Nuggets' Michael Porter: Wraps up rough postseason

Director Kimberley Rampersad injects an air of freewheeling abandon into this classic Cole Porter musical.

Shaw Festival’s ‘Anything Goes’ is a delirious romp

Over the past five years, Peak has generated about $3.6 billion in cash exits and over 30 portfolio companies have gone public.

Peak XV Partners nets over ₹1,200 crore after exiting stake in Porter, clocking 11-fold return

Dolly Parton and Porter Wagoner worked together for years. She said their dynamic could be a complete disaster.

Dolly Parton Said Working With Porter Wagoner Was a 'Disaster' for Her

The Canadian carrier is pulling back from some US routes as demand for cross-border travel has plummeted.

Porter Airlines Exits San Diego & Scraps Montreal-Las Vegas Plans

A Thursday public forum hosted by the League of Women Voters of Porter County will discuss the impact of redistricting the geographical boundaries of the Valparaiso City Council seats.

League of Women Voters hosting Valpo City Council redistricting forum

Uber India is expanding its courier service to include large deliveries of up to 750 kg—an enterprise-focused segment dominated by logistics startup Porter. Can Uber make a space for itself in this vast but largely untapped?

Mint Explainer: Can Uber shake up the market Porter dominates?

Christian 'King' Combs is the son of Sean 'Diddy' Combs and Kim Porter. Learn all about Christian here.

Christian Combs: 5 Things to Know About Diddy’s Son

A man wanted in his home country of Moldova was found to be in unlawful possession of 131 credit cards that didn't match his identity following a traffic stop on the Indiana Toll Road in Porter County this past weekend.

Man from Moldova accused in credit card fraud scheme

Sean 'Diddy' Combs once talked about Kim Porter and Black mothers ahead of Mother's Day. Here's what he said while breaking down.

Sean 'Diddy' Combs Once Broke Down in Tears Discussing Kim Porter Before Mother's Day

Porter

porter

Heroku's been taking it on the chin lately for their response to what looks to be a pretty-damn-serious security incident—and for good reason because about the whole event has been . their communication abysmal Personally, this is a pretty big letdown, because I've been riding the for quite some time. As a software developer with a history of working for teeny-tiny startups (in addition to a fair amount of freelancing), Heroku's Platform-as-a-Service Solution(PaaS) —has been a lifesaver for all the cool kids out there. Heroku train When you're crunched for time and resources, offloading things like server maintenance, security, database management, and all the other that accompany running a software company is incredibly valuable; and Heroku's add-on marketplace is just icing on the cake. tasks Trust me, there's nothing more satisfying than spinning up all the internal and external resources you need within a single pane of glass. As a freelancer, this sort of organization makes billing clients (and eventually transferring application ownership) a snap. Heroku Alternatives But... all of that is gone now. It has been outweighed by a complete and total lack of trust in a company that I've historically put a of trust in. As a result, I've been exploring a few Heroku alternatives that are all new to the PaaS space (or, at least, relatively new to ). lot relatively me To be clear, I'm skipping the most well-known solutions like 's App Platform and 's App Engine, because I think most people are already aware of them, so flogging that particular horse is probably just a waste of bits and bytes. DigitalOcean Google Cloud That said, I've stumbled across a handful of solutions that are both unique pretty "indie" feeling—a great combination in the "tools by developers, for developers" category if you ask me. awesome and Fly.io I've heard of a few times over the years, but it wasn't until just the last few days that I've really taken the opportunity to try it out; and, I've got to say, it's pretty damn awesome. Fly.io While not nearly as "feature robust" as Heroku (read: no "marketplace"), it is a Docker-driven solution with an generous free tier, and one of the most impressive commitments to technical writing I've ever seen (which, if I'm being honest, is only outshone by DigitalOcean's approach). incredibly As the founder of , I personally own and manage any of the integrations and websites that we rely on, and have chosen Fly.io as our new destination. The transition from Heroku to Fly.io was about as painless as you could imagine, and the terminal-driven management has been a great experience. The MUD Coders Guild If you are on the fence and don't have a huge application footprint, you definitely can't go wrong with Fly. Render is a new solution for me, but it most closely resembles Heroku as far as features and functionality go (although that isn't to imply that it is no better than Heroku). A winner in the 2019 TechCrunch Startup Battlefield (an event I will forever associate with Pied Piper and Middle-Out Encryption thanks to HBO's ), Render offers all the bells and whistles that we've come to expect in a PaaS platform: Render Silicon Valley Autoscaling Managed databases Preview environments Docker deployments And cron support actual I have yet to dig deeply into it, but will likely be moving some of my more complicated freelance projects over to Render when the opportunity presents itself (and, just as an aside, their free tier is about as generous as you can ask for). too Porter I've examined in the past as part of an roundup for TechTarget and liked what I saw. Porter Open Source PaaS really What sets Porter apart from the other solutions on this list is that it is an open-source self-hosted option. While they do offer a managed cloud solution that relies on your backend infrastructure, the self-hosted option is super compelling as it gives you total control over your infrastructure. and own While I am personally not in the "manage all my things" game, this is an excellent solution for people who are looking to make the leap from hosting PaaS to managing their own infrastructure. Conclusion Obviously, there are a hell of a lot more platform-as-a-service providers out there than just these three. From big to small, proprietary to open source, it's a pretty big space. That said, these three are the more compelling ones in my mind, and I will be watching them as they continue to grow. If these don't quite fit your needs and are looking for more options to try, take a look at this . There are some great solutions available. Awesome-PaaS list Also published at . flower.codes

Try these 3 Alternatives to Heroku

Hacktivists Take on Misinformation in a New Internet Age

Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2 Related Work and 2.1 Technology Convergence Approaches 2 Related Work and 2.1 Technology Convergence Approaches 2.2 Technology Convergence Measurements 2.2 Technology Convergence Measurements 2.3 Technology Convergence Models 2.3 Technology Convergence Models 3 Data 3 Data 4 Method and 4.1 Proximity Indices 4 Method and 4.1 Proximity Indices 4.2 Interpolation and Fitting Data 4.2 Interpolation and Fitting Data 4.3 Clustering 4.3 Clustering 4.4 Forecasting 4.4 Forecasting 5 Results and Discussion and 5.1 Overall Results 5 Results and Discussion and 5.1 Overall Results 5.2 Case Study 5.2 Case Study 5.3 Limitations and Future Works 5.3 Limitations and Future Works 6 Conclusion and References 6 Conclusion and References Appendix Appendix 6 Conclusion In this study, we introduce a method that uses text mining and bibliometrics techniques, utilizing the ”OpenAlex” catalog, to create and predict technological proximity indices specific to encryption technologies. A case study applying our method highlights the convergence between blockchain and public-key cryptography. The insights gained from our method can offer valuable guidance for stakeholders and enthusiasts navigating the impacts of encryption technology. We recognize certain constraints in our study. Our literature corpus was limited to ”OpenAlex,” which may not comprehensively represent the core interests and activities in the research community working on encryption technologies. Additionally, the non-normalized nature of our indices hinders direct comparisons among various data sources. These limitations also suggest potential paths for future research to expand our findings, enriching the field of scientific monitoring within the encryption technology community. Supplementary information. The code of this project is on https://github.com/technometrics-lab/Proximity-indices-applied-to-OpenAlex. Supplementary information. https://github.com/technometrics-lab/Proximity-indices-applied-to-OpenAlex Acknowledgments. We thank Jacques Roitel, whose work was the original base of this paper. Additionally, we would like to thank the other interns working at armasuisse at the time this research was led for their helpful coding advice: L´eo Meynent, Marc Egli, Francesco Intoci, Lucas Crijns, and Alexander Glavackij. Acknowledgments References [1] Zhou, Y., Dong, F., Kong, D., Liu, Y.: Unfolding the convergence process of scientific knowledge for the early identification of emerging technologies. Technological Forecasting and Social Change 144, 205–220 (2019). https: //doi.org/10.1016/j.techfore.2019.03.014. Accessed 2022-09-30 [2] Wang, Z., Porter, A.L., Wang, X., Carley, S.: An approach to identify emergent topics of technological convergence: A case study for 3D printing. Technological Forecasting and Social Change 147, 723–732 (2019). https://doi.org/10.1016/j.techfore.2018.12.015. Accessed 2022-11-24 [3] Carley, S.F., Newman, N.C., Porter, A.L., Garner, J.G.: An indicator of technical emergence. Scientometrics 115(1), 35–49 (2018). https://doi. org/10.1007/s11192-018-2654-5. Accessed 2022-09-30 [4] Halaweh, M.: Emerging Technology: What is it. Journal of technology management & innovation 8(3), 108–115 (2013). https://doi. org/10.4067/S0718-27242013000400010. Publisher: Universidad Alberto Hurtado. Facultad de Econom´ıa y Negocios. Accessed 2022-09-12 [5] Porter, A.L., Garner, J., Carley, S.F., Newman, N.C.: Emergence scoring to identify frontier R&D topics and key players. Technological Forecasting and Social Change 146, 628–643 (2019). https://doi.org/10.1016/j. techfore.2018.04.016. Accessed 2022-09-13 [6] Curran, C.-S., Broring, S., Leker, J.: Anticipating converging industries using publicly available data. Technological Forecasting and Social Change 77(3), 385–395 (2010). https://doi.org/10.1016/j.techfore.2009. 10.002. Accessed 2022-10-21 [7] Song, C.H., Elvers, D., Leker, J.: Anticipation of converging technology areas — A refined approach for the identification of attractive fields of innovation. Technological Forecasting and Social Change 116, 98–115 (2017). https://doi.org/10.1016/j.techfore.2016.11.001. Accessed 2022-09-30 [8] Huang, L., Cao, X., Cai, Y., Ren, H., Xing, T., Ye, P.: Detecting Technological Recombination using Semantic Analysis and Dynamic Network Analysis, 11 [9] Song, K., Kim, K.S., Lee, S.: Discovering new technology opportunities based on patents: Text-mining and F-term analysis. Technovation 60-61, 1–14 (2017). https://doi.org/10.1016/j.technovation.2017.03.001. Accessed 2022-09-30 [10] Blouin, M., Sery, N., Cluzeau, D., Brun, J.-J., Bedecarrats, A.: Balkanized Research in Ecological Engineering Revealed by a Bibliometric Analysis of Earthworms and Ecosystem Services. Environmental Management 52(2), 309–320 (2013). https://doi.org/10.1007/s00267-013-0079-8. Accessed 2022-10-19 [11] Chand Bhatt, P., Kumar, V., Lu, T.-C., Daim, T.: Technology convergence assessment: Case of blockchain within the IR 4.0 platform. Technology in Society 67, 101709 (2021). https://doi.org/10.1016/j.techsoc.2021. 101709. Accessed 2022-10-20 [12] Kim, T.S., Sohn, S.Y.: Machine-learning-based deep semantic analysis approach for forecasting new technology convergence. Technological Forecasting and Social Change 157, 120095 (2020). https://doi.org/10.1016/ j.techfore.2020.120095. Accessed 2022-10-20 [13] Li, H., An, H., Wang, Y., Huang, J., Gao, X.: Evolutionary features of academic articles co-keyword network and keywords co-occurrence network: Based on two-mode affiliation network. Physica A: Statistical Mechanics and its Applications 450, 657–669 (2016). https://doi.org/10.1016/j. physa.2016.01.017. Accessed 2022-09-09 [14] Chen, H., Zhang, Y., Zhu, D.: Identifying Technological Topic Changes in Patent Claims Using Topic Modeling. In: Daim, T.U., Chiavetta, D., Porter, A.L., Saritas, O. (eds.) Anticipating Future Innovation Pathways Through Large Data Analysis. Innovation, Technology, and Knowledge Management, pp. 187–209. Springer, Cham (2016). https://doi.org/10. 1007/978-3-319-39056-7 11 [15] Cojocaru, S., Bragaru, C., Ciuchi, O.: The role of language in constructing social realities. The Appreciative Inquiry and the reconstruction of organisational ideology. Revista de Cercetare si Interventie Sociala 36, 31–43 (2012) [16] He, C., Shi, F., Tan, R.: A synthetical analysis method of measuring technology convergence. Expert Systems with Applications 209, 118262 (2022). https://doi.org/10.1016/j.eswa.2022.118262. Accessed 2022-10-21 [17] Klarin, A., Suseno, Y., Lajom, J.: Systematic Literature Review of Convergence: A Systems Perspective and Re-evaluation of the Convergence Process. IEEE Transactions on Engineering Management, 1–13 (2021). https://doi.org/10.1109/TEM.2021.3126055 [18] MacRoberts, M.H., MacRoberts, B.R.: Problems of citation analysis. Scientometrics 36(3), 435–444 (1996). https://doi.org/10.1007/BF02129604. Accessed 2022-11-23 [19] Liu, P., Xia, H.: Structure and evolution of co-authorship network in an interdisciplinary research field. Scientometrics 103(1), 101–134 (2015). https://doi.org/10.1007/s11192-014-1525-y. Accessed 2022-11-30 [20] Lu, L., Zhou, T.: Link prediction in complex networks: A survey. Physica A: Statistical Mechanics and its Applications 390(6), 1150–1170 (2011). [https://doi.org/10.1016/j.physa.2010.11.027. Accessed 2022-10-17 ](https://doi.org/10.1016/j.physa.2010.11.027. Accessed 2022-10-17 ) [21] Kim, J., Kim, S., Lee, C.: Anticipating technological convergence: Link prediction using Wikipedia hyperlinks. Technovation 79, 25–34 (2019). https://doi.org/10.1016/j.technovation.2018.06.008. Accessed 2022-10-21 [22] Breitzman, A., Thomas, P.: The Emerging Clusters Model: A tool for identifying emerging technologies across multiple patent systems. Research Policy 44(1), 195–205 (2015). https://doi.org/10.1016/j.respol.2014.06. 006. Accessed 2022-10-21 [23] Kumar, T., Vaidyanathan, S., Ananthapadmanabhan, H., Parthasarathy, S., Ravindran, B.: Hypergraph clustering by iteratively reweighted modularity maximization. Applied Network Science 5(1), 1–22 (2020). https://doi.org/10.1007/s41109-020-00300-3. Number: 1 Publisher: SpringerOpen. Accessed 2022-10-20 [24] Schoen, A., Villard, L., Laurens, P., Cointet, J.-P., Heimeriks, G., Alkemade, F.: The Network Structure of Technological Developments; Technological Distance as a Walk on the Technology Map (2012) [25] Kim, J., Lee, S.: Forecasting and identifying multi-technology convergence based on patent data: the case of IT and BT industries in 2020. Scientometrics 111(1), 47–65 (2017). https://doi.org/10.1007/ s11192-017-2275-4. Accessed 2022-10-21 [26] Lee, C., Kwon, O., Kim, M., Kwon, D.: Early identification of emerging technologies: A machine learning approach using multiple patent indicators. Technological Forecasting and Social Change 127, 291–303 (2018). https://doi.org/10.1016/j.techfore.2017.10.002. Accessed 2022-10-17 [27] Kajikawa, Y., Takeda, Y.: Structure of research on biomass and bio-fuels: A citation-based approach. Technological Forecasting and Social Change 75(9), 1349–1359 (2008). https://doi.org/10.1016/j.techfore.2008.04.007. Accessed 2022-10-18 [28] Mitrea, C., Lee, C., Wu, Z.: A Comparison between Neural Networks and Traditional Forecasting Methods: A Case Study. International Journal of Engineering Business Management 1 (2009). https://doi.org/10.5772/ 6777 [29] Priem, J., Piwowar, H., Orr, R.: OpenAlex: A fully-open index of scholarly works, authors, venues, institutions, and concepts. arXiv. arXiv:2205.01833 [cs] (2022). https://doi.org/10.48550/arXiv.2205.01833. http://arxiv.org/abs/2205.01833 Accessed 2022-10-03 [30] Brown, B.B., et al.: Delphi process: a methodology used for the elicitation of opinions of experts. Rand Corporation Santa Monica, CA (1968) [31] Rousseeuw, P.J.: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Journal of computational and applied mathematics 20, 53–65 (1987) 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 Authors:
(1) Alessandro Tavazz, Cyber-Defence Campus, armasuisse Science and Technology, Building I, EPFL Innovation Park, 1015, Lausanne, Switzerland, Institute of Mathematics, EPFL, 1015, Lausanne, Switzerland and a Corresponding author (tavazale@gmail.com);
(2) Dimitri Percia David, Cyber-Defence Campus, armasuisse Science and Technology, Building I, EPFL Innovation Park, 1015, Lausanne, Switzerland and Institute of Entrepreneurship & Management, University of Applied Sciences of Western Switzerland (HES-SO Valais-Wallis), Techno-Pole 1, Le Foyer, 3960, Sierre, Switzerland;
(3) Julian Jang-Jaccard, Cyber-Defence Campus, armasuisse Science and Technology, Building I, EPFL Innovation Park, 1015, Lausanne, Switzerland;
(4) Alain Mermoud, Cyber-Defence Campus, armasuisse Science and Technology, Building I, EPFL Innovation Park, 1015, Lausanne, Switzerland. Authors: Authors: (1) Alessandro Tavazz, Cyber-Defence Campus, armasuisse Science and Technology, Building I, EPFL Innovation Park, 1015, Lausanne, Switzerland, Institute of Mathematics, EPFL, 1015, Lausanne, Switzerland and a Corresponding author (tavazale@gmail.com); (2) Dimitri Percia David, Cyber-Defence Campus, armasuisse Science and Technology, Building I, EPFL Innovation Park, 1015, Lausanne, Switzerland and Institute of Entrepreneurship & Management, University of Applied Sciences of Western Switzerland (HES-SO Valais-Wallis), Techno-Pole 1, Le Foyer, 3960, Sierre, Switzerland; (3) Julian Jang-Jaccard, Cyber-Defence Campus, armasuisse Science and Technology, Building I, EPFL Innovation Park, 1015, Lausanne, Switzerland; (4) Alain Mermoud, Cyber-Defence Campus, armasuisse Science and Technology, Building I, EPFL Innovation Park, 1015, Lausanne, Switzerland.

Concluding Remarks: Blockchain and Cryptography Convergence Insights

Seoul, Republic of Korea, May 1st, 2025/Chainwire/--Bitcoin Seoul 2025, Asia’s largest Bitcoin-focused conference, will take place from June 4 to 6, 2025, at two of Seoul’s most iconic venues: Signiel Seoul and SKY31 Convention. Bitcoin Seoul 2025 Bitcoin Seoul 2025 Following its successful debut in 2024, Bitcoin Seoul quickly established itself as a key fixture in the global Bitcoin conference circuit. The inaugural event featured leading Bitcoin thinkers such as Saifedean Ammous and Jimmy Song, and attracted thousands of industry professionals and community members to Seoul to exchange insights on Bitcoin’s evolution and future. Building on this momentum, the 2025 edition promises an expanded scale and a deeper examination of Bitcoin’s global trajectory. More than just a conference, Bitcoin Seoul 2025 will feature a multidimensional program spanning Bitcoin strategy, regulation, finance, policy, and real-world adoption. Amid the growing trend of publicly listed companies in Asia and Europe adopting Bitcoin as a treasury asset, executives who have led these initiatives—including from MetaPlanet and The Blockchain Group—will be participating in the event to share first-hand experiences from the corporate frontlines. Additionally, Dennis Porter, who spearheaded the Bitcoin strategic reserve movement in the United States, will offer insights into Bitcoin’s expanding adoption at the corporate and governmental levels. Highlighting real-world adoption El Salvador’s Mi Primer Bitcoin and Bitcoin Beach—trailblazers in national Bitcoin integration—will lead a special session titled "El Salvador Bitcoin Adoption Showcase." The event will also welcome Bitcoin community leaders from around the world, including the United States, Australia, Hong Kong, Vietnam, and Indonesia, who will share firsthand experiences of community-driven Bitcoin adoption across different continents and regions. The 2025 program will feature: Bitcoin Policy Summit: Seoul Edition — Insights into regulatory trends and Bitcoin-related public policy
Bitcoin Finance Forum — addressing institutional investment, Bitcoin treasury management, and macroeconomic perspectives;
Global Bitcoin Community Assembly — A global forum for Bitcoin grassroots and community leaders Bitcoin Policy Summit: Seoul Edition — Insights into regulatory trends and Bitcoin-related public policy Bitcoin Finance Forum — addressing institutional investment, Bitcoin treasury management, and macroeconomic perspectives; Global Bitcoin Community Assembly — A global forum for Bitcoin grassroots and community leaders In addition, attendees will be able to experience live Lightning Network payments at the on-site Lightning Market, showcasing Bitcoin’s real-world utility. Event Structure: VIP Day (June 4): Exclusive sessions and a private reception for global executives and institutional participants
Industry Day (June 5): Focused on enterprise use cases and strategic insights from publicly listed companies and institutional players.
Public Day (June 6): Dedicated to Bitcoin finance, adoption stories, and infrastructure innovations, welcoming community members, builders, and enthusiasts. VIP Day (June 4): Exclusive sessions and a private reception for global executives and institutional participants Industry Day (June 5): Focused on enterprise use cases and strategic insights from publicly listed companies and institutional players. Public Day (June 6): Dedicated to Bitcoin finance, adoption stories, and infrastructure innovations, welcoming community members, builders, and enthusiasts. As institutional interest in Bitcoin accelerates following the approval of spot Bitcoin ETFs in the United States, Bitcoin Seoul 2025 positions Seoul as a key node in the emerging global Bitcoin finance ecosystem. Countries including South Korea, Japan, and Hong Kong are rapidly integrating Bitcoin-based financial products and treasury strategies — reflecting a broader shift in the global financial landscape. Bitcoin Seoul 2025 aims to capture this momentum and further elevate Seoul’s status as a leading hub for Bitcoin-driven innovation and dialogue. This year, dozens of domestic and international companies are slated to sponsor the event. Among them is Bithumb, one of Korea’s leading cryptocurrency exchanges, recently ranked #1 in the Korea Exchange Brand Reputation Index, signaling strong market trust. Ryan, the organizer of Bitcoin Seoul, commented: “Bitcoin Seoul 2025 will unite the global Bitcoin community, extending far beyond Asia to connect innovators worldwide. We are committed to creating a forum that integrates Bitcoin policy, finance, adoption, and community development.” About Bitcoin Seoul Bitcoin Seoul is the largest Bitcoin-only conference in Asia and serves as a central hub connecting the global and Asian Bitcoin ecosystems. The team is dedicated to creating key momentum for the sustainable growth of Bitcoin businesses and communities, while accelerating global Bitcoin adoption. Bitcoin Seoul Bitcoin Seoul By providing a dynamic stage for innovation and collaboration, we aim to contribute to the mainstream adoption of Bitcoin. More than just a conference, their mission is to foster connection, expansion, and action within the Bitcoin ecosystem. For more information on registration, sponsorship, or speaking opportunities, users can visit: https://bitcoinseoul.kr https://bitcoinseoul.kr https://bitcoinseoul.kr Contact Event Manager Sophia Park Bitcoin Seoul 2025 contact@bitcoinseoul.kr This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program __her__e This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program __her__e her

Bitcoin Seoul 2025 To Host Global Industry Leaders For Asia’s Largest Bitcoin-Focused Conference

Bitcoin Seoul 2025 የዓለም አቀፍ ኢንዱስትሪ መሪዎችን ለስያያያ ውስጥ ትልቁ Bitcoin-focused ኮርፖሬሽን ይሰጣል

Bitcoin Seúl 2025 acogerá a líderes de la industria global para la mayor conferencia centrada en Bitcoin de Asia

Bitcoin Seúl 2025 acollerá líderes globais da industria para a maior conferencia centrada en Bitcoin de Asia

Bitcoin סיאול 2025 לארח מנהיגים תעשייתיים גלובליים עבור האסיה הגדולה ביותר Bitcoin-focused כנס

Bitcoin Seoul 2025 ospiterà i leader del settore globale per la più grande conferenza focalizzata su Bitcoin in Asia

ビットコインソウル2025、アジア最大のビットコインに焦点を当てた会議のグローバル産業リーダーを開催

Биткойн Сеул 2025 жылдары Азияның ең үздік Bitcoin-фокусированная конференциясына Global Industry Leaders туралы

Bitcoin Seoul 2025 uzņems globālos nozares līderus Āzijas lielākajā Bitcoin koncentrētajā konferencē

Bitcoin Seoul 2025 będzie gospodarzem globalnych liderów branży na największej konferencji koncentrującej się na Bitcoinie w Azji

Битцоин Сеул 2025 ће бити домаћин глобалних лидера индустрије за највећу конференцију фокусирану на Битцоин у Азији

Bitcoin Seoul 2025 sẽ tổ chức các nhà lãnh đạo ngành công nghiệp toàn cầu cho hội nghị tập trung Bitcoin lớn nhất châu Á

比特币首尔2025将主办亚洲最大比特币专注会议的全球行业领袖

Update, November 1: Federal Trade Commission Chair Lina Khan responded in writing to the report led by Senator Elizabeth Warren and triggered by The Markup’s investigation into tax preparation companies’ use of the Meta Pixel. Khan’s letter acknowledged Warren’s request for FTC action and said that, “in response to public reporting on this issue,” the FTC recently warned the companies involved that they could face financial penalties for mishandling customers’ tax data. The letter also highlighted related FTC work on web tracking, including of sensitive medical information—an issue that The Markup has also investigated. “We continue to look closely at this important area,” Khan wrote. Update, November 1: Update, November 1: Federal Trade Commission Chair Lina Khan responded in writing responded in writing to the report led by Senator Elizabeth Warren and triggered by The Markup’s investigation into tax preparation companies’ use of the Meta Pixel. Khan’s letter acknowledged Warren’s request for FTC action and said that, “in response to public reporting on this issue,” the FTC recently warned the FTC recently warned the companies involved that they could face financial penalties for mishandling customers’ tax data. The letter also highlighted related FTC work on web tracking, including of sensitive medical information—an issue that The Markup has also investigated. “We continue to look closely at this important area,” Khan wrote. an issue that The Markup has also investigated Meta and major tax preparation companies inappropriately shared millions of taxpayers’ financial data for years, according to a congressional report released today that was spurred by a Markup article. a congressional report a Markup article Our investigation, which was published in November, revealed how tax filing services including H&R Block, TaxAct, and TaxSlayer were transmitting data to Facebook’s parent company, Meta, through a tool called the Meta Pixel. The data was sent as taxpayers filed their taxes and included personal information like first and last names, income, filing status, and refund amounts. Some data was also sent to Google through its analytics tools, and Google was also a subject of the congressional investigation. Today’s report from lawmakers was informed by interviews with representatives of Meta, Google, and major tax prep services. It cited and confirmed The Markup’s report and chided the tax companies for being ​​”shockingly careless with their treatment of taxpayer data” and the tech firms for acting “with stunning disregard for taxpayer privacy.” The report determined that the tax prep companies installed tracking tools from Meta and Google on their services without a full understanding of how tax data might be collected and used, and that the companies were “still not fully aware of the current status of millions of taxpayers’ data.” Tax data is tightly regulated, with penalties for improper sharing including fines and jail time. The report found the companies involved likely didn’t receive proper consent to share the data and could face criminal penalties. The lawmakers provided the report today to various federal enforcement agencies and asked them in a letter to investigate and prosecute any company or individual who broke the law. The agencies include the Internal Revenue Service, the Treasury Inspector General for Tax Administration, the Department of Justice, and the Federal Trade Commission. Meta, H&R Block, and TaxSlayer didn’t immediately respond to requests for comment. Angela Krieger, a spokesperson for Google, said the company has “strict policies and technical features” to stop Google Analytics users from collecting sensitive data and that it is site owners’ responsibility to police the information they collect. Dermot Halpin, executive chair of TaxAct, said in a statement emailed after publication that the company cooperated with Warren’s staff and had disabled the “standard analytics tools” to evaluate concerns. “Protecting the rights and privacy of our customers is our top priority, and we are committed to engaging with stakeholders to address any concerns and to help advance public policy,” he said. The government enforcement agencies the letter was sent to did not respond to a request for comment, except the FTC, which declined to comment. The investigation was led by Massachusetts senator Elizabeth Warren and signed on to by Sens. Ron Wyden of Oregon, Richard Blumenthal of Connecticut, Tammy Duckworth of Illinois, Bernie Sanders of Vermont, and Sheldon Whitehouse of Rhode Island, as well as California representative Katie Porter. All are Democrats except Sanders, who is an independent. The Meta Pixel is a widely used piece of tracking code that businesses and organizations can place on their websites to better target ads on Facebook. When web users visit a website with a pixel, the tool can record information about the visit and send it back to Facebook, and companies can then use that information to tailor ads. A business may put a pixel on their checkout page to advertise new products to past customers on Facebook, for example. But while the code is used on millions of sites around the web, Meta cautions against using it to collect potentially sensitive information, like financial and health data. Nonetheless, as part of a project called Pixel Hunt, The Markup has found several cases in which sensitive data has been repeatedly sent to Meta, including from major hospitals, telehealth companies, and the U.S. Department of Education. Pixel Hunt major hospitals telehealth companies the U.S. Department of Education Meta claims to have automated mechanisms to filter out sensitive data, but the lawmakers’ report claims those safeguards are “woefully inadequate” and appear to exist only to provide “a modicum of deniability.” According to the report, Meta told congressional staff that it sent notifications to tax prep companies about the data after The Markup requested comment ahead of publication, but the tax prep companies said they never received those notifications. The tax prep companies also contacted Meta multiple times after The Markup’s article was published to learn about the final status of their customers’ data, according to the report, but walked away without a satisfying answer. In one instance, according to comments from TaxSlayer provided to the lawmakers, a Meta advertising representative specifically advised using a feature to collect data on pages viewed by web visitors. TaxSlayer told lawmakers’ staff that it was unaware how much data would be collected. Unlike many other countries, the United States does not have a widely available, free tax-filing option run by the government itself, essentially forcing many taxpayers to go through tax preparation companies. The report urges the IRS to change that, concluding that the “investigation raises serious doubts about the ability of the tax prep industry to safeguard taxpayer information and highlights the urgent need for the IRS to develop its own online tax filing system—to protect taxpayer privacy and provide a better alternative for taxpayers to file their returns.” Update July 13, 2023 This article has been updated to add a response from TaxAct that was received after publication. Credits: Colin Lecher Credits: Colin Lecher Colin Lecher Also published here Also published here here Photo by Olga DeLawrence on Unsplash Photo by Olga DeLawrence on Unsplash Olga DeLawrence Unsplash

Meta and Tax Prep Companies “Recklessly” Shared Taxpayers’ Data, According to Congressional Report

Table of Links Abstract and 1 Introduction 2. Data 3. Measuring Media Slant and 3.1. Text pre-processing and featurization 3.2. Classifying transcripts by TV source 3.3. Text similarity between newspapers and TV stations and 3.4. Topic model 4. Econometric Framework 4.1. Instrumental variables specification 4.2. Instrument first stage and validity 5. Results 5.1. Main results 5.2. Robustness checks 6. Mechanisms and Heterogeneity 6.1. Local vs. national or international news content 6.2. Cable news media slant polarizes local newspapers 7. Conclusion and References Online Appendices A. Data Appendix A.1. Newspaper articles A.2. Alternative county matching of newspapers and A.3. Filtering of the article snippets A.4. Included prime-time TV shows and A.5. Summary statistics B. Methods Appendix, B.1. Text pre-processing and B.2. Bigrams most predictive for FNC or CNN/MSNBC B.3. Human validation of NLP model B.4. Distribution of Fox News similarity in newspapers and B.5. Example articles by Fox News similarity B.6. Topics from the newspaper-based LDA model C. Results Appendix C.1. First stage results and C.2. Instrument exogeneity C.3. Placebo: Content similarity in 1995/96 C.4. OLS results C.5. Reduced form results C.6. Sub-samples: Newspaper headquarters and other counties and C.7. Robustness: Alternative county matching C.8. Robustness: Historical circulation weights and C.9. Robustness: Relative circulation weights C.10. Robustness: Absolute and relative FNC viewership and C.11. Robustness: Dropping observations and clustering C.12. Mechanisms: Language features and topics C.13. Mechanisms: Descriptive Evidence on Demand Side C.14. Mechanisms: Slant contagion and polarization B. Methods Appendix Here, we present additional material related to the measurement of cable news slant. B.1. Text pre-processing We preprocess all texts (i.e., TV channel transcripts and newspaper articles). We convert them to lowercase and remove non-meaningful stopwords (like and or or ), all nonletter characters, and extra white spaces. Second, for each word, we perform stemming (employing the Porter stemming algorithm). Finally, we form bigrams (phrases of two words). B.2. Bigrams most predictive for FNC or CNN/MSNBC Table B.1 shows some selected bigram examples with positive (predictive for FNC transcripts) or negative (predictive for CNN/MSNBC) values of ψˆ b. Table B.2 provides a more comprehensive list – the 200 bigrams most predictive for a transcript being from FNC or CNN/MSNBC, respectively. That is, the list is ordered such that the FNCrelated bigrams are the 200 bigrams with the largest absolute coefficients in the logistic regression from Section 3). Conversely, CNN/MSNBC-related ones are the 200 bigrams with the most negative coefficients. This paper is available on arxiv under CC 4.0 license. Authors:
(1) Philine Widmer, ETH Zürich and philine.widmer@gess.ethz.ch;
(2) Sergio Galletta, ETH Zürich and sergio.galletta@gess.ethz.ch;
(3) Elliott Ash, ETH Zürich and ashe@ethz.ch. Table of Links Abstract and 1 Introduction 2. Data Abstract and 1 Introduction 2. Data 3. Measuring Media Slant and 3.1. Text pre-processing and featurization 3. Measuring Media Slant and 3.1. Text pre-processing and featurization 3.2. Classifying transcripts by TV source 3.2. Classifying transcripts by TV source 3.3. Text similarity between newspapers and TV stations and 3.4. Topic model 3.3. Text similarity between newspapers and TV stations and 3.4. Topic model 4. Econometric Framework 4.1. Instrumental variables specification 4.1. Instrumental variables specification 4.2. Instrument first stage and validity 4.2. Instrument first stage and validity 5. Results 5.1. Main results 5.1. Main results 5.2. Robustness checks 5.2. Robustness checks 6. Mechanisms and Heterogeneity 6.1. Local vs. national or international news content 6.1. Local vs. national or international news content 6.2. Cable news media slant polarizes local newspapers 6.2. Cable news media slant polarizes local newspapers 7. Conclusion and References 7. Conclusion and References Online Appendices Online Appendices A. Data Appendix A.1. Newspaper articles A.1. Newspaper articles A.2. Alternative county matching of newspapers and A.3. Filtering of the article snippets A.2. Alternative county matching of newspapers and A.3. Filtering of the article snippets A.4. Included prime-time TV shows and A.5. Summary statistics A.4. Included prime-time TV shows and A.5. Summary statistics B. Methods Appendix, B.1. Text pre-processing and B.2. Bigrams most predictive for FNC or CNN/MSNBC B. Methods Appendix, B.1. Text pre-processing and B.2. Bigrams most predictive for FNC or CNN/MSNBC B.3. Human validation of NLP model B.3. Human validation of NLP model B.4. Distribution of Fox News similarity in newspapers and B.5. Example articles by Fox News similarity B.4. Distribution of Fox News similarity in newspapers and B.5. Example articles by Fox News similarity B.6. Topics from the newspaper-based LDA model B.6. Topics from the newspaper-based LDA model C. Results Appendix C.1. First stage results and C.2. Instrument exogeneity C.1. First stage results and C.2. Instrument exogeneity C.3. Placebo: Content similarity in 1995/96 C.3. Placebo: Content similarity in 1995/96 C.4. OLS results C.4. OLS results C.5. Reduced form results C.5. Reduced form results C.6. Sub-samples: Newspaper headquarters and other counties and C.7. Robustness: Alternative county matching C.6. Sub-samples: Newspaper headquarters and other counties and C.7. Robustness: Alternative county matching C.8. Robustness: Historical circulation weights and C.9. Robustness: Relative circulation weights C.8. Robustness: Historical circulation weights and C.9. Robustness: Relative circulation weights C.10. Robustness: Absolute and relative FNC viewership and C.11. Robustness: Dropping observations and clustering C.10. Robustness: Absolute and relative FNC viewership and C.11. Robustness: Dropping observations and clustering C.12. Mechanisms: Language features and topics C.12. Mechanisms: Language features and topics C.13. Mechanisms: Descriptive Evidence on Demand Side C.13. Mechanisms: Descriptive Evidence on Demand Side C.14. Mechanisms: Slant contagion and polarization C.14. Mechanisms: Slant contagion and polarization B. Methods Appendix Here, we present additional material related to the measurement of cable news slant. B.1. Text pre-processing We preprocess all texts (i.e., TV channel transcripts and newspaper articles). We convert them to lowercase and remove non-meaningful stopwords (like and or or ), all nonletter characters, and extra white spaces. Second, for each word, we perform stemming (employing the Porter stemming algorithm). Finally, we form bigrams (phrases of two words). B.2. Bigrams most predictive for FNC or CNN/MSNBC Table B.1 shows some selected bigram examples with positive (predictive for FNC transcripts) or negative (predictive for CNN/MSNBC) values of ψˆ b. Table B.2 provides a more comprehensive list – the 200 bigrams most predictive for a transcript being from FNC or CNN/MSNBC, respectively. That is, the list is ordered such that the FNCrelated bigrams are the 200 bigrams with the largest absolute coefficients in the logistic regression from Section 3). Conversely, CNN/MSNBC-related ones are the 200 bigrams with the most negative coefficients. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv Authors: (1) Philine Widmer, ETH Zürich and philine.widmer@gess.ethz.ch; (2) Sergio Galletta, ETH Zürich and sergio.galletta@gess.ethz.ch; (3) Elliott Ash, ETH Zürich and ashe@ethz.ch. Authors: Authors: (1) Philine Widmer, ETH Zürich and philine.widmer@gess.ethz.ch; (2) Sergio Galletta, ETH Zürich and sergio.galletta@gess.ethz.ch; (3) Elliott Ash, ETH Zürich and ashe@ethz.ch.

How We Measured Cable News Slant: Researching Media Bias

Table of Links Abstract and 1 Introduction 2 Background 3 On the slow growth law 4 Members of Deep Π0 1 classes 5 Strong depth is Negligible 6 Variants of Strong Depth References References [BDM23] Laurent Bienvenu, Valentino Delle Rose, and Wolfgang Merkle. Relativized depth. Theoretical Computer Science, 949:113694, 2023. [BDNM15] Laurent Bienvenu, Rodney G. Downey, Andr´e Nies, and Wolfgang Merkle. Solovay functions and their applications in algorithmic randomness. Journal of Computer and System Sciences, 81(8):1575–1591, 2015. [Ben95] Charles H. Bennett. Logical depth and physical complexity. In The Universal Turing Machine A Half-Century Survey, pages 207–235. Springer, 1995. [BHPS14] Laurent Bienvenu, Rupert H¨olzl, Christopher P. Porter, and Paul Shafer. Randomness and semi-measures. preprint, arXiv:1310.5133, 2014. [BP12] Laurent Bienvenu and Christopher P. Porter. Strong reductions in effective randomness. Theoretical Computer Science, 459:55–68, 2012. [BP16] Laurent Bienvenu and Christopher P Porter. Deep classes. Bulletin of Symbolic Logic, 22(2):249–286, 2016. [DMN17] Rod Downey, Michael McInerney, and Keng Meng Ng. Lowness and logical depth. Theoretical Computer Science, 702:23–33, 2017. [HP17] Rupert H¨olzl and Christopher P Porter. Randomness for computable measures and initial segment complexity. Annals of Pure and Applied Logic, 168(4):860–886, 2017. [JLL94] David W Juedes, James I Lathrop, and Jack H Lutz. Computational depth and reducibility. Theoretical Computer Science, 132(1-2):37–70, 1994. [Kau91] Steven M. Kautz. Degrees of random sequences. PhD thesis, Cornell University, 1991. [KHMS11] Bjørn Kjos-Hanssen, Wolfgang Merkle, and Frank Stephan. Kolmogorov complexity and the recursion theorem. Transactions of the American Mathematical Society, 363(10):5465–5480, 2011. [Lev73] Leonid A Levin. On the notion of a random sequence. In Soviet. Math. Dokl., volume 14, pages 1413–1416, 1973. [Lev84] Leonid Levin. Randomness conservation inequalities; information and independence in mathematical theories. Information and Control, 61:15–37, 1984. [Lev13] Leonid Levin. Forbidden information. Journal of the ACM, 60(2):9, 2013. [LZ70] L. A. Levin and A. K. Zvonkin. The complexity of finite objects and the basing of the concepts of information and randomness on the theory of algorithms. Uspehi Mat. Nauk, 25(6(156)):85–127, 1970. [MS17] Philippe Moser and Frank Stephan. Depth, highness and dnr degrees. Discrete Mathematics & Theoretical Computer Science, 19(special issue FCT’15), 2017. [MSU98] Andrei A Muchnik, Alexei L Semenov, and Vladimir A Uspensky. Mathematical metaphysics of randomness. Theoretical Computer Science, 207(2):263–317, 1998. [Nie09] Andr´e Nies. Computability and randomness, volume 51. Oxford University Press, 2009. [SF77] Claus-Peter Schnorr and P Fuchs. General random sequences and learnable sequences. The Journal of Symbolic Logic, 42(3):329–340, 1977. Appendix A. Proof of Lemma 3 Working towards the proof of Lemma 3, we first establish the following result. We thus have the identity Then by our initial assumption on t and t′, we have The lemma follows by taking the negative logarithm of this inequality We can now prove Lemma 3. The (i)→(ii) implication is immediate. For the (ii)→(i) implication, suppose X is a sequence and h a computable increasing function such that for any time bound t. If k ∈ [h(n), h(n + 1)), we have We now apply the previous lemma with σ = X↾h(n), τ = X↾[h(n), k) and E the map such that, on input ρ, checks whether ρ has length h(n) for some n and if so returns all strings whose length is between 0 and h(n + 1) − h(n) (otherwise E(ρ) is empty). The lemma gives us a computable time bound s such that This being true for all n and all k ∈ [h(n), h(n + 1)), we have and thus X is order-deep. Finally, the (ii)↔(iii) equivalence can be established using Lemma 1(iii) and Theorem 2. This paper is available on arxiv under CC BY 4.0 DEED license. Authors:
(1) Laurent Bienvenu;
(2) Christopher P. Porter. Photo by Matt Hardy on Unsplash Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Background 2 Background 3 On the slow growth law 3 On the slow growth law 4 Members of Deep Π0 1 classes 4 Members of Deep Π0 1 classes 5 Strong depth is Negligible 5 Strong depth is Negligible 6 Variants of Strong Depth 6 Variants of Strong Depth References References References [BDM23] Laurent Bienvenu, Valentino Delle Rose, and Wolfgang Merkle. Relativized depth. Theoretical Computer Science, 949:113694, 2023. [BDNM15] Laurent Bienvenu, Rodney G. Downey, Andr´e Nies, and Wolfgang Merkle. Solovay functions and their applications in algorithmic randomness. Journal of Computer and System Sciences, 81(8):1575–1591, 2015. [Ben95] Charles H. Bennett. Logical depth and physical complexity. In The Universal Turing Machine A Half-Century Survey, pages 207–235. Springer, 1995. [BHPS14] Laurent Bienvenu, Rupert H¨olzl, Christopher P. Porter, and Paul Shafer. Randomness and semi-measures. preprint, arXiv:1310.5133, 2014. [BP12] Laurent Bienvenu and Christopher P. Porter. Strong reductions in effective randomness. Theoretical Computer Science, 459:55–68, 2012. [BP16] Laurent Bienvenu and Christopher P Porter. Deep classes. Bulletin of Symbolic Logic, 22(2):249–286, 2016. [DMN17] Rod Downey, Michael McInerney, and Keng Meng Ng. Lowness and logical depth. Theoretical Computer Science, 702:23–33, 2017. [HP17] Rupert H¨olzl and Christopher P Porter. Randomness for computable measures and initial segment complexity. Annals of Pure and Applied Logic, 168(4):860–886, 2017. [JLL94] David W Juedes, James I Lathrop, and Jack H Lutz. Computational depth and reducibility. Theoretical Computer Science, 132(1-2):37–70, 1994. [Kau91] Steven M. Kautz. Degrees of random sequences. PhD thesis, Cornell University, 1991. [KHMS11] Bjørn Kjos-Hanssen, Wolfgang Merkle, and Frank Stephan. Kolmogorov complexity and the recursion theorem. Transactions of the American Mathematical Society, 363(10):5465–5480, 2011. [Lev73] Leonid A Levin. On the notion of a random sequence. In Soviet. Math. Dokl., volume 14, pages 1413–1416, 1973. [Lev84] Leonid Levin. Randomness conservation inequalities; information and independence in mathematical theories. Information and Control, 61:15–37, 1984. [Lev13] Leonid Levin. Forbidden information. Journal of the ACM, 60(2):9, 2013. [LZ70] L. A. Levin and A. K. Zvonkin. The complexity of finite objects and the basing of the concepts of information and randomness on the theory of algorithms. Uspehi Mat. Nauk, 25(6(156)):85–127, 1970. [MS17] Philippe Moser and Frank Stephan. Depth, highness and dnr degrees. Discrete Mathematics & Theoretical Computer Science, 19(special issue FCT’15), 2017. [MSU98] Andrei A Muchnik, Alexei L Semenov, and Vladimir A Uspensky. Mathematical metaphysics of randomness. Theoretical Computer Science, 207(2):263–317, 1998. [Nie09] Andr´e Nies. Computability and randomness, volume 51. Oxford University Press, 2009. [SF77] Claus-Peter Schnorr and P Fuchs. General random sequences and learnable sequences. The Journal of Symbolic Logic, 42(3):329–340, 1977. Appendix A. Proof of Lemma 3 Working towards the proof of Lemma 3, we first establish the following result. We thus have the identity Then by our initial assumption on t and t′, we have The lemma follows by taking the negative logarithm of this inequality We can now prove Lemma 3. The (i)→(ii) implication is immediate. For the (ii)→(i) implication, suppose X is a sequence and h a computable increasing function such that for any time bound t. If k ∈ [h(n), h(n + 1)), we have We now apply the previous lemma with σ = X↾h(n), τ = X↾[h(n), k) and E the map such that, on input ρ, checks whether ρ has length h(n) for some n and if so returns all strings whose length is between 0 and h(n + 1) − h(n) (otherwise E(ρ) is empty). The lemma gives us a computable time bound s such that This being true for all n and all k ∈ [ h ( n ), h ( n + 1)), we have n k ∈ h n h n and thus X is order-deep. X Finally, the (ii)↔(iii) equivalence can be established using Lemma 1(iii) and Theorem 2. 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 Authors: (1) Laurent Bienvenu; (2) Christopher P. Porter. Authors: Authors: (1) Laurent Bienvenu; (2) Christopher P. Porter. Photo by Matt Hardy on Unsplash Matt Hardy Unsplash

Bridging Computational Notions of Depth: Working Towards the Proof of Lemma 3

Table of Links Abstract and 1 Introduction 2 Background 3 On the slow growth law 4 Members of Deep Π0 1 classes 5 Strong depth is Negligible 6 Variants of Strong Depth References Appendix A. Proof of Lemma 3 6. Variants of Strong Depth Proof. Suppose that X is not weakly deep. Then there is some computable measure µ such that X is µ-Martin-Lof random. By the Levin-Schnorr theorem for a priori complexity with respect to the measure µ (implicit in [Lev73]), there is some c such that KA(X↾n) ≥ − log µ(X↾n) − c for all n ∈ ω. Equivalently, we have Since every computable measure is a computable semimeasure, the conclusion follows. For the other direction, suppose that there is some computable, continuous semimeasure and some c ∈ ω such that for all n ∈ ω, It thus follows from the Levin-Schnorr theorem for a priori complexity that X is µ-Martin-Lof random and hence is not weakly deep. We define a sequence to be KA-deep if (see the proof of [BDM23, Lemma 2.6] for discrete semimeasures which directly translates to the case of continuous semimeasures). Thus we can conclude: 6.2. Depth and monotone complexity. We can obtain a similar characterization of weak depth in terms of monotone complexity. Define a sequence to be Km-deep if This notion was studied by Schnorr and Fuchs [SF77], who used the term super-learnable to refer to the failure of being Km-deep. In particular, Schnorr and Fuchs proved that a sequence is super-learnable if and only if it is Martin-Lof random with respect to a computable measure. Given that a sequence is weakly deep if and only if it is not Martin-Lof random with respect to a computable measure, we have the following. This paper is available on arxiv under CC BY 4.0 DEED license. Authors:
(1) Laurent Bienvenu;
(2) Christopher P. Porter. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Background 2 Background 3 On the slow growth law 3 On the slow growth law 4 Members of Deep Π0 1 classes 4 Members of Deep Π0 1 classes 5 Strong depth is Negligible 5 Strong depth is Negligible 6 Variants of Strong Depth 6 Variants of Strong Depth References References Appendix A. Proof of Lemma 3 Appendix A. Proof of Lemma 3 6. Variants of Strong Depth Proof . Suppose that X is not weakly deep. Then there is some computable measure µ such that X is µ-Martin-Lof random. By the Levin-Schnorr theorem for a priori complexity with respect to the measure µ (implicit in [Lev73]), there is some c such that Proof KA(X↾n) ≥ − log µ(X↾n) − c for all n ∈ ω. Equivalently, we have Since every computable measure is a computable semimeasure, the conclusion follows. For the other direction, suppose that there is some computable, continuous semimeasure and some c ∈ ω such that for all n ∈ ω, It thus follows from the Levin-Schnorr theorem for a priori complexity that X is µ-Martin-Lof random and hence is not weakly deep. We define a sequence to be KA-deep if KA-deep (see the proof of [BDM23, Lemma 2.6] for discrete semimeasures which directly translates to the case of continuous semimeasures). Thus we can conclude: 6.2. Depth and monotone complexity. We can obtain a similar characterization of weak depth in terms of monotone complexity. Define a sequence to be Km-deep if Depth and monotone complexity. This notion was studied by Schnorr and Fuchs [SF77], who used the term super-learnable to refer to the failure of being Km -deep. In particular, Schnorr and Fuchs proved that a sequence is super-learnable if and only if it is Martin-Lof random with respect to a computable measure. Given that a sequence is weakly deep if and only if it is not Martin-Lof random with respect to a computable measure, we have the following. super-learnable Km 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 Authors: (1) Laurent Bienvenu; (2) Christopher P. Porter. Authors: Authors: (1) Laurent Bienvenu; (2) Christopher P. Porter.

Bridging Computational Notions of Depth: Variants of Strong Depth

Table of Links Abstract and 1 Introduction 2 Background 3 On the slow growth law 4 Members of Deep Π0 1 classes 5 Strong depth is Negligible 6 Variants of Strong Depth References Appendix A. Proof of Lemma 3 5. Strong Depth is Negligible Theorem 25. The class of strongly deep sequences is negligible. Proof. For the sake of contradiction, assume there exists a functional Φ such that It is clear that q is computable. Moveover, q is a discrete semimeasure, since On the other hand, for almost all n: Note, by contrast, that the collection of weakly deep sequences is not negligible. Indeed, as shown by Muchnik et al. [MSU98], no 1-generic sequence is Martin-L¨of random with respect to a computable measure, and thus every 1-generic is weakly deep. Moreover, as shown by Kautz [Kau91], every 2-random sequence computes a 1-generic, and hence the collection of 1-generics is not negligible. This paper is available on arxiv under CC BY 4.0 DEED license. Authors:
(1) Laurent Bienvenu;
(2) Christopher P. Porter. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Background 2 Background 3 On the slow growth law 3 On the slow growth law 4 Members of Deep Π0 1 classes 4 Members of Deep Π0 1 classes 5 Strong depth is Negligible 5 Strong depth is Negligible 6 Variants of Strong Depth 6 Variants of Strong Depth References References Appendix A. Proof of Lemma 3 Appendix A. Proof of Lemma 3 5. Strong Depth is Negligible Theorem 25. The class of strongly deep sequences is negligible. Theorem 25. The class of strongly deep sequences is negligible. Proof. For the sake of contradiction, assume there exists a functional Φ such that It is clear that q is computable. Moveover, q is a discrete semimeasure, since q q On the other hand, for almost all n : n Note, by contrast, that the collection of weakly deep sequences is not negligible. Indeed, as shown by Muchnik et al. [MSU98], no 1-generic sequence is Martin-L¨of random with respect to a computable measure, and thus every 1-generic is weakly deep. Moreover, as shown by Kautz [Kau91], every 2-random sequence computes a 1-generic, and hence the collection of 1-generics is not negligible. 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 Authors: (1) Laurent Bienvenu; (2) Christopher P. Porter. Authors: Authors: (1) Laurent Bienvenu; (2) Christopher P. Porter.

Bridging Computational Notions of Depth: Here's Why Strong Depth is Negligible

Table of Links Abstract and 1 Introduction 2 Background 3 On the slow growth law 4 Members of Deep Π0 1 classes 5 Strong depth is Negligible 6 Variants of Strong Depth References Appendix A. Proof of Lemma 3 By Lemma 3, we can conclude that X is order-deep. One immediate consequence of Theorem 9 is the following. The converse of this result does not hold. As an immediate consequence of Theorem 9 and the above results from [BP16], we have: Next, we have: This paper is available on arxiv under CC BY 4.0 DEED license. Authors:
(1) Laurent Bienvenu;
(2) Christopher P. Porter. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Background 2 Background 3 On the slow growth law 3 On the slow growth law 4 Members of Deep Π0 1 classes 4 Members of Deep Π0 1 classes 5 Strong depth is Negligible 5 Strong depth is Negligible 6 Variants of Strong Depth 6 Variants of Strong Depth References References Appendix A. Proof of Lemma 3 Appendix A. Proof of Lemma 3 By Lemma 3, we can conclude that X is order-deep. One immediate consequence of Theorem 9 is the following. The converse of this result does not hold. As an immediate consequence of Theorem 9 and the above results from [BP16], we have: Next, we have: 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 Authors: (1) Laurent Bienvenu; (2) Christopher P. Porter. Authors: Authors: (1) Laurent Bienvenu; (2) Christopher P. Porter.

Stories, News & Mentions about PORTER

Categories

Trending Topics

Stories, News & Mentions about PORTER

Porter’s Stories on HackerNoon

Porter's News & Mentions

Categories

Trending Topics