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1811 Dictionary in the Vulgar Tongue: Section S

Vue.js, the open source JavaScript framework, helps build beautiful web interfaces. Its excellent features can be strongly leveraged when it is paired with other web tools. Nowadays, many developers are replacing with Vue.js. Angular.js and React.js This brings us to the topic of the article — should I go for Vue or Angular? In this article, we attempt to discuss these two frameworks and make a comparison based on which you can make a favorable decision for your project. , the brainchild of an ex-Google employee, Evan You, was released in 2014 and has already gained more than 57,000 GitHub stars in its kitty. Many developers vouch for Vue because it is very easy to learn. If you have strong fundamentals in HTML, CSS and JavaScript, then learning Vue.js is just a matter of hours. Vue.js What makes Vue attractive to developers is that it is fresh, lightweight and comes with little or no complexities. Though Vue is extremely flexible and simple, it is very powerful and offers two-way data binding feature, just like Angular and Virtual DOM feature like React. Being less opinionated, Vue lets you structure your app in whichever way you want it. Angular doesn’t let you do that because you will have to do many things the “Angular way”. Upwork, Netflix, Freelancer, Paypal, Lego and iStock Photo are examples of Angular.js apps. Collate and Remote Pad GUI are examples of apps made with Vue.js Vue.js — the Versatile JavaScript Framework Being a cross-platform, highly progressive framework, Vue becomes the first choice for many developers who need to develop single page applications. In the typical MVC architecture for developing web applications, Vue acts as the View, meaning it lets you see display portions of the data. Vue has a number of features apart from the basic ones mentioned above. Let’s look at those: 1. Easily Adoptable If you have been using some other framework, then you can easily adopt Vue because the core library is focused on the view layer, and you can easily pick it up and integrate it with third party libraries to use with existing projects. 2. Lightweight As it focuses mainly on the ViewModel or the two-way data binding, Vue is lightweight, with fairly basic docs. And Vue is an interface layer, meaning you can use it as a light feature in pages, providing a better option than full-blown SPA. 3. Lower Learning Curve Developers working with HTML will find that Vue has a low learning curve. This makes it perfect for less experienced developers and beginners to learn and understand Vue quickly. 4. Two-Way Binding Vue provides the v-model directive (for updating data on user input events) that makes it easy to have a two-way binding on form inputs and texture elements. It can choose the right way to update the elements with regards to the input type. 5. Virtual DOM The performance factor of Vue is slightly elevated due to its lightweight virtual-DOM implementation, based on . This is one of the main new features of Virtual DOM and makes computation inexpensive because you can directly make the updates. When you need to make the changes in the actual DOM, you can use the function that does it just once. Snabbdom 6. HTML based Template Syntax This allows you to directly bind the rendered DOM to the underlying Vue instance’s data. This is a useful feature because it lets you extend the basic HTML elements to save reusable codes. Angular.js — the Dynamic JavaScript Framework is a full featured Javascript framework that supports Model-View-Controller programming structure and is perfect for building dynamic, single page web apps. Angular.js Developed and supported by Google in 2009, Angular.js contains a library of JS code based on standard JavaScript and HTML. Angular.js was initially a tool that enabled designers to interact with both backend and frontend. Some of the best features of Angular.js are: 1. Model-View-ViewModel (MVVM) For building client-side web applications, Angular.js incorporates basic principles behind the original MVC software design pattern. However, it does not implement the MVC, in what we know in the traditional sense, but rather in an . MVVM or Model-View-ViewModel pattern 2. Dependency Injection Angular.js comes with a built-in dependency injection subsystem feature that makes an application easier to develop and test. Dependency Injection allows you to get the dependencies by asking for it, rather than searching for it. This is greatly helpful to the developer. 3. Testing Separate unit testing for controllers and directives is possible in Angular.js. And it allows the developers to do an end-to-end and unit test runner setup, which means you can test from the user-perspective as well. 4. Cross-browser Compliant An interesting feature of Angular.js is that the applications written in the framework works well in multiple browsers. Angular.js can automatically handle the JS code required for each browser. 5. Directives like elements, attributes, css can be used to create custom HTML tags. These are markers on DOM elements as you can extent the directive vocabulary and make your own directives, or convert them into reuse components . Directives (DOM template for rendering instructions) 6. Deep Linking As Angular.js is mainly used for making single page applications, you have to make use of the Deep Linking feature to allow you to load sub-templates on the same page. The purpose of deep linking is to look at the location URL and arrange for it to map to the current state of the page. The deep linking feature does this by setting URLs by looking at the state of the page and taking you to the specific content rather than traversing the application from the home page. Deep linking allows web applications to be easily searched by all the major search engines. Vue.js vs. Angular.js — Which is the Best? Now, comes the million dollar question. Which is the best out of the two — Angular.js or Vue.js? Let’s go deeper into this by looking at the following factors: Learning Curve As already mentioned before, Vue.js is relatively simple to learn and understand than Angular.js. You need time to get used to Angular. Developers are of the opinion that they are both great for projects, but most of them like to use Vue because it is simpler and scales really well when you add to the project. Vuex Though a few of the syntaxes of Vue and Angular are similar, like API and design (this is because Vue was actually inspired from Angular.js in its early stages of development), Vue has endeavored to improve itself in areas where developers find it difficult with Angular.js. You can build a non-trivial app with Vue.js in a few hours; this is not possible with Angular.js. Flexibility Angular.js is opinionated, it actually gives strong opinions on how your app should be structured, Vue is gentler, and offers a modular, flexible solution for creating apps. Vue is probably considered a library instead of a framework. By default it doesn’t come with a router, http request service, etc. You have to install the “plugins” that you want. Again, very flexible and also compatible with most libraries you may want to use. Developers who don’t like to listen to opinionated frameworks gladly adopt Vue for their projects. However, there are developers who prefer to choose Angular.js because they prefer a support in order to make decisions on the overall structure of their apps. This would help them save time for coding. Document Object Model (DOM) With the minimal amount of components for re-rendering, Vue lets you precompile your templates to pure JavaScript. This virtual DOM allows for massive optimisations. This is the major difference between the two. Vue allows for simpler programming model, while Angular.js manipulates DOM in a cross-browser compatible way. Speed/Performance While both Angular JS and Vue delivers comparable performance, we can say that Vue is slightly ahead, thanks to its lighter-weight Virtual DOM implementations. The simpler programming model enables Vue to provide a better performance and hence, it emerges the winner. Vue can be used without the build system as you can just include it into the HTML file. This makes Vue approachable, thereby improving its performance. The reason why Angular.js becomes slow is that it uses dirty checking, a concept of digest cycle that comes as a loop in which the Angular.js monitors continuously to see if there are any changes to the variables. It is a change detection technique. Two-way Data Binding Both frameworks supports two-way data bindings equally, but Angular.js is more complicated because of its heavy weight nature when compared to Vue.js. The two-way data binding is much simpler in Vue, while in Angular, it is way down. When to Choose Vue.js Developers looking to kickstart their career by making products in the easiest way, can choose Vue. This would be a more helpful option if your Javascript basics are not too strong or if you are dogged by strict deadlines. It is also a good idea to choose Vue if your front end is Laravel because the Laravel community considers Vue to be their most preferred framework. It cuts the total process time by 50% and free up space on the server. The thing with Angular is that it requires using because all the documentation and learning resources are TypeScript based. Of course, Typescript is a good option when you are creating large-scale applications and you can achieve greater productivity when your Java and C# background is very strong. Typescript But this wouldn’t be a good choice for small-scale uses because it could lead to more overhead costs. Using Angular without Typescript can be virtually impossible. In such cases, the obvious choice would be Vue, and you also have the added advantage of using Typescript with Vue through official typings and official decorator. You can also choose Vue if you like your freedom while structuring your application because Angular has some strong opinions and offers official support for a number of build systems. If you have familiarity with just Es5 Javascript and HTML, then you can go ahead with your project using Vue, but Angular entails that you familiarize with several concepts before becoming productive. Using the standalone version of Vue would be good if you want to compile the templates in the browser and developers go for it for its simplicity- there are no file formats of special build steps. But it could affect performance a tad bit. However, kindly note that the first component render would be longer than the rest of the process because the template would have to be compiled to JS first. Vue single-file components are perfect if you are looking to build performance critical SPAs or need features scoped CSS. When to Choose Angular.js Your first choice would be Angular.js if the aim is to build large and complex application because it offers complete and comprehensive solution for client-side app development. Angular is a viable option for developers looking to deal with client side and server side modes. The main reason devs like Angular.js is that they get to focus on any kind of design with any JQuery-call or DOM configuration distractions. Angular.js would also be good for developers creating heavy web applications with several components and complex requirements. When you choose Angular, native developers find it easier to understand the application functionality and coding structure. You can also go for Angular if you want to choose the existing component in a new project because all you need to do is copy and paste the codes. Angular.js would help you considerably through its two-way data binding feature as it manages the synchronization between DOM and the model. This makes it a more beneficial tool for web app development. Developers looking to make lighter and faster web applications can make use of the MVC structure in Angular and separate logic and data components. Thus, it speeds up development process. It is also worth mentioning that Vue’s companion libraries for routing and state management are officially supported and updated with the core library. But this is not so with Angular, because the community manages these libraries, leading to more fragmented ecosystem. Comparison of the Codes of Vue.js and Angular.js It’s interesting to analyse the codes of both the frameworks. The codes containing markup, style and behavior can help you compose highly efficient reusable interfaces. In Angular, entities like controllers and directives are contained in the module, while in Vue, the module contains the component logic. Vue Components Vue.extend({data: function(){ return {…} },created: function() {…},ready: function() {…},components: {…},methods: {…},watch: {…}//(other props excluded)}); Angular Modules angular.module(‘myModule’, […]); Directives are more powerful in Angular.js. They mean a lot; similar to the function of a component in Vue.js. Vue Directives Vue.directive(‘my-directive’, {bind: function () {…},update: function (newValue, oldValue) {…},unbind: function () {…}}); Angular Directives myModule.directive(‘directiveName’, function (injectables) {return {restrict: ‘A’,template: ‘<div></div>’,controller: function() { … },compile: function() {…},link: function() { … }//(other props excluded) };}); As Vue.js was inspired from Angular.js, the former has borrowed the latter’s templating syntax. Hence the syntax for loops, interpolation and conditionals are all very similar. However, templating for both is very easy. Look at the code snippets given below: Vue Interpolation {{myVariable}} Angular Interpolation {{myVariable}} Vue Loops <li v-repeat=”items” class=”item-{{$index}}”>{{myProperty}}</li> Angular Loops <li ng-repeat=”item in items” class=”item-{{$index}}”>{{item.myProperty}}</li> Vue Conditionals <div v-if=”myVar”></div><div v-show=”myVar”></div> Angular Conditionals <div ng-if=”myVar”></div><div ng-show=”myVar”></div> Credits: Fadeit However, the coding of Vue.js makes page rendering very easy and it beats both Angular and React on this count. The fact is that Vue.js is more like a library than a framework, so it does not provide all the functionalities of Angular.js. You will have to rely on third party codes for Vue.js, while Angular provides features like HTTP request service or router. You can try mixing and matching the libraries as you go. If you are used to Angular.js, then you may not be comfortable with Vue because it doesn’t tackle the challenges that is already covered in Angular.js. Before winding up, let’s take a quick look at These are nothing but websites, or rather web pages, that utilizes the most modern web technologies like and to give the user an app-like experience. PWAs are, more or less, hybrid apps that present the user with the benefits of both mobile web apps and native mobile apps. or . Progressive Web Apps PWAs service workers web app manifests is the most popular JavaScript framework used to create Progressive Web Apps. It not only builds PWAs, but also deploys the app in the native app store through Cordova. The combination of Ionic and Angular.js along with HTML5, CSS3 and Cordova, works magic by delivering the best quality PWAs. Ionic Version Releases of Angular.js and Vue.js The latest stable version of Vue.js, , got released on June 8, 2017. Prior to this release, there were 13 other versions that were released this year starting from version 2.1.9. v2.3.4 was released in March 2017. The earlier versions are Angular 1 and 2; there is no Angular 3. Version 5 of Angular will be released during September/October 2017 months. Version 6 in March 2018 and Version 7 is expected in September/October 2018. Angular 4 Conclusion Vue.js is lightweight, and behaves like the fitter little brother of Angular.js, making it a better option if you want a less opinionated framework. And just like a big brother, Angular.js shows you the way to build complex, yet good quality apps. So, ultimately, the answer to which is the perfect tool boils down to the nature of your project and your learning capability. But, nevertheless, both these JavaScript frameworks can yield the best results for your app development. Are you thinking of developing a web app in Vue.js or Angular.js? We’ll be happy to guide you. [Contact Us Today!](http://<a href="javascript:void(0);" onclick="getQuote();">Contact Us Today!</a>) Originally published in Cabot Solutions Blog on June 6, 2017.

A Comparative Study of Progressive JS Frameworks: Angular.js & Vue.js

With all the new libraries and frameworks it is pretty hard to keep up with all of them, and that is if you can even decide which ones are worth spending time one, over the last year or so I was exposed to many a new tech stack, with React for work and just personally playing around with React-Native, Aurelia and Angular2. Each of them attached to a new project, partly justified by wanting to try it out or form my own opinion. Previously I had written about Aurelia, which I was very impressed with after than Angular 2 disaster, if you like, you can read more about it here: _Recently had a small personal project that I wanted to rebuild, a project I had initially started quite some time back…_medium.com Aurelia: First impressions This time round I decided to dive into a lot of good things are being said about it on the web, with it apparently being faster than react, with it’s implementation of a simple and powerful Virtual DOM focused on performance. On top of that is is notably smaller than React sitting around 14kb. Vue.JS, Snabbdom, Of all the frameworks and libraries I have worked with over the years, one thing that stood out to me about Vue.JS was the documentation, very detailed and easy to follow, covering multiple use cases and all the various options, where applicable, for each of it’s built in methods. Now for a look at the code, the following example is for a very simple component, written in absolute bare-bones, just for you to get an idea of how things are structured.. Vue.JS uses a template file containing both the template body and a script section, and these files are saved with a extension. .vue Vue.JS itself is completely template agnostic, you can use handlebar/directive template as above, you can also use , or even build it up very manually using es5 or es6 string interpolation if you prefer. JSX This file pretty much handles it all, you will define the HTML structure as well as relevant scripting logic, and either define a block or import a style sheet like in the example. <style> The script tag is where all the real work begins, we start by importing Vue and whatever components we intend on using within the component. name: 'Events',components: {'header-bar': Header,'search-bar': Search,'list-data': List,'footer-bar': Footer,}, Above we have a snippet from the default export object, we start with the components name, followed by a object. This object defines a key which is the tag name for the HTML element within our template with its value being the component we imported a little further up. components Next we have some of our methods to control initial logic and define usable functions. data() {return {data: [],searchTerm: {},}}, The function is used to setup default data for initial rendering of the component, here the data key is setting itself as an empty array as later when we fetch the data it will become and array of objects, and we do not want to break the render by defaulting with invalid data types. data() created() {// API/Service calls would go herereturn {data: [{},{}],};}, is similar to reacts life cycle method, this is the best place within the life of the component to go fetch any data that is not available on initiation of the component, in this case to go fetch the actual list items. created() componentWillMount methods: {search() {// Search method written here},} is where you define functions that will be used within the component itself, or passed down to a child component as props, as is the case with , the child component will receive this method via the props, and this will then be fired off when a user interacts with the search component. methods() search() Search One thing that was not specifically included in the example but was was referenced was props, like react and probably many other libraries at this stage, Vue.JS also supports props, and like react they can be anything that a child component needs, be it static text, a function, and array of data needing to be looped over, or an object with key value pairs for simple dynamic display. Props are quite simple to define, within the you would add another key, called ‘props’ with an array of all the props it is expecting to receive. default export Above would then be an example of the search component, as you can see it is taking in 2 props, the submit method and term, which is a model for handling the search value that will be passed into the function. This was just a taste of what is possible with Vue.JS, you will see many more examples by visiting their documentation at .If you wish to quickly spin up an application and start playing around with Vue.JS, I can suggest taking a look at the Yeoman generator created by . Vue.JS docs FountainJS Working with Vue.JS was a great pleasure, I found the learning curve very shallow, however that could purely be based on my experience, as mentioned before I have worked with a few in the past. The default template structure feels very similar to how it was working with Angular, so developers coming from that background may pick it up a bit faster than they would react. I cannot really go un-learn react to see if it influences how easy it was to pick up Vue.JS. _This is really exciting: our team has just wrapped up the work on State of Vue.js -a comprehensive report crafted for…_www.monterail.com State of Vue.js - Key Takeaways from the Report _You probably already know this: the first step to learning something in any subject is acknowledging that you don't…_www.monterail.com People to Watch If You're a Vue.js Developer [Infographic] | | Twitter Instagram YouTube

VueJS: First Impressions

In a move that could reshape the Bitcoin ecosystem, Satoshi Protocol has raised $2 million in seed funding. The Dubai-based startup, which claims to be the first stablecoin protocol backed by Bitcoin, is eyeing expansion and enhanced security measures. CMS Holdings and RockTree Capital led the round. Cypher Capital, Metalpha, and a handful of other investors also jumped on board. The cash injection comes at a crucial time for the young company. Satoshi Protocol isn't just another crypto project. It's tackling a real problem: bringing stablecoin utility to Bitcoin users. The idea? Let folks use their Bitcoin as collateral to mint a stablecoin called $SAT. It's a bit like having your Bitcoin cake and eating it too. "We're not just building another stablecoin," says Naka, the company's founder and CEO. "We're creating a tool that Bitcoin users actually need." The protocol has been busy. It's already integrated with several Bitcoin-adjacent platforms like BOB, Bitlayer, and BEVM. A recent campaign with Binance Web3 Wallet pulled in over 172,000 users. Not too shabby for a newcomer. But it's not all smooth sailing. The crypto world is notoriously volatile, and stablecoins have had their share of drama. Satoshi Protocol will need to navigate these choppy waters carefully. Still, some heavy hitters are betting on their success. Vineet Budki from Cypher Capital sees potential. "This could really boost liquidity options for Bitcoin users," he notes. The road ahead is long. Satoshi Protocol plans to beef up security, expand to more Layer 2 solutions, and push for global adoption. It's ambitious, but then again, so was Bitcoin. As the crypto landscape evolves, projects like Satoshi Protocol could play a pivotal role. They're not just building on Bitcoin – they're aiming to enhance its utility and liquidity. The success of such initiatives could have far-reaching implications for the broader cryptocurrency ecosystem. The integration of stablecoin functionality with Bitcoin's network presents both opportunities and challenges. On one hand, it could potentially increase Bitcoin's appeal to a wider range of users and use cases, particularly in decentralized finance (DeFi) applications. This could lead to increased adoption and liquidity for Bitcoin. As Satoshi Protocol moves forward with its $2 million in seed funding, industry observers will be watching closely. The project's ability to deliver on its promises and overcome technical and regulatory challenges could provide valuable insights into the future direction of Bitcoin-based financial innovations. Don’t forget to like and share the story! Vested Interest Disclosure: This author is an independent contributor publishing via our business blogging program. HackerNoon has reviewed the report for quality, but the claims herein belong to the author. #DYOR. In a move that could reshape the Bitcoin ecosystem, Satoshi Protocol has raised $2 million in seed funding. The Dubai-based startup, which claims to be the first stablecoin protocol backed by Bitcoin, is eyeing expansion and enhanced security measures. CMS Holdings and RockTree Capital led the round. Cypher Capital , Metalpha, and a handful of other investors also jumped on board. The cash injection comes at a crucial time for the young company. Satoshi Protocol Cypher Capital Satoshi Protocol isn't just another crypto project. It's tackling a real problem: bringing stablecoin utility to Bitcoin users. The idea? Let folks use their Bitcoin as collateral to mint a stablecoin called $SAT. It's a bit like having your Bitcoin cake and eating it too. "We're not just building another stablecoin," says Naka, the company's founder and CEO. "We're creating a tool that Bitcoin users actually need." The protocol has been busy. It's already integrated with several Bitcoin-adjacent platforms like BOB, Bitlayer, and BEVM. A recent campaign with Binance Web3 Wallet pulled in over 172,000 users. Not too shabby for a newcomer. But it's not all smooth sailing. The crypto world is notoriously volatile, and stablecoins have had their share of drama. Satoshi Protocol will need to navigate these choppy waters carefully. Still, some heavy hitters are betting on their success. Vineet Budki from Cypher Capital sees potential. "This could really boost liquidity options for Bitcoin users," he notes. The road ahead is long. Satoshi Protocol plans to beef up security, expand to more Layer 2 solutions, and push for global adoption. It's ambitious, but then again, so was Bitcoin. As the crypto landscape evolves, projects like Satoshi Protocol could play a pivotal role. They're not just building on Bitcoin – they're aiming to enhance its utility and liquidity. The success of such initiatives could have far-reaching implications for the broader cryptocurrency ecosystem. The integration of stablecoin functionality with Bitcoin's network presents both opportunities and challenges. On one hand, it could potentially increase Bitcoin's appeal to a wider range of users and use cases, particularly in decentralized finance (DeFi) applications. This could lead to increased adoption and liquidity for Bitcoin. As Satoshi Protocol moves forward with its $2 million in seed funding, industry observers will be watching closely. The project's ability to deliver on its promises and overcome technical and regulatory challenges could provide valuable insights into the future direction of Bitcoin-based financial innovations. Don’t forget to like and share the story! Vested Interest Disclosure: This author is an independent contributor publishing via our business blogging program. HackerNoon has reviewed the report for quality, but the claims herein belong to the author. #DYOR. Vested Interest Disclosure: This author is an independent contributor publishing via our business blogging program . HackerNoon has reviewed the report for quality, but the claims herein belong to the author. #DYOR. Vested Interest Disclosure: business blogging program business blogging program

Satoshi Protocol Secures $2M Seed Funding for Bitcoin Backed Stablecoin

সাতোশি প্রোটোকল বিটকয়েন ব্যাকড স্টেবলকয়েনের জন্য $2M বীজ তহবিল সুরক্ষিত করে

Satoshi Protocol sichert sich 2 Millionen US-Dollar Startkapital für Bitcoin-gestützten Stablecoin

El protocolo Satoshi asegura una financiación inicial de 2 millones de dólares para una moneda estable respaldada por Bitcoin

Le protocole Satoshi obtient un financement de démarrage de 2 millions de dollars pour le Stablecoin soutenu par Bitcoin

सातोशी प्रोटोकॉल ने बिटकॉइन समर्थित स्टेबलकॉइन के लिए $2 मिलियन की सीड फंडिंग हासिल की

サトシ・プロトコル、ビットコイン担保ステーブルコインに200万ドルのシード資金を確保

Satoshi 프로토콜은 비트코인 기반 Stablecoin에 대한 200만 달러의 시드 자금을 확보합니다.

Protocolo Satoshi garante financiamento inicial de US$ 2 milhões para Stablecoin apoiado por Bitcoin

Протокол Сатоши обеспечивает начальное финансирование в размере 2 миллионов долларов США для стейблкоина, поддерживаемого биткойнами

Satoshi Protokolü, Bitcoin Destekli Stablecoin için 2 Milyon Dolarlık Başlangıç Fonu Sağladı

Giao thức Satoshi đảm bảo nguồn tài trợ ban đầu trị giá 2 triệu đô la cho Stablecoin được hỗ trợ bằng Bitcoin

Satoshi Protocol 为比特币支持的稳定币获得 200 万美元种子资金

ZURICH, Switzerland, July 8th, 2024, Chainwire Quick take: Certo protocol, decentralized stablecoin lending, previously working with USDT, has added support for USDC deposits and borrows.


stUSD is an interest-earning stablecoin utilizing Certo — a P2P lending protocol designed to work with tokenized real-world assets in the form of U.S. Treasuries. Certo, as detailed on certo.finance, represents a pioneering approach in the realm of decentralized finance (DeFi). It is a peer-to-peer (P2P) lending platform that brings real-world assets into the space. Specifically, Certo facilitates the use of tokenized U.S. Treasuries as collateral in a lending stablecoins — and a lender of traditional stablecoins, the user receive the interest accrued to the borrowers. stUSD is Certo’s dollar-denominated receipt token, which can be seen as a form of interest-earning stablecoin. This digital currency maintains a stable relationship to the U.S. dollar by using a stable collateral of tokenized U.S. Treasuries to maintain price stability, serving as a reliable medium of exchange and a value store for the whole DeFi ecosystem. More importantly, stUSD is designed to generate interest for its holders, which accrues over time based on the underlying lending activities conducted through the Certo protocol. This feature makes stUSD a potential choice for price stability and interest in the volatile landscape of cryptocurrencies. Certo has been under development for some time, with its ambitious goal to bridge the gap between DeFi and real-world assets. Initially, when Certo launched its testnet earlier this year, it exclusively supported deposits and borrowing in Tether (USDT), a widely used stablecoin in the cryptocurrency market. This initial phase allowed Certo to test its systems, ensure robust security measures, and gather valuable feedback from early users within a controlled environment. Today, Certo takes a significant step forward by announcing the addition of support for USD Coin (USDC) deposits and borrows on its testnet platform. This expansion is pivotal as USDC is renowned for its wide acceptance across financial and crypto markets. By incorporating USDC, Certo aims to attract a broader user base and increase the platform’s versatility, allowing more users to participate in testing and refining the protocol’s features. With the inclusion of USDC, participants in the Certo ecosystem now have the flexibility to deposit both USDT and USDC to receive stUSD. This enhancement allows users to preview how their investments accrue interest over time, directly within the Certo interface. This dual-stablecoin option not only provides greater convenience but also enriches the user experience by demonstrating the practical benefits of stUSD in a more diverse and adaptable framework. While today’s announcement marks a significant milestone, it is important to note that Certo is still operating within its testnet phase. This stage is critical as it allows the developers to finetune the protocol’s functionality, ensure the stability of the system under various scenarios, and most importantly, secure user feedback. The testnet phase is essential for Certo to meet its goal of creating a seamless and secure bridge between cryptocurrencies and real-world assets, ensuring that once live, the platform can operate effectively and reliably in the broader DeFi ecosystem. Through initiatives like these, Certo is not just expanding its capabilities but also paving the way for more innovative solutions in the financial technology space. About Certo Certo is at the forefront of developing a secure, stable, and scalable platform, aiming to bridge the gap between traditional fiat currencies and the digital economy. With a focus on security, transparency, and community-driven development, Certo seeks to provide a robust foundation for financial transactions worldwide. Contact Certo Certo Finance pr@certo.finance This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here. ZURICH, Switzerland, July 8th, 2024, Chainwire ZURICH, Switzerland, July 8th, 2024, Chainwire Quick take: Certo protocol, decentralized stablecoin lending, previously working with USDT, has added support for USDC deposits and borrows. stUSD is an interest-earning stablecoin utilizing Certo — a P2P lending protocol designed to work with tokenized real-world assets in the form of U.S. Treasuries. Certo protocol, decentralized stablecoin lending, previously working with USDT, has added support for USDC deposits and borrows. Certo protocol, decentralized stablecoin lending, previously working with USDT, has added support for USDC deposits and borrows. stUSD is an interest-earning stablecoin utilizing Certo — a P2P lending protocol designed to work with tokenized real-world assets in the form of U.S. Treasuries. stUSD is an interest-earning stablecoin utilizing Certo — a P2P lending protocol designed to work with tokenized real-world assets in the form of U.S. Treasuries. Certo, as detailed on certo.finance, represents a pioneering approach in the realm of decentralized finance (DeFi). It is a peer-to-peer (P2P) lending platform that brings real-world assets into the space. Specifically, Certo facilitates the use of tokenized U.S. Treasuries as collateral in a lending stablecoins — and a lender of traditional stablecoins, the user receive the interest accrued to the borrowers. stUSD is Certo’s dollar-denominated receipt token, which can be seen as a form of interest-earning stablecoin. This digital currency maintains a stable relationship to the U.S. dollar by using a stable collateral of tokenized U.S. Treasuries to maintain price stability, serving as a reliable medium of exchange and a value store for the whole DeFi ecosystem. More importantly, stUSD is designed to generate interest for its holders, which accrues over time based on the underlying lending activities conducted through the Certo protocol. This feature makes stUSD a potential choice for price stability and interest in the volatile landscape of cryptocurrencies. Certo has been under development for some time, with its ambitious goal to bridge the gap between DeFi and real-world assets. Initially, when Certo launched its testnet earlier this year, it exclusively supported deposits and borrowing in Tether (USDT), a widely used stablecoin in the cryptocurrency market. This initial phase allowed Certo to test its systems, ensure robust security measures, and gather valuable feedback from early users within a controlled environment. Today, Certo takes a significant step forward by announcing the addition of support for USD Coin (USDC) deposits and borrows on its testnet platform. This expansion is pivotal as USDC is renowned for its wide acceptance across financial and crypto markets. By incorporating USDC, Certo aims to attract a broader user base and increase the platform’s versatility, allowing more users to participate in testing and refining the protocol’s features. With the inclusion of USDC, participants in the Certo ecosystem now have the flexibility to deposit both USDT and USDC to receive stUSD. This enhancement allows users to preview how their investments accrue interest over time, directly within the Certo interface. This dual-stablecoin option not only provides greater convenience but also enriches the user experience by demonstrating the practical benefits of stUSD in a more diverse and adaptable framework. While today’s announcement marks a significant milestone, it is important to note that Certo is still operating within its testnet phase. This stage is critical as it allows the developers to finetune the protocol’s functionality, ensure the stability of the system under various scenarios, and most importantly, secure user feedback. The testnet phase is essential for Certo to meet its goal of creating a seamless and secure bridge between cryptocurrencies and real-world assets, ensuring that once live, the platform can operate effectively and reliably in the broader DeFi ecosystem. Through initiatives like these, Certo is not just expanding its capabilities but also paving the way for more innovative solutions in the financial technology space. About Certo Certo is at the forefront of developing a secure, stable, and scalable platform, aiming to bridge the gap between traditional fiat currencies and the digital economy. With a focus on security, transparency, and community-driven development, Certo seeks to provide a robust foundation for financial transactions worldwide. Contact Certo Certo Finance pr@certo.finance This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here. This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here . here here

Certo Expands Testnet To Include USDC Deposits For stUSD, Its Interest-Earning Stablecoin

Leveraging SwarmUI & Stable Diffusion 3 on Cloud Platforms: A Guide to Kaggle (No-Cost), Massed Comp

Exploring Drone Dynamics: Stability and Force Generation in Multimedia Design

🔗 Tutorial Video Link :  ➡️ https://youtu.be/HKX8_F1Er_w https://youtu.be/HKX8_F1Er_w?embedable=true Do not skip any part of this tutorial to master how to use Stable Diffusion 3 (SD3) with the most advanced generative AI open-source APP SwarmUI. Automatic1111 SD Web UI or Fooocus are not supporting the SD3 yet. Therefore, I am starting to make tutorials for SwarmUI as well. StableSwarmUI is officially developed by StabilityAI, and your mind will be blown away after you watch this tutorial and learn its amazing features. StableSwarmUI uses ComfyUI as the back end, thus, it has all the good features of ComfyUI, and it brings you easy-to-use features of Automatic1111 StableDiffusion Web UI with them. I really liked SwarmUI and planning to do more tutorials for it. 🔗 The Public Post (no login or account required) Shown In The Video With The Links ➡️ https://www.patreon.com/posts/stableswarmui-3-106135985 0:00 Introduction to the Stable Diffusion 3 (SD3) and SwarmUI and what is in the tutorial 4:12 Architecture and features of SD3 5:05 What each different model files of Stable Diffusion 3 means 6:26 How to download and install SwarmUI on Windows for SD3 and all other Stable Diffusion models 8:42 What kind of folder path you should use when installing SwarmUI 10:28 If you get installation error how to notice and fix it 11:49 Installation has been completed and now how to start using SwarmUI 12:29 Which settings I change before start using SwarmUI and how to change your theme like dark, white, gray 12:56 How to make SwarmUI save generated images as PNG 13:08 How to find description of each settings and configuration 13:28 How to download SD3 model and start using on Windows 13:38 How to use model downloader utility of SwarmUI 14:17 How to set models folder paths and link your existing models folders in SwarmUI 14:35 Explanation of Root folder path in SwarmUI 14:52 VAE of SD3 do we need to download? 15:25 Generate and model section of the SwarmUI to generate images and how to select your base model 16:02 Setting up parameters and what they do to generate images 17:06 Which sampling method is best for SD3 17:22 Information about SD3 text encoders and their comparison 18:14 First time generating an image with SD3 19:36 How to regenerate same image 20:17 How to see image generation speed and step speed and more information 20:29 Stable Diffusion 3 it per second speed on RTX 3090 TI 20:39 How to see VRAM usage on Windows 10 22:08 And testing and comparing different text encoders for SD3 22:36 How to use FP16 version of T5 XXL text encoder instead of default FP8 version 25:27 The image generation speed when using best config for SD3 26:37 Why VAE of the SD3 is many times better than previous Stable Diffusion models, 4 vs 8 vs 16 vs 32 channels VAE 27:40 How to and where to download best AI upscaler models 29:10 How to use refiner and upscaler models to improve and upscale generated images 29:21 How to restart and start SwarmUI 32:01 The folders where the generated images are saved 32:13 Image history feature of SwarmUI 33:10 Upscaled image comparison 34:01 How to download all upscaler models at once 34:34 Presets feature in depth 36:55 How to generate forever / infinite times 37:13 Non-tiled upscale caused issues 38:36 How to compare tiled vs non-tiled upscale and decide best 39:05 275 SwarmUI presets (cloned from Fooocus) I prepared and the scripts I coded to prepare them and how to import those presets 42:10 Model browser feature 43:25 How to generate TensorRT engine for huge speed up 43:47 How to update SwarmUI 44:27 Prompt syntax and advanced features 45:35 How to use Wildcards (random prompts) feature 46:47 How to see full details / metadata of generated images 47:13 Full guide for extremely powerful grid image generation (like X/Y/Z plot) 47:35 How to put all downloaded upscalers from zip file 51:37 How to see what is happening at the server logs 53:04 How to continue grid generation process after interruption 54:32 How to open grid generation after it has been completed and how to use it 56:13 Example of tiled upscaling seaming problem 1:00:30 Full guide for image history 1:02:22 How to directly delete images and star them 1:03:20 How to use SD 1.5 and SDXL models and LoRAs 1:06:24 Which sampler method is best 1:06:43 How to use image to image 1:08:43 How to use edit image / inpainting 1:10:38 How to use amazing segmentation feature to automatically inpaint any part of images 1:15:55 How to use segmentation on existing images for inpainting and get perfect results with different seeds 1:18:19 More detailed information regarding upscaling and tiling and SD3 1:20:08 Seams perfect explanation and example and how to fix it 1:21:09 How to use queue system 1:21:23 How to use multiple GPUs with adding more backends 1:24:38 Loading model in low VRAM mode 1:25:10 How to fix colors over saturation 1:27:00 Best image generation configuration for SD3 1:27:44 How to apply upscale to your older generated images quickly via preset 1:28:39 Other amazing features of SwarmUI 1:28:49 Clip tokenization and rare token OHWX 🔗 Tutorial Video Link :  ➡️ https://youtu.be/HKX8_F1Er_w https://youtu.be/HKX8_F1Er_w https://youtu.be/HKX8_F1Er_w?embedable=true https://youtu.be/HKX8_F1Er_w?embedable=true Do not skip any part of this tutorial to master how to use Stable Diffusion 3 (SD3) with the most advanced generative AI open-source APP SwarmUI. Automatic1111 SD Web UI or Fooocus are not supporting the SD3 yet. Therefore, I am starting to make tutorials for SwarmUI as well. StableSwarmUI is officially developed by StabilityAI, and your mind will be blown away after you watch this tutorial and learn its amazing features. StableSwarmUI uses ComfyUI as the back end, thus, it has all the good features of ComfyUI, and it brings you easy-to-use features of Automatic1111 StableDiffusion Web UI with them. I really liked SwarmUI and planning to do more tutorials for it. 🔗 The Public Post (no login or account required) Shown In The Video With The Links ➡️ https://www.patreon.com/posts/stableswarmui-3-106135985 https://www.patreon.com/posts/stableswarmui-3-106135985 0:00 Introduction to the Stable Diffusion 3 (SD3) and SwarmUI and what is in the tutorial 4:12 Architecture and features of SD3 5:05 What each different model files of Stable Diffusion 3 means 6:26 How to download and install SwarmUI on Windows for SD3 and all other Stable Diffusion models 8:42 What kind of folder path you should use when installing SwarmUI 10:28 If you get installation error how to notice and fix it 11:49 Installation has been completed and now how to start using SwarmUI 12:29 Which settings I change before start using SwarmUI and how to change your theme like dark, white, gray 12:56 How to make SwarmUI save generated images as PNG 13:08 How to find description of each settings and configuration 13:28 How to download SD3 model and start using on Windows 13:38 How to use model downloader utility of SwarmUI 14:17 How to set models folder paths and link your existing models folders in SwarmUI 14:35 Explanation of Root folder path in SwarmUI 14:52 VAE of SD3 do we need to download? 15:25 Generate and model section of the SwarmUI to generate images and how to select your base model 16:02 Setting up parameters and what they do to generate images 17:06 Which sampling method is best for SD3 17:22 Information about SD3 text encoders and their comparison 18:14 First time generating an image with SD3 19:36 How to regenerate same image 20:17 How to see image generation speed and step speed and more information 20:29 Stable Diffusion 3 it per second speed on RTX 3090 TI 20:39 How to see VRAM usage on Windows 10 22:08 And testing and comparing different text encoders for SD3 22:36 How to use FP16 version of T5 XXL text encoder instead of default FP8 version 25:27 The image generation speed when using best config for SD3 26:37 Why VAE of the SD3 is many times better than previous Stable Diffusion models, 4 vs 8 vs 16 vs 32 channels VAE 27:40 How to and where to download best AI upscaler models 29:10 How to use refiner and upscaler models to improve and upscale generated images 29:21 How to restart and start SwarmUI 32:01 The folders where the generated images are saved 32:13 Image history feature of SwarmUI 33:10 Upscaled image comparison 34:01 How to download all upscaler models at once 34:34 Presets feature in depth 36:55 How to generate forever / infinite times 37:13 Non-tiled upscale caused issues 38:36 How to compare tiled vs non-tiled upscale and decide best 39:05 275 SwarmUI presets (cloned from Fooocus) I prepared and the scripts I coded to prepare them and how to import those presets 42:10 Model browser feature 43:25 How to generate TensorRT engine for huge speed up 43:47 How to update SwarmUI 44:27 Prompt syntax and advanced features 45:35 How to use Wildcards (random prompts) feature 46:47 How to see full details / metadata of generated images 47:13 Full guide for extremely powerful grid image generation (like X/Y/Z plot) 47:35 How to put all downloaded upscalers from zip file 51:37 How to see what is happening at the server logs 53:04 How to continue grid generation process after interruption 54:32 How to open grid generation after it has been completed and how to use it 56:13 Example of tiled upscaling seaming problem 1:00:30 Full guide for image history 1:02:22 How to directly delete images and star them 1:03:20 How to use SD 1.5 and SDXL models and LoRAs 1:06:24 Which sampler method is best 1:06:43 How to use image to image 1:08:43 How to use edit image / inpainting 1:10:38 How to use amazing segmentation feature to automatically inpaint any part of images 1:15:55 How to use segmentation on existing images for inpainting and get perfect results with different seeds 1:18:19 More detailed information regarding upscaling and tiling and SD3 1:20:08 Seams perfect explanation and example and how to fix it 1:21:09 How to use queue system 1:21:23 How to use multiple GPUs with adding more backends 1:24:38 Loading model in low VRAM mode 1:25:10 How to fix colors over saturation 1:27:00 Best image generation configuration for SD3 1:27:44 How to apply upscale to your older generated images quickly via preset 1:28:39 Other amazing features of SwarmUI 1:28:49 Clip tokenization and rare token OHWX

A Stable Diffusion 3 Tutorial With Amazing SwarmUI SD Web UI That Utilizes ComfyUI: Zero to Hero

Authors:
(1) Agustin Moreno;
(2) Francesco Ruscelli. Table of Links Abstract
Introduction
Preliminaries
The B-signature
GIT sequence: low dimensions
GIT sequence: arbitrary dimension
Appendix A. Stability, the Krein–Moser theorem, and refinements and References Abstract We address the general problem of studying linear stability and bifurcations of periodic orbits for Hamiltonian systems of arbitrary degrees of freedom. We study the topology of the GIT sequence introduced by the first author and Urs frauenfelder in [FM], in arbitrary dimension. In particular, we note that the combinatorics encoding the linear stability of periodic orbits is governed by a quotient of the associahedron. Our approach gives a topological/combinatorial proof of the classical Krein–Moser theorem, and refines it for the case of symmetric orbits. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Agustin Moreno; (2) Francesco Ruscelli. Authors: Authors: (1) Agustin Moreno; (2) Francesco Ruscelli. Table of Links Abstract Introduction Preliminaries The B-signature GIT sequence: low dimensions GIT sequence: arbitrary dimension Appendix A. Stability, the Krein–Moser theorem, and refinements and References Abstract Abstract Introduction Introduction Preliminaries Preliminaries The B-signature The B-signature GIT sequence: low dimensions GIT sequence: low dimensions GIT sequence: arbitrary dimension GIT sequence: arbitrary dimension Appendix A. Stability, the Krein–Moser theorem, and refinements and References Appendix A. Stability, the Krein–Moser theorem, and refinements and References Abstract We address the general problem of studying linear stability and bifurcations of periodic orbits for Hamiltonian systems of arbitrary degrees of freedom. We study the topology of the GIT sequence introduced by the first author and Urs frauenfelder in [FM], in arbitrary dimension. In particular, we note that the combinatorics encoding the linear stability of periodic orbits is governed by a quotient of the associahedron. Our approach gives a topological/combinatorial proof of the classical Krein–Moser theorem, and refines it for the case of symmetric orbits. 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

Addressing the General Problem of Studying Linear Stability and Bifurcations of Periodic Orbits

রৈখিক স্থিতিশীলতা এবং পর্যায়ক্রমিক কক্ষপথের বিভাজন অধ্যয়নের সাধারণ সমস্যা সমাধান করা

Behandlung des allgemeinen Problems der Untersuchung linearer Stabilität und Bifurkationen periodischer Bahnen

Abordar el problema general del estudio de la estabilidad lineal y las bifurcaciones de órbitas periódicas

Aborder le problème général de l'étude de la stabilité linéaire et des bifurcations des orbites périodiques

आवर्त कक्षाओं के रैखिक स्थायित्व और द्विभाजन के अध्ययन की सामान्य समस्या का समाधान

周期軌道の線形安定性と分岐を研究する一般的な問題への取り組み

선형 안정성과 주기 궤도 분기 연구의 일반적인 문제 해결

Resolvendo o problema geral do estudo da estabilidade linear e bifurcações de órbitas periódicas

К общей проблеме исследования линейной устойчивости и бифуркаций периодических орбит

Periyodik Yörüngelerin Doğrusal Kararlılığı ve Çatallanmalarının İncelenmesine İlişkin Genel Sorunun Ele Alınması

Giải quyết vấn đề chung của việc nghiên cứu sự ổn định tuyến tính và sự phân nhánh của quỹ đạo định kỳ

解决研究周期轨道的线性稳定性和分岔的一般问题

Authors:
(1) Bobby He, Department of Computer Science, ETH Zurich (Correspondence to: bobby.he@inf.ethz.ch.);
(2) Thomas Hofmann, Department of Computer Science, ETH Zurich. Table of Links Abstract and Introduction Related Work Preliminaries Simplifying Transformer Blocks Further Experimental Analysis Discussion, Reproducibility Statement, Acknowledgements and References A Duality Between Downweighted Residual and Restricting Updates In Linear Layers B Block Layouts C Additional Experiments D Implementation Details 3 PRELIMINARIES A deep transformer architecture of depth L is formed by sequentially stacking L transformer blocks. The most common block is Pre-LN, depicted in Fig. 1 (left), which we treat as a baseline for comparing training speed, both in terms of per-update and runtime. It differs from the original Post-LN block only in the position of the normalisation layers relative to the skip connections, but is more popular as the Post-LN block suffers from poor training stability and signal propagation in deep layers (Xiong et al., 2020; Liu et al., 2020; Noci et al., 2022; He et al., 2023). with scalar gain weights αFF, βFF, αSA, βSA fixed to 1 by default. Here, “MHA” stands for MultiHead Attention (detailed below), and “Norm” denotes a normalisation layer (Ba et al., 2016; Zhang & Sennrich, 2019). In words, we see that the Pre-LN transformer block consists of two sequential sub-blocks (one attention and one MLP), with normalisation layers and residual connections for both sub-blocks, and crucially the normalisation layers are placed within the residual branch. The MLP is usually single hidden-layer, with hidden dimension that is some multiple of d (e.g. 4 (Vaswani et al., 2017) or 8/3 (Touvron et al., 2023)), and acts on each token in the sequence independently. The MHA sub-block allows tokens to share information between one another using self-attention. For input sequence X, the self-attention mechanism outputs: This paper is available on arxiv under CC 4.0 license. Authors: (1) Bobby He, Department of Computer Science, ETH Zurich (Correspondence to: bobby.he@inf.ethz.ch.); (2) Thomas Hofmann, Department of Computer Science, ETH Zurich. Authors: Authors: (1) Bobby He, Department of Computer Science, ETH Zurich (Correspondence to: bobby.he@inf.ethz.ch.); (2) Thomas Hofmann, Department of Computer Science, ETH Zurich. Table of Links Abstract and Introduction Abstract and Introduction Related Work Related Work Preliminaries Preliminaries Simplifying Transformer Blocks Simplifying Transformer Blocks Further Experimental Analysis Further Experimental Analysis Discussion, Reproducibility Statement, Acknowledgements and References Discussion, Reproducibility Statement, Acknowledgements and References A Duality Between Downweighted Residual and Restricting Updates In Linear Layers A Duality Between Downweighted Residual and Restricting Updates In Linear Layers B Block Layouts B Block Layouts C Additional Experiments C Additional Experiments D Implementation Details D Implementation Details 3 PRELIMINARIES A deep transformer architecture of depth L is formed by sequentially stacking L transformer blocks. The most common block is Pre-LN, depicted in Fig. 1 (left), which we treat as a baseline for comparing training speed, both in terms of per-update and runtime. It differs from the original Post-LN block only in the position of the normalisation layers relative to the skip connections, but is more popular as the Post-LN block suffers from poor training stability and signal propagation in deep layers (Xiong et al., 2020; Liu et al., 2020; Noci et al., 2022; He et al., 2023). with scalar gain weights αFF, βFF, αSA, βSA fixed to 1 by default. Here, “MHA” stands for MultiHead Attention (detailed below), and “Norm” denotes a normalisation layer (Ba et al., 2016; Zhang & Sennrich, 2019). In words, we see that the Pre-LN transformer block consists of two sequential sub-blocks (one attention and one MLP), with normalisation layers and residual connections for both sub-blocks, and crucially the normalisation layers are placed within the residual branch. The MLP is usually single hidden-layer, with hidden dimension that is some multiple of d (e.g. 4 (Vaswani et al., 2017) or 8/3 (Touvron et al., 2023)), and acts on each token in the sequence independently. The MHA sub-block allows tokens to share information between one another using self-attention. For input sequence X, the self-attention mechanism outputs: 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

Improving Training Stability in Deep Transformers: Pre-LN vs. Post-LN Blocks

MONACO CITY, Monaco, June 18th, 2024/Chainwire/--Memereum (MEME), a new altcoin, has demonstrated notable performance during its initial coin offering (ICO) presale, selling over 23 million tokens and nearing the 24 million mark. The project has attracted more than 8,000 users to its platform, while the Ethereum challenger Solana remains below the $150 price level. The pre-sale began at $0.01 and by a strategic move by the team, is now at $0.039. Those who invested in Memereum at the beginning have seen their investments grow almost 400%. Memereum's appeal stems from its unique position as the first blockchain insurance with its own insured decentralized exchange, MemeSwap. Memereum (MEME) is currently priced at $0.039 but will launch at $0.45 on BitVenus, Toobit, Azbit, and MemeSwap, more than 10 times its original price. The Memereum ICO also offers automatic 183% APY staking for holders and free airdrop competitions. Solana (SOL): Analysts Predict a Potential Rise To $215 Solana (SOL), one of the top altcoins in the crypto market, is experiencing mixed sentiment on the price chart, remaining under the $150 mark. According to CoinMarketCap, Solana has recorded losses of 9.71% on the weekly chart and shown losses of 14.65% on the monthly chart. Despite the mixed sentiment, some predict Solana's price could rise to $215 in the coming weeks. Furthermore, Solana aims to carve out its niche in the digital asset space and establish itself as a rival to Ethereum. About Memereum (MEME) Strong interest in Memereum (MEME) can be attributed to its innovative approach in the blockchain sector and growing community support. Similarly, Solana is currently experiencing mixed market sentiment but continues to participate in the market actively. Users can click here to join Memereum's ongoing presale. Contact Bessie Cooper Memereum support@memereum.net This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here. MONACO CITY, Monaco, June 18th, 2024/Chainwire/--Memereum (MEME), a new altcoin, has demonstrated notable performance during its initial coin offering (ICO) presale, selling over 23 million tokens and nearing the 24 million mark. The project has attracted more than 8,000 users to its platform, while the Ethereum challenger Solana remains below the $150 price level. The pre-sale began at $0.01 and by a strategic move by the team, is now at $0.039. Those who invested in Memereum at the beginning have seen their investments grow almost 400%. Memereum's appeal stems from its unique position as the first blockchain insurance with its own insured decentralized exchange, MemeSwap. Memereum (MEME) is currently priced at $0.039 but will launch at $0.45 on BitVenus, Toobit, Azbit, and MemeSwap, more than 10 times its original price. The Memereum ICO also offers automatic 183% APY staking for holders and free airdrop competitions. Solana (SOL): Analysts Predict a Potential Rise To $215 Solana (SOL), one of the top altcoins in the crypto market, is experiencing mixed sentiment on the price chart, remaining under the $150 mark. According to CoinMarketCap, Solana has recorded losses of 9.71% on the weekly chart and shown losses of 14.65% on the monthly chart. Despite the mixed sentiment, some predict Solana's price could rise to $215 in the coming weeks. Furthermore, Solana aims to carve out its niche in the digital asset space and establish itself as a rival to Ethereum. About Memereum (MEME) Strong interest in Memereum (MEME) can be attributed to its innovative approach in the blockchain sector and growing community support. Similarly, Solana is currently experiencing mixed market sentiment but continues to participate in the market actively. Users can click here to join Memereum's ongoing presale. Contact Bessie Cooper Memereum support@memereum.net This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here. This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here . here

Memereum Sells Over 23 Million Tokens In Presale As SOL Stabilizes Below $150

SOL $150 এর নিচে স্থিতিশীল হওয়ায় Memereum প্রেসালে 23 মিলিয়নেরও বেশি টোকেন বিক্রি করে

Memereum verkauft über 23 Millionen Token im Vorverkauf, während sich SOL unter 150 USD stabilisiert

Memereum vende más de 23 millones de tokens en preventa mientras SOL se estabiliza por debajo de $ 150

Memereum vend plus de 23 millions de jetons en prévente alors que SOL se stabilise en dessous de 150 $

मेमेरेम ने प्री-सेल में 23 मिलियन से अधिक टोकन बेचे, जबकि एसओएल 150 डॉलर से नीचे स्थिर हुआ

Memereum はプレセールで 2,300 万以上のトークンを販売、SOL は 150 ドル以下で安定

Memereum은 SOL이 $150 미만으로 안정화됨에 따라 사전 판매에서 2,300만 개 이상의 토큰을 판매합니다.

Memereum vende mais de 23 milhões de tokens em pré-venda enquanto SOL se estabiliza abaixo de US$ 150

Memereum продает более 23 миллионов токенов в предпродаже, поскольку SOL стабилизируется ниже $150

Memereum, SOL'un 150 Doların Altında Sabitlenmesiyle Ön Satışta 23 Milyondan Fazla Token Sattı

Memereum bán hơn 23 triệu token trong đợt bán trước khi SOL ổn định dưới 150 đô la

Memereum 在预售中售出超过 2300 万个代币，SOL 价格稳定在 150 美元以下

With Stable Diffusion 3 freshly released, I thought it would be nice to make a simple Web-Interface for it. About a month ago, me and a couple of friends released a library for making websites with Python, and this just seemed like too good of an opportunity to pass up. The interface includes support for the classic SD1, SDXL, and the new SD3. Inference is done using the diffusers library from Huggingface, and the interface is built with Rio. Given how new SD3 is in diffusers, you'll spot the odd issue here and there, but I'm sure that'll improve now with thousands of people using it. This is a simple Web-Interface for Stable Diffusion, based on our new Rio framework. We've gotten a lot of requests for larger sample projects, so given the highly anticipated release of Stable Diffusion 3, I figured this would be a great example. With all of that out of the way, let's get started! Install at least one model from the list below to begin using Difoosion. Rio: https://github.com/rio-labs/rio This makes use of Stable Diffusion, which is a sizable AI model. While it can technically run on the CPU, an Nvidia GPU with at least 8GB of VRAM is highly recommended. You can find installation instructions in the project's README: https://gitlab.com/mad-moo/difoosion Get Started Clone this repository git clone git@gitlab.com:Vivern/difoosion.git Install the project and its dependencies (Use a venv if you like) cd difoosion
python -m pip install -e . This will download some large packages like diffusers and torch. Give it a few minutes to complete. Run the interface python -m rio run --release After a few seconds, this will display a URL in the console. Open this URL in your browser to start using the interface. Install Models When you first connect, you won't have any models installed yet. The site will automatically allow you to download one of the built-in ones. diffusers doesn't seem to offer any way to track the download progress of models. That's why you won't be able to see how far the download has progressed in the interface. Check the terminal to see updates. Get cracking! Type a prompt of what you'd like to see, click "Generate," and wait for your masterpiece to be created :) Tech Stack All models are run with the diffusers library from huggingface. There is a thin wrapper around the library to workaround some issues and make it easier to use. The web interface is built with Rio, a new web framework that is designed to be 100% Python, and as easy to use as possible. I'm one of the Rio developers, and this project was meant to both test Rio out in a bigger project, as well as be a showcase & reference to other Rio developers. Dependencies are managed with rye. Caveats Stable Diffusion 3 is still very new, and support in diffusers immature. This has led to a couple of known problems: Generating non-square images can lead to errors from pytorch. Stick to aspect ratios of 1:1 for now. Freeing up memory is very unreliable. On some of my devices, the model keeps gobbling up more and more RAM as time goes on, while on others, it seems to free up just fine. Keep a close eye on your memory usage. With Stable Diffusion 3 freshly released, I thought it would be nice to make a simple Web-Interface for it. About a month ago, me and a couple of friends released a library for making websites with Python, and this just seemed like too good of an opportunity to pass up. The interface includes support for the classic SD1, SDXL, and the new SD3. Inference is done using the diffusers library from Huggingface, and the interface is built with Rio . Given how new SD3 is in diffusers , you'll spot the odd issue here and there, but I'm sure that'll improve now with thousands of people using it. diffusers Rio diffusers This is a simple Web-Interface for Stable Diffusion, based on our new Rio framework. We've gotten a lot of requests for larger sample projects, so given the highly anticipated release of Stable Diffusion 3, I figured this would be a great example. With all of that out of the way, let's get started! Install at least one model from the list below to begin using Difoosion. Rio: https://github.com/rio-labs/rio https://github.com/rio-labs/rio This makes use of Stable Diffusion, which is a sizable AI model. While it can technically run on the CPU, an Nvidia GPU with at least 8GB of VRAM is highly recommended. You can find installation instructions in the project's README: https://gitlab.com/mad-moo/difoosion This makes use of Stable Diffusion, which is a sizable AI model. While it can technically run on the CPU, an Nvidia GPU with at least 8GB of VRAM is highly recommended. https://gitlab.com/mad-moo/difoosion Get Started Clone this repository Clone this repository git clone git@gitlab.com:Vivern/difoosion.git git clone git@gitlab.com:Vivern/difoosion.git Install the project and its dependencies (Use a venv if you like) Install the project and its dependencies (Use a venv if you like) cd difoosion
python -m pip install -e . cd difoosion
python -m pip install -e . This will download some large packages like diffusers and torch . Give it a few minutes to complete. diffusers torch Run the interface Run the interface python -m rio run --release python -m rio run --release After a few seconds, this will display a URL in the console. Open this URL in your browser to start using the interface. Install Models Install Models When you first connect, you won't have any models installed yet. The site will automatically allow you to download one of the built-in ones. diffusers doesn't seem to offer any way to track the download progress of models. That's why you won't be able to see how far the download has progressed in the interface. Check the terminal to see updates. diffusers Get cracking! Get cracking! Type a prompt of what you'd like to see, click "Generate," and wait for your masterpiece to be created :) Tech Stack All models are run with the diffusers library from huggingface. There is a thin wrapper around the library to workaround some issues and make it easier to use. All models are run with the diffusers library from huggingface . There is a thin wrapper around the library to workaround some issues and make it easier to use. diffusers library from huggingface The web interface is built with Rio, a new web framework that is designed to be 100% Python, and as easy to use as possible. I'm one of the Rio developers, and this project was meant to both test Rio out in a bigger project, as well as be a showcase & reference to other Rio developers. The web interface is built with Rio , a new web framework that is designed to be 100% Python, and as easy to use as possible. I'm one of the Rio developers, and this project was meant to both test Rio out in a bigger project, as well as be a showcase & reference to other Rio developers. Rio Dependencies are managed with rye. Dependencies are managed with rye . rye Caveats Stable Diffusion 3 is still very new, and support in diffusers immature. This has led to a couple of known problems: diffusers Generating non-square images can lead to errors from pytorch. Stick to aspect ratios of 1:1 for now. Generating non-square images can lead to errors from pytorch. Stick to aspect ratios of 1:1 for now. Freeing up memory is very unreliable. On some of my devices, the model keeps gobbling up more and more RAM as time goes on, while on others, it seems to free up just fine. Keep a close eye on your memory usage. Freeing up memory is very unreliable. On some of my devices, the model keeps gobbling up more and more RAM as time goes on, while on others, it seems to free up just fine. Keep a close eye on your memory usage.

Difoosion - A Simple Web-Interface for Stable Diffusion Models

The Hidden Cost of Hypergrowth: Scale Without Sacrificing Stability

Author:
(1) CALLA TSCHANZ. Table of Links Abstract and Intro
Background on tropical perspective
The expanded construction
GIT stability
Stack perspective
The canonical moduli stack
References 4. GIT stability In this section, we set up some results analogous to those of [GHH19] to describe various GIT stability conditions on the scheme X[n] with respect to the possible choices of G-linearised line bundles described in the previous section. In particular, we show that these stability conditions do not depend on the scheme structure of the length m zero-dimensional subschemes, but instead can be reduced to combinatorial criteria on configurations of n points. 4.1 Hilbert-Mumford criterion In this section, we shall recall the definition of Hilbert-Mumford invariants and give a numerical criterion for stability and semi-stability in terms of these invariants. Let H be a reductive group acting on a scheme S, which is proper over an algebraically closed field k. Let L be a H-linearised ample line bundle. Then a 1-parameter subgroup of H (denoted 1-PS for convenience) is defined to be a homomorphism 4.2 Action of 1-parameter subgroup 4.3 Bounded and combinatorial weights In this section, we explain the relation between what [GHH19] call the bounded and combinatorial weights of the Hilbert-Mumford invariants. Keeping the notation as consistent as possible with [GHH19], let be the universal family, with first and second projections p and q. The line bundle is relatively ample when l ≫ 0 and is G-linearised, exactly as in Section 2.2.1 of [GHH19]. Relationship between bounded and combinatorial weights. The following lemmas describe how the Hilbert-Mumford invariant can be decomposed into a sum of invariants. Note that, whereas the combinatorial weight depends on the choice of linearised line bundle, the bounded weight does not. Similarly to [GHH19], we can show that the bounded weight, as its name suggests, can be given an upper bound. The following result is based on Lemma 2.3 of [GHH19], with some slight modifications to suit our setting. Let us discuss now how the bounded weight affects the overall stability condition. The following lemma is immediate from [GHH19], but we recall their proof here for convenience. Proof. As we have shown that the bounded weight can be expressed as it is just a matter of choosing a big enough value of l to make the combinatorial weight overpower the bounded weight. This allows us effectively to treat the bounded weight as negligible and ignore it in our computations. Remark 4.3.5. Note, here, that such a Z will not necessarily be smoothly supported, nor will every point of the support of Z necessarily be contained in a ∆-component. Repeating this process over all k ∈ {1, . . . , n} will give us a description of L and we may form the G-linearised line bundle M from this line bundle in the way described at the start of this section. For more details on why this yields a positive combinatorial weight, see the proof of the following lemma. Note that this is not the only GIT stability condition for which Z is stable. Proof. It is clear that the combinatorial weight may be written as a sum 4.4 Semistable locus and GIT quotient Proof. This follows from Lemmas 4.3.3 and 4.3.7. Indeed, by Lemma 4.3.3, if the combinatorial weight can be written in the form Proof. Let us choose an arbitrary G-linearised line bundle M, not necessarily constructed as above, with respect to which Z has Hilbert-Mumford invariant Proof. This follows directly from Lemmas 4.4.1 and 4.4.2. We can now describe the GIT quotients resulting from these constructions. Let Then we recall from Lemma 3.1.13, the isomorphism For all choices of linearised line bundle described in the above, the GIT quotient on the base therefore behaves as follows Proof. This result follows directly from the relative Hilbert-Mumford criterion of [GHH15]. This paper is available on arxiv under CC 4.0 license. Author: (1) CALLA TSCHANZ. Author: Author: (1) CALLA TSCHANZ. Table of Links Abstract and Intro Background on tropical perspective The expanded construction GIT stability Stack perspective The canonical moduli stack References Abstract and Intro Abstract and Intro Background on tropical perspective Background on tropical perspective The expanded construction The expanded construction GIT stability GIT stability Stack perspective Stack perspective The canonical moduli stack The canonical moduli stack References References 4. GIT stability In this section, we set up some results analogous to those of [GHH19] to describe various GIT stability conditions on the scheme X[n] with respect to the possible choices of G-linearised line bundles described in the previous section. In particular, we show that these stability conditions do not depend on the scheme structure of the length m zero-dimensional subschemes, but instead can be reduced to combinatorial criteria on configurations of n points. 4.1 Hilbert-Mumford criterion In this section, we shall recall the definition of Hilbert-Mumford invariants and give a numerical criterion for stability and semi-stability in terms of these invariants. Let H be a reductive group acting on a scheme S, which is proper over an algebraically closed field k. Let L be a H-linearised ample line bundle. Then a 1-parameter subgroup of H (denoted 1-PS for convenience) is defined to be a homomorphism 4.2 Action of 1-parameter subgroup 4.3 Bounded and combinatorial weights In this section, we explain the relation between what [GHH19] call the bounded and combinatorial weights of the Hilbert-Mumford invariants. Keeping the notation as consistent as possible with [GHH19], let be the universal family, with first and second projections p and q. The line bundle is relatively ample when l ≫ 0 and is G-linearised, exactly as in Section 2.2.1 of [GHH19]. Relationship between bounded and combinatorial weights. The following lemmas describe how the Hilbert-Mumford invariant can be decomposed into a sum of invariants. Relationship between bounded and combinatorial weights. Note that, whereas the combinatorial weight depends on the choice of linearised line bundle, the bounded weight does not. Similarly to [GHH19], we can show that the bounded weight, as its name suggests, can be given an upper bound. The following result is based on Lemma 2.3 of [GHH19], with some slight modifications to suit our setting. Let us discuss now how the bounded weight affects the overall stability condition. The following lemma is immediate from [GHH19], but we recall their proof here for convenience. Proof . As we have shown that the bounded weight can be expressed as Proof it is just a matter of choosing a big enough value of l to make the combinatorial weight overpower the bounded weight. This allows us effectively to treat the bounded weight as negligible and ignore it in our computations. l Remark 4.3.5. Note, here, that such a Z will not necessarily be smoothly supported, nor will every point of the support of Z necessarily be contained in a ∆-component. Remark Repeating this process over all k ∈ {1, . . . , n} will give us a description of L and we may form the G-linearised line bundle M from this line bundle in the way described at the start of this section. For more details on why this yields a positive combinatorial weight, see the proof of the following lemma. Note that this is not the only GIT stability condition for which Z is stable. Proof . It is clear that the combinatorial weight may be written as a sum Proof 4.4 Semistable locus and GIT quotient Proof . This follows from Lemmas 4.3.3 and 4.3.7. Indeed, by Lemma 4.3.3, if the combinatorial weight can be written in the form Proof Proof . Let us choose an arbitrary G-linearised line bundle M, not necessarily constructed as above, with respect to which Z has Hilbert-Mumford invariant Proof Proof . This follows directly from Lemmas 4.4.1 and 4.4.2. Proof We can now describe the GIT quotients resulting from these constructions. Let Then we recall from Lemma 3.1.13, the isomorphism For all choices of linearised line bundle described in the above, the GIT quotient on the base therefore behaves as follows Proof . This result follows directly from the relative Hilbert-Mumford criterion of [GHH15]. Proof 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

Expansions for Hilbert Schemes: GIT Stability

হিলবার্ট স্কিমগুলির সম্প্রসারণ: জিআইটি স্থিতিশীলতা

Erweiterungen für Hilbert-Schemata: GIT-Stabilität

Ampliaciones para los esquemas Hilbert: estabilidad de GIT

Extensions pour les schémas Hilbert : stabilité GIT

हिल्बर्ट योजनाओं के लिए विस्तार: जीआईटी स्थिरता

ヒルベルトスキームの拡張: GIT の安定性

Hilbert 체계 확장: GIT 안정성

Expansões para esquemas de Hilbert: estabilidade do GIT

Расширения схем Гильберта: стабильность GIT

Hilbert Şemaları için Genişletmeler: GIT Kararlılığı

Mở rộng cho các sơ đồ Hilbert: Tính ổn định của GIT

希尔伯特方案的扩展：GIT 稳定性

Brief Update Building on the foundation of innovation detailed in my previous articles (BAMK - Pioneering the Nakamoto Dollar on Bitcoin, Bitcoin’s First Synthetic Dollar - The $NUSD by BAMK, and Nakamoto Dollar - BAMK Paper), BAMK has made significant strides with NUSD, the Nakamoto Dollar which we’ll look at below. But first, some numbers: BAMK•OF•NAKAMOTO•DOLLAR ($BAMK) price is currently sitting at 8.55 sats after seeing a high of 10.94 sats in recent days.
BAMK•OF•NAKAMOTO•DOLLAR ($BAMK) Market Cap (MCAP) for the circulating supply is $8,003,375 and Fully Diluted Valuation (FDV) is $128,139,425.
NUSD•NUSD•NUSD•NUSD / $NUSD Total Value Locked (TVL) is $1,325,600 and USDe reserves (backed by Ethena sUSDe) $1,335,982. Rewind BAMK recently created NUSD, the Nakamoto Dollar, the first of its kind stablecoin implemented as a BRC20 and Rune directly on the Bitcoin blockchain. The concept of NUSD is rooted in the synthetic dollar idea pioneered by Arthur Hayes. BAMK has effectively leveraged Ethena's synthetic dollar to back NUSD as both a BRC20 token and a Rune on Bitcoin. The project aims to provide a crypto-native yield and a stable asset on Bitcoin without reliance on traditional banking systems. The protocol includes the BAMK token as a governance and reward token feeding organic marketing activities as well as yield into NUSD. Background and Development NUSD offers a unique value proposition by allowing users to earn yield directly on the Bitcoin blockchain, which we haven’t seen before. At present, the yield offered is roughly between eight hundred and a thousand percent. The protocol's initial open mint model ensured a fair distribution and actived community participation. BAMK has a fixed supply, with most of it (19.6B) currently uncirculated and instead set aside for future rewards and governance. The yield flywheel of NUSD has two main components: the price of $BAMK and the Total Value Locked (TVL) of $NUSD. Simply buying and holding NUSD in a wallet allows users to collect BAMK yield at each Bitcoin block, which you can now see calculated here. As of now, there are no staking or holding requirements, and payouts are calculated pro-rata by block until the first payout at block 886,454. The payout system will reward holders of $NUSD in a ‘first in, first out’ system where if you got in at the first block that $BAMK was rewarded you will be the first to be paid out, and if you are the last, you will be the last to be paid out. See below from Bamks Git here: Allocation: 31,250 BAMK per block, pro-rata, user_holdings/NUSD_TVL
Duration: 41,962 blocks (~291 days) Start block: 844,492*
End block: 886,454
Vesting: 31,250 BAMK per block after block 886,454, for the next 41,962 blocks The team behind BAMK is currently mostly un-doxxed, but we can work out that Jack Liu appears to be directly involved and is acting spokesperson, which means that likely, this is the same team behind RelayX and Ordswap. All good things, all good things. Jack explains in a video (linked below) recently put out by Mark Jeffrey that the team has been together for about five years, they’re very resilient, and they’re focusing on building non-custodial projects. From that video, you get a feeling of their commitment to transparency and organic growth in navigating the challenges of the very new Bitcoin DeFi space. Risks and Benefits Holding NUSD presents both risks and benefits.  As a synthetic dollar, it carries the risk of Ethena’s backing. However, the reason you would want to hold NUSD is that you can take profits from Bitcoin or RUNES directly on-chain without the need for centralized exchanges, in other words, you can move in and out of NUSD and BTC without ever having to go through another party or exchange. This greatly enhances its appeal to users looking for decentralized financial solutions. And if you're an optimist, that should signal other ideas about what else NUSD might be used for in the future hint hint-wink wink. Additionally, you earn yield, which, at the moment, is roughly between eight hundred and a thousand percent. NUSD is currently backed by USDe and eventually, the plan is for it to be fully backed by BTC once the infrastructure allows for it. Being able to deposit BTC for NUSD finally offers a yield opportunity on Bitcoin. The yield can be influenced by changes in NUSD TVL or price fluctuations of BAMK. This is of course both another risk and opportunity. At current ratios, the APY has been sitting around 1000%, making it a very lucrative option for early NUSD holders. Future Development BAMK's roadmap includes several exciting developments for NUSD, such as the introduction of an authorized mint and the implementation of Automated Market Maker (AMM) swap pools. Centralized exchanges will also give the project validity and support, further boosting liquidity and integration with other stablecoins and blockchain networks, addressing one of the critical components for the success of any stablecoin. At least that is what we have seen in the past with other stablecoin projects. While we wait for the move from USDe to BTC, which could take some time, it sounds as if the team is almost ready to roll out a direct mint/redeem feature on the site which is very exciting for all involved. Market Potential The market potential for stablecoins like NUSD on Bitcoin, the ‘mother chain’ is for lack of a better word, mind-boggling, especially as Bitcoin continues to grow and suck in further capital from both retail and institutional investors following ETF approval and rollouts. The valuation and Total Value Locked (TVL) for NUSD are currently modest but are anticipated to increase as the project gains traction. Addressing issues such as negative funding rates, which can be managed by encouraging withdrawals and redeeming the synthetic dollar. This should further stabilize and enhance the attractiveness of NUSD. I should stress at this point that this is very early days, BAMK is essentially a brand new project as is the Runes protocol on Bitcoin, and, Ethena the ‘engine under the hood’ backing this thing is about six months old. The ideal situation for the ecosystem is for NUSD TVL to go up, BAMK price to go up, yield to maintain these levels or rise, and for all of this to repeat. However, if BAMK's price falls, yields won’t be as attractive since payouts are in BAMK tokens. It’s important to remember that while a developed stable should yield around 10-20% max, the current high yields are due to the early stage of the project. Additional Resources For more information on BAMK and its projects, you can visit the following resources: BAMK Official Website: Explore the latest updates, projects, and developments from BAMK.
BAMK Documentation: Access comprehensive documentation about BAMK’s protocols, tokens, and governance.
NUSD Yield Calculator: Calculate potential yields from holding NUSD using BAMK's yield calculator.
BAMK Leaderboard: Check out the top holders and participants in the BAMK ecosystem on the leaderboard.
BAMK Directory: Discover a directory of BAMK-related resources, projects, and community links. For further insights, you can watch the latest Bamk Video BAMK video by Mark Jeffrey (Twitter). Additionally, The Block Runner has provided a detailed analysis in their YouTube Video here: video. Conclusion BAMK’s NUSD represents a groundbreaking step in the evolution of stablecoins on the Bitcoin blockchain. By combining the security and stability of a synthetic dollar with the innovative approach of BRC20 and Rune implementations, BAMK is paving the way for a new era in decentralized finance. Transparency, liquidity, and organic growth will be the pillars supporting the continued success and expansion of NUSD in the ever-evolving crypto landscape. This post was sponsored by Crypto Content Producer Valerioshi: Valerioshi’s Degen Reports on YouTube. Valerioshi’s Degen Reports on Substack. Valerioshi on X. Brief Update Building on the foundation of innovation detailed in my previous articles ( BAMK - Pioneering the Nakamoto Dollar on Bitcoin , Bitcoin’s First Synthetic Dollar - The $NUSD by BAMK , and Nakamoto Dollar - BAMK Paper ), BAMK has made significant strides with NUSD, the Nakamoto Dollar which we’ll look at below. But first, some numbers: BAMK - Pioneering the Nakamoto Dollar on Bitcoin Bitcoin’s First Synthetic Dollar - The $NUSD by BAMK Nakamoto Dollar - BAMK Paper BAMK•OF•NAKAMOTO•DOLLAR ($BAMK) price is currently sitting at 8.55 sats after seeing a high of 10.94 sats in recent days. BAMK•OF•NAKAMOTO•DOLLAR ($BAMK) Market Cap (MCAP) for the circulating supply is $8,003,375 and Fully Diluted Valuation (FDV) is $128,139,425. NUSD•NUSD•NUSD•NUSD / $NUSD Total Value Locked (TVL) is $1,325,600 and USDe reserves (backed by Ethena sUSDe) $1,335,982. BAMK•OF•NAKAMOTO•DOLLAR ($BAMK) price is currently sitting at 8.55 sats after seeing a high of 10.94 sats in recent days. BAMK•OF•NAKAMOTO•DOLLAR ($BAMK) Market Cap (MCAP) for the circulating supply is $8,003,375 and Fully Diluted Valuation (FDV) is $128,139,425. NUSD•NUSD•NUSD•NUSD / $NUSD Total Value Locked (TVL) is $1,325,600 and USDe reserves ( backed by Ethena sUSDe ) $1,335,982. backed by Ethena sUSDe Rewind BAMK recently created NUSD, the Nakamoto Dollar, the first of its kind stablecoin implemented as a BRC20 and Rune directly on the Bitcoin blockchain. The concept of NUSD is rooted in the synthetic dollar idea pioneered by Arthur Hayes. BAMK has effectively leveraged Ethena's synthetic dollar to back NUSD as both a BRC20 token and a Rune on Bitcoin. The project aims to provide a crypto-native yield and a stable asset on Bitcoin without reliance on traditional banking systems. The protocol includes the BAMK token as a governance and reward token feeding organic marketing activities as well as yield into NUSD. Background and Development NUSD offers a unique value proposition by allowing users to earn yield directly on the Bitcoin blockchain, which we haven’t seen before. At present, the yield offered is roughly between eight hundred and a thousand percent. The protocol's initial open mint model ensured a fair distribution and actived community participation. BAMK has a fixed supply, with most of it (19.6B) currently uncirculated and instead set aside for future rewards and governance. The yield flywheel of NUSD has two main components: the price of $BAMK and the Total Value Locked (TVL) of $NUSD. Simply buying and holding NUSD in a wallet allows users to collect BAMK yield at each Bitcoin block, which you can now see calculated here . As of now, there are no staking or holding requirements, and payouts are calculated pro-rata by block until the first payout at block 886,454. The payout system will reward holders of $NUSD in a ‘first in, first out’ system where if you got in at the first block that $BAMK was rewarded you will be the first to be paid out, and if you are the last, you will be the last to be paid out. calculated here See below from Bamks Git here : Bamks Git here Allocation: 31,250 BAMK per block, pro-rata, user_holdings/NUSD_TVL Duration: 41,962 blocks (~291 days) Start block: 844,492* End block: 886,454 Vesting: 31,250 BAMK per block after block 886,454, for the next 41,962 blocks Allocation: 31,250 BAMK per block, pro-rata, user_holdings/NUSD_TVL Duration: 41,962 blocks (~291 days) Start block: 844,492* End block: 886,454 Vesting: 31,250 BAMK per block after block 886,454, for the next 41,962 blocks The team behind BAMK is currently mostly un-doxxed, but we can work out that Jack Liu appears to be directly involved and is acting spokesperson, which means that likely, this is the same team behind RelayX and Ordswap. All good things, all good things. Jack Liu Jack explains in a video (linked below) recently put out by Mark Jeffrey that the team has been together for about five years, they’re very resilient, and they’re focusing on building non-custodial projects. From that video, you get a feeling of their commitment to transparency and organic growth in navigating the challenges of the very new Bitcoin DeFi space. Mark Jeffrey Risks and Benefits Holding NUSD presents both risks and benefits.  As a synthetic dollar, it carries the risk of Ethena’s backing. However, the reason you would want to hold NUSD is that you can take profits from Bitcoin or RUNES directly on-chain without the need for centralized exchanges, in other words, you can move in and out of NUSD and BTC without ever having to go through another party or exchange. This greatly enhances its appeal to users looking for decentralized financial solutions. And if you're an optimist, that should signal other ideas about what else NUSD might be used for in the future hint hint-wink wink . Additionally, you earn yield, which, at the moment, is roughly between eight hundred and a thousand percent. hint hint-wink wink NUSD is currently backed by USDe and eventually, the plan is for it to be fully backed by BTC once the infrastructure allows for it. Being able to deposit BTC for NUSD finally offers a yield opportunity on Bitcoin. The yield can be influenced by changes in NUSD TVL or price fluctuations of BAMK. This is of course both another risk and opportunity. At current ratios, the APY has been sitting around 1000%, making it a very lucrative option for early NUSD holders. Future Development BAMK's roadmap includes several exciting developments for NUSD, such as the introduction of an authorized mint and the implementation of Automated Market Maker (AMM) swap pools. Centralized exchanges will also give the project validity and support, further boosting liquidity and integration with other stablecoins and blockchain networks, addressing one of the critical components for the success of any stablecoin. At least that is what we have seen in the past with other stablecoin projects. While we wait for the move from USDe to BTC, which could take some time, it sounds as if the team is almost ready to roll out a direct mint/redeem feature on the site which is very exciting for all involved. Market Potential The market potential for stablecoins like NUSD on Bitcoin, the ‘mother chain’ is for lack of a better word, mind-boggling, especially as Bitcoin continues to grow and suck in further capital from both retail and institutional investors following ETF approval and rollouts. The valuation and Total Value Locked (TVL) for NUSD are currently modest but are anticipated to increase as the project gains traction. Addressing issues such as negative funding rates, which can be managed by encouraging withdrawals and redeeming the synthetic dollar. This should further stabilize and enhance the attractiveness of NUSD. I should stress at this point that this is very early days, BAMK is essentially a brand new project as is the Runes protocol on Bitcoin, and, Ethena the ‘engine under the hood’ backing this thing is about six months old. The ideal situation for the ecosystem is for NUSD TVL to go up, BAMK price to go up, yield to maintain these levels or rise, and for all of this to repeat. However, if BAMK's price falls, yields won’t be as attractive since payouts are in BAMK tokens. It’s important to remember that while a developed stable should yield around 10-20% max, the current high yields are due to the early stage of the project. Additional Resources For more information on BAMK and its projects, you can visit the following resources: BAMK Official Website: Explore the latest updates, projects, and developments from BAMK. BAMK Documentation: Access comprehensive documentation about BAMK’s protocols, tokens, and governance. NUSD Yield Calculator: Calculate potential yields from holding NUSD using BAMK's yield calculator. BAMK Leaderboard: Check out the top holders and participants in the BAMK ecosystem on the leaderboard. BAMK Directory: Discover a directory of BAMK-related resources, projects, and community links. BAMK Official Website : Explore the latest updates, projects, and developments from BAMK. BAMK Official Website BAMK Official Website BAMK Documentation : Access comprehensive documentation about BAMK’s protocols, tokens, and governance. BAMK Documentation BAMK Documentation NUSD Yield Calculator : Calculate potential yields from holding NUSD using BAMK's yield calculator. NUSD Yield Calculator NUSD Yield Calculator BAMK Leaderboard : Check out the top holders and participants in the BAMK ecosystem on the leaderboard. BAMK Leaderboard BAMK Leaderboard BAMK Directory : Discover a directory of BAMK-related resources, projects, and community links. BAMK Directory BAMK Directory For further insights, you can watch the latest Bamk Video BAMK video BAMK video by Mark Jeffrey (Twitter). Mark Jeffrey Additionally, The Block Runner has provided a detailed analysis in their YouTube Video here: The Block Runner video . video Conclusion BAMK’s NUSD represents a groundbreaking step in the evolution of stablecoins on the Bitcoin blockchain. By combining the security and stability of a synthetic dollar with the innovative approach of BRC20 and Rune implementations, BAMK is paving the way for a new era in decentralized finance. Transparency, liquidity, and organic growth will be the pillars supporting the continued success and expansion of NUSD in the ever-evolving crypto landscape. This post was sponsored by Crypto Content Producer Valerioshi: Valerioshi’s Degen Reports on YouTube. Valerioshi’s Degen Reports on YouTube . Valerioshi’s Degen Reports on YouTube Valerioshi’s Degen Reports on Substack. Valerioshi’s Degen Reports on Substack . Valerioshi’s Degen Reports on Substack Valerioshi on X . Valerioshi on X Valerioshi on X

NUSD by BAMK.FI: The First Stablecoin Implemented as a BRC20 and Rune on Bitcoin (Updated)

Authors:
(1) Agustin Moreno;
(2) Francesco Ruscelli. Table of Links Abstract
Introduction
Preliminaries
The B-signature
GIT sequence: low dimensions
GIT sequence: arbitrary dimension
Appendix A. Stability, the Krein–Moser theorem, and refinements and References 4. GIT sequence: low dimensions We now discuss global topological methods in the study of periodic orbits, following the exposition in [AFKM]. These methods encode: bifurcations; stability; eigenvalue configurations; obstructions to existence of regular families; and B-signs, in a visual and resource-efficient way. The GIT sequence is the sequence of maps and spaces given by Then, by the above, the stability point is the result of applying the GIT sequence of maps to the given matrix. 4.1. GIT sequence: 2D. We start with the simplest case, i.e. the case of an autonomous Hamiltonian of two degrees of freedom, so that the reduced monodromy matrix is an element in Sp(2) = SL(2, R). The Broucke stability diagram is then simply the real line, split into three components; see Figure 1. If two orbits lie in different components of the diagram, then there are always bifurcations in any family joining them, as the topology of the diagram implies that any path between them has to cross the ±1 eigenvalues (corresponding respectively to bifurcation or period-doubling bifurcation). One can think that the stability index “collapses” the two elliptic branches in the middle layer of Figure 1 together. These two branches are distinguished by the B-signs, coinciding with the Krein signs [Kre2; Kre3]. There is an extra top layer for symmetric orbits, where now each hyperbolic branch separates into two, and there is a collapsing map from the top to middle layer. Note that to go from one branch to the other (say from the positive hyperbolic branch I to the positive hyperbolic branch II), the topology of the top layer implies that the eigenvalue 1 needs to be crossed. This means that one should expect bifurcations in any (symmetric) family joining them, even if they project to the same component of the Broucke diagram. In this way, the information given by the diagram is much more refined for the case of symmetric orbits. If we say that two orbits are qualitatively equivalent if they can be joined by a regular orbit cylinder, then the topology of the spaces in the GIT sequence give criteria to determine whenever two orbits are not qualitatively equivalent. To sum up: • B-signs “separate” hyperbolic branches, for symmetric orbits. • If two orbits lie in different components of the Broucke diagram, there are always bifurcations in any path joining them. • If two symmetric orbits lie in the same component of the Broucke diagram, but if B-signs differ, one should also expect bifurcation in any (symmetric) path joining them[1]. 4.2. GIT sequence: 3D. Now we apply the same idea, but for autonomous Hamiltonian systems with three degrees of freedom, for which reduced monodromy matrices are elements in Sp(4). The GIT sequence [FM] adds two layers to this diagram, as shown in Figure 3. The top layer has two extra branches than the middle one, for each hyperbolic eigenvalue. While the combinatorics and the global topology of the spaces involved is more complicated than the 2D case, the intuitive idea is still the same, i.e. that the amount of information for symmetric orbits is richer, and that we can distinguish more orbits up to qualitative equivalence. Note that as in this dimension we have two pairs of eigenvalues, the B-signature is a pair (±, ±) of signs, and therefore the top layer has 4 branches over each component of the Broucke diagram (except the nonreal component). This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. [1] We cautiosuly use the word “expect” rather than give a mathematical statement, as theoretically orbits could tangentially pass through the Maslov cycle without birfurcating. Authors: (1) Agustin Moreno; (2) Francesco Ruscelli. Authors: Authors: (1) Agustin Moreno; (2) Francesco Ruscelli. Table of Links Abstract Introduction Preliminaries The B-signature GIT sequence: low dimensions GIT sequence: arbitrary dimension Appendix A. Stability, the Krein–Moser theorem, and refinements and References Abstract Abstract Introduction Introduction Preliminaries Preliminaries The B-signature The B-signature GIT sequence: low dimensions GIT sequence: low dimensions GIT sequence: arbitrary dimension GIT sequence: arbitrary dimension Appendix A. Stability, the Krein–Moser theorem, and refinements and References Appendix A. Stability, the Krein–Moser theorem, and refinements and References 4. GIT sequence: low dimensions We now discuss global topological methods in the study of periodic orbits, following the exposition in [AFKM]. These methods encode: bifurcations; stability; eigenvalue configurations; obstructions to existence of regular families; and B-signs, in a visual and resource-efficient way. The GIT sequence is the sequence of maps and spaces given by Then, by the above, the stability point is the result of applying the GIT sequence of maps to the given matrix. 4.1. GIT sequence: 2D. We start with the simplest case, i.e. the case of an autonomous Hamiltonian of two degrees of freedom, so that the reduced monodromy matrix is an element in Sp(2) = SL(2, R). GIT sequence: 2D. The Broucke stability diagram is then simply the real line, split into three components; see Figure 1. If two orbits lie in different components of the diagram, then there are always bifurcations in any family joining them, as the topology of the diagram implies that any path between them has to cross the ±1 eigenvalues (corresponding respectively to bifurcation or period-doubling bifurcation). One can think that the stability index “collapses” the two elliptic branches in the middle layer of Figure 1 together. These two branches are distinguished by the B-signs, coinciding with the Krein signs [Kre2; Kre3]. There is an extra top layer for symmetric orbits, where now each hyperbolic branch separates into two, and there is a collapsing map from the top to middle layer. Note that to go from one branch to the other (say from the positive hyperbolic branch I to the positive hyperbolic branch II), the topology of the top layer implies that the eigenvalue 1 needs to be crossed. This means that one should expect bifurcations in any (symmetric) family joining them, even if they project to the same component of the Broucke diagram. In this way, the information given by the diagram is much more refined for the case of symmetric orbits. If we say that two orbits are qualitatively equivalent if they can be joined by a regular orbit cylinder, then the topology of the spaces in the GIT sequence give criteria to determine whenever two orbits are not qualitatively equivalent. To sum up: • B-signs “separate” hyperbolic branches, for symmetric orbits. • If two orbits lie in different components of the Broucke diagram, there are always bifurcations in any path joining them. • If two symmetric orbits lie in the same component of the Broucke diagram, but if B-signs differ, one should also expect bifurcation in any (symmetric) path joining them[1]. 4.2. GIT sequence: 3D . Now we apply the same idea, but for autonomous Hamiltonian systems with three degrees of freedom, for which reduced monodromy matrices are elements in Sp(4). GIT sequence: 3D The GIT sequence [FM] adds two layers to this diagram, as shown in Figure 3. The top layer has two extra branches than the middle one, for each hyperbolic eigenvalue. While the combinatorics and the global topology of the spaces involved is more complicated than the 2D case, the intuitive idea is still the same, i.e. that the amount of information for symmetric orbits is richer, and that we can distinguish more orbits up to qualitative equivalence. Note that as in this dimension we have two pairs of eigenvalues, the B-signature is a pair (±, ±) of signs, and therefore the top layer has 4 branches over each component of the Broucke diagram (except the nonreal component). 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 [1] We cautiosuly use the word “expect” rather than give a mathematical statement, as theoretically orbits could tangentially pass through the Maslov cycle without birfurcating.

Combinatorics of linear stability for Hamiltonian systems in arbitrary dimension: GIT sequence: low 

নির্বিচারে হ্যামিলটোনিয়ান সিস্টেমের জন্য রৈখিক স্থিতিশীলতার সংমিশ্রণ: GIT ক্রম: কম 

Kombinatorik der linearen Stabilität für Hamiltonsysteme in beliebiger Dimension: GIT-Sequenz: niedrig

Combinatoria de estabilidad lineal para sistemas hamiltonianos en dimensión arbitraria: secuencia GIT: baja 

Combinatoire de stabilité linéaire pour les systèmes hamiltoniens en dimension arbitraire : séquence GIT : faible 

मनमाने आयाम में हैमिल्टोनियन प्रणालियों के लिए रैखिक स्थिरता का संयोजन: जीआईटी अनुक्रम: निम्न

任意次元のハミルトン系の線形安定性の組合せ論：GITシーケンス：低

임의 차원의 해밀턴 시스템에 대한 선형 안정성 조합: GIT 시퀀스: 낮음 

Combinatória de estabilidade linear para sistemas hamiltonianos em dimensão arbitrária: sequência GIT: baixa 

Комбинаторика линейной устойчивости гамильтоновых систем произвольной размерности: последовательность GIT: низкая 

Keyfi boyutta Hamilton sistemleri için doğrusal kararlılığın kombinatoriği: GIT dizisi: düşük 

Tổ hợp ổn định tuyến tính cho các hệ Hamilton theo chiều tùy ý: Trình tự GIT: thấp 

任意维汉密尔顿系统的线性稳定性组合：GIT 序列：低

Authors:
(1) Agustin Moreno;
(2) Francesco Ruscelli. Table of Links Abstract
Introduction
Preliminaries
The B-signature
GIT sequence: low dimensions
GIT sequence: arbitrary dimension
Appendix A. Stability, the Krein–Moser theorem, and refinements and References 1. Introduction The stability of periodic orbits is a central topic in the study of Hamiltonian systems, going back to the problem of stability of the solar system in celestial mechanics. Ubiquitous in the study of ODEs, the notion of stability arises whenever studying orbits in families and their bifurcations, a practice which entails both theoretical and practical interest. For instance, from the perspective of space mission design, orbits used for parking a spacecraft around a target Moon should be as stable as possible, in order to minimize fuel corrections and station-keeping. From a mathematical point of view, the key notions of stability of a system come in three flavors, related by the following implications: Non-linear (Lyapunov) stability ⇒ linear stability ⇒ spectral stability. Non-linear stability, roughly speaking, means that trajectories which start near a given periodic orbit stay near the orbit for all time. Linear stability corresponds to stability of the origin for the linearized dynamics, i.e. the orbits of the linearized system should stay bounded. For a Hamiltonian system, this means that the eigenvalues of the monodromy matrix of the corresponding orbit should lie in the unit circle, and be semi-simple. Spectral stability, on the other hand, requires that eigenvalues all lie in the unit circle, but allows them to have multiplicity (so that orbits can escape to infinity in polynomial time, rather than exponential). In this paper, we will focus on the notion of linear stability. In the presence of symmetry, the study of linear stability of periodic orbits which are preserved by the symmetry can be significantly refined. With this end in mind, the first author and Urs Frauenfelder introduced in [FM] the notion of the GIT sequence, as a refinement of the Broucke stability diagram [Br69], via the notion of B-signature. The GIT sequence consists of a sequence of three spaces and maps between them whose topology encodes stability and bifurcations of periodic orbits, as well as their eigenvalue configurations, and provides obstructions to the existence of regular cylinder of orbits. In low dimensions, the spaces can be visualized in the plane or in three-dimensional space, which makes them amenable for numerical work. We should note that while the GIT sequence is designed to study linear stability, it blurs its distinction with spectral stability. Indeed, recall that the Krein–Moser theorem gives a criterion for when a Krein biurcation may occur (i.e. two elliptic eigenvalues of the monodromy matrix come together and then bifurcate out of the circle). Our refinement gives a similar criterion for the situation when two hyperbolic eigenvalues come together at a hyperbolic eigenvalue of multiplicity two and then become complex, but for the case of symmetric orbits. We call such a transition a HN -transition, and the high-multiplicity eigenvalue, the transit eigenvalue. Whether or not such a transition may occur is completely determined by the B-signature of the transit eigenvalue. Namely, the following result is a consequence of our topological study of the symplectic group. Theorem A. Consider a Hamiltonian with arbitrary degrees of freedom, admitting a symmetry. Let t 7→ γt , t ∈ [0, 1], be a family of symmetric periodic orbits, undergoing an HN -transition. Then the B-signature of the transit eigenvalue is indefinite. The definition of B-signature will be given in Section 3, and the proof of this theorem is obtained in Appendix A. Acknowledgements. The authors are grateful to Urs Frauenfelder, whose ideas inspired this paper. A. Moreno is currently supported by the Sonderforschungsbereich TRR 191 Symplectic Structures in Geometry, Algebra and Dynamics, funded by the DFG (Projektnummer 281071066 – TRR 191), and also by the DFG under Germany’s Excellence Strategy EXC 2181/1 - 390900948 (the Heidelberg STRUCTURES Excellence Cluster). This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Agustin Moreno; (2) Francesco Ruscelli. Authors: Authors: (1) Agustin Moreno; (2) Francesco Ruscelli. Table of Links Abstract Introduction Preliminaries The B-signature GIT sequence: low dimensions GIT sequence: arbitrary dimension Appendix A. Stability, the Krein–Moser theorem, and refinements and References Abstract Abstract Introduction Introduction Preliminaries Preliminaries The B-signature The B-signature GIT sequence: low dimensions GIT sequence: low dimensions GIT sequence: arbitrary dimension GIT sequence: arbitrary dimension Appendix A. Stability, the Krein–Moser theorem, and refinements and References Appendix A. Stability, the Krein–Moser theorem, and refinements and References 1. Introduction The stability of periodic orbits is a central topic in the study of Hamiltonian systems, going back to the problem of stability of the solar system in celestial mechanics. Ubiquitous in the study of ODEs, the notion of stability arises whenever studying orbits in families and their bifurcations, a practice which entails both theoretical and practical interest. For instance, from the perspective of space mission design, orbits used for parking a spacecraft around a target Moon should be as stable as possible, in order to minimize fuel corrections and station-keeping. From a mathematical point of view, the key notions of stability of a system come in three flavors, related by the following implications: Non-linear (Lyapunov) stability ⇒ linear stability ⇒ spectral stability. Non-linear stability, roughly speaking, means that trajectories which start near a given periodic orbit stay near the orbit for all time. Linear stability corresponds to stability of the origin for the linearized dynamics, i.e. the orbits of the linearized system should stay bounded. For a Hamiltonian system, this means that the eigenvalues of the monodromy matrix of the corresponding orbit should lie in the unit circle, and be semi-simple. Spectral stability, on the other hand, requires that eigenvalues all lie in the unit circle, but allows them to have multiplicity (so that orbits can escape to infinity in polynomial time, rather than exponential). In this paper, we will focus on the notion of linear stability. linear In the presence of symmetry, the study of linear stability of periodic orbits which are preserved by the symmetry can be significantly refined. With this end in mind, the first author and Urs Frauenfelder introduced in [FM] the notion of the GIT sequence, as a refinement of the Broucke stability diagram [Br69], via the notion of B-signature. The GIT sequence consists of a sequence of three spaces and maps between them whose topology encodes stability and bifurcations of periodic orbits, as well as their eigenvalue configurations, and provides obstructions to the existence of regular cylinder of orbits. In low dimensions, the spaces can be visualized in the plane or in three-dimensional space, which makes them amenable for numerical work. We should note that while the GIT sequence is designed to study linear stability, it blurs its distinction with spectral stability. Indeed, recall that the Krein–Moser theorem gives a criterion for when a Krein biurcation may occur (i.e. two elliptic eigenvalues of the monodromy matrix come together and then bifurcate out of the circle). Our refinement gives a similar criterion for the situation when two hyperbolic eigenvalues come together at a hyperbolic eigenvalue of multiplicity two and then become complex, but for the case of symmetric orbits. We call such a transition a HN -transition, and the high-multiplicity eigenvalue, the transit eigenvalue. Whether or not such a transition may occur is completely determined by the B-signature of the transit eigenvalue. Namely, the following result is a consequence of our topological study of the symplectic group. Theorem A. Consider a Hamiltonian with arbitrary degrees of freedom, admitting a symmetry. Let t 7→ γt , t ∈ [0, 1], be a family of symmetric periodic orbits, undergoing an HN -transition. Then the B-signature of the transit eigenvalue is indefinite. Theorem A. Consider a Hamiltonian with arbitrary degrees of freedom, admitting a symmetry. Let t 7→ γt , t ∈ [0, 1], be a family of symmetric periodic orbits, undergoing an HN -transition. Then the B-signature of the transit eigenvalue is indefinite. The definition of B-signature will be given in Section 3, and the proof of this theorem is obtained in Appendix A. Acknowledgements . The authors are grateful to Urs Frauenfelder, whose ideas inspired this paper. A. Moreno is currently supported by the Sonderforschungsbereich TRR 191 Symplectic Structures in Geometry, Algebra and Dynamics, funded by the DFG (Projektnummer 281071066 – TRR 191), and also by the DFG under Germany’s Excellence Strategy EXC 2181/1 - 390900948 (the Heidelberg STRUCTURES Excellence Cluster). Acknowledgements 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

Combinatorics of linear stability for Hamiltonian systems in arbitrary dimension: Introduction

নির্বিচারে হ্যামিলটোনিয়ান সিস্টেমের জন্য রৈখিক স্থিতিশীলতার সংমিশ্রণ: ভূমিকা

Kombinatorik der linearen Stabilität für Hamiltonsysteme beliebiger Dimension: Einführung

Combinatoria de estabilidad lineal para sistemas hamiltonianos en dimensión arbitraria: Introducción

Combinatoire de la stabilité linéaire pour les systèmes hamiltoniens en dimension arbitraire : Introduction

मनमाने आयाम में हैमिल्टोनियन प्रणालियों के लिए रैखिक स्थिरता का संयोजन: परिचय

任意次元のハミルトン系の線形安定性の組合せ論：序論

임의 차원의 해밀턴 시스템에 대한 선형 안정성 조합: 소개

Combinatória de estabilidade linear para sistemas hamiltonianos em dimensão arbitrária: Introdução

Комбинаторика линейной устойчивости гамильтоновых систем произвольной размерности. Введение.

Keyfi boyutta Hamilton sistemleri için doğrusal kararlılığın kombinatoriği: Giriş

Tổ hợp ổn định tuyến tính cho hệ Hamilton theo chiều tùy ý: Giới thiệu

任意维汉密尔顿系统线性稳定性的组合：简介

Authors:
(1) Agustin Moreno;
(2) Francesco Ruscelli. Table of Links Abstract
Introduction
Preliminaries
The B-signature
GIT sequence: low dimensions
GIT sequence: arbitrary dimension
Appendix A. Stability, the Krein–Moser theorem, and refinements and References Appendix A. Stability, the Krein–Moser theorem, and refinements Now we explain how the GIT sequence topologically encodes the (linear) stability of periodic orbits, and compare it to the basic notions of Krein theory, and the Krein–Moser stability theorem. We will also explain how to obtain Theorem A. We follow the exposition in Ekeland’s book [Eke90] (see also [Ab01]). Consider a linear symplectic ODE One can show that the ODE x˙ = JA(t)x is (strongly) stable if and only if R(T) is (strongly) stable [Eke90]. Moreover, stability is equivalent to R(T) being diagonalizable (i.e. all eigenvalues are semi-simple), with its spectrum lying in the unit circle [Eke90]. Now, consider an elliptic pair {λ, λ} of eigenvalues of a symplectic matrix R. Then any other symplectic matrix close to R will also have simple eigenvalues in the unit circle different from ±1 (otherwise an eigenvalue would have to bifurcate into two, as every eigenvalue comes in quadruples, which is not possible if eigenspaces are 1-dimensional). Therefore in this situation, R is strongly stable. The case of eigenvalues with higher multiplicity is dealt with via Krein theory. Whenever two elliptic eigenvalues come together, this gives a criterion for when they cannot possibly escape the circle and transition into a complex quadruple. This works as follows. if x, y are the corresponding eigenvectors. Moreover, if we consider the generalized eigenspaces Definition A.2. (Krein-positivity/negativity) If λ is an eigenvalue of the symplectic matrix R with |λ| = 1, then the signature (p, q) of Gλ is called the Krein-type or Krein signature of λ. If q = 0, i.e. Gλ is positive definite, λ is said to be Krein-positive. If p = 0, i.e. Gλ is negative definite, λ is said to be Krein-negative. If λ is either Krein-negative or Krein-positive, we say that it is Krein-definite. Otherwise, we say that it is Krein-indefinite. If λ is of Krein-type (p, q), then λ is of Krein-type (q, p) [Eke90]. If λ satisfies |λ| = 1 and it is not semi-simple, then it is easy to show that it is Krein-indefinite [Eke90]. Moreover, ±1 are always Krein-indefinite if they are eigenvalues, as they have real eigenvectors x, which are therefore G-isotropic, i.e. G(x, x) = 0. The following, originally proved by Krein in [Kre1; Kre2; Kre3; Kre4] and independently rediscovered by Moser in [M78], gives a characterization of strong stability in terms of Krein theory: Theorem 3 (Krein–Moser). R is strongly stable if and only if it is stable and all its eigenvalues are Krein-definite. See [Eke90] for a proof. Note that this generalizes the case where all eigenvalues are simple, different from ±1 and in the unit circle, as discussed above. Now, the way that the GIT sequence ties up with Krein theory is the following. Proposition A.1 ([FM]). For a Wonenburger matrix, the Krein signature coincides with the B-signature, for elliptic eigenvalues. Example A.3. As a simple example, to illustrate Proposition A.1, consider the Wonenburger matrices As a corollary of the Krein–Moser theorem and of Proposition A.1, we obtain the following. Theorem 4. Let R be a Wonenburger matrix. Then R is strongly stable if and only if it is stable and all its eigenvalues are B-definite. In higher dimensions, whether or not a given high-multiplicity elliptic or hyperbolic eigenvalue of a Wonenburger matrix can be perturbed to be a complex quadruple is determined by whether or not its B-signature is definite; see e.g. Figure 9 and Remark 5.2. This gives a topological proof of the Krein–Moser theorem in all dimensions, and in fact generalizes it for the hyperbolic case, in the case of Wonenburger matrices, proving Theorem A in the Introduction. References [Ab01] Abbondandolo, Alberto. Morse theory for Hamiltonian systems. Chapman & Hall/CRC Research Notes in Mathematics, 425. Chapman & Hall/CRC, Boca Raton, FL, 2001. xii+189 pp. ISBN: 1-58488- 202-6 [Ay22] Aydin, Cengiz. From Babylonian lunar observations to Floquet multipliers and Conley-Zehnder Indices. Preprint arXiv:2206.07803, 2022. [AFKM] Aydin, Cengiz; Frauenfelder, Urs; Koh, Dayung; Moreno, Agustin. Symplectic methods in space mission design. Proceedings of the 2023 AAS/AIAA Astrodynamics Specialist Conference, 2023. [Br69] Broucke, R. Stability of periodic orbits in the elliptic, restricted three-body problem. AIAA J. 7,1003 (1969). [Eke90] Ekeland, Ivar. Convexity methods in Hamiltonian mechanics. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 19. Springer-Verlag, Berlin, 1990. x+247 pp. ISBN: 3-540-50613-6 [FM] Frauenfelder, Urs; Moreno, Agustin. On GIT quotients of the symplectic group, stability and bifurcations of periodic orbits, Journal of Symplectic Geometry. To appear. [FMb] Frauenfelder, Urs; Moreno, Agustin. On doubly symmetric periodic orbits. Celestial Mechanics & Dynamical Astronomy, 135 (2023), no. 2, Paper No. 20. [HD98] Howard, James E.; Dullin, Holger R. Linear stability of natural symplectic maps. Phys. Lett. A 246 (1998), no. 3-4, 273–283. [HM87] Howard, J. E.; MacKay, R. S. Calculation of linear stability boundaries for equilibria of Hamiltonian systems. Phys. Lett. A 122 (1987), no. 6-7, 331–334. Kre1] Krein, M.: Generalization of certain investigations of A.M. Liapunov on linear differential equations with periodic coefficients. Doklady Akad. Nauk USSR 73 (1950) 445-448. Kre2] Krein, M.: On the application of an algebraic proposition in the theory of monodromy matrices. Uspekhi Math. Nauk 6 (1951) 171-177. [Kre3] Krein, M.: On the theory of entire matrix-functions of exponential type. Ukrainian Math. Journal 3 (1951) 164-173. [Kre4] Krein, M.: On some maximum and minimum problems for characteristic numbers and Liapunov stability zones. Prikl. Math. Mekh. 15 (1951) 323-348. [M78] Moser, Jürgen. A fixed point theorem in symplectic geometry. Acta Math. 141 (1978), no. 1-2, 17–34. (A. Moreno) Universität Heidelberg, Mathematisches Institut, Heidelberg, Germany Email address: agustin.moreno2191@gmail.com (F. Ruscelli) Universität Heidelberg, Mathematisches Institut, Heidelberg, Germany Email address: fruscelli@mathi.uni-heidelberg.de This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Agustin Moreno; (2) Francesco Ruscelli. Authors: Authors: (1) Agustin Moreno; (2) Francesco Ruscelli. Table of Links Abstract Introduction Preliminaries The B-signature GIT sequence: low dimensions GIT sequence: arbitrary dimension Appendix A. Stability, the Krein–Moser theorem, and refinements and References Abstract Abstract Introduction Introduction Preliminaries Preliminaries The B-signature The B-signature GIT sequence: low dimensions GIT sequence: low dimensions GIT sequence: arbitrary dimension GIT sequence: arbitrary dimension Appendix A. Stability, the Krein–Moser theorem, and refinements and References Appendix A. Stability, the Krein–Moser theorem, and refinements and References Appendix A. Stability, the Krein–Moser theorem, and refinements Now we explain how the GIT sequence topologically encodes the (linear) stability of periodic orbits, and compare it to the basic notions of Krein theory, and the Krein–Moser stability theorem. We will also explain how to obtain Theorem A. We follow the exposition in Ekeland’s book [Eke90] (see also [Ab01]). Consider a linear symplectic ODE One can show that the ODE x˙ = JA(t)x is (strongly) stable if and only if R(T) is (strongly) stable [Eke90]. Moreover, stability is equivalent to R(T) being diagonalizable (i.e. all eigenvalues are semi-simple), with its spectrum lying in the unit circle [Eke90]. Now, consider an elliptic pair {λ, λ} of eigenvalues of a symplectic matrix R. Then any other symplectic matrix close to R will also have simple eigenvalues in the unit circle different from ±1 (otherwise an eigenvalue would have to bifurcate into two, as every eigenvalue comes in quadruples, which is not possible if eigenspaces are 1-dimensional). Therefore in this situation, R is strongly stable. The case of eigenvalues with higher multiplicity is dealt with via Krein theory. Whenever two elliptic eigenvalues come together, this gives a criterion for when they cannot possibly escape the circle and transition into a complex quadruple. This works as follows. if x, y are the corresponding eigenvectors. Moreover, if we consider the generalized eigenspaces Definition A.2. (Krein-positivity/negativity) If λ is an eigenvalue of the symplectic matrix R with |λ| = 1, then the signature (p, q) of Gλ is called the Krein-type or Krein signature of λ. If q = 0, i.e. Gλ is positive definite, λ is said to be Krein-positive. If p = 0, i.e. Gλ is negative definite, λ is said to be Krein-negative. If λ is either Krein-negative or Krein-positive, we say that it is Krein-definite. Otherwise, we say that it is Krein-indefinite. Definition A.2. (Krein-positivity/negativity) If λ is of Krein-type (p, q), then λ is of Krein-type (q, p) [Eke90]. If λ satisfies |λ| = 1 and it is not semi-simple, then it is easy to show that it is Krein-indefinite [Eke90]. Moreover, ±1 are always Krein-indefinite if they are eigenvalues, as they have real eigenvectors x, which are therefore G-isotropic, i.e. G(x, x) = 0. The following, originally proved by Krein in [Kre1; Kre2; Kre3; Kre4] and independently rediscovered by Moser in [M78], gives a characterization of strong stability in terms of Krein theory: Theorem 3 (Krein–Moser). R is strongly stable if and only if it is stable and all its eigenvalues are Krein-definite. Theorem 3 (Krein–Moser). R is strongly stable if and only if it is stable and all its eigenvalues are Krein-definite. See [ Eke90 ] for a proof. Note that this generalizes the case where all eigenvalues are simple, different from ±1 and in the unit circle, as discussed above. Now, the way that the GIT sequence ties up with Krein theory is the following. Eke90 Proposition A.1 ([FM]). For a Wonenburger matrix, the Krein signature coincides with the B-signature, for elliptic eigenvalues. Proposition A.1 ([FM]). For a Wonenburger matrix, the Krein signature coincides with the B-signature, for elliptic eigenvalues. Example A.3. As a simple example, to illustrate Proposition A.1, consider the Wonenburger matrices Example A.3. As a corollary of the Krein–Moser theorem and of Proposition A.1, we obtain the following. Theorem 4. Let R be a Wonenburger matrix. Then R is strongly stable if and only if it is stable and all its eigenvalues are B-definite. Theorem 4. Let R be a Wonenburger matrix. Then R is strongly stable if and only if it is stable and all its eigenvalues are B-definite. In higher dimensions, whether or not a given high-multiplicity elliptic or hyperbolic eigenvalue of a Wonenburger matrix can be perturbed to be a complex quadruple is determined by whether or not its B-signature is definite; see e.g. Figure 9 and Remark 5.2. This gives a topological proof of the Krein–Moser theorem in all dimensions, and in fact generalizes it for the hyperbolic case, in the case of Wonenburger matrices, proving Theorem A in the Introduction. References [Ab01] Abbondandolo, Alberto. Morse theory for Hamiltonian systems. Chapman & Hall/CRC Research Notes in Mathematics, 425. Chapman & Hall/CRC, Boca Raton, FL, 2001. xii+189 pp. ISBN: 1-58488- 202-6 [Ay22] Aydin, Cengiz. From Babylonian lunar observations to Floquet multipliers and Conley-Zehnder Indices. Preprint arXiv:2206.07803, 2022. [AFKM] Aydin, Cengiz; Frauenfelder, Urs; Koh, Dayung; Moreno, Agustin. Symplectic methods in space mission design. Proceedings of the 2023 AAS/AIAA Astrodynamics Specialist Conference, 2023. [Br69] Broucke, R. Stability of periodic orbits in the elliptic, restricted three-body problem. AIAA J. 7,1003 (1969). [Eke90] Ekeland, Ivar. Convexity methods in Hamiltonian mechanics. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 19. Springer-Verlag, Berlin, 1990. x+247 pp. ISBN: 3-540-50613-6 [FM] Frauenfelder, Urs; Moreno, Agustin. On GIT quotients of the symplectic group, stability and bifurcations of periodic orbits, Journal of Symplectic Geometry. To appear. [FMb] Frauenfelder, Urs; Moreno, Agustin. On doubly symmetric periodic orbits. Celestial Mechanics & Dynamical Astronomy, 135 (2023), no. 2, Paper No. 20. [HD98] Howard, James E.; Dullin, Holger R. Linear stability of natural symplectic maps. Phys. Lett. A 246 (1998), no. 3-4, 273–283. [HM87] Howard, J. E.; MacKay, R. S. Calculation of linear stability boundaries for equilibria of Hamiltonian systems. Phys. Lett. A 122 (1987), no. 6-7, 331–334. Kre1] Krein, M.: Generalization of certain investigations of A.M. Liapunov on linear differential equations with periodic coefficients. Doklady Akad. Nauk USSR 73 (1950) 445-448. Kre2] Krein, M.: On the application of an algebraic proposition in the theory of monodromy matrices. Uspekhi Math. Nauk 6 (1951) 171-177. [Kre3] Krein, M.: On the theory of entire matrix-functions of exponential type. Ukrainian Math. Journal 3 (1951) 164-173. [Kre4] Krein, M.: On some maximum and minimum problems for characteristic numbers and Liapunov stability zones. Prikl. Math. Mekh. 15 (1951) 323-348. [M78] Moser, Jürgen. A fixed point theorem in symplectic geometry. Acta Math. 141 (1978), no. 1-2, 17–34. (A. Moreno) Universität Heidelberg, Mathematisches Institut, Heidelberg, Germany Email address: agustin.moreno2191@gmail.com (F. Ruscelli) Universität Heidelberg, Mathematisches Institut, Heidelberg, Germany Email address: fruscelli@mathi.uni-heidelberg.de 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

Appendix A. Stability, the Krein–Moser theorem, and refinements and References

পরিশিষ্ট A. স্থিতিশীলতা, ক্রেইন-মোজার উপপাদ্য, এবং পরিমার্জন এবং উল্লেখ

Anhang A. Stabilität, Krein-Moser-Theorem, Verfeinerungen und Referenzen

Apéndice A. Estabilidad, teorema de Krein-Moser y refinamientos y referencias

Annexe A. Stabilité, théorème de Krein-Moser, affinements et références

परिशिष्ट A. स्थिरता, क्रेन-मोजर प्रमेय, और परिशोधन और संदर्भ

付録A. 安定性、クライン・モーザー定理、改良点と参考文献

부록 A. 안정성, Krein-Moser 정리, 개선 사항 및 참고 자료

Apêndice A. Estabilidade, teorema de Krein-Moser e refinamentos e referências

Приложение A. Устойчивость, теорема Крейна–Мозера, уточнения и литература

Ek A. Kararlılık, Krein-Moser teoremi, iyileştirmeler ve Referanslar

Phụ lục A. Tính ổn định, định lý Krein–Moser, các cải tiến và tài liệu tham khảo

附录 A. 稳定性、Krein–Moser 定理以及改进和参考文献

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