The cybersecurity outlet The Record originally reported that under Trump’s new Defense Secretary Pete Hegseth, U.S. Cyber Command has been ordered to “stand down from all planning against Russia, including offensive digital actions.” The outlet cites three anonymous sources who are familiar ...

Trump's Defense Secretary Hegseth Orders Cyber Command to 'Stand Down' on All Russia Operations

Amid President Donald Trump’s attacks on government scientists and science funding, researchers are arranging rallies to “Stand Up for Science” in Washington, D.C., and nationwide on March 7

‘Stand Up for Science’ Rallies Will Protest Trump Attacks on Research | Scientific American

We recently published a list of 10 Firms Stand Out Amid Market Downturn. In this article, we are going to take a look at where Unity Software Inc. (NYSE:U) stands against other firms that stand out amid market downturn. Pessimistic sentiment persisted on the stock market on Thursday as investors ...

Why Unity Software Inc. (U) Went Up On Thursday?

It comes as Ipswich Town says expanding the Cobbold Stand is a mid to long-term plan.

Football club 'agrees to buy' land for expansion - Yahoo Sports

While Gary Lineker tried to de-escalate tense moment with Manchester City manager, former Newcastle striker was having none of it

Alan Shearer showed rigour and bravery to stand up to Pep Guardiola’s rant over fixture congestion

Stand

stand

VANCOUVER, Canada, March 18th, 2025/Chainwire/--The artificial intelligence landscape is evolving. Traditional AI models remain centralized, relying on static text data and corporate control. iAgent is introducing a decentralized AI framework where AI agents are trained, owned, and monetized on-chain using real-world visual data. iAgent iAgent Backed by a recent $3 million investment, iAgent has forged several strategic partnerships with leading projects such as Base, LayerZero, Avalanche, Aethir, Arbitrum, and XAI Games. With over 700,000 users on its AGNTxp platform, iAgent is at the forefront of AI x Gaming x DePIN innovation. Now, with TGE live, iAgent is laying the foundation for AI Agents to become a new digital asset that can be trained, validated, and exchanged transparently. "AI should be decentralized, transparent, and monetizable. iAgent is ensuring AI models belong to those who train them, not corporations." — Jamie Batzorig, Co-Founder of iAgent. "AI should be decentralized, transparent, and monetizable. iAgent is ensuring AI models belong to those who train them, not corporations." — Jamie Batzorig, Co-Founder of iAgent. iAgent’s Product Hub: Powering the AI Economy iAgent’s ecosystem consists of a suite of interconnected products aimed at supporting AI development, deployment, and monetization through a decentralized framework. Each component is designed to enhance the verifiability, scalability, and accessibility of AI models across various ecosystems. Visual Learning Model (VLM): Adaptive AI Training Unlike traditional AI that relies on text-based training (LLMs), iAgent’s Visual Learning Models (VLMs) enable AI agents to learn from real-world gameplay footage. This approach allows AI to analyze, strategize, and adapt dynamically, making them more intelligent and applicable in real-world scenarios. iAgent’s VLM-powered AI utilizes real-player interactions to enhance its adaptability, enabling continuous optimization for performance in competitive gaming environments and other applications: Current live for Counter Strike 2, Off the Grid & Citizen Conflict. Players have already contributed 25 TB+ gameplay data.
Over 10,000+ hours of gameplay footage recorded Players have already contributed 25 TB+ gameplay data. Over 10,000+ hours of gameplay footage recorded ERC-** Agent Standard: A New AI Digital Asset Class iAgent’s ERC-** standard will bring AI Agents on-chain as verifiable, secure, and interoperable digital assets. This aims to enable true ownership, trading, and cross-chain utilization without centralized control. While enhancing trust and transparency through provable authenticity and ownership history. AI Agent Marketplace: The Open AI Economy The AI Agent Marketplace serves as the foundation of iAgent’s decentralized ecosystem, enabling seamless AI model deployment, trading, and monetization. Developers can list AI-powered agents for rental or sale, while businesses and game studios can purchase or integrate AI models tailored to their needs. iAgent DEV Hub: Decentralized AI Infrastructure The iAgent DEV Hub acts as the backbone of the protocol, offering developers and AI researchers a comprehensive suite of tools, SDKs, and APIs to build and optimize AI models. It provides a trustless AI validation framework, leveraging on-chain verification nodes, cross-DePIN compute integration, and AI execution tracking. AI in Gaming: The Next Evolution of Intelligent Agents Gaming offers high-quality, labeled data, making it a suitable environment for training advanced AI models. iAgent is introducing adaptive AI agents to gaming, facilitating: AI-powered game assistants – AI agents that analyze in-game movements, provide real-time coaching and improve player performance in FPS games like Valorant.
Smart NPCs that evolve dynamically – NPCs in RPGs like World of Warcraft that learn and adapt to a player’s choices, creating truly immersive experiences.
AI anti-cheat and security systems – AI in games like CS2 that detects aimbots and wallhacks in real-time, ensuring fair gameplay.
Predictive AI for in-game economies – AI models that track in-game trends, helping players optimize asset trading in games like Diablo 4. AI-powered game assistants – AI agents that analyze in-game movements, provide real-time coaching and improve player performance in FPS games like Valorant. Smart NPCs that evolve dynamically – NPCs in RPGs like World of Warcraft that learn and adapt to a player’s choices, creating truly immersive experiences. AI anti-cheat and security systems – AI in games like CS2 that detects aimbots and wallhacks in real-time, ensuring fair gameplay. Predictive AI for in-game economies – AI models that track in-game trends, helping players optimize asset trading in games like Diablo 4. iAgent’s decentralized AI infrastructure will expand beyond gaming, creating an open AI economy applicable across industries. "Gaming is the first major use case, but our AI infrastructure will extend to multiple sectors. AI models will be owned, monetized, and deployed across various real-world applications." — MHL Solutions, iAgent Advisor. "Gaming is the first major use case, but our AI infrastructure will extend to multiple sectors. AI models will be owned, monetized, and deployed across various real-world applications." — MHL Solutions, iAgent Advisor. Roadmap: From Foundation to AI Economy 2023-2024: Establishing the iAgent Protocol Development of Visual Learning Models (VLMs) and AI ownership framework.
AGNTxp launch, onboarding 700K+ users and generating 75K+ AI identities.
AI data collection platform, accumulating 25+ TB+ gameplay data.
Genesis Node Sale to decentralize AI model validation and verification. Development of Visual Learning Models (VLMs) and AI ownership framework. AGNTxp launch, onboarding 700K+ users and generating 75K+ AI identities. AI data collection platform, accumulating 25+ TB+ gameplay data. Genesis Node Sale to decentralize AI model validation and verification. 2025: Scaling AI Deployment & Monetization March 2025: TGE live, launching $AGNT as the core AI economy token.
On-chain governance rollout, enabling staking & liquid staking. TGE live, launching $AGNT as the core AI economy token. On-chain governance rollout, enabling staking & liquid staking. April 2025: AI Agent Marketplace launch, enabling AI deployment, trading, and rental.
ERC-** Standard proposal, formalizing AI ownership and validation. AI Agent Marketplace launch, enabling AI deployment, trading, and rental. ERC-** Standard proposal, formalizing AI ownership and validation. May 2025: AGNT-Hub powered by $AGNT. AGNT-Hub powered by $AGNT. June 2025: AI Agent Explorer & Analytics Platform, enabling transparent AI tracking. AI Agent Explorer & Analytics Platform, enabling transparent AI tracking. Q3 2025: Integration of VLM-powered AI into partner games in the AAA and indie gaming ecosystem.
Visual Data Monetization framework, allowing users to sell gameplay data to train AI. Integration of VLM-powered AI into partner games in the AAA and indie gaming ecosystem. Visual Data Monetization framework, allowing users to sell gameplay data to train AI. Q4 2025: Protocol Testnet Launch, deploying decentralized AI compute infrastructure.
Mainnet launch, establishing the fully operational iAgent Protocol. Protocol Testnet Launch, deploying decentralized AI compute infrastructure. Mainnet launch, establishing the fully operational iAgent Protocol. AGNT: Advancing Practical Applications in AI and Blockchain As the core of the iAgent ecosystem, AGNT enables: AI Training & Trading – AI models can be owned, sold, and deployed through the marketplace.
Compute & Staking Rewards – GPU node operators are incentivized for providing AI training power.
Visual Data Monetization – Users can get AGNT by contributing high-quality labeled data.
Governance Participation – AGNT holders shape the evolution of iAgent’s decentralized AI infrastructure. AI Training & Trading – AI models can be owned, sold, and deployed through the marketplace. Compute & Staking Rewards – GPU node operators are incentivized for providing AI training power. Visual Data Monetization – Users can get AGNT by contributing high-quality labeled data. Governance Participation – AGNT holders shape the evolution of iAgent’s decentralized AI infrastructure. AI is Becoming an Asset Class, and iAgent is Leading the Way. The AI, gaming, and DePIN industry is set to grow from $553.7 billion today to $2.8 trillion by 2030. iAgent aims to build the infrastructure for this growth. About iAgent Protocol iAgent’s Visual Learning Model allows gamers to train custom AI agents from their gameplay footage, powered by decentralized computing. By leveraging blockchain technology, it introduces a new digital asset class, enabling users to Create, Own, and Monetize their AI agents in gaming. iAgent’s iAgent’s Founded by a powerhouse team of industry veterans and innovators, iAgent's leadership team includes eight C-level executives with a combined 20+ years of experience at Fortune 500 companies, driving strategic growth and innovation. On the tech front, the team comprises 12 top-tier AI and blockchain engineers, bringing expertise from global giants like Bosch, Meta, Airbus, and Samsung. The best minds shaping the future of AI x Gaming x DePIN together. Website | Twitter | Telegram | Discord | Whitepaper | Linktree Website Website Twitter Twitter Telegram Telegram Discord Discord Whitepaper Whitepaper Linktree Linktree Contact Co-Founder & CEO Jamie Batzorig iAgent Corporation jamie@iagentpro.com 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

iAgent Secures $3M, Launches $AGNT, And Will Introduce a New ERC-**Standard For AI Agents

iAgent beveilig $3 miljoen, stel $AGNT bekend en sal 'n nuwe ERC-**-standaard vir KI-agente bekendstel

iAgent zajistí 3 miliony dolarů, spouští AGNT $ a představí nový standard ERC-** pro AI agenty

iAgent obtiene 3 millones de dólares, lanza $AGNT y presentará un nuevo estándar ERC-** para agentes de IA

iAgent lève 3 millions de dollars, lance $AGNT et introduira une nouvelle norme ERC-** pour les agents IA

iAgent ने $3M हासिल किया, $AGNT लॉन्च किया, और AI एजेंटों के लिए एक नया ERC-**मानक पेश करेगा

iAgent Sekirize $3M, lanse $AGNT, epi li pral prezante yon nouvo ERC-**Standa pou ajan AI.

iAgent が 300 万ドルを調達し、$AGNT を立ち上げ、AI エージェント向けの新しい ERC-** 標準を導入

„iAgent“ užsitikrina 3 mln. USD, paleidžia USD AGNT ir pristatys naują ERC-** DI agentų standartą

iAgent garante US$ 3 milhões, lança $AGNT e apresentará um novo padrão ERC-**para agentes de IA

iAgent Yizewe $ 3M, Itangiza $ AGNT, Kandi Izana ERC Nshya - ** Ibisanzwe kubakozi ba AI

iAgent säkrar $3 miljoner, lanserar $AGNT och kommer att introducera en ny ERC-**-standard för AI-agenter

iAgent 3 миллион долларро таъмин мекунад, $AGNT-ро оғоз мекунад ва ERC-** стандарти нави агентҳои AI-ро ҷорӣ мекунад

MCP: The Universal Standard Making AI Systems Talk (And Why Big Tech Is Betting Everything On It)

এমসিপি: এআই সিস্টেমগুলিকে আলোচনায় আনার সর্বজনীন মান (এবং কেন বিগ টেক এর উপর সবকিছু বাজি ধরছে)

MCP: El estándar universal que hace que los sistemas de IA hablen (y por qué las grandes tecnológicas lo apuestan todo)

MCP: AI システムを機能させる世界標準 (そして大手テクノロジー企業がこれにすべてを賭ける理由)

MCP: AI жүйелерін талқылайтын әмбебап стандарт (және неге Big Tech оған бәрін тігуде)

MCP: ស្តង់ដារជាសកលធ្វើឱ្យប្រព័ន្ធ AI និយាយ (ហើយហេតុអ្វីបានជាបច្ចេកវិទ្យាធំភ្នាល់អ្វីៗគ្រប់យ៉ាងលើវា)

MCP: universalus standartas, leidžiantis kalbėti apie dirbtinio intelekto sistemas (ir kodėl „Big Tech“ stato viską)

MCP: एआई प्रणालीलाई चर्चामा ल्याउने विश्वव्यापी मानक (र किन ठूला प्रविधिहरूले यसमा सबै कुरा बाजी लगाइरहेका छन्)

MCP: O Padrão Universal que Faz os Sistemas de IA Falarem (E Por Que as Big Techs Estão Apostando Tudo Nele)

MCP: AI පද්ධති කතාබහට ලක් කරන විශ්වීය ප්‍රමිතිය (සහ මහා තාක්‍ෂණය ඒ සඳහා සියල්ල ඔට්ටු අල්ලන්නේ ඇයි)

MCP: Univerzálny štandard, vďaka ktorému budú systémy umelej inteligencie hovoriť (a prečo na to veľká technológia vsádza všetko)

MCP: Ang Pangkalahatang Pamantayan sa Paggawa ng AI Systems Talk (At Bakit Itinataya ng Big Tech ang Lahat Dito)

MCP: Універсальний стандарт, що змушує системи штучного інтелекту говорити (і чому велика техніка робить ставку на все)

Building scalable, enterprise Angular apps comes with some challenges, one of which is to organize project in a way, that something maintained by two-three developers will be good to be developed by several teams like this. So the organisation of the project is really important. Especially because an enterprise app can consist of anything between 100 and 500 components and same amount of services. By the way, my name is Tom Smykowski, I’m an expert in building scalable, enterprise applications and in this series I’ll be teaching you how to do it! Before standalone components were introduced, you had to put every component, directive and pipe into a module. Here’s an example of a module: @NgModule({
  declarations: [AppComponent, HeaderComponent],
  imports: [CommonModule, FormsModule],
  providers: [SomeService],
  bootstrap: [AppComponent],
})
export class AppModule {} @NgModule({
  declarations: [AppComponent, HeaderComponent],
  imports: [CommonModule, FormsModule],
  providers: [SomeService],
  bootstrap: [AppComponent],
})
export class AppModule {} There were several problems with this approach. First of all, modules aren’t always necessary. Other libraries like React doesn’t require this construct. For a reason, it increases complexity, increases risk of circular dependencies, makes the codebase harder to understand (you have to figure out what module exports your component, especially difficult when working with 3rd party libraries), lazy loading was a bit complex, and well… there was really a nice pattern to use them. If you put too much in a module, it gets bloated and your app suffers on performance, because Angular is unable to tree-shake them properly. If you create a module for every component… what is the best option… what’s the point of modules at all? These issues led to creation of standalone elements in Angular. Now you import a component, service, or a pipe directly where you use it, from where it’s defined: import { Component } from '@angular/core';
import { CommonModule } from '@angular/common';
import { MeasurementCardComponent } from './measurement-card.component';
import { UnitConverterPipe } from './unit-converter.pipe';
import { StatusDirective } from './status.directive';

@Component({
  selector: 'app-factory-dashboard',
  imports: [
    CommonModule,
    MeasurementCardComponent,
    UnitConverterPipe,
    StatusDirective,
  ],
  // Add other metadata properties here if needed
})
export class FactoryDashboardComponent {
  // Component logic goes here
} import { Component } from '@angular/core';
import { CommonModule } from '@angular/common';
import { MeasurementCardComponent } from './measurement-card.component';
import { UnitConverterPipe } from './unit-converter.pipe';
import { StatusDirective } from './status.directive';

@Component({
  selector: 'app-factory-dashboard',
  imports: [
    CommonModule,
    MeasurementCardComponent,
    UnitConverterPipe,
    StatusDirective,
  ],
  // Add other metadata properties here if needed
})
export class FactoryDashboardComponent {
  // Component logic goes here
} As you can see, it’s easier to figure out and find dependencies of the component using standalone entities. When you are not there yet with your codebase to use standalone entities, you have to know that in Angular 19 components are standalone by default. You don’t have to add standalone: true to the decorator: @Component({
  selector: 'app-factory-dashboard',
  standalone: true,
  // Add other metadata properties here
}) @Component({
  selector: 'app-factory-dashboard',
  standalone: true,
  // Add other metadata properties here
}) You can also use the schematic to automatically switch to standalone: ng generate @angular/core:standalone ng generate @angular/core:standalone It will also change other elements like bootstrapping and routing. So a lot of things will be taken care of automatically. In my experience the schematics works quite good. If you use some special things in your application, you may need to do some manual adjustments. But as long as you sticked to Angular standards, it should go smoothly. To summarize by updating and switching to standalone components, your app complexity will drop, maintainability increase, build size will drop and initial load time drop. All of these contribute strongly to building scalable Angular app. In my experience of working on Angular apps serving millions of users, standalone components are mature, and serving purpose they were designed for. So, I encourage you to switch to standalone entities. I’ve prepared a free checklist how to make your Angular app scalable and ready for enterprise demand. If you’re interested, you can get this checklist for free here. I’ve prepared a free checklist how to make your Angular app scalable and ready for enterprise demand. If you’re interested, you can get this checklist for free here. checklist for free here checklist for free here If you have any questions, ask these in the comment section!

Building Enterprise Angular Apps? You’re Doing It Wrong (Unless You Use Standalone Components)

Table of Links Abstract and 1. Introduction Clock in Orbit
2.1 Coordinate Time
2.2 Local Frame for the Moon


Clock Rate Differences Between Earth and Moon


Clocks at Earth-Moon Lagrance Points
4.1 Clock at Lagrange point L1
4.2. Clock at Lagrange point L2
4.3. Clock at Lagrange point L4 or L5


Conclusions Appendix 1: Fermi Coordinates with Origin at the Center of the Moon Appendix 2: Construction of Freely Falling Center of Mass Frame Appendix 3: Equations of Motion of Earth and Moon Appendix 4: Comparing Results in Rotating and Non-Rotating Coordinate Systems Acknowledgments and References 2. CLOCKS IN ORBIT An instructive example of establishing a coordinate time on Earth is the GPS time. The constellation clocks are set to beat at the average coordinate rate corresponding to clocks at rest on the surface of the rotating Earth by applying a “factory frequency offset” to the clocks before launch, which is [4] This model is based on using an eccentric Keplerian orbit in the local inertial frame centered on Earth’s center of mass. The center of mass of the Earth and Moon approximately follows a Keplerian orbit. However, for the EarthMoon system, one cannot have a Keplerian orbit in a coordinate system centered on the Earth and a Keplerian orbit in a coordinate system centered on the Earth-Moon center of mass with the same orbit parameters. There are also relativistic effects arising from changes in time and length scales, Lorentz contraction, and changes in tidal effects. Authors:
(1) Neil Ashby, National Institute of Standards and Technology, Boulder, CO 80305 (Neil.Ashby@Colorado.Edu);
(2) Bijunath R. Patla, National Institute of Standards and Technology, Boulder, CO 80305 (bijunath.patla@nist.gov). This paper is available on arxiv under CC0 1.0 license. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Clock in Orbit
2.1 Coordinate Time
2.2 Local Frame for the Moon Clock Rate Differences Between Earth and Moon Clocks at Earth-Moon Lagrance Points
4.1 Clock at Lagrange point L1
4.2. Clock at Lagrange point L2
4.3. Clock at Lagrange point L4 or L5 Conclusions Clock in Orbit 2.1 Coordinate Time 2.2 Local Frame for the Moon Clock in Orbit Clock in Orbit 2.1 Coordinate Time 2.1 Coordinate Time 2.2 Local Frame for the Moon 2.2 Local Frame for the Moon Clock Rate Differences Between Earth and Moon Clock Rate Differences Between Earth and Moon Clock Rate Differences Between Earth and Moon Clocks at Earth-Moon Lagrance Points 4.1 Clock at Lagrange point L1 4.2. Clock at Lagrange point L2 4.3. Clock at Lagrange point L4 or L5 Clocks at Earth-Moon Lagrance Points 4.1 Clock at Lagrange point L1 4.1 Clock at Lagrange point L1 4.2. Clock at Lagrange point L2 4.2. Clock at Lagrange point L2 4.3. Clock at Lagrange point L4 or L5 4.3. Clock at Lagrange point L4 or L5 Conclusions Conclusions Conclusions Appendix 1: Fermi Coordinates with Origin at the Center of the Moon Appendix 1: Fermi Coordinates with Origin at the Center of the Moon Appendix 2: Construction of Freely Falling Center of Mass Frame Appendix 2: Construction of Freely Falling Center of Mass Frame Appendix 3: Equations of Motion of Earth and Moon Appendix 3: Equations of Motion of Earth and Moon Appendix 4: Comparing Results in Rotating and Non-Rotating Coordinate Systems Appendix 4: Comparing Results in Rotating and Non-Rotating Coordinate Systems Acknowledgments and References Acknowledgments and References 2. CLOCKS IN ORBIT An instructive example of establishing a coordinate time on Earth is the GPS time. The constellation clocks are set to beat at the average coordinate rate corresponding to clocks at rest on the surface of the rotating Earth by applying a “factory frequency offset” to the clocks before launch, which is [4] This model is based on using an eccentric Keplerian orbit in the local inertial frame centered on Earth’s center of mass. The center of mass of the Earth and Moon approximately follows a Keplerian orbit. However, for the EarthMoon system, one cannot have a Keplerian orbit in a coordinate system centered on the Earth and a Keplerian orbit in a coordinate system centered on the Earth-Moon center of mass with the same orbit parameters. There are also relativistic effects arising from changes in time and length scales, Lorentz contraction, and changes in tidal effects. Authors: (1) Neil Ashby, National Institute of Standards and Technology, Boulder, CO 80305 (Neil.Ashby@Colorado.Edu); (2) Bijunath R. Patla, National Institute of Standards and Technology, Boulder, CO 80305 (bijunath.patla@nist.gov). Authors: Authors: (1) Neil Ashby, National Institute of Standards and Technology, Boulder, CO 80305 ( Neil.Ashby@Colorado.Edu ); Neil.Ashby@Colorado.Edu (2) Bijunath R. Patla, National Institute of Standards and Technology, Boulder, CO 80305 ( bijunath.patla@nist.gov ). bijunath.patla@nist.gov This paper is available on arxiv under CC0 1.0 license. This paper is available on arxiv under CC0 1.0 license. available on arxiv available on arxiv

Why It's So Difficult To Establish a Lunar Time Standard

Table of Links Acknowledgements 1 Introduction to thesis 1.1 History and Evidence 1.2 Facts on dark matter 1.3 Candidates to dark matter 1.4 Dark matter detection 1.5 Outline of the thesis 2 Dark matter through ALP portal and 2.1 Introduction 2.2 Model 2.3 Existing constraints on ALP parameter space 2.4 Dark matter analysis 2.5 Summary 3 A two component dark matter model in a generic 𝑈(1)𝑋 extension of SM and 3.1 Introduction 3.2 Model 3.3 Theoretical and experimental constraints 3.4 Phenomenology of dark matter 3.5 Relic density dependence on 𝑈(1)𝑋 charge 𝑥𝐻 3.6 Summary 4 A pseudo-scalar dark matter case in 𝑈(1)𝑋 extension of SM and 4.1 Introduction 4.2 Model 4.3 Theoretical and experimental constraints 4.4 Dark Matter analysis 4.5 Summary 5 Summary Appendices A Standard model B Friedmann equations C Type I seasaw mechanism D Feynman diagrams in two-component DM model Bibliography 2.2 Model The model that we consider is the minimal combination of type-I seesaw and effective ALP interaction with additional Z2 symmetry apart from the SM gauge symmetry [108, 109]. The matter content of the model is shown in Table. 2.1. This paper is available on arxiv under CC BY 4.0 DEED license. Author:
(1) Shivam Gola, The Institute of Mathematical Sciences, Chennai. Table of Links Acknowledgements Acknowledgements 1 Introduction to thesis 1 Introduction to thesis 1.1 History and Evidence 1.1 History and Evidence 1.2 Facts on dark matter 1.2 Facts on dark matter 1.3 Candidates to dark matter 1.3 Candidates to dark matter 1.4 Dark matter detection 1.4 Dark matter detection 1.5 Outline of the thesis 1.5 Outline of the thesis 2 Dark matter through ALP portal and 2.1 Introduction 2 Dark matter through ALP portal and 2.1 Introduction 2.2 Model 2.2 Model 2.3 Existing constraints on ALP parameter space 2.3 Existing constraints on ALP parameter space 2.4 Dark matter analysis 2.4 Dark matter analysis 2.5 Summary 2.5 Summary 3 A two component dark matter model in a generic 𝑈(1)𝑋 extension of SM and 3.1 Introduction 3 A two component dark matter model in a generic 𝑈(1)𝑋 extension of SM and 3.1 Introduction 3.2 Model 3.2 Model 3.3 Theoretical and experimental constraints 3.3 Theoretical and experimental constraints 3.4 Phenomenology of dark matter 3.4 Phenomenology of dark matter 3.5 Relic density dependence on 𝑈(1)𝑋 charge 𝑥𝐻 3.5 Relic density dependence on 𝑈(1)𝑋 charge 𝑥𝐻 3.6 Summary 3.6 Summary 4 A pseudo-scalar dark matter case in 𝑈(1)𝑋 extension of SM and 4.1 Introduction 4 A pseudo-scalar dark matter case in 𝑈(1)𝑋 extension of SM and 4.1 Introduction 4.2 Model 4.2 Model 4.3 Theoretical and experimental constraints 4.3 Theoretical and experimental constraints 4.4 Dark Matter analysis 4.4 Dark Matter analysis 4.5 Summary 4.5 Summary 5 Summary 5 Summary Appendices Appendices A Standard model A Standard model B Friedmann equations B Friedmann equations C Type I seasaw mechanism C Type I seasaw mechanism D Feynman diagrams in two-component DM model D Feynman diagrams in two-component DM model Bibliography Bibliography 2.2 Model The model that we consider is the minimal combination of type-I seesaw and effective ALP interaction with additional Z2 symmetry apart from the SM gauge symmetry [108, 109]. The matter content of the model is shown in Table. 2.1. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv Author: (1) Shivam Gola, The Institute of Mathematical Sciences, Chennai. Author: Author: (1) Shivam Gola, The Institute of Mathematical Sciences, Chennai.

Dark Matter Research: A Look at the Standard Model

The DS Acronym: DolphinScheduler or DeepSeek Once upon a time, when people in the tech circle mentioned DS, what came to mind was a lively “little dolphin” - Apache DolphinScheduler (abbreviated as DS). This distributed task scheduling system, born in 2019, was once the “dream job” for big data engineers with its visual DAG interface, multi-tenancy support, and deep integration with the Hadoop/Spark ecosystem. However, the wheels of fate began to spin rapidly in early 2025: Hangzhou AI company DeepSeek (Deep Quest) burst onto the scene with its inference model R1 and open-source large model V3, touting “low cost and high performance.” Not only did it sweep the capital market, but it also redefined the acronym “DS” overnight - from now on, “DS” was no longer a scheduling tool but the “new darling” of the AI circle. Some developers joked, “When I used to write DS configuration documents and colleagues asked, ‘What is DS?’ I would reply, ‘Dolphin Scheduler.’ Now when I ask, they immediately respond, ‘Oh, that AI that writes poetry more emotionally than Qu Yuan?’” The “Top-Flow Battle” in the Tech Circle: DolphinScheduler's Grievance and the AI Newcomer's Ambition 1. DolphinScheduler: The Forgotten “Original DS” As the “old-timer” in the big data scheduling field, DolphinScheduler should have comfortably held the throne of the acronym. Its distributed architecture and drag-and-drop DAG design once conquered countless ETL engineers, even rivaling Airflow. However, its user profile has always been that of a “behind-the-scenes hero” - busy daily solving Spark environment variable errors, debugging email alert nicknames, or going crazy when ZooKeeper nodes crash. This “hardcore but low-key” image has kept the DS acronym confined to technical documents, never breaking through the circle. 2. DeepSeek: The “Acronym Hijacker” in the AI Circle In contrast, DeepSeek made its debut with its own buzz: low-cost models (training costs only one-twentieth of GPT-4), domestic GPU compatibility (11 manufacturers competing for cooperation), and even the ability to analyze trade war policies while reciting “The Mountain Spirit” to move users. What's more “unfair” is that it took only a week to make “DS” a hot word on social media, with even sensational bloggers discussing “DS's RL technology breakthrough.” Netizens joked, “DS used to be the acronym for programmers staying up late to fix bugs; now it's the code for AI poetry that trends on hot searches.” The “Technical Philosophy” of Acronym Collision: The Battle Between Tools and Traffic This acronym dispute is essentially a collision between technical value and traffic hegemony: DolphinScheduler represents the long-termism of basic tools - it quietly supports data pipelines but is too “practical” to lack explosive highlights.
DeepSeek interprets the traffic law of the AI era - using emotional interaction (such as poetry empathy) and capital storytelling (such as “the rise of domestic GPUs”) to quickly occupy the mind. Some developers complained, “When I used to use DS for scheduling tasks and my boss asked, ‘What's the use of this tool?’ Now when I use DS (DeepSeek) to write weekly reports, my boss praises, ‘This AI is reliable.’” Peace Proposal: How to Achieve “Common Prosperity” for the “DS” Acronym? Faced with the acronym collision, the tech community has put forward the following “peace initiatives”: Scenario Isolation Method

Big data engineers insist: “DS (DolphinScheduler) schedules tasks, DS (DeepSeek) writes PPT,s clear division of labor, no interference.”
AI researchers retort: “DS (DeepSeek) can tune parameters, DS (DolphinScheduler) can schedule tasks, the combination is the perfect entity!”


Suffix Differentiation Technique

It is proposed to rename DolphinScheduler as “DScheduler” and DeepSeek as “DSeek,” but the public rejected it, saying, “Why not just call them ‘Dolphin’ and ‘Deep Sea Fish’ to avoid internal competition?”


Ultimate Mysticism


Developers suggest: “Let DolphinScheduler integrate with the DeepSeek model to generate poetic logs for scheduling tasks - keeping the acronym while riding the traffic wave.” Example:

Task node 14451413115008,Failed as resolutely as Qu Yuan throwing himself into the Miluo River,But don't panic, after three automatic retries,Finally, ‘SUCCESS’ illuminates the mountains and rivers! The War of Acronyms, the Symbiosis of Technology Perhaps, the battle over the “DS” acronym is a microcosm of technological evolution: DolphinScheduler reminds us that the value of basic tools never fades - even if the acronym is “stolen,” it remains the unsung hero of the data pipeline.
DeepSeek proves that breaking through the circle in technology needs “poetry and the distance” - an AI that can write code is common, but one that can empathize with Qu Yuan is rare. Finally, an appeal to all developers: If you happen to encounter a confused newcomer asking, ‘What is DS?’ Please kindly reply:——For big data, use Dolphin; for AI, use Deep Sea Fish,Both are DS,But it is recommended to check the documentation first,To avoid awkward conversations in meetings. The DS Acronym: DolphinScheduler or DeepSeek Once upon a time, when people in the tech circle mentioned DS , what came to mind was a lively “little dolphin” - Apache DolphinScheduler (abbreviated as DS). This distributed task scheduling system, born in 2019, was once the “dream job” for big data engineers with its visual DAG interface, multi-tenancy support, and deep integration with the Hadoop/Spark ecosystem. However, the wheels of fate began to spin rapidly in early 2025: Hangzhou AI company DeepSeek (Deep Quest) burst onto the scene with its inference model R1 and open-source large model V3 , touting “low cost and high performance.” Not only did it sweep the capital market, but it also redefined the acronym “DS” overnight - from now on, “DS” was no longer a scheduling tool but the “new darling” of the AI circle. DS Apache DolphinScheduler DeepSeek R1 V3 Some developers joked, “When I used to write DS configuration documents and colleagues asked, ‘What is DS?’ I would reply, ‘Dolphin Scheduler.’ Now when I ask, they immediately respond, ‘Oh, that AI that writes poetry more emotionally than Qu Yuan?’” The “Top-Flow Battle” in the Tech Circle: DolphinScheduler's Grievance and the AI Newcomer's Ambition 1. DolphinScheduler: The Forgotten “Original DS” As the “old-timer” in the big data scheduling field, DolphinScheduler should have comfortably held the throne of the acronym. Its distributed architecture and drag-and-drop DAG design once conquered countless ETL engineers, even rivaling Airflow. However, its user profile has always been that of a “behind-the-scenes hero” - busy daily solving Spark environment variable errors, debugging email alert nicknames, or going crazy when ZooKeeper nodes crash. This “hardcore but low-key” image has kept the DS acronym confined to technical documents, never breaking through the circle. 2. DeepSeek: The “Acronym Hijacker” in the AI Circle In contrast, DeepSeek made its debut with its own buzz: low-cost models (training costs only one-twentieth of GPT-4), domestic GPU compatibility (11 manufacturers competing for cooperation), and even the ability to analyze trade war policies while reciting “The Mountain Spirit” to move users. What's more “unfair” is that it took only a week to make “DS” a hot word on social media, with even sensational bloggers discussing “DS's RL technology breakthrough.” Netizens joked, “DS used to be the acronym for programmers staying up late to fix bugs; now it's the code for AI poetry that trends on hot searches.” The “Technical Philosophy” of Acronym Collision: The Battle Between Tools and Traffic This acronym dispute is essentially a collision between technical value and traffic hegemony : technical value traffic hegemony DolphinScheduler represents the long-termism of basic tools - it quietly supports data pipelines but is too “practical” to lack explosive highlights. DeepSeek interprets the traffic law of the AI era - using emotional interaction (such as poetry empathy) and capital storytelling (such as “the rise of domestic GPUs”) to quickly occupy the mind. DolphinScheduler represents the long-termism of basic tools - it quietly supports data pipelines but is too “practical” to lack explosive highlights. DolphinScheduler long-termism of basic tools DeepSeek interprets the traffic law of the AI era - using emotional interaction (such as poetry empathy) and capital storytelling (such as “the rise of domestic GPUs”) to quickly occupy the mind. DeepSeek traffic law of the AI era Some developers complained, “When I used to use DS for scheduling tasks and my boss asked, ‘What's the use of this tool?’ Now when I use DS (DeepSeek) to write weekly reports, my boss praises, ‘This AI is reliable.’” Peace Proposal: How to Achieve “Common Prosperity” for the “DS” Acronym? Faced with the acronym collision, the tech community has put forward the following “peace initiatives”: Scenario Isolation Method

Big data engineers insist: “DS (DolphinScheduler) schedules tasks, DS (DeepSeek) writes PPT,s clear division of labor, no interference.”
AI researchers retort: “DS (DeepSeek) can tune parameters, DS (DolphinScheduler) can schedule tasks, the combination is the perfect entity!” Suffix Differentiation Technique

It is proposed to rename DolphinScheduler as “DScheduler” and DeepSeek as “DSeek,” but the public rejected it, saying, “Why not just call them ‘Dolphin’ and ‘Deep Sea Fish’ to avoid internal competition?” Ultimate Mysticism


Developers suggest: “Let DolphinScheduler integrate with the DeepSeek model to generate poetic logs for scheduling tasks - keeping the acronym while riding the traffic wave.” Example:

Task node 14451413115008,Failed as resolutely as Qu Yuan throwing himself into the Miluo River,But don't panic, after three automatic retries,Finally, ‘SUCCESS’ illuminates the mountains and rivers! Scenario Isolation Method Big data engineers insist: “DS (DolphinScheduler) schedules tasks, DS (DeepSeek) writes PPT,s clear division of labor, no interference.”
AI researchers retort: “DS (DeepSeek) can tune parameters, DS (DolphinScheduler) can schedule tasks, the combination is the perfect entity!” Scenario Isolation Method Big data engineers insist: “DS (DolphinScheduler) schedules tasks, DS (DeepSeek) writes PPT,s clear division of labor, no interference.” AI researchers retort: “DS (DeepSeek) can tune parameters, DS (DolphinScheduler) can schedule tasks, the combination is the perfect entity!” Big data engineers insist: “DS (DolphinScheduler) schedules tasks, DS (DeepSeek) writes PPT,s clear division of labor, no interference.” AI researchers retort: “DS (DeepSeek) can tune parameters, DS (DolphinScheduler) can schedule tasks, the combination is the perfect entity!” Suffix Differentiation Technique It is proposed to rename DolphinScheduler as “DScheduler” and DeepSeek as “DSeek,” but the public rejected it, saying, “Why not just call them ‘Dolphin’ and ‘Deep Sea Fish’ to avoid internal competition?” Suffix Differentiation Technique It is proposed to rename DolphinScheduler as “DScheduler” and DeepSeek as “DSeek,” but the public rejected it, saying, “Why not just call them ‘Dolphin’ and ‘Deep Sea Fish’ to avoid internal competition?” It is proposed to rename DolphinScheduler as “DScheduler” and DeepSeek as “DSeek,” but the public rejected it, saying, “Why not just call them ‘Dolphin’ and ‘Deep Sea Fish’ to avoid internal competition?” Ultimate Mysticism Developers suggest: “Let DolphinScheduler integrate with the DeepSeek model to generate poetic logs for scheduling tasks - keeping the acronym while riding the traffic wave.” Example:

Task node 14451413115008,Failed as resolutely as Qu Yuan throwing himself into the Miluo River,But don't panic, after three automatic retries,Finally, ‘SUCCESS’ illuminates the mountains and rivers! Ultimate Mysticism Developers suggest: “Let DolphinScheduler integrate with the DeepSeek model to generate poetic logs for scheduling tasks - keeping the acronym while riding the traffic wave.” Example:

Task node 14451413115008,Failed as resolutely as Qu Yuan throwing himself into the Miluo River,But don't panic, after three automatic retries,Finally, ‘SUCCESS’ illuminates the mountains and rivers! Developers suggest: “Let DolphinScheduler integrate with the DeepSeek model to generate poetic logs for scheduling tasks - keeping the acronym while riding the traffic wave.” Example: Task node 14451413115008,Failed as resolutely as Qu Yuan throwing himself into the Miluo River,But don't panic, after three automatic retries,Finally, ‘SUCCESS’ illuminates the mountains and rivers! Developers suggest: “Let DolphinScheduler integrate with the DeepSeek model to generate poetic logs for scheduling tasks - keeping the acronym while riding the traffic wave.” Example: Task node 14451413115008,Failed as resolutely as Qu Yuan throwing himself into the Miluo River,But don't panic, after three automatic retries,Finally, ‘SUCCESS’ illuminates the mountains and rivers! Task node 14451413115008,Failed as resolutely as Qu Yuan throwing himself into the Miluo River,But don't panic, after three automatic retries,Finally, ‘SUCCESS’ illuminates the mountains and rivers! The War of Acronyms, the Symbiosis of Technology Perhaps, the battle over the “DS” acronym is a microcosm of technological evolution: DolphinScheduler reminds us that the value of basic tools never fades - even if the acronym is “stolen,” it remains the unsung hero of the data pipeline. DeepSeek proves that breaking through the circle in technology needs “poetry and the distance” - an AI that can write code is common, but one that can empathize with Qu Yuan is rare. DolphinScheduler reminds us that the value of basic tools never fades - even if the acronym is “stolen,” it remains the unsung hero of the data pipeline. DolphinScheduler the value of basic tools never fades DeepSeek proves that breaking through the circle in technology needs “poetry and the distance” - an AI that can write code is common, but one that can empathize with Qu Yuan is rare. DeepSeek breaking through the circle in technology needs “poetry and the distance” Finally, an appeal to all developers: If you happen to encounter a confused newcomer asking, ‘What is DS?’ Please kindly reply:——For big data, use Dolphin; for AI, use Deep Sea Fish,Both are DS,But it is recommended to check the documentation first,To avoid awkward conversations in meetings. If you happen to encounter a confused newcomer asking, ‘What is DS?’ Please kindly reply:——For big data, use Dolphin; for AI, use Deep Sea Fish,Both are DS,But it is recommended to check the documentation first,To avoid awkward conversations in meetings.

Tech Circles Can't Decide What 'DS' Stands For

Table of Links Acknowledgements 1 Introduction to thesis 1.1 History and Evidence 1.2 Facts on dark matter 1.3 Candidates to dark matter 1.4 Dark matter detection 1.5 Outline of the thesis 2 Dark matter through ALP portal and 2.1 Introduction 2.2 Model 2.3 Existing constraints on ALP parameter space 2.4 Dark matter analysis 2.5 Summary 3 A two component dark matter model in a generic 𝑈(1)𝑋 extension of SM and 3.1 Introduction 3.2 Model 3.3 Theoretical and experimental constraints 3.4 Phenomenology of dark matter 3.5 Relic density dependence on 𝑈(1)𝑋 charge 𝑥𝐻 3.6 Summary 4 A pseudo-scalar dark matter case in 𝑈(1)𝑋 extension of SM and 4.1 Introduction 4.2 Model 4.3 Theoretical and experimental constraints 4.4 Dark Matter analysis 4.5 Summary 5 Summary Appendices A Standard model B Friedmann equations C Type I seasaw mechanism D Feynman diagrams in two-component DM model Bibliography 1.3 Candidates to dark matter In this section, we briefly mention some of the popular DM candidates. Looking into the Standard Model Thermal dark matter These are DM candidates, which were produced thermally in the early universe when it was in the plasma state. One can do such a study and calculate the DM relic density using the Boltzmann equation. A popular mechanism following thermal DM is the freeze-out mechanism [33]. It assumes that DM is in thermal equilibrium with the SM bath in the very early stages of the universe, but as the universe expands and the interaction rate becomes ineffective against the expansion rate, DM number density or relic density freezes out. It is found that if DM is in the GeV - TeV mass range and couples weakly to SM, it can easily satisfy the correct relic density. This is called the WIMP miracle, and such particles are named weakly interacting massive particles (WIMPs). A brief on the freeze-out mechanism is described here [32, 33], Strongly interacting massive particles (SIMPs) is another interesting DM candidate that lies in the MeV mass range and interacts strongly with both particles [56, 57]. These thermal DM candidates are being searched in several experiments. Non-thermal dark matter These are the candidates that are not in thermal equilibrium with SM in the early universe. Many mechanisms can produce a non-thermal DM, e.g. Freeze-in [58], exponential production [59], misalignment mechanism [60], gravitational production, etc. Freeze-in is a popular mechanism to produce DM non-thermally in the early universe. It starts with a negligible abundance of DM in the early universe, but it grows and freezes in via a tiny coupling with the bath particles from the hidden sector (dark sector). DM mass or coupling can be tuned to have the correct relic. Such DM candidates are called feebly interacting massive particles (FIMPs). A FIMP candidate is hard to detect in the lab due to its tiny coupling with bath particles [58]. In particular, MACHOs are astrophysical objects like isolated planets, brown dwarfs (failed stars), neutron stars, black holes, etc. These objects have been ruled out by a survey done by the MACHO collaboration and the EROS-2 group using the microlensing technique [64]. This paper is available on arxiv under CC BY 4.0 DEED license. Author:
(1) Shivam Gola, The Institute of Mathematical Sciences, Chennai. Table of Links Acknowledgements Acknowledgements 1 Introduction to thesis 1 Introduction to thesis 1.1 History and Evidence 1.1 History and Evidence 1.2 Facts on dark matter 1.2 Facts on dark matter 1.3 Candidates to dark matter 1.3 Candidates to dark matter 1.4 Dark matter detection 1.4 Dark matter detection 1.5 Outline of the thesis 1.5 Outline of the thesis 2 Dark matter through ALP portal and 2.1 Introduction 2 Dark matter through ALP portal and 2.1 Introduction 2.2 Model 2.2 Model 2.3 Existing constraints on ALP parameter space 2.3 Existing constraints on ALP parameter space 2.4 Dark matter analysis 2.4 Dark matter analysis 2.5 Summary 2.5 Summary 3 A two component dark matter model in a generic 𝑈(1)𝑋 extension of SM and 3.1 Introduction 3 A two component dark matter model in a generic 𝑈(1)𝑋 extension of SM and 3.1 Introduction 3.2 Model 3.2 Model 3.3 Theoretical and experimental constraints 3.3 Theoretical and experimental constraints 3.4 Phenomenology of dark matter 3.4 Phenomenology of dark matter 3.5 Relic density dependence on 𝑈(1)𝑋 charge 𝑥𝐻 3.5 Relic density dependence on 𝑈(1)𝑋 charge 𝑥𝐻 3.6 Summary 3.6 Summary 4 A pseudo-scalar dark matter case in 𝑈(1)𝑋 extension of SM and 4.1 Introduction 4 A pseudo-scalar dark matter case in 𝑈(1)𝑋 extension of SM and 4.1 Introduction 4.2 Model 4.2 Model 4.3 Theoretical and experimental constraints 4.3 Theoretical and experimental constraints 4.4 Dark Matter analysis 4.4 Dark Matter analysis 4.5 Summary 4.5 Summary 5 Summary 5 Summary Appendices Appendices A Standard model A Standard model B Friedmann equations B Friedmann equations C Type I seasaw mechanism C Type I seasaw mechanism D Feynman diagrams in two-component DM model D Feynman diagrams in two-component DM model Bibliography Bibliography 1.3 Candidates to dark matter In this section, we briefly mention some of the popular DM candidates. Looking into the Standard Model Looking into the Standard Model Thermal dark matter Thermal dark matter These are DM candidates, which were produced thermally in the early universe when it was in the plasma state. One can do such a study and calculate the DM relic density using the Boltzmann equation. A popular mechanism following thermal DM is the freeze-out mechanism [33]. It assumes that DM is in thermal equilibrium with the SM bath in the very early stages of the universe, but as the universe expands and the interaction rate becomes ineffective against the expansion rate, DM number density or relic density freezes out. It is found that if DM is in the GeV - TeV mass range and couples weakly to SM, it can easily satisfy the correct relic density. This is called the WIMP miracle, and such particles are named weakly interacting massive particles (WIMPs). A brief on the freeze-out mechanism is described here [32, 33], Strongly interacting massive particles (SIMPs) is another interesting DM candidate that lies in the MeV mass range and interacts strongly with both particles [56, 57]. These thermal DM candidates are being searched in several experiments. Non-thermal dark matter Non-thermal dark matter These are the candidates that are not in thermal equilibrium with SM in the early universe. Many mechanisms can produce a non-thermal DM, e.g. Freeze-in [58], exponential production [59], misalignment mechanism [60], gravitational production, etc. Freeze-in is a popular mechanism to produce DM non-thermally in the early universe. It starts with a negligible abundance of DM in the early universe, but it grows and freezes in via a tiny coupling with the bath particles from the hidden sector (dark sector). DM mass or coupling can be tuned to have the correct relic. Such DM candidates are called feebly interacting massive particles (FIMPs). A FIMP candidate is hard to detect in the lab due to its tiny coupling with bath particles [58]. In particular, MACHOs are astrophysical objects like isolated planets, brown dwarfs (failed stars), neutron stars, black holes, etc. These objects have been ruled out by a survey done by the MACHO collaboration and the EROS-2 group using the microlensing technique [64]. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv Author: (1) Shivam Gola, The Institute of Mathematical Sciences, Chennai. Author: Author: (1) Shivam Gola, The Institute of Mathematical Sciences, Chennai.

Some of the Most Popular Dark Matter Candidates: Looking Into the Standard Model 

Coin3D Introduces a New Standard for Interactive 3D Asset Generation

Authors:
(1) Jongmin Lee, Department of Mathematical Science, Seoul National University;
(2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Abstract and 1 Introduction 1.1 Notations and preliminaries 1.2 Prior works 2 Anchored Value Iteration 2.1 Accelerated rate for Bellman consistency operator 2.2 Accelerated rate for Bellman optimality opera 3 Convergence when y=1 4 Complexity lower bound 5 Approximate Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 7 Conclusion, Acknowledgments and Disclosure of Funding and References A Preliminaries B Omitted proofs in Section 2 C Omitted proofs in Section 3 D Omitted proofs in Section 4 E Omitted proofs in Section 5 F Omitted proofs in Section 6 G Broader Impacts H Limitations 4 Complexity lower bound We now present a complexity lower bound establishing optimality of Anc-VI. The so-called “span condition” of Theorem 5 is arguably very natural and is satisfied by standard VI and Anc-VI. The span condition is commonly used in the construction of complexity lower bounds on first-order optimization methods [13, 14, 23, 25, 59, 65] and has been used in the prior state-ofthe-art lower bound for standard VI [37, Theorem 3]. However, designing an algorithm that breaks the lower bound of Theorem 5 by violating the span condition remains a possibility. In optimization theory, there is precedence of lower bounds being broken by violating seemingly natural and minute conditions [35, 40, 98]. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Jongmin Lee, Department of Mathematical Science, Seoul National University; (2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Authors: Authors: (1) Jongmin Lee, Department of Mathematical Science, Seoul National University; (2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Abstract and 1 Introduction Abstract and 1 Introduction 1.1 Notations and preliminaries 1.1 Notations and preliminaries 1.2 Prior works 1.2 Prior works 2 Anchored Value Iteration 2 Anchored Value Iteration 2.1 Accelerated rate for Bellman consistency operator 2.1 Accelerated rate for Bellman consistency operator 2.2 Accelerated rate for Bellman optimality opera 2.2 Accelerated rate for Bellman optimality opera 3 Convergence when y=1 3 Convergence when y=1 4 Complexity lower bound 4 Complexity lower bound 5 Approximate Anchored Value Iteration 5 Approximate Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 7 Conclusion, Acknowledgments and Disclosure of Funding and References 7 Conclusion, Acknowledgments and Disclosure of Funding and References A Preliminaries A Preliminaries B Omitted proofs in Section 2 B Omitted proofs in Section 2 C Omitted proofs in Section 3 C Omitted proofs in Section 3 D Omitted proofs in Section 4 D Omitted proofs in Section 4 E Omitted proofs in Section 5 E Omitted proofs in Section 5 F Omitted proofs in Section 6 F Omitted proofs in Section 6 G Broader Impacts G Broader Impacts H Limitations H Limitations 4 Complexity lower bound We now present a complexity lower bound establishing optimality of Anc-VI. The so-called “span condition” of Theorem 5 is arguably very natural and is satisfied by standard VI and Anc-VI. The span condition is commonly used in the construction of complexity lower bounds on first-order optimization methods [13, 14, 23, 25, 59, 65] and has been used in the prior state-ofthe-art lower bound for standard VI [37, Theorem 3]. However, designing an algorithm that breaks the lower bound of Theorem 5 by violating the span condition remains a possibility. In optimization theory, there is precedence of lower bounds being broken by violating seemingly natural and minute conditions [35, 40, 98]. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Anc-VI Sets a New Standard for Reinforcement Learning Optimization

Authors:
(1) Jongmin Lee, Department of Mathematical Science, Seoul National University;
(2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Abstract and 1 Introduction 1.1 Notations and preliminaries 1.2 Prior works 2 Anchored Value Iteration 2.1 Accelerated rate for Bellman consistency operator 2.2 Accelerated rate for Bellman optimality opera 3 Convergence when y=1 4 Complexity lower bound 5 Approximate Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 7 Conclusion, Acknowledgments and Disclosure of Funding and References A Preliminaries B Omitted proofs in Section 2 C Omitted proofs in Section 3 D Omitted proofs in Section 4 E Omitted proofs in Section 5 F Omitted proofs in Section 6 G Broader Impacts H Limitations 2.1 Accelerated rate for Bellman consistency operator First, for general state-action spaces, we present the accelerated convergence rate of Anc-VI for the Bellman consistency operator. This paper is available on arxiv under CC BY 4.0 DEED license. [1] Arguably, T π is affine, not linear, but we follow the convention of [69] say T π is linear. Authors: (1) Jongmin Lee, Department of Mathematical Science, Seoul National University; (2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Authors: Authors: (1) Jongmin Lee, Department of Mathematical Science, Seoul National University; (2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Abstract and 1 Introduction Abstract and 1 Introduction 1.1 Notations and preliminaries 1.1 Notations and preliminaries 1.2 Prior works 1.2 Prior works 2 Anchored Value Iteration 2 Anchored Value Iteration 2.1 Accelerated rate for Bellman consistency operator 2.1 Accelerated rate for Bellman consistency operator 2.2 Accelerated rate for Bellman optimality opera 2.2 Accelerated rate for Bellman optimality opera 3 Convergence when y=1 3 Convergence when y=1 4 Complexity lower bound 4 Complexity lower bound 5 Approximate Anchored Value Iteration 5 Approximate Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 7 Conclusion, Acknowledgments and Disclosure of Funding and References 7 Conclusion, Acknowledgments and Disclosure of Funding and References A Preliminaries A Preliminaries B Omitted proofs in Section 2 B Omitted proofs in Section 2 C Omitted proofs in Section 3 C Omitted proofs in Section 3 D Omitted proofs in Section 4 D Omitted proofs in Section 4 E Omitted proofs in Section 5 E Omitted proofs in Section 5 F Omitted proofs in Section 6 F Omitted proofs in Section 6 G Broader Impacts G Broader Impacts H Limitations H Limitations 2.1 Accelerated rate for Bellman consistency operator First, for general state-action spaces, we present the accelerated convergence rate of Anc-VI for the Bellman consistency operator. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv [1] Arguably, T π is affine, not linear, but we follow the convention of [69] say T π is linear.

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