partnership, limited liability company, joint venture, trust or other enterprise, and a natural person. Any reference in these bylaws to a section of the DGCL shall be deemed to refer to such section as amended from time to time and any successor provisions thereto. Continue Reading . Here About HackerNoon Legal PDF Series: We bring you the most important technical and insightful public domain court case filings. This court case 2023-0409 retrieved on October 4, 2023, from is part of the public domain. The court-created documents are works of the federal government, and under copyright law, are automatically placed in the public domain and may be shared without legal restriction. int.nyt.com

Twitter Sued By Former Executives: Details on Corporate Contracts, Fiscal Year, and More

Wives and Daughters by Elizabeth Cleghorn Gaskell, is part of the HackerNoon Books Series. You can jump to any chapter in this book . "OFF WITH THE OLD LOVE, AND ON WITH THE NEW." here CHAPTER LVI. "OFF WITH THE OLD LOVE, AND ON WITH THE NEW." The next morning saw Mrs. Gibson in a much more contented frame of mind. She had written and posted her letter, and the next thing was to keep Cynthia in what she called a reasonable state, or, in other words, to try and cajole her into docility. But it was so much labour lost. Cynthia had already received a letter from Mr. Henderson before she came down to breakfast,—a declaration of love, a proposal of marriage as clear as words could make it; together with an intimation that, unable to wait for the slow delays of the post, he was going to follow her down to Hollingford, and would arrive at the same time that she had done herself on the previous day. Cynthia said nothing about this letter to any one. She came late into the breakfast-room, after Mr. and Mrs. Gibson had finished the actual business of the meal; but her unpunctuality was quite accounted for by the fact that she had been travelling all the night before. Molly was not as yet strong enough to get up so early. Cynthia hardly spoke, and did not touch her food. Mr. Gibson went about his daily business, and Cynthia and her mother were left alone. "My dear," said Mrs. Gibson, "you are not eating your breakfast as you should do. I am afraid our meals seem very plain and homely to you after those in Hyde Park Street?" "No," said Cynthia; "I'm not hungry, that's all." "If we were as rich as your uncle, I should feel it to be both a duty and a pleasure to keep an elegant table; but limited means are a sad clog to one's wishes. I don't suppose that, work as he will, Mr. Gibson can earn more than he does at present; while the capabilities of the law are boundless. Lord Chancellor! Titles as well as fortune!" Cynthia was almost too much absorbed in her own reflections to reply, but she did say,—"Hundreds of briefless barristers. Take the other side, mamma." "Well; but I have noticed that many of these have private fortunes." "Perhaps. Mamma, I expect Mr. Henderson will come and call this morning." "Oh, my precious child! But how do you know? My darling Cynthia, am I to congratulate you?" "No! I suppose I must tell you. I have had a letter this morning from him, and he's coming down by the 'Umpire' to-day." "But he has offered? He surely must mean to offer, at any rate?" Cynthia played with her teaspoon before she replied; then she looked up, like one startled from a dream, and caught the echo of her mother's question. "Offered! yes, I suppose he has." "And you accept him? Say 'yes,' Cynthia, and make me happy!" "I shan't say 'yes' to make any one happy except myself, and the Russian scheme has great charms for me." She said this to plague her mother, and lessen Mrs. Gibson's exuberance of joy, it must be confessed; for her mind was pretty well made up. But it did not affect Mrs. Gibson, who affixed even less truth to it than there really was. The idea of a residence in a new, strange country, among new, strange people, was not without allurement to Cynthia. "You always look nice, dear; but don't you think you had better put on that pretty lilac silk?" "I shall not vary a thread or a shred from what I have got on now." "You dear, wilful creature! you know you always look lovely in whatever you put on." So, kissing her daughter, Mrs. Gibson left the room, intent on the lunch which should impress Mr. Henderson at once with an idea of family refinement. Cynthia went upstairs to Molly; she was inclined to tell her about Mr. Henderson, but she found it impossible to introduce the subject naturally, so she left it to time to reveal the future as gradually as it might. Molly was tired with a bad night; and her father, in his flying visit to his darling before going out, had advised her to stay upstairs for the greater part of the morning, and to keep quiet in her own room till after her early dinner, so Time had not a fair chance of telling her what he had in store in his budget. Mrs. Gibson sent an apology to Molly for not paying her her usual morning visit, and told Cynthia to give Mr. Henderson's probable coming as a reason for her occupation downstairs. But Cynthia did no such thing. She kissed Molly, and sate silently by her, holding her hand; till at length she jumped up, and said, "You shall be left alone now, little one. I want you to be very well and very bright this afternoon: so rest now." And Cynthia left her, and went to her own room, locked the door, and began to think. Some one was thinking about her at the same time, and it was not Mr. Henderson. Roger had heard from Mr. Gibson that Cynthia had come home, and he was resolving to go to her at once, and have one strong, manly attempt to overcome the obstacles whatever they might be—and of their nature he was not fully aware—that she had conjured up against the continuance of their relation to each other. He left his father—he left them all—and went off into the woods, to be alone until the time came when he might mount his horse and ride over to put his fate to the touch. He was as careful as ever not to interfere with the morning hours that were tabooed to him of old; but waiting was very hard work when he knew that she was so near, and the time so near at hand. Yet he rode slowly, compelling himself to quietness and patience when he was once really on the way to her. "Mrs. Gibson at home? Miss Kirkpatrick?" he asked of the servant, Maria, who opened the door. She was confused, but he did not notice it. "I think so—I'm not sure! Will you walk up into the drawing-room, sir? Miss Gibson is there, I know." So he went upstairs, all his nerves on the strain for the coming interview with Cynthia. It was either a relief or a disappointment, he was not sure which, to find only Molly in the room:—Molly, half lying on the couch in the bow-window which commanded the garden; draped in soft white drapery, very white herself, and a laced half-handkerchief tied over her head to save her from any ill effects of the air that blew in through the open window. He was so ready to speak to Cynthia that he hardly knew what to say to any one else. "I am afraid you are not so well," he said to Molly, who sat up to receive him, and who suddenly began to tremble with emotion. "I'm a little tired, that's all," said she; and then she was quite silent, hoping that he might go, and yet somehow wishing him to stay. But he took a chair and placed it near her, opposite to the window. He thought that surely Maria would tell Miss Kirkpatrick that she was wanted, and that at any moment he might hear her light quick footstep on the stairs. He felt he ought to talk, but he could not think of anything to say. The pink flush came out on Molly's cheeks; once or twice she was on the point of speaking, but again she thought better of it; and the pauses between their faint disjointed remarks became longer and longer. Suddenly, in one of these pauses, the merry murmur of distant happy voices in the garden came nearer and nearer; Molly looked more and more uneasy and flushed, and in spite of herself kept watching Roger's face. He could see over her into the garden. A sudden deep colour overspread him, as if his heart had sent its blood out coursing at full gallop. Cynthia and Mr. Henderson had come in sight; he eagerly talking to her as he bent forward to look into her face; she, her looks half averted in pretty shyness, was evidently coquetting about some flowers, which she either would not give, or would not take. Just then, for the lovers had emerged from the shrubbery into comparatively public life, Maria was seen approaching; apparently she had feminine tact enough to induce Cynthia to leave her present admirer, and to go a few steps to meet her to receive the whispered message that Mr. Roger Hamley was there, and wished to speak to her. Roger could see her startled gesture; she turned back to say something to Mr. Henderson before coming towards the house. Now Roger spoke to Molly—spoke hurriedly, spoke hoarsely. "Molly, tell me! Is it too late for me to speak to Cynthia? I came on purpose. Who is that man?" "Mr. Henderson. He only came to-day—but now he is her accepted lover. Oh, Roger, forgive me the pain!" "Tell her I have been, and am gone. Send out word to her. Don't let her be interrupted." And Roger ran downstairs at full speed, and Molly heard the passionate clang of the outer door. He had hardly left the house before Cynthia entered the room, pale and resolute. "Where is he?" she said, looking around, as if he might yet be hidden. "Gone!" said Molly, very faint. "Gone. Oh, what a relief! It seems to be my fate never to be off with the old lover before I am on with the new, and yet I did write as decidedly as I could. Why, Molly, what's the matter?" for now Molly had fainted away utterly. Cynthia flew to the bell, summoned Maria, water, salts, wine, anything; and as soon as Molly, gasping and miserable, became conscious again, she wrote a little pencil-note to Mr. Henderson, bidding him return to the "George," whence he had come in the morning, and saying that if he obeyed her at once, he might be allowed to call again in the evening, otherwise she would not see him till the next day. This she sent down by Maria, and the unlucky man never believed but that it was Miss Gibson's sudden indisposition in the first instance that had deprived him of his charmer's company. He comforted himself for the long solitary afternoon by writing to tell all his friends of his happiness, and amongst them uncle and aunt Kirkpatrick, who received his letter by the same post as that discreet epistle of Mrs. Gibson's, which she had carefully arranged to reveal as much as she wished, and no more. "Was he very terrible?" asked Cynthia, as she sate with Molly in the stillness of Mrs. Gibson's dressing-room. "Oh, Cynthia, it was such pain to see him, he suffered so!" "I don't like people of deep feelings," said Cynthia, pouting. "They don't suit me. Why couldn't he let me go without this fuss? I'm not worth his caring for!" "You have the happy gift of making people love you. Remember Mr. Preston,—he too wouldn't give up hope." "Now I won't have you classing Roger Hamley and Mr. Preston together in the same sentence. One was as much too bad for me as the other is too good. Now I hope that man in the garden is the ,—I'm that myself, for I don't think I'm vicious, and I know I'm not virtuous." juste milieu "Do you really like him enough to marry him?" asked Molly earnestly. "Do think, Cynthia. It won't do to go on throwing your lovers off; you give pain that I'm sure you do not mean to do,—that you cannot understand." "Perhaps I can't. I'm not offended. I never set up for what I am not, and I know I'm not constant. I've told Mr. Henderson so—" She stopped, blushing and smiling at the recollection. "You have! and what did he say?" "That he liked me just as I was; so you see he's fairly warned. Only he's a little afraid, I suppose,—for he wants me to be married very soon, almost directly, in fact. But I don't know if I shall give way,—you hardly saw him, Molly,—but he's coming again to-night, and mind, I'll never forgive you if you don't think him very charming. I believe I cared for him when he offered all those months ago, but I tried to think I didn't; only sometimes I really was so unhappy, I thought I must put an iron band round my heart to keep it from breaking, like the Faithful John of the German story,—do you remember, Molly?—how when his master came to his crown and his fortune and his lady-love, after innumerable trials and disgraces, and was driving away from the church where he'd been married in a coach and six, with Faithful John behind, the happy couple heard three great cracks in succession, and on inquiring, they were the iron-bands round his heart, that Faithful John had worn all during the time of his master's tribulation, to keep it from breaking." In the evening Mr. Henderson came. Molly had been very curious to see him; and when she saw him she was not sure whether she liked him or not. He was handsome, without being conceited; gentlemanly, without being foolishly fine. He talked easily, and never said a silly thing. He was perfectly well-appointed, yet never seemed to have given a thought to his dress. He was good-tempered and kind; not without some of the cheerful flippancy of repartee which belonged to his age and profession, and which his age and profession are apt to take for wit. But he wanted something in Molly's eyes—at any rate, in this first interview, and in her heart of hearts she thought him rather commonplace. But of course she said nothing of this to Cynthia, who was evidently as happy as she could be. Mrs. Gibson, too, was in the seventh heaven of ecstasy, and spoke but little; but what she did say, expressed the highest sentiments in the finest language. Mr. Gibson was not with them for long, but while he was there he was evidently studying the unconscious Mr. Henderson with his dark penetrating eyes. Mr. Henderson behaved exactly as he ought to have done to everybody: respectful to Mr. Gibson, deferential to Mrs. Gibson, friendly to Molly, devoted to Cynthia. The next time Mr. Gibson found Molly alone, he began,—"Well! and how do you like the new relation that is to be?" "It's difficult to say. I think he's very nice in all his bits, but—rather dull on the whole." "I think him perfection," said Mr. Gibson, to Molly's surprise; but in an instant afterwards she saw that he had been speaking ironically. He went on. "I don't wonder she preferred him to Roger Hamley. Such scents! such gloves! And then his hair and his cravat!" "Now, papa, you're not fair. He is a great deal more than that. One could see that he had very good feeling; and he is very handsome, and very much attached to her." "So was Roger. However, I must confess I shall be only too glad to have her married. She's a girl who'll always have some love-affair on hand, and will always be apt to slip through a man's fingers if he doesn't look sharp; as I was saying to Roger—" "You have seen him, then, since he was here?" "Met him in the street." "How was he?" "I don't suppose he'd been going through the pleasantest thing in the world; but he'll get over it before long. He spoke with sense and resignation, and didn't say much about it; but one could see that he was feeling it pretty sharply. He's had three months to think it over, remember. The Squire, I should guess, is showing more indignation. He is boiling over, that any one should reject his son! The enormity of the sin never seems to have been apparent to him till now, when he sees how Roger is affected by it. Indeed, with the exception of myself, I don't know one reasonable father; eh, Molly?" Whatever else Mr. Henderson might be, he was an impatient lover; he wanted to marry Cynthia directly—next week—the week after; at any rate before the long vacation, so that they could go abroad at once. Trousseaux, and preliminary ceremonies, he gave to the winds. Mr. Gibson, generous as usual, called Cynthia aside a morning or two after her engagement, and put a hundred-pound note into her hands. "There! that's to pay your expenses to Russia and back. I hope you'll find your pupils obedient." To his surprise, and rather to his discomfiture, Cynthia threw her arms round his neck and kissed him. "You are the kindest person I know," said she; "and I don't know how to thank you in words." "If you tumble my shirt-collars again in that way, I'll charge you for the washing. Just now, too, when I'm trying so hard to be trim and elegant, like your Mr. Henderson." "But you do like him, don't you?" said Cynthia, pleadingly. "He does so like you." "Of course. We're all angels just now, and you're an arch-angel. I hope he'll wear as well as Roger." Cynthia looked grave. "That was a very silly affair," she said. "We were two as unsuitable people—" "It has ended, and that's enough. Besides, I've no more time to waste; and there's your smart young man coming here in all haste." Mr. and Mrs. Kirkpatrick sent all manner of congratulations; and Mrs. Gibson, in a private letter, assured Mrs. Kirkpatrick that her ill-timed confidence about Roger should be considered as quite private. For as soon as Mr. Henderson had made his appearance in Hollingford, she had written a second letter, entreating them not to allude to anything she might have said in her first; which she said was written in such excitement on discovering the real state of her daughter's affections, that she had hardly known what she had said, and had exaggerated some things, and misunderstood others: all that she did know now was, that Mr. Henderson had just proposed to Cynthia, and was accepted, and that they were as happy as the day was long, and ("excuse the vanity of a mother,") made a most lovely couple. So Mr. and Mrs. Kirkpatrick wrote back an equally agreeable letter, praising Mr. Henderson, admiring Cynthia, and generally congratulatory; insisting into the bargain that the marriage should take place from their house in Hyde Park Street, and that Mr. and Mrs. Gibson and Molly should all come up and pay them a visit. There was a little postscript at the end. "Surely you do not mean the famous traveller, Hamley, about whose discoveries all our scientific men are so much excited. You speak of him as a young Hamley, who went to Africa. Answer this question, pray, for Helen is most anxious to know." This P.S. being in Helen's handwriting. In her exultation at the general success of everything, and desire for sympathy, Mrs. Gibson read parts of this letter to Molly; the postscript among the rest. It made a deeper impression on Molly than even the proposed kindness of the visit to London. There were some family consultations; but the end of them all was that the Kirkpatrick invitation was accepted. There were many small reasons for this, which were openly acknowledged; but there was one general and unspoken wish to have the ceremony performed out of the immediate neighbourhood of the two men whom Cynthia had previously—rejected; that was the word now to be applied to her treatment of them. So Molly was ordered and enjoined and entreated to become strong as soon as possible, in order that her health might not prevent her attending the marriage; Mr. Gibson himself, though he thought it his duty to damp the exultant anticipations of his wife and her daughter, being not at all averse to the prospect of going to London, and seeing half-a-dozen old friends, and many scientific exhibitions, independently of the very fair amount of liking which he had for his host, Mr. Kirkpatrick himself. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Elizabeth Cleghorn Gaskell (2003). Wives and Daughters. Urbana, Illinois: Project Gutenberg. Retrieved https://www.gutenberg.org/cache/epub/4274/pg4274-images.html This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at , located at . www.gutenberg.org https://www.gutenberg.org/policy/license.html

"OFF WITH THE OLD LOVE, AND ON WITH THE NEW."

Scientific American Supplement, No. 365, December 30, 1882 by Various, is part of the HackerNoon Books Series. You can jump to any chapter in this book . APPARATUS FOR MEASURING ELECTRICITY AT THE UPPER SCHOOL OF TELEGRAPHY. here APPARATUS FOR MEASURING ELECTRICITY AT THE UPPER SCHOOL OF TELEGRAPHY. —On a former occasion I described an instrument to which, in 1873, I gave the name , and which is nothing else than a tuning fork whose motion is kept up electrically in such a way as to last indefinitely, provided that the elements of the pile are renewed gradually, and that from time to time the metallic contact is changed, which causes, at every oscillation, the current to pass from the pile into the magnet, which keeps up the vibration. Electro Tuning Forks and their Uses. Electro-Tuning Fork We reproduce herewith, in Fig. 1, a cut showing in projection one of the simplest forms of the apparatus. If we imagine the platinum or steel style, , of the figure to be done away with, as well as the platinized plate, I, and its communication with the negative pole of the pile, P, we shall have the ordinary instrument kept in operation electrically by the aid of the electro-magnet, E, the style, , the interrupting plate, I, and the pile. s s If we preserve the parts above mentioned, the instrument will possess the property of having vibrations of a constant amplitude if sufficient energy be kept up in the pile. In fact, when the amplitude is sufficiently great to cause the style, , to touch the plate, I, it will be seen that at such a moment the current no longer passes through the electromagnet, and the vibration is no longer maintained. The amplitude cannot exceed an extent which shall permit the style, , to touch I. s s Under such conditions, the duration of the vibrations remains exactly constant, as does also the vibratory intensity of the entire instrument. The measurement of time, then, by an instrument of this kind is, indeed, as perfect as it could well be. This complication in the arrangement of the apparatus has no importance as regards those tuning forks the number of whose vibrations exceeds a hundred per second, for in such a case these are given an amplitude of a few millimeters only; but it would be of importance with regard to instruments whose number of vibrations is very small, and to which it might be desirable to give great amplitude; for then, as I have long ago shown, the duration of the oscillation would depend a little on the amplitude, but a very little, it is true. I shall not refer now to the applications of these instruments in chronography, but will rather point out first the applications in which they are destined to produce an effective power. For this purpose it is necessary to make them pretty massive. The number of the vibrations depends upon such massiveness, and it is necessity to know the relation which exists between these two quantities in order to be able to construct an instrument under determinate conditions. I made in former years such a research with regard to tuning forks of prismatic form, that is to say, of a constant rectangular section continuing even into the bent portion where the parallel branches are united by a semicylinder, at the middle of which is the wrought iron rod as well as the branches. The of the instrument is the dimension parallel to the vibrations; its is the dimension which is perpendicular to them, and its is reckoned from the extremity of the branches up to the middle of the curved portion. thickness width length It is found that the number of vibrations is independent of the width, proportional to the thickness, and very nearly inverse ratio of the square of the length, provided the latter exceeds ten centimeters. If we represent the length by , the thickness by , and the number of vibrations by , we shall have the following formula: l e n = × ( / 2) n k e l in which is a constant quantity whose value depends upon the nature of the metal of which the tuning fork is made. k This constant varies very little from steel to malleable cast iron, and it may be taken as equal to 818270. Thus, then, we have a means of constructing a tuning fork in which two of the three quantities, , , , are given in advance. Experience proves that no errors are committed exceeding one or two per cent. n e l It is seen from this that there is a means of increasing the mass of the instrument without changing anything in the thickness, the length or, consequently, the number of vibrations, and this is by increasing the . breadth It is in this way that I have succeeded in having long massive tuning forks made of malleable iron, giving no more than 12 to 15 vibrations per second, and vibrating with perfect regularity. Fig. 2, annexed, shows one of these instruments of about 55 centimeters length, whose breadth, E, is from 5 to 6 centimeters, and which makes about fifteen double vibrations per second only. This number might be still further reduced, but at the expense of our being led to exaggerate the longitudinal dimensions of the apparatus in such a way as to make it inconvenient. The object may be attained more simply by loading the branches with slides supporting leaden weights, M, of 500 grammes each. By fixing these slides at different points on the branches, the number of vibrations can be made to vary from simple to double, and even triple. Thus, by fixing them at the extremity of the branches the number of the vibrations is reduced to 5 or 6. There will be seen in the figure the electro-magnet which keeps up the vibration. This is formed of three simple electro-magnets, whose bobbins have a resistance of no more than 10 ohms, and which are united in series. The interrupting plate, P, against which the style, , rests at each vibration, is capable of a forward movement, or one of recoil, by the aid of a screw, V, and of an eccentric movement which is produced by a small handle, , and during which its plane remains invariable. This arrangement permits the point of contact of the style and plate to be varied without changing the precision with which the contact takes place, and all the points of the plate to be slowly used in succession before replacing it. The motion is produced by means of a relatively weak pile, whose poles are connected to the terminals, A and A'. Three Callaud elements of triple surface, renewed one after the other every month at the most, are sufficient to keep up the vibrations continuously, day and night, without interruption, and that too even when the instrument is employed in producing a small mechanical power, as we shall see further on. s m We have now seen how electro-tuning forks may be constructed of large dimensions, of large mass, and giving a small number of vibrations per second. Such instruments are well fitted to perform the role of electrical interrupters, and it was in such a character that one of them figured in the Exhibition of the Upper School of Telegraphy as a type of an interrupter for testing piles. When it is desired to test a pile to ascertain the practicability of employing it in telegraphy, it is necessary to make it perform a work which shall be as nearly as possible identical with that which it will be called on to do, until it is used up, to estimate the duration of such work, to measure regularly the constants of the pile, the electro-motive power, and the internal resistance. Usually, in telegraphy, this work consists in sending over a line of a certain resistance intermittent currents, through the intermedium of suitable manipulators. It suffices then to cause the branches of the electro tuning fork to play the role of one of these manipulators. For doing this the tuning fork carries two insulating ebonite or ivory strips, B B (Fig. 3), which, at every oscillation, abut against vertical brass springs, . Each of these latter is located in front of the platinized point of a screw, , which is affixed to a small metallic tongue. The springs and tongues are insulated from each other, and are mounted on a piece which may be moved by a screw, V, so as to cause the springs of the strips, B B', to approach or recede according to the amplitude of the instrument's vibrations. Each spring and tongue is connected with terminals affixed to the base of the apparatus. One of the poles of one element, P, of the pile is connected with the tongue and corresponding screw, while the other pole is connected with the screw in front of it through the intermedium of a galvanometer, 2, which gives the intensity of the intermittent current, and of a resistance coil, 2, which performs the role of an artificial telegraph line. The apparatus being set in operation, it will be seen that the current from the pile is emitted once at every vibration. r v g b Thus there may be exhausted as many pile elements as there are springs, and that, too, simultaneously; and the contacts of the screws and springs can be regulated in such a way that the duration of the emissions shall be the same for all. At the laboratory of the School of Telegraphy one of these instruments has operated without interruption, day and night, during eighteen months. The apparatus shown in Fig. 4 is also an interrupting electro-tuning fork, but it makes a much greater number of vibrations than the preceding, and may serve for other electric tests. The operation of the tuning fork is kept up electrically by the aid of the screw, , and the corresponding plate; of the style, , and of the fine wire spiral spring, , both insulated from the fork, from the electro-magnet, N, and from the two wires, F F', which communicate with a pile. v s f The interrupting system is symmetrical with the first. It consists of the style, , of the spiral spring, , of the screw, , and of the plate that this carries at its extremity. The terminal, B, which carries the spring, , and the rod which carries the screw being insulated from each other, it is only necessary to cause to terminate therein the extremities of a circuit comprising one pile, in order to produce in the circuit a number of interruptions equal to that of the tuning fork's vibrations. Provided the lengths of the springs, and , are proper, such vibrations will not be altered. s f v f f f' Moreover, the instrument is so arranged as to produce vibrations whose during the whole time the experiments last. This is done by modifying the of the vibrations; for the greater the amplitude, the longer likewise the duration of the contact of the style, , on the corresponding plate, and the shorter the duration of the interruption. In order to modify the amplitude, the action of the electro-magnet on the branches of the apparatus is made to vary. To effect this, the electro-magnet is made movable perpendicularly by the aid of a screw, V, between two slides, so that the core, N, may be moved with respect to the median line of the branches, and even be raised above them. Its action diminishes, necessarily, while it is being raised, and the amplitude of the vibrations likewise diminishes gradually and continuously. It may thus be made, without difficulty, to vary from two to three tenths of a millimeter to three or four millimeters or more. duration can be varied at pleasure and kept constant amplitude s But it is not sufficient to cause the amplitude to vary; it is necessary to measure it and to keep it constant at the value desired. The measurement is effected by the aid of a very simple apparatus that I have before described under the name of the . This is a small square of paper carrving a design like that shown in Fig. 5, and which is seen in Fig. 4 glued to one of the masses, M, which serve to vary the number of the instrument's vibrations. This figure is in fact, an angle, one of whose sides is graduated into millimeters, for example, and the other forms the edge of a wide black band. The apex of the angle is above and the divided side is perpendicular to the direction of the vibrations. vibrating micrometer Under such conditions, when the fork is vibrating, the apex of the angle, by virtue of the persistence of impressions upon the retina, to advance along the graduation in measure as the amplitude of the vibrations increases. If an angle has been drawn such that the slope of one of its sides to the other is one-tenth, it is easy to see that for each millimeter passed over by the apex of the angle, the amplitude will increase by two-tenths of a millimeter. seems apparently This is the way, then, that the amplitude is measured. On another hand, it suffices to keep the apex of the angle of the micrometer immovable, in order to be sure of the constancy of the tuning fork's amplitude; and this is done, when necessary, by causing the screw, V, to move slightly. The instrument represented in Fig. 4 is, moreover, fixed to a support devised by Mr. A. Duboscq, so as to make it possible to give the tuning fork every position possible with respect to a vertical plane; to raise it or lower it, and to move it backward or forward so that it may be employed for chimography, and in all those experiments in which electro-tuning folks are used. E. MERCADIER. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Various (2006). Scientific American Supplement, No. 365, December 30, 1882. Urbana, Illinois: Project Gutenberg. Retrieved https://www.gutenberg.org/cache/epub/18763/pg18763-images.html This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at , located at . www.gutenberg.org https://www.gutenberg.org/policy/license.html

APPARATUS FOR MEASURING ELECTRICITY AT THE UPPER SCHOOL OF TELEGRAPHY

North and South by Elizabeth Cleghorn Gaskell, is part of the HackerNoon Books Series. You can jump to any chapter in this book . CHAPTER XLVIII. here CHAPTER XLVIII. “NE’ER TO BE FOUND AGAIN.” “My own, my father’s friend! I cannot part with thee! I ne’er have shown, thou ne’er hast known, How dear thou art to me.” Anon. The elements of the dinner-parties which Mrs. Lennox gave, were these; her friends contributed the beauty, Captain Lennox the easy knowledge of the subjects of the day; and Mr. Henry Lennox, and the sprinkling of rising men who were received as his friends, brought the wit, the cleverness, the keen and extensive knowledge of which they knew well enough how to avail themselves without seeming pedantic, or burdening the rapid flow of conversation. These dinners were delightful; but even here Margaret’s dissatisfaction found her out. Every talent, every feeling, every acquirement; nay, even every tendency towards virtue, was used up as materials for fireworks; the hidden, sacred fire, exhausted itself in sparkle and crackle. They talked about art in a merely sensuous way, dwelling on outside effects, instead of allowing themselves to learn what it has to teach. They lashed themselves up into an enthusiasm about high subjects in company, and never thought about them when they were alone; they squandered their capabilities of appreciation into a mere flow of appropriate words. One day, after the gentlemen had come up into the drawing-room, Mr. Lennox drew near to Margaret, and addressed her in almost the first voluntary words he had spoken to her since she had returned to live in Harley Street. “You did not look pleased at what Shirley was saying at dinner.” “Didn’t I? My face must be very expressive,” replied Margaret. “It always was. It has not lost the trick of being eloquent.” “I did not like,” said Margaret, hastily, “his way of advocating what he knew to be wrong—so glaringly wrong—even in jest.” “But it was very clever. How every word told! Did you remember the happy epithets?” “Yes.” “And despise them, you would like to add. Pray don’t scruple, though he is my friend.” “There! that is the exact tone in you, that”—she stopped short. He listened for a moment to see if she would finish her sentence; but she only reddened, and turned away; before she did so, however, she heard him say, in a very low, clear voice,— “If my tones, or modes of thought, are what you dislike, will you do me the justice to tell me so, and so give me the chance of learning to please you.” All these weeks there was no intelligence of Mr. Bell’s going to Milton. He had spoken of it at Helstone as of a journey which he might have to take in a very short time from then; but he must have transacted his business by writing. Margaret thought, ere now, and she knew that if he could, he would avoid going to a place which he disliked, and moreover would little understand the secret importance which she affixed to the explanation that could only be given by word of mouth. She knew that he would feel that it was necessary that it should be done; but whether in summer, autumn, or winter, it would signify very little. It was now August, and there had been no mention of the Spanish journey to which he had alluded to Edith, and Margaret tried to reconcile herself to the fading away of this illusion. But one morning she received a letter, saying that next week he meant to come up to town; he wanted to see her about a plan which he had in his head; and, moreover, he intended to treat himself to a little doctoring, as he had begun to come round to her opinion, that it would be pleasanter to think that his health was more in fault than he, when he found himself irritable and cross. There was altogether a tone of forced cheerfulness in the letter, as Margaret noticed afterwards; but at the time her attention was taken up by Edith’s exclamations. “Coming up to town! Oh dear! and I am so worn out by the heat that I don’t believe I have strength enough in me for another dinner. Besides, everybody has left but our dear stupid selves, who can’t settle where to go to. There would be nobody to meet him.” “I’m sure he would much rather come and dine with us quite alone than with the most agreeable strangers you could pick up. Besides, if he is not well he won’t wish for invitations. I am glad he has owned it at last. I was sure he was ill from the whole tone of his letters, and yet he would not answer me when I asked him, and I had no third person to whom I could apply for news.” “Oh! he is not very ill, or he would not think of Spain.” “He never mentions Spain.” “No! but his plan that is to be proposed evidently relates to that. But would you really go in such weather as this?” “Oh, it will get cooler every day. Yes! Think of it. I am only afraid I have thought and wished too much—in that absorbing wilful way which is sure to be disappointed—or else gratified, to the letter, while in the spirit it gives no pleasure.” “But that’s superstitious, I’m sure, Margaret.” “No, I don’t think it is. Only it ought to warn me, and check me from giving way to such passionate wishes. It is a sort of ‘Give me children, or else I die.’ I’m afraid my cry is, ‘Let me go to Cadiz, or else I die.’” “My dear Margaret! You’ll be persuaded to stay there; and then what shall I do? Oh! I wish I could find somebody for you to marry here, that I could be sure of you!” “I shall never marry.” “Nonsense, and double nonsense! Why, as Sholto says, you’re such an attraction to the house, that he knows ever so many men who will be glad to visit here next year for your sake.” Margaret drew herself up haughtily. “Do you know, Edith, I sometimes think your Corfu life has taught you——” “Well!” “Just a shade or two of coarseness.” Edith began to sob so bitterly, and to declare so vehemently that Margaret had lost all love for her, and no longer looked upon her as a friend, that Margaret came to think that she had expressed too harsh an opinion for the relief of her own wounded pride, and ended by being Edith’s slave for the rest of the day; while that little lady, overcome by wounded feeling, lay like a victim on the sofa, heaving occasionally a profound sigh, till at last she fell asleep. Mr. Bell did not make his appearance even on the day to which he had for a second time deferred his visit. The next morning there came a letter from Wallis, his servant, stating that his master had not been feeling well for some time, which had been the true reason of his putting off his journey; and that at the very time when he should have set out for London, he had been seized with an apoplectic fit; it was, indeed, Wallis added, the opinion of the medical men—that he could not survive the night; and more than probable, that by the time Miss Hale received this letter his poor master would be no more. Margaret received this letter at breakfast-time, and turned very pale as she read it; then, silently putting into Edith’s hands, she left the room. Edith was terribly shocked as she read it, and cried in a sobbing, frightened, childish way, much to her husband’s distress. Mrs. Shaw was breakfasting in her own room, and upon him devolved the task of reconciling his wife to the near contact into which she seemed to be brought with death, for the first time that she could remember in her life. Here was a man who was to have dined with them to-day lying dead or dying instead! It was some time before she could think of Margaret. Then she started up, and followed her upstairs into her room. Dixon was packing up a few toilette articles, and Margaret was hastily putting on her bonnet, shedding tears all the time, and her hands trembling so that she could hardly tie the strings. “Oh, dear Margaret! how shocking! What are you doing? Are you going out? Sholto would telegraph or do anything you like.” “I am going to Oxford. There is a train in half-an-hour. Dixon has offered to go with me, but I could have gone by myself. I must see him again. Besides, he may be better, and want some care. He has been like a father to me. Don’t stop me, Edith.” “But I must. Mamma won’t like it at all. Come and ask her about it, Margaret. You don’t know where you’re going. I should not mind if he had a house of his own; but in his Fellow’s rooms! Come to mamma, and do ask her before you go. It will not take a minute.” Margaret yielded, and lost her train. In the suddenness of the event, Mrs. Shaw became bewildered and hysterical, and so the precious time slipped by. But there was another train in a couple of hours; and after various discussions on propriety and impropriety, it was decided that Captain Lennox should accompany Margaret, as the one thing to which she was constant was her resolution to go, alone or otherwise, by the next train, whatever might be said of the propriety or impropriety of the step. Her father’s friend, her own friend, was lying at the point of death; and the thought of this came upon her with such vividness, that she was surprised herself at the firmness with which she asserted something of her right to independence of action; and five minutes before the time of starting, she found herself sitting in a railway carriage opposite to Captain Lennox. It was always a comfort to her to think that she had gone, though it was only to hear that he had died in the night. She saw the rooms that he had occupied, and associated them ever after most fondly in her memory with the idea of her father, and his one cherished and faithful friend. They had promised Edith before starting, that if all had ended as they feared, they would return to dinner; so that long, lingering look around the room in which her father had died, had to be interrupted, and a quiet farewell taken of the kind old face that had so often come out with pleasant words, and merry quips and cranks. Captain Lennox fell asleep on their journey home; and Margaret could cry at leisure, and bethink her of this fatal year, and all the woes it had brought to her. No sooner was she fully aware of one loss than another came—not to supersede her grief for the one before, but to re-open wounds and feelings scarcely healed. But at the sound of the tender voices of her aunt and Edith, of merry little Sholto’s glee at her arrival, and at the sight of the well-lighted rooms, with their mistress, pretty in her paleness and her eager sorrowful interest, Margaret roused herself from her heavy trance of almost superstitious hopelessness, and began to feel that even around her joy and gladness might gather. She had Edith’s place on the sofa; Sholto was taught to carry Aunt Margaret’s cup of tea very carefully to her; and by the time she went up to dress, she could thank God for having spared her dear old friend a long or a painful illness. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Elizabeth Cleghorn Gaskell (2003). North and South. Urbana, Illinois: Project Gutenberg. Retrieved https://www.gutenberg.org/cache/epub/4276/pg4276-images.html This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at , located at . www.gutenberg.org https://www.gutenberg.org/policy/license.html

“NE’ER TO BE FOUND AGAIN.”

Scientific American Supplement, No. 365, December 30, 1882 by Various, is part of the HackerNoon Books Series. You can jump to any chapter in this book . APPARATUS FOR MANUFACTURING GASEOUS OR AERATED BEVERAGES. here APPARATUS FOR MANUFACTURING GASEOUS OR AERATED BEVERAGES. The apparatus employed at present for making gaseous beverages are divided into two classes—intermittent apparatus based on chemical compression, and continuous ones based on mechanical compression. The first are simple in appearance and occupy small space, but their use is attended with too great inconveniences and losses to allow them to be employed in cases where the manufacture is of any extent, so the continuous apparatus are more and more preferred by those engaged in the industry. Continuous apparatus, however, other than those that we now propose to occupy ourselves with, are not without some defects, for the gas is produced in them intermittingly and at intervals, and more rapidly than it is used, thus necessitating the use of a gasometer, numerous and large washers, complicated piping, and, besides, of an acid cock. To get rid of such drawbacks, it became necessary to seek a means of rendering the production of the gas continuous, and of regulating it automatically without the aid of the operator. Mr. Mondollot has obtained such a result through a happy modification of the primitive system of the English engineer Bramah. He preserves the suction and force pump but, while applying it to the same uses, he likewise employs it, by the aid of a special arrangement, so as to distribute the sulphuric acid automatically over the chalk in the generator, and to thus obtain a regular and continuous disengagement of carbonic acid gas. The dangers and difficulties in the maneuver of an acid cock are obviated, the gasometer and its cumbersome accessories are dispensed with, and the purification is more certain, owing to the regularity with which the gas traverses the washers. In the accompanying plate we have figured three types of these apparatus. The first that we shall describe is arranged for the use of bicarbonate of soda. This apparatus consists (1) of a , C D, (2) of a double G G, (3) of a , P, and (4) of a , S (See Figs 1 to 9). generator washer suction pump saturator —This consists of a cylindrical leaden receptacle, D, on the bottom of which rests a leaden bell containing apertures, , at its base. A partition, , into which is screwed a leaden tube, C, containing apertures divides the interior of the bell into two compartments. The upper of these latter is surmounted by a mouth, B, closed by a clamp, and through which the bicarbonate of soda is introduced. A definite quantity of water and sulphuric acid having been poured into the receptacle, D, a level tends to take place between the latter and the bell, C, the liquid passing through the apertures. But the acidulated water, coming in contact with the soda, sets free carbonic acid gas, which, having no exit, forces the water back and stops the production of gas until the apparatus is set in motion. At this moment, the suction of the pump causes a new inflow of acidulated water upon the soda, from whence another disengagement of gas, and then a momentary forcing of the water, whose level thus alternately rises and falls and causes a continuous production of gas proportionate with the suction of the pump. The Generator. c c The consumption of soda and acid is about 2 kilogrammes each for charging 100 siphons or 150 bottles. The bicarbonate is known to be used up when the liquid in the generator is seen to descend to the bottom of the water level, , fixed to the vessel, D. n (Figs 1 and 4)—The gas, on leaving the generator, enters the washer through a bent copper pipe, R. The washer is formed of two ovoid glass flasks G G, mounted on a bronze piece, L, to which they are fixed by screw rings, , of the same metal. The two flasks, G G, communicate with each other only through the tinned-copper tube , which is held in the mounting , of the same metal. This latter is screwed into the piece, L, and contains numerous apertures, through which the gas coming in from the pipe, R, passes to reach the upper flask, G. The gas is washed by bubbling up through water that has been introduced through the cock, R. After it has traversed both flasks, it escapes through the copper pipe, , into which it is sucked by the pump, P. The Washer l q q p (Figs 1, 5 and 6)—This consists of a cylindrical chamber, P, of bronze, bolted to a bracket on the frame, and cast in a piece, with the suction valve chamber, P, in which the valve, p, plays. It is surmounted by the distributing valve chamber P2. This latter is held by means of two nuts screwed on to the extremity of the rods, p3, connected with the shell, E, of the distributing-cock, E. In the shell, E, terminates, on one side, the pipe, , through which enters the gas from the washer, and, on the other, the pipe , that communicates with a feed-reservoir not shown in the cuts. The cock E, permits of the simultaneous regulation of the entrance of the gas and water. Its position is shown by an index , passing over a graduated dial, . From the distributing valve chamber, P2 the pipe, , leads the mixture of water and gas under pressure into The Pump p i e e s , S (Figs 1, 7 and 9)—This consists of a large copper vessel, , affixed to the top of the frame through the intermedium of a bronze collar , and a self closing bottom H. This latter is provided with two pipes, one of which, , leads the mixture of water and carbonic acid forced by the pump, and the other, , communicates with the siphons or bottles to be filled. The pipe, , is not affixed directly to the bottom, but is connected therewith through the intermedium of a cock, . The object of the broken form of this pipe is to cause the pressure to act according to the axis of the screw, , which is maneuvered by the key, 2. The Saturator s h s b b r r r The water under pressure, having been forced into the vessel, S, is submitted therein to an agitation that allows it to dissolve a larger quantity of gas. Such agitation is produced by two pairs of paddles, J J, mounted at the extremity of an axle actuated by the wheel, A, through the intermedium of gearings, and . g g The course of the operation in the saturator may be followed by an inspection of the water level, , seen at the front and side in Figs. 2 and 3. This apparatus, in which the pressure reaches 4 to 6 atmospheres in the manufacture of Seltzer water or gaseous lemonade in bottles, and from 10 to 12 atmospheres in that of Seltzer water in siphons, is provided also with a pressure gauge, , and a safety valve, both screwed, as is also the tube, 2, into a sphere, S, on the top of the saturator. n m n (Figs 2, 3, and 10)—When chalk is acted upon by sulphuric acid, there is formed an insoluble sulphate which, by covering the chalk, prevents the action of the acid from continuing if care be not taken to constantly agitate the materials. This has led to a change in the arrangement of the generator in the apparatus designed for the use of chalk. Apparatus for Using Carbonate of Lime It consists in this case of a leaden vessel, D, having a hemispherical bottom set into a cylindrical cast iron base, K, and of an agitator similar to that shown in Fig. 11, for keeping the chalk in suspension in the water. These latter materials are introduced through the mouth, B (Fig. 3). Then a special receptacle, C, of lead, shown in detail in Fig. 10, and the cock, , of which is kept closed, is filled with sulphuric acid. The acid is not introduced directly into the vessel, C, but is poured into the cylinder, C, whose sides contain numerous apertures which prevent foreign materials from passing into the siphon tube , and obstructing it. c c To put the apparatus in operation, the acid cock, , is opened and the wheel, A, is turned, thus setting in motion both the pump piston, P, and the agitator, within S and D. Then the play of the pump produces a suction in the washers and from thence in the generator and causes the acid in the vessel, C, to flow into the generator through the leaden siphon tubes, . Coming in contact with the chalk in suspension, the acid produces a disengagement of gas which soon establishes sufficient pressure to stop the flow of the acid and drive it back into the siphon tube. The play of the pump continuing, a new suction takes place and consequently a momentary flow of acid and a new disengagement of gas. Thus the production of the latter is continuous, and is regulated by the very action of the pump, without the operator having to maneuver an acid-cock. The latter he only has to open when he sets the apparatus in operation, and to close it when he stops it. c c The arrangement of the washer is the same as in the preceding apparatus, save that a larger cylindrical copper reservoir, G', is substituted for the lower flask. The pump and saturator offer nothing peculiar. A bent tube, , which communicates with the generator, D, on one side, and with a cylindrical tube, V, ending in a glass vessel on the other, serves as a safety-valve for both the generator and the acid vessel. u The consumption of chalk is about 2.5 kilogrammes, and the same of acid, for charging 100 siphons or 150 bottles. The apparatus shown in the figure is capable of charging 600 siphons or 900 bottles per day. (Fig. 11).—This apparatus consists of two very distinct parts. The saturator, pump, and driving shaft are supported by a hollow base, in whose interior are placed a copper washer and the water-inlet controlled by a float-cock. This part of the apparatus is not shown in the plate. The generator, partially shown in Fig. 11, is placed on a base of its own, and is connected by a pipe with the rest of the apparatus. It consists of two similar generators, D, made of copper lined with lead, and working alternately, so as to avoid all stoppages in the manufacture when the materials are being renewed. The pipe, , connecting the two parts of the apparatus forks so as to lead the gas from one or the other of the generators, whence it passes into the copper washer within the base, then into the glass indicating washer, and then to the pump which forces it into the saturator. An Apparatus Completely Mechanical in Operation d Each of the generators communicates by special pipes, , with a single safety vessel, V, that operates the same as in the preceding apparatus. The agitator, Q, is of bronze, and is curved as shown in Fig. 11. a The production of this type of apparatus is dependent upon the number of siphons that can be filled by a siphon filler working without interruption.— Machines, Outils et Appareils. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Various (2006). Scientific American Supplement, No. 365, December 30, 1882. Urbana, Illinois: Project Gutenberg. Retrieved https://www.gutenberg.org/cache/epub/18763/pg18763-images.html This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at , located at . www.gutenberg.org https://www.gutenberg.org/policy/license.html

APPARATUS FOR MANUFACTURING GASEOUS OR AERATED BEVERAGES

Things To Make by Archibald Williams is part of the HackerNoon Books Series. You can jump to any chapter in this book . A WOODEN WORKBOX here XXXIII. A WOODEN WORKBOX. The box illustrated by Fig. 181 was copied from an article of Norwegian manufacture. Its construction is an extremely simple matter, provided that one can get a piece of easily bent wood (birch, for instance), not exceeding 3/16 inch in thickness, for the sides. [Illustration: FIG. 180.—Showing how to draw an ellipse.] [Illustration: FIG. 181.—Norwegian workbox.] The bottom of the box is made of 5/16 or 3/8 inch wood, cut to an oval or elliptical shape. To mark out an ellipse about 8 inches long and 5-1/2 inches wide—this will be a. convenient size—stick two pins into the board 5-1/8 inches apart, pass a loop of thread 14 inches in circumference round these, and run the point of a pencil round the pins in the path which it has to take when confined by the slack of the loop (Fig. 180). Fret-saw along the line. The wood strip for the side is 4-1/2 inches deep, and 1-1/2 inches longer than the circumference of the bottom. The ends are thinned off somewhat, as shown in Fig. 181, to prevent the lap having a clumsy appearance, and the surface is smoothed all over with sandpaper. Bore a number of small nail holes 3/16 inch from one edge, and then steam the wood over a big saucepan or other suitable vessel until it is quite lissom. When attaching the side piece to the bottom, begin at the middle, and work first towards what will be the inside end of the lap, and then towards the outside end. Nails are driven in through the holes already drilled. When nailing is finished, clip the top of the overlap with a hand-vice or screw spanner, to prevent the tops of the ends sliding over one another, and bore a line of holes l/4 inch apart, and at the same distance from the outer end. Fine copper wire drawn to and fro through alternate holes from one end of the row to the other and back again, will secure the joint. The lid overlaps the side 1/4 inch in all directions and has a square notch cut in it at one end to pass under the piece A, and at the other a deeper, circular-ended nick to enable it to pass over the key B when that is turned into the position shown in the illustration. A is cut out of 1/4-inch wood; B, in one piece, out of 1/2-inch. Their length under the heads exceeds the inside depth of the box by the thickness of the lid. A is affixed rigidly to the side by small screws or wire, while B must be attached in a manner, which will allow the head to rotate. Cut two nicks round the shank, and two horizontal slots at the same height through the end of the box. A couple of brass rings must then be procured of such a size that, when flattened into a somewhat oval shape, they will project beyond the slots sufficiently to allow a piece of wire to pass through them and prevent their being drawn back again. Quarter-inch wood will do for the lid. A handle is made out of a couple of inches of small cane bent into a semicircle, let through the lid at each end, glued, and cut off flush. The exterior may be decorated by a design in poker-work, or be stained and varnished. This is left to the maker’s discretion. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Archibald Williams (2005). Things To Make. Urbana, Illinois: Project Gutenberg. Retrieved https://www.gutenberg.org/cache/epub/14664/pg14664-images.html This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at , located at . www.gutenberg.org https://www.gutenberg.org/policy/license.html

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