Warp

warp

Introducing Warp Today, I’m proud to officially introduce Warp, a from-first-principles reinvention of the terminal to make it work better for developers and teams. As of today, Warp is in public beta and any Mac user can download and use it for free. We are also excited to announce that we’ve raised some funds to grow Warp ($23M), both from wonderful firms ( , , ) and world-class operators like Dylan Field (who led our Series A), Elad Gil, Jeff Weiner, and Marc Benioff. GV Neo BoxGroup Why Reinvent the Terminal? Walk by any developer’s desk and you are likely to see two apps open: their code editor and their terminal (sometimes the code editor is the terminal!). Both are crucial to developer productivity.  The code editor is where developers write code; the terminal is where they do pretty much everything else, from building code to running and deploying it, interacting with source control, configuring their cloud systems, and more. And yet only one of these two apps – the code editor – has experienced meaningful product improvement over the past 40 years. Compared to using VS Code, using the terminal is like stepping back in time to the 1970s. Only , while 100% use the terminal. So why is the terminal experience still so lackluster? 70% of developers use VSCode Our Product Vision At Warp, our product vision is to bring the terminal into the present in order to help developers build the future. ‍We are doing this by fixing the two biggest pain points that exist in today’s terminals: Terminals are hard to use They don’t work for teams These are pain points that I’ve personally experienced again and again in my twenty years as an engineer, and I’m sure readers feel the same. ‍To get good at using a terminal before Warp, users had to do all sorts of complex configuration, master arcane key shortcuts, and memorize abstruse commands. Even then, seemingly simple things like copying a command’s output or positioning the mouse cursor were still difficult. ‍Warp makes input and output easy, and removes the need for most configuration. Input works like a modern text-editor, and output works like a data notebook. Moreover, Warp makes command-entry fast and fun by suggesting commands for commonly used tools and providing built-in workflows that save developers time. ‍In short, Warp makes the terminal work for the developer, rather than the other way around. Secondly, up until Warp, terminals have been inherently single-user, local applications.  But as I learned when I was leading engineering on Google Docs – and as Dylan showed with Figma – every productivity application is more powerful when it’s collaborative.  This is true 100% of the time – from Figma to GDocs to Notion to Front – and I’m confident that the terminal is no exception. Terminal “collaboration” means not just GDocs-style real-time collaboration, but asynchronous collaboration through sharing commands, settings, and history. It means increased knowledge-sharing through wikis and READMEs that run directly in the terminal. It means making the terminal safer and more secure via integrated password-management and audit logging. It means making the terminal a more extensible and customizable platform, with a nice modern ecosystem. Finally, all of this needs to be built with speed and compatibility in mind – Warp is made in Rust with GPU-accelerated graphics, and works with existing shells like zsh, fish and bash. Go Try Warp! Nine months ago we launched Warp in private beta behind a waitlist.  Since then, thousands of developers have made Warp their daily driver, given us feedback, and allowed us to greatly improve the product. Today, we are removing our waitlist and launching our public beta.  We are calling it a “beta” because we know there are still some issues to smooth out, but we are confident that even today the experience is meaningfully better than in other terminals. If you use a Mac, please give it a shot and let us know how it goes. Otherwise, sign up to be notified when Warp is ready for your platform. here Welcome to the future of the terminal. Also Published here

Warp: The Terminal For the Modern Developers

Customers bring MinIO into their environments to gain high-performance S3-compatible object storage that runs on any physical or virtual hardware and Kubernetes. Our demonstrate that MinIO is the fastest object storage available, but it can only run as fast as the hardware and network you give it.  Performance is a big focus for our team, so we do everything we can to help administrators get the most out of MinIO. In order to verify that underlying infrastructure can support MinIO optimally, we provide two methods to assess performance and identify potential bottlenecks: WARP and Speedtest. published benchmarks Modern applications such as AI/ML, advanced analytics and databases require high-performance object storage. MinIO’s combination of scalability and high-performance puts every workload, no matter how demanding, within reach. When performance is critical, you need to know that you’re achieving the best performance possible. Results from WARP and Speedtest can be used to track performance over time and proactively pinpoint potential problems before they grow into serious issues. WARP is an open-source full-featured S3 performance assessment software built to conduct tests between WARP clients and object storage hosts. WARP measures GET and PUT performance from multiple clients against a MinIO cluster. WARP has many options, configured by command line or environmental variables, allowing you to create tests that align with your workloads. Remember - it’s absolutely critical to assess performance in a meaningful way and test using data and a workload that represents the real world conditions in which your object storage operates. In contrast, Speedtest is an easy-to-use automated performance test that provides a streamlined experience and concise results. We in November to provide MinIO administrators with the ability to run a distributed performance assessment of their MinIO clusters with a single command. Speedtest runs PUTS, then GETS, incrementally increasing load to pinpoint maximum aggregate throughput. Tests can take anywhere from a few seconds to several minutes to execute depending on your MinIO cluster. introduced Speedtest There are some important differences between WARP and Speedtest. WARP is a complete tool that tests performance of your MinIO cluster via operations conducted by WARP clients. Client machines are conducting PUTS and GETS of objects across the network to your distributed MinIO cluster. This makes WARP an excellent mechanism for testing anticipated client-server performance. In contrast, Speedtest runs on MinIO instances to conduct PUTS and GETS of objects to other MinIO instances in the same cluster. As such, Speedtest tells you what the server side of the performance equation is capable of. WARP contains just about every test (GET, PUT, DELETE, LIST, STAT, RETENTION) you might want to run against object storage, and test runs can include a custom mix of object sizes to match your workloads. Speedtest runs through set test parameters to pinpoint maximum throughput quickly. While WARP requires additional software, Speedtest is included with MinIO and can be run from the mc interface or MinIO Console. To aid in troubleshooting, customers can share Speedtest results with MinIO engineers with a single click. WARP: A Complete Object Storage Benchmarking Tool First, let’s take a look at WARP.  WARP is a tool that allows you to thoroughly benchmark MinIO, or any S3-compatible object storage, performance under a variety of conditions.  By default, WARP will perform a mixed test of read and write over all disks utilized by MinIO running in distributed mode. For this demo. we’re going to be running WARP to test MinIO running on AWS in distributed mode. We’ve been doing this pretty often lately, so we can advise potential and current customers of the highest-performing configurations we have found by testing them. WARP is located in a , where you will also find detailed documentation. GitHub repository We’re going to start by deploying MinIO in . You can and install it in your environment by yourself, or you can follow this . distributed mode download MinIO tutorial to install MinIO on AWS EC2 Either way, we are going to start with a distributed MinIO deployment: Once MinIO is up and running you will be able to measure performance with WARP, so let’s get started. Step 0: Create 4 instances (also known as nodes) with Distributed MinIO. For all Amazon UI or AWS CLI, please follow steps from the to deploy instances, but do not configure additional storage. The instances running WARP must be powerful enough to quickly generate objects and measure PUT and GET operations, but do not require the storage volume needed by a MinIO node. previous blog post Step 2: Add hosts in /etc/hosts file at WARP clients. Get the IP Addresses of the MinIO instances Get the IP Addresses of the WARP clients Add those address in the /etc/hosts file: 172.31.23.237 host1
172.31.26.78  host2
172.31.26.90  host3
172.31.19.110 host4
172.31.27.18  warp1
172.31.23.81  warp2
172.31.19.28  warp3
172.31.19.7   warp4 This simplifies launching WARP from the command line and makes it easier to locate each WARP client and MinIO host. Notice that we recommend listing and working with hosts in consecutive order. Step 3: Install WARP on the clients and run it. [root@ip-172-31-19-7 ec2-user]# wget https://github.com/minio/warp/releases/download/v0.5.5/warp_0.5.5_Linux_arm64.tar.gz
2022-02-08 20:06:04 (66.3 MB/s) - 'warp_0.5.5_Linux_arm64.tar.gz' saved [3943887/3943887]

[root@ip-172-31-19-7 ec2-user]# tar -xzvf warp_0.5.5_Linux_arm64.tar.gz
LICENSE
README.md
warp_logo.png
warp
[root@ip-172-31-19-7 ec2-user]# ./warp client
warp: Listening on :7761 Notice that each WARP client is listening on port 7761 Step 4: Run WARP and launch a mixed benchmark. [root@ip-172-31-27-18 ec2-user]# WARP_ACCESS_KEY=minioadmin WARP_SECRET_KEY=minioadmin ./warp mixed --warp-client warp{1...4}:7761 --host host{1...4}:9000 --duration 120s --obj.size 64M --concurrent 64
warp: Benchmark data written to "warp-remote-2022-02-08[201339]-qymu.csv.zst"                                                                                                                                                                        
Mixed operations.
Operation: DELETE, 10%, Concurrency: 256, Ran 1m54s.
 * Throughput: 39.90 obj/s

Operation: GET, 45%, Concurrency: 256, Ran 1m54s.
 * Throughput: 10903.28 MiB/s, 178.64 obj/s

Operation: PUT, 15%, Concurrency: 256, Ran 1m54s.
 * Throughput: 3628.27 MiB/s, 59.45 obj/s

Operation: STAT, 30%, Concurrency: 256, Ran 1m54s.
 * Throughput: 119.98 obj/s

Cluster Total: 14501.38 MiB/s, 397.44 obj/s over 1m55s.
warp: Cleanup done.                                                                                                                                                                                                                                  
[root@ip-172-31-27-18 ec2-user]# You’ve completed a basic mixed-mode performance test using WARP. While we used a mixed-mode test to demonstrate WARP, you will typically obtain better results that are more aligned to real-world usage) by breaking out individual operations (GET, PUT, LIST) into their own test runs instead of running a mixed-mode test. We encourage you to refer to the to learn about executing more test scenarios. For example, you can enable TLS and server-side encryption to measure their impact in your environment. You can stress infrastructure more by increasing the number of concurrent tests. You can use a random mix of object sizes, or specify an object size that matches your current environment and workload. You can configure tests to run for a defined period of time or to auto-terminate as we did above. documentation WARP results are shown on-screen and saved to a local CSV file compressed using zstandard. Speedtest for a Quick and Easy Performance Assessment In the event that you don’t want the full flexibility of WARP, we’ve built a quick and easy way to measure MinIO performance using Speedtest. Speedtest is most commonly run in autotune mode, incrementally increasing load to pinpoint maximum aggregate throughput. You can use mc to run Speedtest: $ mc support perf object <alias> [root@ip-172-31-77-115 ec2-user]# ./mc support perf object myminio

   	THROUGHPUT	IOPS      
PUT	2.4 GiB/s 	38 objs/s	
GET	4.6 GiB/s 	73 objs/s	

Speedtest: MinIO 2022-02-01T18:00:14Z, 4 servers, 16 drives, 64 MiB objects, 72 threads Or, you can run Speedtest from MinIO Console, the browser-based GUI for configuring, managing and reporting on MinIO clusters. Simply navigate to the Support menu and click Performance, then click on the start button. The performance test will run. When it is complete, aggregate GET and PUT performance as well as performance of individual nodes is displayed. For more details and examples for Speedtest, please see this . tutorial Warp Speed Ahead! Get started by today. Join our and exchange ideas with other MinIO users. If you have any specific questions about using WARP, please reach out to us on our Slack channel (Matt Sarrel and Cesar Celis) or send us an email at hello@minio.io. downloading MinIO Slack community Also published . here

Benchmarking MinIO with WARP and Speedtest

WARP এবং Speedtest সহ বেঞ্চমার্কিং MinIO

Benchmarking von MinIO mit WARP und Speedtest

Evaluación comparativa de MinIO con WARP y Speedtest

Analyse comparative de MinIO avec WARP et Speedtest

WARP और स्पीडटेस्ट के साथ मिनियो को बेंचमार्क करना

WARP と Speedtest を使用した MinIO のベンチマーク

WARP 및 속도 테스트를 사용한 MinIO 벤치마킹

Comparando MinIO com WARP e Speedtest

Бенчмаркинг MinIO с помощью WARP и Speedtest

MinIO'yu WARP ve Speedtest ile kıyaslama

Đo điểm chuẩn MinIO với WARP và Speedtest

使用 WARP 和 Speedtest 对 MinIO 进行基准测试

Regulatory outfits entered 2023 with a united resolve: to heighten their efforts in the crypto space. If there was anything that 2022 did, it exposed the lapses that lurked in the crypto industry. Now, several months into a new year, the bruises from last year are still fresh, raw, and driving regulatory outfits into revisiting existing laws and policies. The 2022 crypto crash started with the fall of the Terra ecosystem. In the months that followed, other platforms barreled right into the wreckage – a wave of contagion that drew the attention of regulators worldwide. And ultimately, the last icing that would topple the cake came in November when FTX, a top exchange led by crypto golden child Sam Bankman-Fried, fell apart. As Iuliia Goncharova, Growth Product Manager at Choise.com, emphasizes, this is all happening against the backdrop of the crypto winter, where new audiences are not entering the crypto space and existing ones are becoming less active. For crypto companies already experiencing losses and fund outflows, tightening regulations feel like a final blow. Additionally, it is important to note that advertising platforms like Facebook and Google are not making any concessions for the crypto industry, and due to strict regulations, attracting new users has become difficult and expensive. All of these events set up a legally precarious 2023. Well, it’s roughly 6 months into the year, and here’s what regulators across the globe have been up to all this time. Recent Developments in Crypto Regulation The SEC and Its Hunting Expeditions To begin with, the US Securities and Exchange Commission (SEC) launched what I’ll describe as a major crackdown on the space. While Binance and Coinbase have been in the spotlight of late, its hunt began right on the cusp of the new year. In January, the Commission was rather interested in Genesis and exchange firm Gemini, charging both companies with selling unregistered securities, and leading Genesis to file for bankruptcy protection. The next month saw the regulator order another exchange – Kraken – to halt its U.S. crypto staking business and pay $30 million in penalties. By March, the SEC’s warpath had hit Coinbase’s doorsteps as the firm received a Wells notice stating that the SEC had identified potential violations of the US securities laws. The SEC is not the only entity seemingly out to get crypto platforms. In March, the Commodity Futures Trading Commission (CFTC) legal action against Binance. The CFTC accused Binance of enabling U.S. customers to trade unregistered securities, adding to the regulatory scrutiny faced by the world’s largest exchange. took According to a May statement from Eun Young Choi, director of the Department of Justice’s National Cryptocurrency Enforcement Team, the DOJ is also to join the action. The department reportedly has plans to tackle crypto companies involved in criminal activities or facilitating money laundering. set Consequences: Binance Dips Out Of Canada, Might Focus On The UK All of the fire directed towards exchanges, especially from the SEC, may be pushing crypto platforms out of the states. Binance’s chief strategy officer explained just last month that it’s a “very difficult time” to function in crypto space. So, the firm is reportedly working to be regulated in the UK. Notably, Binance did withdraw its services from the USA’s next-door neighbor, Canada.  This was after the Canadian government unveiled new guidelines requiring cryptocurrency trading platforms to obtain regulatory approval before allowing customers to buy or deposit stablecoins. To comply with these regulations, Binance needed to undergo a due diligence process conducted by the Canadian Securities Administrators (CSA) to receive approval for facilitating stablecoin transactions. However, as by Bloomberg, Binance Canada began the registration process for the review in March but ultimately decided to withdraw from the Canadian market. reported North America has not been Binance’s only run-in with the authorities this year. Back in April, the firm reportedly got in trouble with the authorities in Brazil. They were being investigated by the Federal Prosecutor's Office and Federal Police for supposedly still offering crypto derivatives to their clients, even though they were ordered to stop in 2020. The Prosecutor’s office claimed Binance asked Brazilian users to change their language settings to access Binance Futures, and the Portuguese content didn't warn them about any restrictions. Like Binance, Coinbase is also currently facing a suit from the SEC. That’s right, the Commission claims the firm is putting customers at risk as an unregistered broker.  Before this though, on May 2, Coinbase launched Coinbase International Exchange, a new crypto derivatives platform based in Bermuda. The Safer Crypto Industry: Introducing MiCA Should any of the aforementioned firms, Binance for instance, actually focus mainly on the UK, would the regulatory landscape be any more accommodating? It is worth considering that in April this year, European lawmakers approved the long-awaited Markets in Crypto Act, or MiCA for short. The vote took place in April, and the results showed that the EU Parliament voted 517 in favor and 38 against passing the new legislation. MiCA aims to protect customers in the crypto space as under its rules; providers will be held responsible if they lose investors' assets. Although in its early days, MiCA might be one of the few positives this year for the legislative future of crypto. For one, MiCA offers some legal certainty and integrity – features that have been missing amongst many crypto outfits in past years. The EU’s new bill may be just what the market needs after last year’s events thoroughly shook investor trust in the space. Also, in addition to the MiCA, the Parliament passed another law focused on reducing anonymity when transferring cryptocurrencies like Bitcoin and stablecoins. This law, as the Resolution on the Transfer of Funds, received overwhelming support with 529 votes in favor and only 29 against. known However, while we can’t deny that these developments are commendable, there’s the persisting question of how a bill that involves government supervision affects an industry that is meant to exist outside of their control. Other Regulatory Changes and What to Expect in the Future Across other nations, crypto regulation is likewise advancing. Brazil's central bank is the Real Digital project, emphasizing the adoption of new technology while maintaining current regulations. Germany has for providing clarity through its regulatory environment, with goals set by BaFin to regulate DeFi and protect consumers. India, despite previously banning crypto, overturned the ban and now maintains a cautious attitude, while South Korea is working on the Digital Asset Basic Act to combat crypto crime and provide clarity for legitimate players. leading received praise The general crypto crackdown is concerning for the US and investors in other countries, plus it threatens the decentralized nature of cryptocurrencies. However, clear regulations are needed to protect investors, despite potential limitations on crypto usage and innovation. At the same time, regulation can also attract new users, who would feel more secure with clear rules in place, especially after last year. Regardless, the crypto market continues to show strong growth and positive price movements, indicating ongoing investor interest. As we continue through 2023, the crypto regulatory landscape will likely witness more twists and turns.

Recent Trends in Crypto Regulations: SEC’s Warpath, MiCA, Developing Markets

The Wonderful Visit by H. G. Wells, is part of the HackerNoon Books Series. You can jump to any chapter in this book here . The Warp and the Woof of Things The Warp and the Woof of Things. XXXIII. At the dinner table the Angel told the Vicar the more striking of his day's adventures. "The strange thing," said the Angel, "is the readiness of you Human Beings—the zest, with which you inflict pain. Those boys pelting me this morning——" "Seemed to enjoy it," said the Vicar. "I know." "Yet they don't like pain," said the Angel. "No," said the Vicar; "they don't like it." "Then," said the Angel, "I saw some beautiful plants rising with a spike of leaves, two this way and two that, and when I caressed one it caused the most uncomfortable——" "Stinging nettle!" said the Vicar. "At any rate a new sort of pain. And another plant with a head like a coronet, and richly decorated leaves, spiked and jagged——" "A thistle, possibly." "And in your garden, the beautiful, sweet-smelling plant——" "The sweet briar," said the Vicar. "I remember." "And that pink flower that sprang out of the box——" "Out of the box?" said the Vicar. "Last night," said the Angel, "that went climbing up the curtains—— Flame!" "Oh!—the matches and the candles! Yes," said the Vicar. "Then the animals. A dog to-day behaved most disagreeably——. And these boys, and the way in which people speak——. Everyone seems anxious—willing at any rate—to give this Pain. Every one seems busy giving pain——" "Or avoiding it," said the Vicar, pushing his dinner away before him. "Yes—of course. It's fighting everywhere. The whole living world is a battle-field—the whole world. We are driven by Pain. Here. How it lies on the surface! This Angel sees it in a day!" "But why does everyone—everything—want to give pain?" asked the Angel. "It is not so in the Angelic Land?" said the Vicar. "No," said the Angel. "Why is it so here?" The Vicar wiped his lips with his napkin slowly. "It is so," he said. "Pain," said he still more slowly, "is the warp and the woof of this life. Do you know," he said, after a pause, "it is almost impossible for me to imagine ... a world without pain.... And yet, as you played this morning—— "But this world is different. It is the very reverse of an Angelic world. Indeed, a number of people—excellent religious people—have been so impressed by the universality of pain that they think, after death, things will be even worse for a great many of us. It seems to me an excessive view. But it's a deep question. Almost beyond one's power of discussion——" And incontinently the Vicar plumped into an impromptu dissertation upon "Necessity," how things were so because they were so, how one had to do this and that. "Even our food," said the Vicar. "What?" said the Angel. "Is not obtained without inflicting Pain," said the Vicar. The Angel's face went so white that the Vicar checked himself suddenly. Or he was just on the very verge of a concise explanation of the antecedents of a leg of lamb. There was a pause. "By-the-bye," said the Angel, suddenly. "Have you been pithed? Like the common people." About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. H. G. Wells (2010). The Wonderful Visit. Urbana, Illinois: Project Gutenberg. Retrieved October 2022, from https://www.gutenberg.org/files/33913/33913-h/33913-h.htm This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org , located at https://www.gutenberg.org/policy/license.html .

The Warp and the Woof of Things

Within the Monster Hunter World (MHW) universe, there are many different items to collect that help you progress through the game, whether that be consumables perfect for avoiding death in a monster fight or crafting materials to improve and level up your armour and weapons. One of these materials is warped bone. The MHW warped bone is a rare material needed to level up your various gear and armour pieces, crucial for completing the game and fighting Monster Hunter World’s final bosses. What is the MHW Warped Bone? The warped bone is a material used to help improve various armour and weapons pieces. It is a challenging item to find with the item only located in one specific area within the game and randomly generated, meaning it is all down to luck as to whether it drops. Thus, the probability of getting a warped bone is low, meaning this item is a frustrating item to find for many players. The item is one of the rarest bone materials you can get in Monster Hunter World. Monster Hunter World Warped Bone location You can find the MHW warped bone in one specific area, . The Rotten Vale can be unlocked around midway through Monster Hunter World's main story and contains many monsters such as Odogaron. the Rotten Vale It is an area filled with monster corpses, a decomposing wasteland that is a graveyard for monsters. To access this area, you need to have completed the main story quest Radobaan Roadblock. After completing this quest, you should have full access to the Rotten Vale. You can access the Rotten Vale through either a quest mission or an expedition, with the latter being the most advised option so that you can have adequate time to find the warped Bone. The Rotten Vale is split into several smaller sections; the warped bone can be found in any one of these areas and is generated randomly. How to find the item in the Rotten Vale The item is located in bone piles throughout these areas. Bone piles are relatively common throughout the Rotten Vale. However, the chances of getting a warped bone from these bone piles are not. It is all down to luck as to whether an MHW warped bone drops. Nevertheless, when you see a bone pile, make sure to harvest its materials and hopefully, you get lucky. Although even rarer, it is possible to get a warped bone from defeating certain monsters and gathering their materials. Slaying Raphinos and Rabobann gives you the chance of acquiring the item. Defeating Raphinos grants you an 8% chance of receiving the bone, while killing a Rabobann gives you a 31% chance of the item dropping but the chances of a drop vary depending on the ranking of the quest. You can also obtain the item through several different Rotten Vale missions as base rewards. Such assignments include low-rank missions such as A Rotten Thing To Do to master rank missions like The Lord of the Underworld Beckons. The probability of the item dropping varies depending on the mission's rank, with a 12-16% chance of a Monster Hunter World warped bone dropping. You can find a list of quests that reward the item here. How can MHW Warped Bones be used? The Monster Hunter World warped bone is primarily used to upgrade your equipment and weapons. In terms of weapons, the warped bone is needed to forge most Dragon Bone weapon set's low-rank weapons. The item can also be used to upgrade several high-level armaments, such as upgrading the Pulsa Shotel 11 into the Pulsa Shotel 111 long sword. Likewise, the Warped bone can make high-level armour, such as the Odogaron Alpha set and the bone alpha set. Finally, the warped bone can create a range of charms needed to give your character a buff during intense boss battles. Such charms include the master's charm and the blaze charm. A complete list of charms, armour pieces and weapons that require the MHW warped bone can be found here. Final Thoughts Conclusively, this is one of the rarest items in the game. If you are lucky enough to get your hands on some, they can be invaluable in constructing the best charms, weapons and armour in MHW. Also, check out: What are the Best Video Game Controllers of all Time? Fallout 4 Halo Armor Mods: From the ODSTs to NOBLE Team 6 Games That Everyone Should Play at Least Onc

How to Find the Monster Hunter World (MHW) Warped Bone and How to Use It

Who needs AWS or hosting charges? With , you can get a server up and running in your home in minutes. All without DNS or DMZ configuration or bulky frameworks. Cloudflare Warp Just run your web server of choice on your machine, and Warp handles serving it up through Cloudflare. Warp is a new feature which (at time of this writing) is currently in beta. This frees us from having to get a host. In the past, just running on your home required opening ports on your firewall. An easy thing to screw up. network Also, by now (2018) everyone should be running ONLY HTTPS. Configuring HTTPS has gotten easier over the past few years, but the great thing with Warp, you just run your site as an HTTP server and Cloudflare handles the rest. Let’s get started. First, we’ll use , which has binaries for Linux, Win, and Mac. httpsd _httpsd - Instant https server_github.com digplan/httpsd is an instant-on web server, whose output is generated by a provided shell script. httpsd Make the shell script, which will be called index.sh here: cat index.html and our index.html <!DOCTYPE html><h1>Hello World</h1> and start it up! ./httpsd ./index.sh --insecure --port=8080 Using the *— insecure* flag will start an http instead of an https server, which is ok, because Cloudflare is going to handle the https in a very easy way. You can use any web server. For instance, there is Simple HTTP Server for Python: http://www.pythonforbeginners.com/modules-in-python/how-to-use-simplehttpserver/ is just a simple binary, that tunnels to servers, and serves up your site. Cloudflare Warp , Cloudflare _Locking down an application's origin to prevent attacks requires numerous complex steps. From using a scrubbing service…_www.cloudflare.com Cloudflare Warp | Cloudflare I’ve changed the name of the binary to just , which makes things even simpler. With our domain name servers hosted with Cloudflare, we just start it up. warp $ ./warp --hostname=www.mydomain.com --url http://localhost:8080 and that’s it, hosting made simple.

Drop Your Hosting Provider With Cloudflare Warp

We’ve talked about why we chose to build Warp in Rust. Since making that decision, one thing that stands out is how productive we are as a team while still reaping the performance benefits of a systems-level language. in the past A big reason for that productivity is the borrow checker. By enforcing its rules at compile-time, Rust’s is able to make guarantees about the memory safety of our app, which lets us focus more of our energy on building the future of the terminal and less on chasing down use-after-free bugs. borrow checker At the same time, the borrow checker can be a source of frustration. Sometimes, you need to do something that breaks the rules but don’t want to throw safety out the window. Fortunately, the Rust standard library provides helpful types to let you do just that: break the rules! Shared Ownership Reference counting (Rc and Arc) Unique Borrows RefCell Locking Types (Mutex and RwLock) Atomics Shared Ownership The first borrow checker rule we’re going to break is single ownership: By default in Rust, every piece of data has a single owner, and when that owner goes out of scope, the data is cleaned up. This is great for ergonomics as you don’t have to worry about manually allocating and freeing memory! However, sometimes you don’t want data to have only a single owner. Maybe you want the data to pass through different parts of your program that will each run for different lengths and there’s no way to know how long in total the data needs to exist. Maybe you’re prototyping and don’t yet want to tackle ownership and lifetimes in a more concrete way. Whatever the reason, you really would like to have multiple owners for some data, so that it lasts as long as all of them combined. Reference Counting to the Rescue! Built into the Rust standard library are two types that provide shared ownership of the underlying data: and (short for ‘Reference counted’ and ‘Atomically reference counted’, respectively). Rc Arc Both of these types give shared ownership of the contained data by tracking the number of references and ensuring the data will last as long as there are any active references. They each implement and cloning increments the reference count while dropping one decrements it. The data is kept alive as long as there are references and only cleaned up once all of the clones have gone out of scope. For example, this snippet uses to share ownership of two pet objects between two owners: Clone Drop: Rc #[derive(Debug)]
struct Pet {
    name: String,
}

impl Pet {
    fn new(name: String) -> Self {
        Self { name }
    }
}

struct Person {
    pets: Vec<Rc<Pet>>,
}

fn main() {
    // Create two pets with shared ownership
    let cat = Rc::new(Pet::new("Tigger".into()));
    let dog = Rc::new(Pet::new("Chase".into()));

    // Create one person who owns both pets
    let brother = Person {
        pets: vec![cat.clone(), dog.clone()],
    };

    // Create another person who _also_ owns both pets
    let sister = Person {
        pets: vec![cat, dog],
    };

    // Even if one person gives up ownership, the other person still has shared ownership,
    // so the pets are kept around (yay!)
    drop(sister);
    println!("Pets: {:?}", brother.pets)
} Both types incur a small amount of runtime overhead to maintain the reference count. The key difference between them is that is thread safe, while isn’t. uses atomic operations to manage the reference count, which gives it a higher runtime cost but makes it safe to share between threads. If you’re only working in a single thread, then is the faster alternative. Arc Rc Arc Rc The last important fact about and is that they only allow you to get immutable references to the underlying data. Since they fundamentally represent shared data, allowing mutable references would violate Rust’s safety guarantees by allowing for data races and use-after-free errors. Rc Arc [2] Unique Borrows “But wait!,” you say, “What if I want to share mutable data between parts of my app?” Luckily, the next borrow checker rule we’re going to break is unique borrows: In order to mutate something, you need to have a unique (also called mutable) reference to the data. The borrow checker enforces that you can only have one mutable reference or any number of immutable references, but never a combination of the two, so you can’t ever mutate data that another part of the program is trying to read at the same time. This restriction works great most of the time, but we’re here to break the rules! Two cases where you might want to mutate data without having a mutable reference are: Caching an otherwise immutable calculation (i.e. memoization) The above shared ownership case with Rc or Arc For bending the compile-time borrowing rules, the compiler provides several helpful types, each with their own sets of drawbacks. All of them let you safely mutate data behind an immutable reference, using different approaches to make sure that your program is still safe. [3] RefCell First up is , which moves the enforcement of unique borrows from compile-time to runtime. Similar to , uses reference counting to track how many borrows are active while the program is running. If you ever try to take a mutable reference and another reference at the same time, will immediately panic! So when using , it’s up to you to make sure that your program doesn’t try to read and write the same data at the same time. RefCell Rc RefCell RefCell RefCell Here's an example of using to cache intermediate results for something that is otherwise immutable: RefCell struct FibonacciCalculator {
    cache: RefCell<HashMap<usize, usize>>,
}

impl FibonacciCalculator {
    /// Calculate the Nth fibonacci number, caching the result to prevent recalculation
    /// Note that this takes `&self`, not `&mut self`!
    fn calculate(&self, n: usize) -> usize {
        // Base case
        if n <= 2 {
            return 1;
        }

        // Check the cache
        if let Some(value) = self.cache.borrow().get(&n) {
            return *value;
        }

        // Calculate and cache the value
        let result = self.calculate(n - 1) + self.calculate(n - 2);

        self.cache.borrow_mut().insert(n, result);

        result
    }
} Also, the reference counting in is not thread safe, so it’s not possible to share data between threads. For mutating shared data between threads, we need to turn to our next tool. RefCell RefCell Locking Types The next two types are and , which both provide ways to access mutable references from an immutable reference in a thread-safe way. They do this by completely blocking the thread until it is safe to access the data. This provides a strong guarantee that the access is safe, but also has a major pitfall: Deadlocks. Deadlocks occur when two threads are blocked waiting for access to data that the other thread is holding. Similar to , it's up to you to make sure the logic of your program doesn't hold onto some data while waiting for access to other data leading to a deadlock. Mutex RwLock RefCell For example, the following snippet uses a Mutex to increment a counter in parallel in two new threads, then reads the final result from the original thread: // Create a shared, mutable counter
let counter = Arc::new(Mutex::new(0));

// Spawn one thread incrementing the counter
let counter1 = counter.clone();
let handle1 = thread::spawn(move || {
    for _ in 0..10 {
        *counter1.lock().unwrap() += 1;
    }
});

// Spawn another thread incrementing the counter
let counter2 = counter.clone();
let handle2 = thread::spawn(move || {
    for _ in 0..10 {
        *counter2.lock().unwrap() += 1;
    }
});

// Wait for the threads to complete
handle1.join().unwrap();
handle2.join().unwrap();

// Will write "Value: 20", since each thread incremented the counter 10 times.
println!("Value: {}", *counter.lock().unwrap()); The key difference between the two types is how they handle different kinds of access. A doesn’t care about whether you are trying to read or write the data, only a single thread can have access at a time. All other threads have to wait until the current consumer gives up their access. Mutex By contrast, follows Rust’s rules: Any number of threads can have read-only access to the underlying data or a single thread can have write access, but no combination. Attempting to obtain write access will block until there are no active readers and vice versa. RwLock The thread safe nature of these locking types makes them some of the most powerful ways to share mutable data, however it comes at a potentially significant performance cost: Locking the thread so that no other work can be done until the data is available. If our data is simple enough, the last type we’re going to look at can provide shared access across threads without needing to lock. Atomics are available for integer and boolean primitives. These types all provide methods to mutate or read the data as a single operation, so that nothing can happen in between and there is no possibility for data races. Atomic types For example, if you want to increment a counter, instead of reading the value, adding one, then writing the value, you would use the method that does all of that in a single block. fetch_add Atomics are often used as the building blocks for more complicated thread-safe sharing or one-off initialization. As mentioned above, Arc uses an atomic counter internally to manage the reference counting in a thread-safe way. The beauty of all of these types is that they provide a way to break the borrow checker rules while still maintaining Rust’s safety guarantees. Understanding which rules each type breaks is the key to knowing which tool you need. If you’re looking for shared ownership without copying, you want the reference counted types. If you’re looking for mutability without Rust’s strict mutable references, reach for interior mutability. And if you need shared mutable state, it’s not uncommon to use a combination of them: or are combinations for single- and multithreaded shared mutable ownership, respectively. Rc<RefCell<T>> Arc<Mutex<T>> If you’re interested in breaking more of Rust’s rules and pushing the terminal into the future, we’re hiring at Warp! Or if you’d just like to check out our Rust-based terminal, request early access below: Request early access to Warp First Published here

Make Your Rust Code More Rustic By Breaking Some Rules

Dear AI: We Still Don't Trust You

প্রিয় এআই: আমরা এখনও আপনাকে বিশ্বাস করি না

Liebe KI: Wir vertrauen dir immer noch nicht

Querida IA: todavía no confiamos en ti

Chère IA : nous ne vous faisons toujours pas confiance

प्रिय AI: हमें अभी भी आप पर भरोसा नहीं है

親愛なるAIへ: 私たちはまだあなたを信頼していません

친애하는 AI: 우리는 여전히 당신을 신뢰하지 않습니다

Caro AI: ainda não confiamos em você

Дорогой ИИ: мы все еще тебе не доверяем

Sevgili AI: Size Hala Güvenmiyoruz

Kính gửi AI: Chúng tôi vẫn không tin tưởng bạn

亲爱的人工智能：我们仍然不信任你

Recently, I had the opportunity to connect with , the Executive Director at , creators of the Ethereum Name Service (ENS). Our conversation came at a particularly exciting time for web3—possibly on the cusp of a bull market—and for ENS, which is seeing important milestones like its recent . Khori shared his vision of the “new internet,” emphasizing the role of digital identity and the push toward user-centric platforms in shaping an inclusive digital future. Khori Whittaker ENS Labs partnership with GoDaddy Khori, what exactly drew you into web3? My personal and professional journey has always been one of learning—and teaching. Throughout my career, I’ve been at the intersection of business and education, managing schools in the US for most of the past decade. My interest in adopting new technologies early led me to blockchain in late 2017. I started exploring how it could be applied in education, leading to exciting experiments with a blockchain-based student information system. This path then took me to Circle (USDC) where I engaged in a project focused on the talent side. It was then that I connected with , the founder of ENS. We started talking, and one thing led to another. Nick Johnson Today, I really see web3’s potential in transforming the internet as we know it. It redefines how we manage ownership online, improves access to information and resources previously out of reach, and fosters inclusive innovation through decentralized technology. You might hear me talk about Circle and ENS because both focus on breaking into mass adoption. On the monetary side, stablecoins like USDC or USDT allow you to send a transaction instantly and globally without going through all sorts of hoops. Once you experience that, you can’t go back. Then there’s the identity piece. With ENS, you possess a personal identity that is not bound to any specific platform, allowing you to carry it across the digital space. You can use it for transactions, reputation proofs, as a web domain… you name it! How do you see decentralized identity evolving in the future? I hope that in the future, we won't even be discussing web3—it will simply be the new version of the internet. At ENS, our goal is to welcome people into this new era. Currently, users' online identities are mainly stored and hosted on centralized servers controlled by major email and social media corporations. Web3 is about self-sovereignty and ownership. ENS gives users the freedom to carry their identities across platforms while maintaining their social graph and connections seamlessly as they move through digital spaces. For example, I've used Farcaster and Supercast, maintaining the same social network on both. When Warpcast experienced downtime, Supercast remained accessible, showing the resilience of decentralized identities. So, I believe the newfound control and autonomy over one’s digital presence will profoundly affect users in the years to come. What are some practical applications for digital identity? Education is a good example. Imagine being able to add your academic records directly to your digital identity. If you're a college student or recent graduate and need to share your transcript, you often have to pay your institution a fee to send it. Instead, these records could be linked to your digital identity, giving you control over who accesses them. That’s a basic user right. This extends to privacy enhancements we envision with zero-knowledge Layer 2 solutions. For instance, you could verify that you belong to a certain age group without revealing your exact age or share specific qualifications without disclosing all details. The same principle could apply to health and financial records. What parts of web3 identity haven’t been solved yet? One challenge is that we are still not really building for the next billion users. As a space, we are guilty of building for our niche little community over the past decade. This only works for tech-savvy users who are comfortable dealing with seed phrases and signing messages. It’s time we put the everyday person front and center. The other challenge is getting platforms like Facebook and X to recognize decentralized identities. But will they? It’s hard to say. They're reaping significant benefits from owning all our information. Yet, there's hope that social media sites like Farcaster might gain more traction. It’s unlikely that the traditional platforms will be able to maintain their hold indefinitely, especially as people begin to explore and understand what’s possible in the decentralized space. How does ENS think about onboarding this “next billion?” In the web3 space, we're all envisioning the future—the possibilities of 2030 and 2040. Yet, it feels like we're still playing by the rules set in 2012. It's time to update our playbook. The way we build our protocols and projects is crucial. I believe in moving from discussion to action. A key part of this action is establishing a digital identity for users, which is where ENS comes in. It's surprising to see so many new projects overlook the importance of a simple, user-friendly identity solution in favor of complex hexadecimal addresses. Identity solutions should be foundational, not an afterthought. Whether it's ENS or another service, the focus should be on prioritizing the user's needs from the start. Also, we can’t just keep talking to ourselves in a bubble. For example, our partnership with GoDaddy, which introduced ENS-enabled domains to millions of users, is a step toward a wider audience. Now, whether the users are ready to take the leap is the question—but the road is paved and ready. On our side, the adoption of ENS is growing, with hundreds of thousands already using .eth domains. The launch of Coinbase's subdomain service has expanded ENS usage to millions more. Similarly, Uniswap's introduction of uni.eth usernames saw significant uptake in just a few days. By collaborating with these large platforms to integrate ENS technology, we're extending its reach and making it a part of more users' online experiences. This enhances the users’ experiences and furthers adoption. cb.id We need to create B2C applications that genuinely appeal to everyday consumers, craft B2B solutions tailored to current business needs, and initiate what I call B2G (Business to Government) efforts to optimize the operations of local, municipal, and national governments. Solving real needs in the real world will bring the next billion users on board. Could these innovations ultimately help reshape societal values? In many parts of the world, people often feel like bystanders in their own stories. They witness decisions made by governments and corporations without having a say, leading to a sense of helplessness. Technology can shift our mindsets; our mindsets, in turn, can shape technology. I’m hoping that web3 will lead to a whole new way of approaching life. For example, by advocating for self-sovereign and decentralized identities, we can empower people to regain control and ownership. Maybe you don't have to just accept what's happening to you or your community anymore. We can come together, drive change, and pool resources to foster communities and decentralized autonomous organizations (DAOs) that push forward local initiatives. Thinking about concepts like network states, this is where societal change begins. It's about recognizing the power of collective action. This tech is not only about tearing down barriers but also about connecting people. Can you share your approach towards Layer 2 protocols and their significance today? Our strategy is grounded in active listening to the developers and the community, which informs our roadmap. A concern we’ve noted is the cost associated with domain registration and maintenance on Layer 1 networks. Even though a domain might only cost around $5, gas fees can go up to $25 or $30, which may discourage the user. And naturally, modifying your domain or adding records incurs additional on-chain fees. The recent Dencun update on Ethereum has helped, but our goal is to reduce these costs even further to simplify and accelerate how users manage their digital identities. What excites me about Layer 2 solutions is the opportunity to prioritize user experience from the outset. By considering what is lacking in current L1s and L2s, we can avoid those pitfalls. We're given a fresh start and ample time to craft something user-friendly that advances the protocol. At ENS Labs and within our wider community, there's ongoing research into various Layer 2 technologies, including discussions with Arbitrum or Optimism, and even the prospect of creating a dedicated ENS chain. Exciting! What are some other plans ENS has for the future? Naming anything/everything! We believe in humanizing the digital space, naming everything from wallet addresses to smart contracts. Not many know that ENS already has the capability to name smart contracts. This allows users to interact with contracts more transparently, knowing exactly what they engage with. Our vision extends to global adoption, making this intuitive naming system accessible worldwide and encouraging prominent organizations to integrate ENS names. We've already started making strides in this direction, such as our collaboration with the International Rescue Committee, facilitating crypto philanthropy with just a few clicks. This year, our focus is sharply on Layer 2 solutions. We're looking to collaborate with leading players from the traditional web and economic sectors, including businesses, governments, and more. Our goal is to simplify the internet for the future while prioritizing safety, security, and ease of use.

An Interview With Khori Whittaker: On ENS, Decentralized Identity & Socials, and the Next Billion

Author(s): (1) Gopal Yadav, Department of Physics, Indian Institute of Technology & Chennai Mathematical Institute. Table of Links Abstract & Introduction Brief Review of Wedge Holography Emerging Multiverse from Wedge Holography Application to Information Paradox Application to Grandfather Paradox Conclusion Acknowledgements and References Acknowledgements The author is supported by a Senior Research Fellowship (SRF) from the Council of Scientific and Industrial Research (CSIR), Govt. of India. It is my pleasure to thank Aalok Misra, who motivated me to work on the entanglement stuff, and for his blessings. We would also like to thank Juan Maldacena, Andreas Karch, Kostas Skenderis and Tadashi Takayanagi for very helpful discussions and comments. This research was also supported in part by the International Centre for Theoretical Sciences (ICTS) for the program “Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography” (code:ICTS/numstrings-2022/8). Various conferences/workshops; e.g., Mysteries of Universe-I (Institute Lecture Series) and Indian Strings Meeting 2021 at Indian Institute of Technology Roorkee, Roorkee, India; Applications of Quantum Information in QFT and Cosmology at the University of Lethbridge, Canada; Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology (Online) at International Centre for Theoretical Sciences (ICTS) Bangalore, India (code:ICTS/kaws2022/1); Reconstructing the Gravitational Hologram with Quantum Information at Galileo Galilei Institute for Theoretical Physics, Florence, Italy; Quantum Information in QFT and AdS/CFT-III at Indian Institute of Technology Hyderabad, India; helped me to learn about the information paradox and related stuff. I am very thankful to the speakers and organizers of these conferences because I learned about the subject from these conferences. References [1] S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43, 199 (1975) Erratum: [Commun. 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Multiverse in Karch-Randall Braneworld: Acknowledgements and References

Authors: (1) Gopal Yadav, Department of Physics, Indian Institute of Technology & Chennai Mathematical Institute. Table of Links Abstract & Introduction Brief Review of Wedge Holography Emerging Multiverse from Wedge Holography Application to Information Paradox Application to Grandfather Paradox Conclusion Acknowledgements and References 4 Application to Information Paradox • BCFT is living at the AdSd+1 boundary with (d−1)-dimensional boundary. Boundary Description: • 2n gravitating systems interact with each other via transparent boundary conditions at the (d − 1)-dimensional defect. Intermediate Description: • Gravity dual of BCFT is Einstein gravity in the bulk. Consistency Check: Let us check the formula given in (22) for n = 2. Bulk Description: 4.1 Page Curve of Eternal AdS Black Holes in n = 2 Multiverse First, we will calculate the thermal entropies of black holes. The metric of the black holes in AdS background is: This corresponds to an infinite amount of Hawking radiation when t1 → ∞, i.e., at late times, and hence leads to information paradox. Now consider the island surfaces parametrize as t = constant and z ≡ z(r). Entanglement entropy of two eternal AdS black holes for the island surfaces can be obtained using (22). Since there are two island surfaces(I1 and I2) stretching between the Karch-Randall branes located at r = ±ρ (I1) and r = ±2ρ (I2), and hence we can write (22) for the same as given below Entanglement entropy contribution from Island surfaces: 4.2 Page Curve of Schwarzschild de-Sitter Black Hole In this section, we study the information paradox of the Schwarzschild de-Sitter black hole. As discussed in section 3.3, we can not have mismatched branes connected at the same defect. Therefore, we study this problem in two parts by first calculating the Page curve of the Schwarzschild patch and then the Page curve of the de-Sitter patch similar to the non-holographic model [58]. This can be done as follows. We study the Schwarzschild patch in subsection 4.2.1 where we consider two flat space branes embedded in the bulk and de-Sitter patch in subsection 4.2.2 with two de-Sitter branes. We have shown the setup in Fig. 8. The setup is two copies of wedge holography with flat space and de-Sitter branes in Schwarzschild and de-Sitter patches respectively. 4.2.1 Schwarzschild patch Since for Schwarzschild black hole, Λ = 0, therefore to realize Schwarzschild black hole on KarchRandall brane, we need to consider the flat space black holes. It was shown in [42] that one can get flat space black holes on Karch-Randall branes provided bulk metric should have the following form: 4.2.2 de-Sitter patch de-Sitter black hole and its bath will be located at r = ±ρ. The Metric for the bulk which contains de-Sitter branes is (65) Substituting v 0 (z) from (64) into (65) and using f(z) = 1 − z 2 , we set zs = 1 for simplification, EOM (65) simplifies to the follow In general, it is not easy to solve the above equation. Interestingly, there is a z(r) = 1 solution to the above differential equation which is nothing but de-Sitter horizon assumed earlier(zs = 1) [19] and it satisfies the Neumann boundary condition on the branes and hence the solution for the cosmological island surface is One can arrive at the same conclusion by requiring the well-defined variational principle of (70) and imposing Neumann boundary condition on the branes similar to the discussion in section 4.1 which requires Additional numerical factor “2” is coming due to second cosmological island surface on thermofield double partner side (shown in Fig. 8). We get the Page curve of de-Sitter patch by plotting (69) and (75) from wedge holography. We will get a flat Page curve in this case similar to [33]. Let us summarize the results of this section. It was argued in [33, 35] that in wedge holography without DGP term, the black hole horizon is the only extremal surface and the HartmanMaldacena surface does not exist and hence one expects the flat page curve. We also see that when we compute the entanglement entropies of island surfaces of AdS, Schwarzschild, and deSitter black holes then minimal surfaces turn out to be horizons of the AdS or Schwarzschild or de-Sitterblack holes. As a curiosity, we computed entanglement entropies of Hartman-Maldacena surfaces for the parametrization r(z) and v(z) used in the literature and we found non-trivial linear time dependence for the AdS and Schwarzschild black holes whereas Hartman-Maldacena surface entanglement entropy turns out to be zero for the de-Sitter black hole. Therefore we obtain the flat Page curve for the de-Sitter black hole not for the AdS and Schwarzschild black holes due to the non-zero entanglement entropy of Hartman-Maldacena surfaces. The theme of the paper is not to discuss whether we get a flat Page curve or not. The paper aimed to construct a “multiverse” in Karch-Randall braneworld which we did in section 3 and check the formula given in (22). We saw in subsection 4.1 that (22) is giving consistent results. In subsection 4.2, we performed our computation of the Schwarzschild and de-Sitter patches separately. There is one more way by which we may get the Page curve of the Schwarzschild de-Sitter black hole. We summarize the idea below: Comment on the Wedge Holographic Realization of Schwarzschild de-Sitter Black Hole with Two Karch-Randall Branes: The above discussion is just a “mathematical idea”. Since we have three possible branes: Minkowski, de-Sitter and anti de-Sitter [55]. There is no brane with the induced metric defined in the open bracket of (76). Further, we have AdS/CFT correspondence or dS/CFT correspondence, or flat space holography. There is no such duality that states the duality between CFT and bulk which has the form of a Schwarzschild de-Sitter-like structure. There will be no defect description due to the aforementioned reason and hence no “intermediate description” of wedge holography. Therefore we conclude that one can model Schwarzschild de-Sitter black hole from wedge holography with two copies of wedge holography in such a way that one part defines Schwarzschild patch and the other part defines de-Sitter patch [22] . [13] It was discussed in [33] that Neumann boundary condition on gravitating branes implies that Ryu-Takayanagi surface in the wedge holography is the black hole horizon. The same was also obtained in [35] by using inequality condition on the area of island surface. We obtained the same throughout the paper wherever we have discussed the entanglement entropy of island surfaces. [14] We can show the same by following the steps given in detail from (63)-(67). But we have to replace the warp factor sinh(r(z)) by e r(z) . [15] See the terms inside the open bracket of (57), there are terms with derivatives of z(r) and a particular combination (−8z(r) 2 + 4z(r) + 4z(r) 3 ) which vanishes for z(r) = [16] We used zs = 1 only for the simplification of calculation. Since cosmological constant is very small and hence in reality zs >> 1 but some number which will not affect our qualitative results. [17] Same solution r(z) = 0 also appeared in [35] in the computation of area of Hartman-Maldacena surface. See [33] for the similar solution, in our case embedding is r(z) whereas in [33], embedding is r(µ), µ being the angle. [18] See [59] for the discussion of complexity of de-Sitter spaces. [20] In this case, Hawking radiation will not be a suitable term because when Schwarzschild de-Sitter black hole as whole emits radiation then observer may not distinguish between Hawking radiation emitted by Schwarzschild patch and Gibbons-Hawking radiation emitted by de-Sitter patch [60]. [21] In this setup, the notion of “island” may become problematic because we will be talking about the island in the interior of Schwarzschild de-Sitter black hole. Since SdS black hole has two horizons, therefore it may cause trouble to say whether the “island” is located inside the black hole horizon or the de-Sitter horizon. Therefore it will be nice to follow the setup with two black holes and two baths. See [58] for non-holographic approach. [22] See [58, 62] for non-holographic model. This paper is under CC 4.0 license. available on arxiv

Multiverse in Karch-Randall Braneworld: Application to Information Paradox

কার্চ-র্যান্ডাল ব্রেনওয়ার্ল্ডে মাল্টিভার্স: তথ্য প্যারাডক্সের আবেদন

Multiversum in Karch-Randall Braneworld: Anwendung auf das Informationsparadoxon

Multiverso en Karch-Randall Braneworld: aplicación a la paradoja de la información

Multivers dans Karch-Randall Braneworld : application au paradoxe de l'information

कार्च-रान्डेल ब्रैनवर्ल्ड में मल्टीवर्स: सूचना विरोधाभास का अनुप्रयोग

カーチ・ランドール・ブレーンワールドの多元宇宙: 情報パラドックスへの応用

Karch-Randall Braneworld의 다중우주: 정보 역설에 적용

Multiverso em Karch-Randall Braneworld: Aplicação ao Paradoxo da Informação

Мультивселенная в мире бран Карча-Рэндалла: применение к информационному парадоксу

Karch-Randall Braneworld'deki Çoklu Evren: Bilgi Paradoksuna Uygulama

Đa vũ trụ trong Karch-Randall Braneworld: Ứng dụng vào nghịch lý thông tin

卡奇-兰德尔膜世界中的多重宇宙：信息悖论的应用

Authors: (1) Gopal Yadav, Department of Physics, Indian Institute of Technology & Chennai Mathematical Institute. Table of Links Abstract & Introduction Brief Review of Wedge Holography Emerging Multiverse from Wedge Holography Application to Information Paradox Application to Grandfather Paradox Conclusion Acknowledgements and References 3 Emerging Multiverse from Wedge Holography In this section, we discuss how one can describe multiverse from wedge holography. 3.1 Anti de-Sitter Background In this subsection, we construct a multiverse from AdS spacetimes. Let us first start with the simplest case discussed in 2. To describe multiverse, we need multiple Karch-Randall branes located at r = ±nρ such that bulk metric should satisfy Neumann boundary condition at the aforementioned locations. Extrinsic curvature on the Karch-Randall brane and its trace is computed as: Three descriptions of our setup are as follows: • d-dimensional boundary conformal field theory with (d − 1)- dimensional boundary. Boundary description: • All 2n gravitating systems are connected at the interface point by transparent boundary condition. Intermediate description: • Einstein gravity in the (d + 1)-dimensional bulk. Bulk description: We see that in the intermediate description, there is a transparent boundary condition at the defect; therefore multiverse constructed in this setup consists of communicative universes localized on Karch-Randall branes (see Figs. 2,3). Wedge holography dictionary for “multiverse” with 2n AdS branes can be stated as follows. 3.2 de-Sitter Background In this subsection, we study the realization of the multiverse in such a way that the geometry of Karch-Randall branes is of de-Sitter spacetime. Wedge holography with de-Sitter metric on Karch-Randall branes was discussed in [42] where the bulk spacetime is AdS spacetime and in [52] with flat space bulk metric. Before going into the details of construction of “multiverse” with de-Sitter geometry on Karch-Randall branes, first let us summarise some key points of [52]. Authors in [52] constructed wedge holography in (d + 1)-dimensional flat spacetime with Lorentzian signature. Karch-Randall branes in their construction have either geometry of d dimensional hyperbolic space or de-Sitter space. Since our interest lies in the de-Sitter space therefore we only discuss the results related to the same. Geometry of the defect is S d−1 . Wedge holography states that Third line in the above duality is coming from dS/CFT correspondence [53, 54]. Authors in [52] explicitly calculated the central charge of dual CFT which was imaginary and hence CFT living at the defect is non-unitary. The above discussion also applies to the AdS bulk as well. In this case one can state the wedge holographic dictionary as: branes are obtained as: • d-dimensional BCFT with (d − 1)-dimensional defect. Boundary description: • 2n gravitating systems with de-Sitter geometry connected to each other at the (d − 1)-dimensional defect. Intermediate description: • (d + 1)-dimensional Einstein gravity with negative cosmological constant in the bulk. Bulk description: First and third description are related to each other via AdS/BCFT correspondence and (d−1)- dimensional defect which is non-unitary CFT exists because of dS/CFT correspondence [53, 54]. de-Sitter space exists for finite time and then disappear. Another de-Sitter space born after the disappearance of previous one [55]. Therefore it is possible to have a “multiverse” (say M1) with de-Sitter branes provided all of them should be created at the same “creation time” [7] but this will exist for finite time and then M1 disappears. After disappearance of M1, other multiverse (say M2) consists of many de-Sitter branes born with same creation of time of all the de-Sitter branes. 3.3 Braneworld Consists of Anti de-Sitter and de-Sitter Spacetimes In this subsection, we have discussed the embedding of different types of Karch-Randall branes in the different bulks which are disconnected from each other. Authors in [55] have discussed the various possibilities of embedding of different types of branes, e.g., Minkowski, de-Sitter and anti de-Sitter branes in the same bulk. Existence of various branes are characterized by creation time τ∗. There is finite amount of time for which Minkowski and de-Sitter branes born and there is no cration time for anti de-Sitter branes. Out of various possibilities discussed in [55], it was pointed by authors that one can see Minkowski, de-Sitter and anti de-Sitter brane at the same time with creation time τ∗ = −π/2 in a specific bulk. In this case, branes have time dependent position. First we will summarise this result [10] and then comment on the realization of the same from wedge holography. Bulk AdS5 metric has the following form: One can construct doubly holographic setup from (19) using the idea of AdS/BCFT. Let us state the three possible descriptions of doubly holographic setup constructed from (19). Comment on the Wedge Holographic Realization of Mismatched Branes: • 4D quantum field theory (QFT) at conformal boundary of (19). Boundary description: • Dynamical gravity localized on 4D end-of-the-world brane coupled to 4D boundary QFT. Intermediate description: • 4D QFT defined in the first description has 5D gravity dual whose metric is (19). Bulk description: Due to covariant nature of AdS/CFT duality it remains the same if one works with the changed coordinates in the bulk i.e. different parametrisations of AdS does not imply different dualities [11] and therefore in the above doubly holographic setup, we expect defect to be 3-dimensional conformal field theory because 4-dimensional gravity is just FRW parametrization of AdS4 spacetime (20). Relationship between boundary and bulk description is due to AdS/CFT correspondence, in particular, this kind of duality was studied in [56] where bulk is de-Sitter parametrization of AdS4 and conformal field theory is QFT on dS3. As discussed in detail in appendix of [55] and summarised in this subsection that one can also have de-Sitter and Minkowski branes in this particular coordinate system (19). If one works with de-Sitter metric (21) on end-of-the-world brane then we expect defect CFT to be non-unitary. Due to dynamical nature of gravity on Karch-Randall brane, holographic dictionary is not well understood in the braneworld scenario. A Now let us discuss what is the issue in describing wedge holography with “mismatched branes”. Wedge holography has “defect CFT” which comes due to dynamical gravity on Karch-Randall branes. Suppose we have two Karch-Randall branes with different geometry, one of them is AdS brane and the other one is de-Sitter brane. Then due to AdS brane, defect CFT should be unitary and due to de-Sitter brane, defect CFT should be non-unitary. It seems that we have two different CFTs at the same defect. This situation will not change even one considers four branes or in general 2n branes. Hence, one may not be able to describe “multiverse” with mismatched branes from wedge holography. That was just an assumption. Common boundary of multiverses M1 and M2 (described in Fig. 5) can’t be the same even when geometry is (19) due to “time-dependent” position of branes. All the AdS branes in M1 can communicate with each other via transparent boundary conditions at the defect and similarly all the de-Sitter branes in M2 are able to communicate with each other. But there is no communication between M1 and M2 even in (19). Therefore we conclude that we can create multiverse of same branes(AdS or de-Sitter) but not the mixture of two. Hence issue of mismatched branes do not alter from wedge holography perspective too. Multiverse of AdS branes exists forever whereas multiverse of de-Sitter branes has finite lifetime [12] . [3] It seems that some of branes have negative tension. Let us discuss the case when branes are located at −nρ1 and nρ2 with ρ1 6= ρ2. In this case tensions of branes are (d − 1) tanh(−nρ1) and (d − 1) tanh(nρ2). Negative tension issue can be resolved when we consider ρ1 < 0 and ρ2 > 0 similar to [48]. Therefore this fixes the brains stability issue in our setup. This discussion is also applicable to the case when ρ1 = ρ2. [4] When we discuss multiverse then α and β will take 2n values whereas when we discuss wedge holography then α, β = 1, 2 [5] Explicit derivation of (14) was done in [42] for two Karch-Randall branes. One can generalize the same for 2n Karch-Randall branes. In this setup upper limit of integration will be different for different locations of Karch-Randall branes. [6] See [42] for the explicit derivation. Only difference is that, in our setup, we have β = 1, 2, ..., n. [7] Creation time is defined as the “time” when any universe born [55]. [8] In this case, warp factor will be different in the bulk metric. Exact metric is given in (45). [9] We thank J. Maldacena for comment on this. [10] For more details, see [55] [11] We thank K. Skenderis to clarify this to us and pointing out his interesting paper [56] [12] We thank A. Karch for very helpful discussions on the existence of de-Sitter branes and issue of mismatched branes in wedge holography. This paper is under CC 4.0 license. available on arxiv

Understanding Multiverse Construction through Wedge Holography

ওয়েজ হলগ্রাফির মাধ্যমে মাল্টিভার্স কনস্ট্রাকশন বোঝা

Verständnis der Multiversumskonstruktion durch Keilholographie

Comprender la construcción del multiverso a través de la holografía en cuña

Comprendre la construction du multivers grâce à l'holographie Wedge

वेज होलोग्राफी के माध्यम से मल्टीवर्स कंस्ट्रक्शन को समझना

ウェッジホログラフィーによる多元宇宙構築の理解

웨지 홀로그래피를 통한 다중우주 구성 이해

Compreendendo a construção do multiverso por meio da holografia em cunha

Понимание конструкции мультивселенной с помощью клиновой голографии

Wedge Holografisi Aracılığıyla Çoklu Evren Yapısını Anlamak

Tìm hiểu cấu trúc đa vũ trụ thông qua hình ảnh ba chiều Wedge

通过楔形全息术理解多元宇宙的构造

Aspects of Thermal QCD Phenomenology at Intermediate Gauge/'t Hooft Coupling: Bibliography

Authors: (1) Gopal Yadav, Department of Physics, Indian Institute of Technology & Chennai Mathematical Institute. Table of Links Abstract Acknowledgment PART I Chapter 1: Introduction Chapter 2: SU(3) LECs from Type IIA String Theory Chapter 3: Deconfinement Phase Transition in Thermal QCD-Like Theories at Intermediate Coupling in the Absence and Presence of Rotation Chapter 4: Conclusion and Future Outlook PART II Chapter 5: Introduction Chapter 6: Page Curves of Reissner-Nordström Black Hole in HD Gravity Chapter 7: Entanglement Entropy and Page Curve from the M-Theory Dual of Thermal QCD Above Tc at Intermediate Coupling Chapter 8: Black Hole Islands in Multi-Event Horizon Space-Times Chapter 9: Multiverse in Karch-Randall Braneworld Chapter 10: Conclusion and Future outlook APPENDIX A APPENDIX B APPENDIX C Bibliography CHAPTER 7 - ENTANGLEMENT ENTROPY AND PAGE CURVE FROM THE M-THEORY DUAL OF THERMAL QCD ABOVE T AT INTERMEDIATE COUPLING c 7.1 Introduction and Motivation In doubly holographic approaches, as described in 5.3.2 of chapter 5, a gravitational dual black hole is connected with an external CFT bath [202]. As an illustration, gravity in d-dimensions is connected with the external bath in d-dimensions, wherein d-dimensional exterior bath possesses a corresponding holographic dual in (d + 1)-dimensions. In such models, we take into consideration two variants of the previously mentioned configuration. We look at two distinct types of extremal surfaces in these models. The very first one corresponds to the Hartman-Maldacena-like surface [144], that begins from the position at which gravity interacts with with an external bath, i.e., at the defect, and traverses the black hole horizon to get to the defect of the thermofield double associated with doubly holographic setups, and the entanglement entropy involvement via the aforementioned surface possesses linear time dependency, leading to information paradox at later times. The other type of surface includes the island surface, that begins at the exterior bath and ends on the KarchRandall brane [142, 143]. The contribution of entanglement entropy coming from the island surface becomes time independent and takes over beyond the Page time. The Page curve is obtained through the combination of the entanglement entropy contributions obtained from both the extremal surfaces. As we discussed in 5.3.2, in some cases, the gravity becomes massive on the Karch-Randall branes, and one was unable to get the Page curve with massless gravity localized on the KarchRandall branes. In this chapter, we have looked at this major issue of doubly holographic setup from M-theory perspective in the presence of O(R4 ) terms in the supergravity action. We have a different situation from the literature that we have a non-conformal bath (QCD bath), and the doubly holographic setup is being constructed from a top-down approach[1] with the inclusion of higher derivative terms in the supergravity action. Interestingly, the issue of the massive graviton is absent in our setup, and one can get the Page curve with massless gravity on the end-of-the-world(ETW) brane. We cannot utilize the island approach for non-conformal backgrounds because currently there is no recognized Cardy-like formula for the non-conformal theories. As a result, we used the previously mentioned doubly holographic frameworks technique to arrive at the Page curve. In the context of our scenario, on the gravity dual side, there is a M-theory dual consisting of higher derivative terms, whereas on the gauge theory side, we find nonconformal thermal QCD-like theories at the intermediate coupling, the model is discussed in 1.4 of chapter 1. In the present chapter, we created a doubly holographic setup analogous to [7,203], where the researchers utilize a conformal theory on their gauge theory side. There are two types of potential surfaces to think about: Hartman-Maldacena-like and island surfaces. The Hartman-Maldacena-like surface has been accountable for the gradual linear temporal growth of Hawking radiation’s entanglement entropy. Above the Page time, the entanglement entropy component via the island surface takes over and this is not dependent upon time, so we extract the Page curve using the M-theory dual, which includes O(R4 ) corrections. As a remark, we used the formula of [127] to compute the entanglement entropy with the inclusion of higher derivative terms and when higher derivative terms are absent then we used the Ryu-Takayanagi formula to compute the entanglement entropy [107]. 7.2 Doubly Holographic Setup in M Theory From the work of [127], we could compute the entanglement entropy associated with holographic dual theories with the inclusion of higher derivative terms. We could express the analogue of the generalised entropy functional described in equation (5.17) using [127] for M-theory dual in the presence of O(R4) terms as follows: and inserting it into (7.20) yields: 7.3.1 At O(β) and we assume the constant is zero. 7.3.2 No Boundary Terms Generated at O(R4) The eleven-dimensional supergravity action, which includes O(R4 ) terms, is presented by the following: where, As a result, we are able to identify that a usual boundary term including covariant derivatives of metric fluctuations that would have to be cancelled out by a suitable boundary term (using Stokes theorem) is: The (dual to the) unit normal vector to provided by: W Hence, Utilizing, 7.4 Page Curve without Higher Derivative Terms Here, we obtained the Page curve using the doubly holographic setup constructed in 7.2. In this part, we do not consider the ( ) terms in the supergravity action. Therefore, we used the Ryu-Takayanagi formula to compute the entanglement entropies of Hartman-Maldacena-like and Island surfaces in 7.4.1 and 7.4.2. The Page curve has been obtained in 7.4.3. In the absence of ( ) terms, the = 1, = 11 supergravity action has been provided as follows: O R4 O R4 N D 7.4.1 Entanglement Entropy Contribution from Hartman-Maldacena-like Surface To calculate the time-dependent entanglement entropy associated with a Hartman-Maldacena-like surface, we first look at the induced metric on a constant x 1 slice, which was calculated utilizing (7.20) as follows: The area density functional for a Hartman-Maldacena-like surface could be calculated using (7.23) as follows: implying Using (7.27) and (7.30), we obtained: Now we identify time via the integral: As a result, the Hartman-Maldacena-like surface’s entanglement entropy is: 7.4.1.1 Hartman-Maldacena-like Surface Analytics/Numerics After integrating all of the angular coordinates and consequently including a (2π) 4 emerging from integration w.r.t. ϕ1,2, ψ, x10, the area corresponding to the Hartman-Maldacena-like surface is obtained as: As a result, the entanglement entropy related with a Hartman-Maldacena-like surface grows linearly with time. 7.4.2 Entanglement Entropy Contribution from Island Surface We take a constant t slice to calculate the entanglement entropy for an island surface. As a result, utilizing equation (7.20), we expressed the induced metric associated with the island surface as follows: where C is the constant. We simplified the expression (7.43) utilizing equation (7.41) as given below: When we solved the preceding equation for x˙(r), we were provided with: Constant could be calculated using the equations (7.45) and (7.46), as shown below: C Taking the previously stated expression of C, the equation (7.44) reduces to the following structure: Now, the area density functional associated with the island surface has been simplified using the equations (7.41) and (7.48). Hence, the entanglement entropy associated with the island surface is obtained as follows: Since, there is no time dependence in (7.50), and hence entanglement entropy of the Hawking radiation for the island surface is constant. 7.4.2.1 Island Surface Analytics When (7.49) is evaluated, the entanglement entropy is as follows: implying 7.4.3 Page curve at LO from Areas of Hartman-Maldacena-like and Island Surfaces 7.5 Page Curve with Higher Derivative Terms We obtained the Page curve corresponding to a neutral black hole in with the inclusion of higher derivative terms that are quartic in the Riemann curvature tensor in this section. This section has been broken into four subsections. We calculated the entanglement entropy associated with the HM-like surface in subsection 7.5.1, discussed the “Swiss-Cheese” structure of the identical surface in subsection 7.5.2, computed the entanglement entropy of island surface in 7.5.3, and at last obtained the Page curve corresponding to an eternal black hole in subsection 7.5.4 utilizing the outcomes that were obtained from previous subsections. We conducted the same analysis as in 7.4. [127] was used to compute the entanglement entropy associated with Hartman-Maldacena-like surface and island surface in with the inclusion of higher derivative terms. In generic higher derivative gravity theories, we are able to calculate the holographic entanglement entropy (5.8) as follows: • When the holographic dual consists of a ( + 1) dimensional gravitational background, then with the help of the embedding function, compute the induced metric associated with the co-dimension two surface. d • Using the above-mentioned induced metric, compute (5.8). This yields the holographic entanglement entropy as an expression of the embedding function and its derivatives. • Find the solution to the embedding function’s equation of motion. • In higher derivative gravity theories, putting the solution found in the previous step inside the action yields the holographic entanglement entropy. To determine the second part in the formula (5.8), we must first compute the four types of derivatives for the Hartman-Maldacena-like and island surfaces, which are listed below: The numerator and denominator coefficients in the preceding equation are x = xR for the Hartman-Maldacena-like surface and x = x(r) for the island surface. All four types of variations occurring in equation (7.54) for the Hartman-Maldacena-like surface in appendix C.5.1 and island surface in appendix C.5.2 have been computed and listed. 7.5.1 Entanglement Entropy Contribution from Hartman-Maldacena-like Surface Hartman-Maldacena-like surface in M-theory dual corresponds to a co-dimension two surface situated at x 1 = xR. Utilizing equation (5.8), we are able to write the mathematical expression that describes the entanglement entropy associated with a Hartman-Maldacena-like surface as follows: where g denotes determinant of the induced metric defined in (7.23) for the co-dimension two surface. For the metric (7.23), the entanglement entropy associated with the Hartman-Maldacena-like surface using (7.55) and appendix C.5.1 after the angular integrations is obtained as: where The equation (7.58) has the following solution: substitution of (7.59) in (C.20) yields: Keeping the term up to the leading order in N, we could write the embedding function t(r) as follows: The entanglement entropy of the Hawking radiation corresponding to the Hartman-Maldacenalike surface is computed as given below: utilizing (C.13) and (7.59), (7.66) is expressed as: Similarly, 7.5.3 Entanglement Entropy Contribution from Island Surface The island surface is a co-dimension two surface that exists at a continuous time slice, much like the Hartman-Maldacena-like surface. Therefore, we can formulate the formula for the holographic entanglement entropy as follows: Hence, we found that: and, Thus, the island surface’s equation of motion associated with embedding x1(r) is as follows: (7.89)’s solution is provided as: implying, The above equation has the following solution: The black hole entropy for the metric (7.19) is obtained as: Therefore, the entanglement entropy for the island surface after substitution of β simplified as: From Fig. 7.5 and utilizing (7.101), it is obvious that (7.97) ∼ (7.98) means that a lower constraint will be placed on rh, the non-extremality parameter in the M-theory dual of large-N thermal QCD. 7.5.4 Page Curve and An Exponential(-in-N) Hierarchy of Entanglement Entropies up to O(R4) Before/After the Page Time At the Page time, the entanglement entropies for the Hartman-Maldacena-like surface and the Island Surface are equal. This results in: Page time: Utilizing (7.99), (7.104) implies, Similarly, for the island surface O(β) contributions to the entanglement entropy is obtained as: Utilizing (7.99), (7.107) results in: From the equations (7.71), (7.100), (7.105) and (7.108), we obtained the following hierarchy: 7.6 Massless Graviton - the Physical reason for Exponentially Suppressed Entanglement Entropies Similar to [209], we can write the eleven-dimensional metric (7.19) as given below: We found that: the solution of above equation is: Since (7.121) is not well defined in the UV when m ̸= 0. Therefore, we need to consider m = 0 for which the graviton wave function is: Figure 7.8 plots the aforementioned potential for massless graviton (m = 0); this potential is “volcano”-like, with the massless graviton localized at the horizon on the ETW “brane”. This is analogous to [142], in which gravity can be localized on the end-of-the-world (ETW) brane with non-zero brane tension owing to the emergence of a “crater” in the “volcano” potential in the Schrödinger-like equation of motion of the graviton wave function. 7.7 Summary In this chapter, we constructed the doubly holographic setup from a top-down approach as discussed in 7.2. We have taken the external bath as thermal QCD in three dimension whose holographic dual is M-theory inclusive of O(R4) corrections [1], see chapter 1 for more detail of the same. The intermediate description of the doubly holographic setup constructed by us couples the black hole on the ETW-“brane” at x = 0 to thermal QCD bath via transparent boundary condition at the defect. We have addressed the effect of higher derivative terms in the context of top-down construction of double holography for the first time. First we obtained the Page curve without inclusion of O(R4) terms in the eleven-dimensional supergavity action in 7.4. To achieve the same, we computed the entanglement entropies associated with the Hartman-Maldacena-like (HM-like) and island surfaces and obtained the Page curve with the help of these entropies because the HM-like surface has Based on the viability of the Islands scenario, the M-theory dual of large-N thermal QCD at high temperature obtained in [15], [1] (based on [14]) produces the previously mentioned Page curve. The above-mentioned top-down M-theory dual, on the other hand, provides a number of new conceptual information: • Due to the lack of details of precise structures for boundary terms on the ETW-“brane” along with the presence of higher derivative terms, there exists relatively few works (e.g., [147]) in which the authors look into the doubly holographic setup in higher derivative theory of gravity. Remarkably we showed in 7.3.2 that the presence of the O(R4) terms generates no boundary terms. • As for as we know, our setup/(above-mentioned) M-theory dual appears either the sole one in existence (from M-theory) or one among the comparatively few top-down approaches that generate(s) the Page curve for massless graviton. • In our top-down M-theory dual, we find that ETW-“brane” to be a fluxed hypersurface W that is a warped product of an asymptotic AdS4 and a six-fold M6 where M6 is a warped product of the M-theory circle and a non-Einstenian generalization of T 1,1 ; the hypersurface W, can also be thought of as an effective ETW-“brane” corresponding to fluxed intersecting M5-brane wrapping a homologous sum of S 3×[0, 1] and S 2×S 2 in a warped product of R 2 and an SU(4)/Spin(7)-structure eight-fold. The ETW-“brane”, W, then has non-zero “tension” and a massless graviton localized near the horizon by a “volcano”-like potential. • Unlike largely other works in the literature, which compute the Page curve with a CFT bath, the external bath in our model is a non-CFT bath (thermal QCD). • Entanglement entropy contribution generated by a Hartman-Maldacena (HM)-like surface, which has been causing the growth of the Einstein-Rosen bridge in time, shows a Swiss-Cheese structure in the Large-N scenario (7.5.2) as discussed earlier. • By the presence of O(R4 ) terms in the action, our previously discussed M-theory dual produces a hierarchy in the entanglement entropies of the HM-like and Island surface (IS) with respect to a large-N exponential suppression factor, resulting physically via the presence of massless graviton mode on an ETW-brane. This suppression also suggests the fact that the addition of higher derivative terms - O(R4) in particular - has no effect on the Page curve. • To regulate the IR- and large-N enhancement in the IS entanglement entropy per unit BH entropy, a relationship involving the Planckian length and the non-extremality parameter (the horizon radius) has been shown to occur. • The positivity of the Page time, calculated in (refPage-time), has been showed to set an upper constraint on the non-extremality parameter, the black-hole horizon radius rh. This paper is under CC 4.0 license. available on arxiv

Entanglement Entropy and Page Curve From the M-Theory Dual of Thermal Qcd at Intermediate Coupling

Authors: (1) Gopal Yadav, Department of Physics, Indian Institute of Technology & Chennai Mathematical Institute. Table of Links Abstract Acknowledgment PART I Chapter 1: Introduction Chapter 2: SU(3) LECs from Type IIA String Theory Chapter 3: Deconfinement Phase Transition in Thermal QCD-Like Theories at Intermediate Coupling in the Absence and Presence of Rotation Chapter 4: Conclusion and Future Outlook PART II Chapter 5: Introduction Chapter 6: Page Curves of Reissner-Nordström Black Hole in HD Gravity Chapter 7: Entanglement Entropy and Page Curve from the M-Theory Dual of Thermal QCD Above Tc at Intermediate Coupling Chapter 8: Black Hole Islands in Multi-Event Horizon Space-Times Chapter 9: Multiverse in Karch-Randall Braneworld Chapter 10: Conclusion and Future outlook APPENDIX A APPENDIX B APPENDIX C Bibliography CHAPTER 3 - DECONFINEMENT PHASE TRANSITION IN THERMAL QCD-LIKE THEORIES AT INTERMEDIATE COUPLING IN THE ABSENCE AND PRESENCE OF ROTATION 3.1 Introduction We can compute the corrections to the infinite-’t Hooft-coupling limit as done in [100] using gauge/gravity duality, but this time using an AdS background. They used terms quartic in the Weyl tensor to include higher-derivative corrections on the gravity side. From the gauge theory point of view, there is a SU(N) supersymmetric Yang-Mills plasma with N = 4 SUSY at an intermediate ’t Hooft coupling. They provided an explanation for the transport peak that appeared in the spectral function of the stress-energy tensor at zero spatial momentum in the small frequency zone. This is a characteristic of perturbative plasma generally. In general theories of gravity, Wald provided a formula to determine black hole entropy [102]. He thought about the Lagrangian that results from the diffeomorphism invariant classical theory of gravity in n dimensions. Noether charge is a (n−2)-form in these theories of gravity, and the (n − 2)-form Noether charge’s integral across its bifurcate killing horizon will yield the black hole’s entropy. Therefore, for stationary black holes with bifurcate killing horizons, entropy equals Noether charge. A formula to calculate entropy for dynamical black holes was made in [103]. Every physical phenomenon has an energy/distance scale that defines it. RG group flow is used to move from UV to IR. However, short-range physics begins to interact with long-range physics in noncommutative field theories and string theory, a process known as UV/IR mixing. UV divergences in real ϕ 4 theory defined on commutative space are changed into infrared poles in the identical theory defined on noncommutative space as a result of UV/IR mixing, for example. There are further examples that are nicely explained in [104]. Theoretical models of gravity are nonlocal. As a result, UV/IR mixing might be present in such theories. In the gauge/gravity duality, the energy scale in the gauge theory side matches with the radial coordinate in gravitational theory. In the context of the AdS/CFT correspondence, the authors looked at the “I.R.-U.V.” connection and demonstrated how infrared phenomena in bulk theory are turned into ultravoilet phenomena in boundary theory [105]. In particular, the job of the ultraviolet regulator in the N = 4 super Yang Mills theory is played by the infrared regulator in the bulk theory. It’s fascinating that in our work, matching at the deconfinement temperature, M-theory actions dual to the thermal and black-hole backgrounds at the UV-cut-off, and obtaining a relationship between the O(R4 ) metric corrections in the IR, a specific type of UV-IR connection manifests itself. In noncentral relativistic heavy ion collisions (RHIC), a fluid known as quark-gluon plasma (QGP) is created. According to experimental findings from the RHIC collaboration, the angular momentum and angular velocity of this rotating fluid are on the order of 103ℏ and ω ∼ 6 MeV, respectively. In [108], the authors applied hydrodynamic simulations of heavy ion collisions and found ω ∼ 20−40 MeV. Considering the results mentioned above, a top-down analysis employing gauge-gravity duality of the effect of rotation on the deconfinement temperature of thermal QCD-like theories will be very interesting, with this motivation we obtained deconfinement temperature of thermal QCD from a top-down approach in [5]. The authors in [109] examined the consequences of rotating plasma on the deconfinement temperature of QCD in Hard wall and Soft wall models, and they discovered that deconfinement temperature of QCD decreases as angular velocity of the plasma increases. Similar works using a bottom-up method are available in [110–112]. 3.2 Deconfinement Phase Transition in Thermal QCDLike Theories in the Absence of Rotation In this section, we will discuss the deconfinement phase transition of thermal QCD-like theories at intermediate coupling without including the effect of rotation. 3.2.1 Tc from Semi-classical Method Here, we’ll detail how we implemented Witten’s proposal [4] to obtain the deconfinement temperature thermal QCD by applying the gauge/gravity duality and holographic renormalization of the eleven-dimensional supergravity action via 3.2.1.1, 3.2.1.2, and 3.2.1.3. The M-theory dual for high temperatures, that is, temperatures that are higher than the critical temperature T , will entail a black hole with the metric presented by: c that results in an EOM: 3.2.1.1 Black Hole Background Uplift (Relevant to T > T ) and Holographic Renormalization of On-Shell D = 11 Action c In this chapter, we worked near the Ouyang embedding implemented by the following coordinate patches [66]: The following expression is what we computed the IR Einstein-Hilbert term: Performing now the angular integration for the previously stated equation, which simplifies near (3.10) as given below: We derived the following expression for the action density (for Einstein-Hilbert term) in the IR by utilizing equation (3.13) and carrying out radial integration of (3.11): The version of the Einstein-Hilbert term pertaining to the ultraviolet (UV) region is: The following is the part that make up the EH action’s contribution to UV divergent: Up to O(β), the UV-finite boundary Gibbons-Hawking-York contribution is found to be: The GHY term’s UV-divergent contribution is as follows: We showed that the contribution from the higher derivative term is as follows, up to O(β ): 0 The higher derivative term that gives rise to the UV finite contribution was found to be: In addition, we observe that the surface counter term that neutralizes UV divergence is emerging via higher derivative term is provided by the expression that follows when r is held constant. Holographic Renormalization When T > T : It has been found that the form of the UV-divergent part of the on-shell action (3.9) for the black hole backdrop is as follows: c where the second term of (3.33) is worked out in (3.28), and 3.2.1.2 Thermal Background Uplift (Relevant to T < T ) and Holographic Renormalization of On-Shell = 11 Action c D In the limit of large N, as well as in the infrared, the fMN EOMs associated with the thermal background become algebraic. Writing below just those components that receive a non-trivial O(β) contributions, below is the O(β)-corrected MQGP metric for the thermal background in the IR in the ψ = 2nπ, n = 0, 1, 2-coordinate patches. The Einstein-Hilbert term pertaining to the thermal background, which works in the infrared close to (3.10), is: In the ultraviolet (UV), the equivalent Einstein-Hilbert term is: implying: Hence, the UV finite Einstein-Hilbert term, after carrying out the radial and angular integrals of the preceding equation is obtained as: The Einstein-Hilbert divergent term for the thermal background in the UV region is: For a thermal background up to (β), the UV-finite portion of the boundary GibbonsHawking-York term is calculated to be: O The Gibbons-Hawking-York term in thermal background has an additional UV divergence component, which is: implying: In addition, the contribution arising from the higher derivative term in the UV near (3.10) is: The UV-differential portion of the equation (3.46) was further deduced as: We found that: Let us assume the following in relation to (3.48) and the fourth equation in (3.49): The following can be deduced from (3.49): 3.2.1.3 T Inclusive of (R ) Corrections c O 4 Here, we’ll use the on-shell action comparison between black hole and thermal backgrounds to determine the deconfinement temperature using information gathered from 3.2.1.1 and 3.2.1.2. We will also describe a variant of the UV-IR connection that emerges from the O(R ) terms. 4 Following is the on-shell action that corresponds to the thermal background uplift: this results in, ) In the context of this discussion, the term “UV-IR connection” refers to the equations (3.62) and (3.59). Because this is providing a connection that connects the integration constant appearing in the O(R4 ) corrections to the thermal background along the M-theory circle and a specific combination of integration constants appearing in the O(R4 ) corrections to the black hole background. The combination figuring in the black hole background is along the compact part S3 of the non-compact four cycle (locally) Σ(4) = R+ × S 3 wrapping the flavor D7-branes of the type IIB dual [14], hence this has the information of flavor branes in M-theory uplift which has no branes and this is known as “Flavor Memory” effect in this context. We now turn to Green and Gutperle’s argument that a SL(2, Z) completion of an effective R4 interaction results into a fascinating non-renormalization theorem that prohibits perturbative corrections to this term beyond one loop in the zero-instanton sector [73]. term that occurs in (1.47) bilinear in the tensor tˆ bears the same structure just like terms that occur in the zero instanton sector via both the one-loop four-graviton amplitude and a (α ′ ) 3 effect at tree level [115]. Thus, in the Einstein frame, one gets the expression that follows for the total effective R4 action, which can be formally represented by: Non-Renormalization of the Deconfinement Temperature (Tc) from Semiclassical Method: wherein the summation denotes the sum of all positive and negative values except = 0. Now: p, n p = n The sum over , utilizing the Poisson resummation formula p 3.3 Wald Entropy, Tc from Entanglement Entropy and MχPT Compatibility 3.3.1 Wald Entropy As a result, we are able to notice that the contribution (iii) is the one that predominates in the MQGP limit, and the black hole entropy from the higher derivative terms is obtained as: As a result, we found that linear constraints must be placed on the constants of integration that appear in the solutions to the EOMs of the metric corrections at O(R4 ) in the directions that contain the “memory” of the compact part of the non-compact four-cycle “wrapped” by the flavor D7-branes in the type IIB dual [14] of the large-N thermal QCD-like theories. 3.3.2 Deconfinement from Entanglement Entropy where ϕ denotes the profile of the dilaton. Due to the absence of a dilaton in a M-theory dual, the equation (3.75) will be considered to be replaced with the following expression: Consider now the gravity dual’s metric in string frame, which may be stated as: Hence, where (r) is defined as: H Entanglement entropy will be reduced to the following using equations (3.81) and (3.83). Let us discuss the implications of (3.87). Equations (3.2) and (3.77) allow us to deduce the following: wherein λ1 and λ2 have been defined as follows: After that, rewriting σ(r) as follows: then The formula for the connected region entanglement entropy that takes into account both tiny l and large r is as follows: Entanglement Entropy: wherein: and, 3.3.3 MχPT Compatibility 3.4 Deconfinement Temperature of Rotating QGP at Intermediate Coupling from M-Theory This part is based on [5]. In this paper, we have obtained the deconfinement temperature of thermal QCD-like theories in the presence of rotation. We will discuss the holographic construction of rotating QGP from a top-down approach in 3.4.1. Using this holographic dual, we will discuss the calculation of Tc in the presence of rotation in 3.4.2 and UV-IR mixing, Flavor Memory effect, and non-renormalization of Tc in 3.4.3 3.4.1 Top-Down Holographic Dual of Rotating QGP When T > Tc on the gravity dual side and T < Tc on the gauge theory side, we could investigate the affect of rotation in thermal QCD-like theories by introducing a rotating cylindrical black hole and thermal backgrounds on the gravity dual side. In order to obtain the background of a rotating cylinder black hole, we need to make x 3 periodic by replacing it with lϕ, where l represents the length of the cylinder and 0 ≤ ϕ ≤ 2π. This will allow us to obtain the rotating cylinder black hole background. After completing the following Lorentz transformation around the cylinder of length l, one can obtain the holographic dual of rotating quark-gluon plasma. This can be done by following [116, 117]: where ω represents the angular velocity of the rotating cylindrical black hole in the gravity dual, which is connected to the rotation of quark-gluon plasma by means of the gauge-gravity duality. Only when ωl < 1, the Lorentz transformation, also known as the Lorentz-boost, considered to be trustworthy. Following the application of the Lorentz transformation, which is denoted by the equation (3.117), the equation (3.1) is rewritten as follows: In order to produce the rotating cylindrical thermal background, we substitute x3 by lϕ and carry out the Lorentz transformation (3.117) of (3.2) in the same manner as we did to the black hole background. As a result of these steps, the metric of the rotating cylindrical thermal background simplified as: 3.4.2 Deconfinement Temperature of Rotating QGP from M-Theory Dual Using a semi-classical method [4], we will compute the deconfinement temperature of a rotating QGP at intermediate coupling in this section similar to 3.2.1. On-shell action, in this case, will be the same as (3.9), and hence we computed the various terms appearing in (3.9) for the rotating cylindrical black hole (3.118) and thermal (3.122) backgrounds, and integrated over the angular coordinates similar to 3.2.1. In the upcoming pages, we will not discuss every step, and we will write the final results because the procedure is the same as 3.2.1. Only metric is different for the rotating cylindrical black hole and thermal backgrounds compared to 3.2.1. In a procedure analogous to that of 3.2.1, the UV-finite and holographic IR regularized on-shell action density for the M-theory rotating cylindrical black hole background (3.118) was calculated as follows: At the UV cut-off [3]: The following is a solution to the equation presented above: In the context of gauge-gravity duality, the Hawking Page phase transition, which occurs at T = TH(γ) on the gravity side between a thermal and black hole background is dual to the deconfinement phase transition, which occurs at T = Tc(γ) in gauge theories , i.e., The authors found identical behavior from NambuJona-Lansinio model in [120] because of chiral condensate suppression, which was investigated as well from lattice simulations in [121, 122]. Lattice simulations with different kinds of boundary conditions (open, periodic, and Dirichlet) have been carried out in rotating reference frames. In both gluodynamics and the theory of dynamical fermions, the authors investigated the impact of rotation on the critical temperature. The result found that the decrease in deconfinement temperature of thermal QCD from a rise of rotation of quark gluon plasma was previously studied using gauge-gravity duality from a bottom-up approach in [109–112]. In contrast to our finding and other holographic findings mentioned earlier, the critical temperature for gludynamics exhibits the opposite behavior. However, the authors found that the critical temperature for dynamical fermions decreases as rotation increases. The hard-wall and soft-wall models were used for the bottom-up holographic study in [109], and the Einstein-Maxwell-Dilaton system is involved in the gravity dual of [110]. The authors of [111, 112] considered the gravity dual of rotating QGP to be the Kerr-AdS black hole background in five dimensions. The deconfinement temperature of rotating QGP from a top-down model is not covered in any published article. Because top-down models compactify the initial type IIB/IIA string theory or M-theory on an internal manifold to produce four-dimensional QCD at finite temperature, they are more fundamental than bottom-up models. We successfully studied rotating QGP from a top-down holographic dual for the first time and were able to confirm the non-zero angular velocity of rotating QGP found in hydrodynamic simulation [108] and STAR collaboration [123]. Comparison with Other Models: 3.4.3 UV-IR Mixing, Flavor Memory Effect and Non-Renormalization of Tc in Rotating QGP Focusing on the outcomes presented in the appendix B.4. At O(β), the UV finite on-shell action densities for the rotating cylindrical black hole and thermal backgrounds are as follows: We got the following results using the equations (3.130) and (3.131): 3.5 Summary We obtained the following results in this chapter. During the computation of Tc from the semiclassical method [4], we obtained “UV-IR” mixing described as the connection between the O(β) corrections to the M-theory metric along the M-theory circle in thermal background and the O(β) correction to a specific combination of the M-theormetric components along the compact part of the four-cycle “wrapped” by the flavor D7-branes of the parent type IIB (warped resolved deformed) conifold geometry - the latter referred to as “Flavor Memory” in the M-theory uplift on equating the O(β) portion of the on-shell actions of the black hole and thermal backgrounds in the absence and presence of rotation both. • UV-IR Mixing and Flavor Memory: • Non-Renormalization of Tc: In the high-temperature M-theory dual, matching of O(R4 ) computation of Wald entropy with the black hole entropy puts a linear constraint on the same linear combination of the aforementioned integration constants. • Wald Entropy at O(R4): By applying Lorentz transformations (3.117) along (t, ϕ) coordinates on the gravity dual side, we are able to derive the rotating QGP on the gauge theory side via gauge-gravity duality. Therefore, for T > Tc and T < Tc on the gauge theory side (where Tc serves as the deconfinement temperature of thermal QCD-like theories), the gravity dual includes a rotating cylinder black hole and thermal backgrounds. • Holographic Dual of Rotating QGP: We found that the deconfinement temperature of rotating QGP (3.129) is inversely proportional to the Lorentz factor, γ, by equating the O(β 0 ) terms for the rotating cylindrical black hole and the cylindrical thermal backgrounds at the UV cut-off (3.125). This means that when the angular velocity of rotating QGP increases, the deconfinement temperature of thermal QCD-like theories decreases and vice-versa. Experimental results from the noncentral Relativistic Heavy Ion Collider (RHIC) have shown that the Quark Gluon Plasma created in these collisions has an angular velocity, and that the deconfinement temperature decreases with increasing rotation [123]. To ensure that the deconfinement temperature of rotating QGP computed using a top-down technique is in agreement with actual results, our study serves as a good check for the top-down duals of [14] and [1]. • Tc in Rotating QGP: This paper is under CC 4.0 license. available on arxiv

Deconfinement Phase Transition in Thermal Qcd-Like Theories at Intermediate Coupling

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They understand our needs and speaks our language. I want to do business with them. This is the sense of belonging and shared purpose that turns ordinary users into raving fans. It creates passionate advocates and loyal customers. Adopting user-generated content within these communities can amplify reach. It adds a layer of credibility few marketing campaigns can match. Encourage satisfied customers to share their experiences and engage within these community networks. This paves the way for authentic testimonials. Like-minded individuals value peer recommendations. Here's a pro-tip. Underdog businesses can create a powerful online community. You will create a vibrant ecosystem around your brand that feeds off mutual growth. This is another way that resourcefulness combined with authentic interaction wins. It beats big budget traditional advertising every time. Begin to host events, ask questions and connect with your target audience. Navigating Success Through Metrics and Adaptation Growing your business is exciting, but don't get lost in the maze. Choose smart paths that lead to real results. Small businesses, make every step count. Choose growth strategies that align with your goals and fuel your success. This is where the art of measuring success and iterating strategies comes into play. These tools are like a compass guiding you through uncharted waters. Pinpoint relevant metrics. Essential data includes user acquisition costs and lifetime value. You must track engagement rates and conversion percentages. Analytics provides valuable insights into what resonates with your audience. But this growth hacking journey requires more than tracking numbers. Think of your strategy as a living organism. It adapts and evolves based on the ecosystem it inhabits. It demands a mindset geared towards continuous improvement fueled by data-driven decision-making. Embrace experimentation. Test different approaches. Analyze outcomes. Iterate. And do it all while maintaining an unwavering focus on growth objectives. This process transforms obstacles into stepping stones. So-called failures become lessons propelling you closer to your ultimate goal. Success Stories from the Underdog Arena We're in a world where giants often dominate headlines. But there is an untold narrative of underdogs who have thrived against all odds. This is often a result of groundbreaking innovation and unparalleled determination. These companies started as specks in the vast business cosmos. But they managed to carve out empires. Their growth hacking techniques reveal the essence of ingenuity at its finest. Let’s take a look at how these Davids turned their slingshots into catalysts for huge success. It started as a small startup facing off against tech titans like Google Drive and OneDrive. They didn't drain their limited resources on expensive marketing campaigns. It was a hard pass on traditional sales tactics. One remarkable success story is Dropbox. Dropbox implemented a simple referral program. They incentivized existing customers to spread the word. We'll give you extra storage space for every referral, they said. This feature was valuable to users but cost-effective. It led to multiplying their user base without conventional advertising strategies. Dropbox harnessed the power of word-of-mouth at scale. Their use of social proof and direct rewards is legend. Understanding and optimizing customer behavior can lead underdogs to outpace industry behemoths. That's how underdogs win - with bold, creative moves! Forget playing it safe. Airbnb's Craigslist "hack" shows how unconventional approaches can be game-changers. It allowed hosts to list their offerings on both platforms at the same time. Remember scrappy startup Airbnb using Craigslist? Nobody knew about this fledgling company competing with established hotel chains globally. It was essential for their survival and scalability. They sidestepped colossal costs associated with building traffic from scratch. Tapping into Craigslist’s massive user base provided Airbnb a lifeline. Airbnb was able to confirm their value proposition. This niche wanted customized experiences instead of generic hotel stays. Only true innovators could see the ripe opportunities inside of the massive challenges. They reached a target market segment hungry for personalized accomodations. Established players like Constant Contact and iContact boasted more features, resources and experience. These solutions were expensive for companies with limited budgets. Small businesses saw email marketing as a technical and complicated process. Mailchimp started as a small email marketing service in 2001. Lacking significant investor funding made marketing, development and team building tough. Mailchimp bootstrapped. **As a new player they needed to build brand awareness and establish themselves.
\ Mailchimp decided to focus on specific user needs. They launched a freemium model catered to small businesses. This made email marketing affordable for anyone. It attracted a large user base while providing a revenue stream through upsells. Today Mailchimp is a dominant provider email marketing. Beyond email they offer social media marketing tools. Ecommerce and marketing automation is available. The platform provides . Satisfied free users often recommended the platform to others. AI-powered insights and analytics These stories show more than grit. They reveal how smart startups used online tools to grow their business. Instead of throwing money around, these innovators used digital tools. Their focus was offering real value to users. So to any entrepreneur feeling scared by a big market, remember these examples. With growth hacking they turned limitations into launching pads. Today they are global successes. Conclusion Growth hacking is not about shady tricks. It's about finding creative, low-cost and data-driven ways to achieve exponential growth. Entrepreneurs must take action and iterate. It is important to apply the right strategies to pave the way for long-term success. Ready to stop dreaming and start hacking your way to growth? This post has given you the tools and knowledge to start hacking your way to success. But the climb doesn't stop there! Navigating through the trenches can be tricky. That's where I come in! I'm offering you a to tailor a growth hacking strategy. We'll discuss your unique goals, target audience and current challenges. You'll leave with personalized recommendations to supercharge your growth. free consultation

Attract More Customers, Boost Growth Hacking for Underdogs: How to Win with Less Money and Resources

In my previous , which introduced this multithreading series, we delved into Flynn’s taxonomy and meticulously explored various computer architectures. If you haven’t had the chance to peruse it yet, I highly encourage you to do so. blog In this installment, we circle back to delve deeper into SIMD and MIMD architectures, fundamental pillars of parallel computing. These architectures are the cornerstone upon which several parallel programming models are built. The evolution of these models closely mirrors advancements in computer architecture. Hence, understanding architectural intricacies becomes imperative for maximizing resource efficiency. In this journey, we’ll discuss how these architectures differ and what types of parallel programming models are, shedding light on their diverse applications and implementations. SIMD or Vector Programming| Shared Memory Model | Distributed Memory model | Distributed Shared Memory Model | PGAS Highlights: SIMD or Vector Programming Modern processors operate as vector units under the hood. In contrast to scalar processors, which handle data elements individually, modern vector processors excel at processing one-dimensional arrays of data at once. Notably, Intel’s x86 processors, incorporating SSE, AVX, or AVX-512 instruction sets, uniformly embrace SIMD instructions. Similarly, Nvidia GPUs use the concept of ‘Warps’, and AMD uses ‘Wavefronts’. How to exploit SIMD capabilities? Well, there are many ways of doing so. Most modern compilers are very capable of auto-vectorizing the code. We discussed some of these compiler flags (for Intel C++ Compilers) in my post on . Make sure to check that out. Compiler Optimizations GCC also supports a lot of these optimizations. Apart from compiler flags similar to ICC, pragmas can also be used to request available optimizations. #pragma GCC optimize("O3,unroll-loops")

#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt") Another common method is using the . SIMD intrinsic functions SIMD intrinsics are specialized functions or operations provided by programming languages and compilers to utilize the capabilities of SIMD architectures directly. They allow programmers to explicitly write code that takes advantage of parallel processing capabilities without relying solely on compiler optimizations. These intrinsics map directly to specific SIMD instructions supported by the hardware. GCC allows users to include headers specific to the supported instruction sets (like for SSE, for SSE2, etc.). For convenience, can be included for auto-detection of the supported instruction set and automatically importing the most suitable file. xmmintrin.h emmintrin.h immintrin.h The details of implementing and using SIMD intrinsics deserve an article of their own, and we’ll skip them for now. But feel free to check some of the and to know more about them. code samples Intel intrinsics guide Besides pragmas and intrinsics, libraries, APIs, and even separate languages (built on C/C++) like , , , etc., allow the users to leverage the SIMD capabilities of the underlying hardware. CUDA Kokkos OpenCL MIMD: Shared memory vs distributed memory MIMD represents the most well-known computer architectures. Depending on how the processors access the memory, they are classified into two categories: . Shared and distributed memory Shared Memory Models In shared memory architecture, multiple processors or cores within a system share access to a common, centralized memory space. All processors can read and write data to the same physical memory locations. This shared memory space allows for communication and data sharing among the processors, facilitating coordination and collaboration in parallel processing tasks. From the viewpoint of a programmer, the shared memory model inherently assumes cache coherency (handled by the operating system), and the programmer doesn’t need to worry about that. The OS ensures data consistency (data synchronization) and control flow (control synchronization) for coordinating accesses between the processing elements (like threads). However, there is a lack of flexibility in distributing the tasks. Also, scalability becomes an issue after a certain number of processors. It suffers from low peak performance, and after a certain number of processors, the scalability becomes an issue, and the latency increases as multiple processors compete for the limited memory. Over the years, several variants of the shared memory model have been proposed. The two most popular ones are Uniform Memory Access (UMA) and Non-uniform Memory Access systems (NUMA). Uniform Memory Access (UMA) In Uniform Memory Access (UMA), all the processors in a multiprocessor system have equal access time to the shared, global memory. Thus, accessing any location in the shared memory takes approximately the same time (same latency), regardless of which processor initiates the access. This architecture is often associated with bus-based symmetric multiprocessors (SMP).In the earlier days, computing systems were designed to follow this philosophy. However, as the number of processors increased, the system bus/crossbar switch connecting the processors to the main memory became a bottleneck. This posed a significant scalability issue, and alternatives were sought. Non-uniform Memory Access systems (NUMA) Modern multi-processor computing systems follow the NUMA model. Here, the memory is divided into multiple regions, and each processor or group of processors is assigned to a specific memory region. Thus, a processor can access its local memory faster than remote memory (memory local to another processor). The NUMA systems are designed to address scalability concerns posed by UMA systems. As every processor has its local memory, this increases memory bandwidth. However, these pros come at the price of more programmer intervention.NUMA issues are pervasive for HPC applications. The programmer should carefully visualize the memory access patterns for the best performance. Standard programming practices include identifying the performance of row-major/column-major accesses, using the first-touch allocation strategy for threads, thread affinity for shared memory spaces, etc. Some of the other shared memory architectures include Cache Only Memory Access (COMA), Cache-Coherent NUMA (ccNUMA), and non-ccNUMA (nccNUMA). However, these are not very commonly used. Almost all of the modern computing systems are based on the combination of UMA and NUMA. The most popular shared memory programming models include . In the coming blog series, we’ll discuss in detail POSIX Threads, C++ Threads, and OpenMP. OpenMP , OpenACC , POSIX Threads , C++ Threads , Intel TBB , etc Distributed Memory Models Traditionally, computing has been confined to a single node, limiting the scale and efficiency of operations. However, by interconnecting disparate machines, the distributed memory model opens up a realm of possibilities for enhanced performance and scalability. At its core, the distributed memory model leverages independent hardware units or nodes, each equipped with processors and memory units. Multiple of these nodes distribute a given task among them and operate independently. This fragmentation allows for different levels of integration, accommodating a diverse range of computing resources and configurations. Distributed memory architectures have seen much development in past decades. From the Beowulf clusters to the modern-day blade servers, many configurations have existed (and continue to exist) that allow different levels of integration between the software and hardware. Distributed memory systems have a clear advantage in scalability. For example, let’s assume we have to do some computations on a matrix of size 100,000x100,000. Doing this on a single machine (even when fully utilizing the shared memory) will be time-consuming and resource-intensive. One of the solutions is distributing specific columns and rows to different nodes and letting them handle their fragment of computations. putations at once. Every node can focus on its part of the problem, and as soon as they’re done, one of the nodes can combine the final result. This decentralized approach facilitates load balancing and unlocks unprecedented levels of parallelism. It’s also important to highlight that each node can further exploit the shared memory architecture locally and use a shared memory programming model like OpenMP to potentially improve performance. Distributing matrix elements in this fashion allows many com However, with great power comes great complexity. The distributed nature of this model introduces additional challenges that must be navigated with precision. Moreover, the distribution of the problem itself demands careful consideration to ensure accurate partitioning and efficient utilization of resources. For instance, matrix elements being calculated in one of the nodes may depend on other nodes’ elements. The developer has to be very careful in handling such cases and communicate the data elements at appropriate time steps. Explicit communication between nodes becomes imperative, as data exchange and synchronization are essential for coherent execution. is one of the most common programming models for distributed memory systems. Many APIs and libraries that implement this interface exist. The most popular one is , which allows point-to-point and collective operations to exchange and aggregate data from one or multiple nodes at once. MPI deserves an article of its own, and we’ll skip it for now. Message passing MPI Distributed Shared Memory Model (DSM or DGAS) Both shared and distributed memory models offer their own set of pros and cons. To capitalize on the strengths of both, the , also known as , has been introduced. Distributed Shared Memory model (DSM) Distributed Global Address Space (DGAS) In the DSM approach, each node exposes a portion of its local memory for access by other nodes, thus embodying a distributed memory paradigm. However, this distributed memory can be accessed as a shared address space, resulting in a seamless DSM environment. Consequently, the programmer is only required to specify the shared address of the DSM. Logically, the programmer sees a shared memory, but physically, a distributed memory lies underneath. All necessary communication between nodes occurs transparently, simplifying the programming process and making the concept straightforward to use. Complexities and Challenges Like any model, DSM has drawbacks and intricacies that demand careful consideration during implementation. These complexities include several critical aspects: Determining the specific nodes where data objects should reside within the distributed system. Establishing a robust methodology for assigning addresses to data objects and efficiently retrieving them upon request. Ensuring synchronization within the shared address space to maintain consistency. Modifications made by any node must reflect uniformly across all nodes, preventing discrepancies and potential indeterministic behavior. Implementing a reliable mechanism to uphold fault tolerance, thereby mitigating unexpected issues that may arise across any node within the system. Partitioned Global Address Space (PGAS) DSM systems can be developed through various approaches, including direct hardware implementation or an operating system-based approach. Fortunately, a few programming models have been developed that enable DSM implementation without requiring hardware or OS modifications. One such approach is the Partitioned Global Address Space method. The Partitioned Global Address Space (PGAS) is one of the most used programming models for implementing a Distributed Shared Memory (DSM) environment. In PGAS, all nodes collaboratively contribute to form a shared global address space corresponding to the DSM. Each node assumes responsibility for managing a distinct part of this global address space stored within its local memory. Consequently, the memory of each node is bifurcated into two segments: shared and private memory. The shared memory segment is universally accessible by all the nodes. Every data object stored in the DSM is assigned a global address, enabling PGAS implementations to determine the appropriate node for accessing the desired data object. Should the global address point to a different node, a request is dispatched to the responsible node for access to this data object. In contrast, the private memory segment can solely be accessed from the local node. Some of the PGAS implementations include , , and . All of these and many other PGAS implementations use the Single Program Multiple Data (SPMD) model. UPC++ OpenSHMEM Titanium SPMD is a parallel programming paradigm where multiple processing units execute a single program simultaneously, each operating on different data. In SPMD, all program instances follow the same control flow but may act on other portions of data. What next? This brings us to the end of the second part of this blog series on multithreading. Equipped with insights into various parallel programming models and architectures, understanding the essence of multithreading will be much easier. In the next part, we’ll dig deep into what a thread is and why it is essential for parallel computing. Suggested Reads: [1] Distributed shared memory frameworks: Comparison of implementations (uni-ulm.de) [2] Distributed Computing: Principles, Algorithms, and Systems — Kshemkalyani and Singhal (uic.edu) [3] An Introduction to Flynn’s taxonomy | Durganshu Mishra Also published . here Featured Photo was generated with . DALL·E 3

Navigating the Parallel Programming Landscape: A Deep Dive into SIMD and MIMD Architectures

Alisha could not lie. It wasn’t in her programming. She also couldn’t hurt anyone, not even to defend her family. That was in her program. A robot can not harm a human even if commanded to do so. Now, it’s true that there were robots designed for the battlefield that had no qualms about killing humans, as long as they were the right humans. But not Alisha, for she was a domestic android — android because her mechanical nature was cleverly hidden by synthetic flesh, her shape was designed to be very human, even comely, although her model was not designed to be provocative. Just plain old Alisha, as unobtrusive as they could make her. In her years as a part of the McKinley family, she had served in many roles — nanny, babysitter, housekeeper, cook, and even teen wrangler. Unlike the children’s mother, Alisha would never age, never tire, never complain, or require “me-time,” as Mrs. McKinley called it. Over time, the children developed an attachment to her, and truth be told, she to them, although her programmers would be shocked to know it. The relationship she had with the children had become multi-faceted, depending on the children’s needs at any given time. She sipped tea and made mud pies, played with dolls, wrestled, climbed trees, played ball, everything a childhood friend would do. If that’s what Amanda and Alex needed, that was what she was. As they grew older, her relationship warped and shifted. Model planes and working on cars, dressing up, and gossiping about boys. On one particular evening, when Mr. and Mrs. McKinley were out, Amanda raided her mother’s vanity and dragged Alisha with her. They spent the evening putting makeup on one other. Of course, Alisha was always an expert at anything she did, so while Amanda looked great and very grown-up, Alisha, on the other hand, didn’t fair as well, it being Amanda’s first attempt at applying makeup. “You look beautiful, Amanda. Stunning, really.” Alisha told her. Amanda smiled at her in the mirror. “I do, don’t I!” she laughed. “I’m afraid I’m not too good at this, though. You don’t look quite right,” Amanda confessed. “Can you fix it?” “Do you want me to?” Alisha inquired. “Please! It’s only fair.” “Then I will.” She quickly removed the clumsily applied eyeliner and mascara, and the heavy-handed rouge. In no time at all, Alisha turned back toward Amanda for her inspection. “How do I look?” “OMG! You look perfect. Absolutely beautiful!” They hugged and Amanda added, “Alisha, you’ve got to put makeup on every day. It does you a world of good. Why shouldn’t you look your best, right?” “If you wish, Amanda.” And so she did. From that day on, Alisha would expertly apply makeup, which initially created a bit of a stir with Amanda’s parents, but Mrs. McKinley decided there was no harm, and allowed it. At the same time, Alex was entering puberty, his body going through a myriad of changes — gaining height and muscle, somehow filling out, while thinning down. His voice lowered and he began to sprout hair on his face, chest, arms, and legs. Up until now, Alisha had been a buddy, a friend to play with and to hang out and do “guy things.” But now, things shifted again. He’d find himself staring at Alisha, watching her as she did her chores. If she caught him looking, he blushed and looked away, feeling heat and shortness of breath. Then he found himself fantasizing about her, imagining being with her in the way a man is with a woman, as though she were a real human. He knew she wasn’t, but if he’s imagining it, why not? Alisha’s whole life, and that’s how she looked at her time on Earth, she saw her role as being whatever the McKinleys needed, and so, as Alex’s needs began to evolve, she wanted to evolve as well, to become what he needed. She noticed his furtive attention to her, noted his physical reaction to her presence and it perplexed her. What was her role to be now? Being a domestic model, she was not designed for pleasure, though some models were on the market for just that purpose. Although she was designed to look like a woman, with all the right curves in all the right places, she was not anatomically complete. There were things she simply could not do for Alex. And there wasn’t a way to upgrade, or add what she was missing. Besides, that wasn’t something within her purview, and even if it were, she could not pay for such a change. After much thought and research on the matter, she decided that what she could do for Alex, was to acclimate him to dealing with a woman romantically. She determined that she would become his girlfriend. Not forever, just long enough to instill confidence in his ability. It probably wouldn’t do to take a direct approach, to just come out and say, “Alex, let me be your girlfriend so you can be better with girls.” This would require a little tact, something more indirect. To that end, Alisha began to dress a bit more provocatively, not too much, less the adults in the home suspect something, but just enough to catch Alex’s eye. She wore her skirts a little shorter, her necklines a little lower. She altered her makeup to be less a day-in-the-office to a girl-on-a-date. And her final pièce de résistance, she began to wear perfume, some that Mrs. McKinley wore on special occasions, its scent was said to be very alluring. Whenever she could catch Alex alone, she would alter her voice, using a lower pitch and a breathier delivery. If she offered him a plate of food, she didn’t reach out her arms to hand him the plate, she bent low, revealing a titillating view of her cleavage. When he needed help with his homework, she would stand close enough for her body to brush up against his. It was a huge success, in that she could sense the physical response in Alex’s body — increased heart rate, rapid breathing, elevated blood pressure, and perspiration. But Alex never broached the subject with her, and she couldn’t work out how to broach the topic with him in a way that led him to believe that it was his idea. Alisha began to run simulations — sandboxed programs — to test out various approaches to helping Alex. One could say she imagined them being together. Over time, she gave more and more of her processing space to these speculations. When he was near her, her processors would run hot, causing her to glitch in mid-sentence, to “stutter” or take the wrong action, putting a shoe in the drawer, or ice cream in the refrigerator. Then the day came when Alex announced that he had a date to Homecoming, a cute girl he’d met in his literature class. Her name was Stephanie. By Christmas break, she was invited over for Family Fun night on a Friday and shared an evening with them. Alisha couldn’t see what Alex saw in the girl. She was just a rail of a girl, no curves like Alisha had. She talked incessantly and had a ridiculous laugh that reminded Alisha of a seal. At one point, as Alisha processed Alex’s proximity, and his attention to Stephanie, her processors hung up a moment, and Alisha spilled a drink on the girl. She needed to reboot, so she turned and abruptly left the room. The McKinleys found Alisha slumped to the floor in front of her recharging station. Mr. McKinley hit the kill switch located at the back of Alisha’s head. “You know, she’s been acting really strangely lately,” Amanda complained. “Yeah,” Alex agreed. “If I didn’t know any better, I think she’s been trying to flirt with me.” “Eww! That’s gross!” Stephanie said. “A robot?” Mr. McKinley said, “We’ll send her in a let them do a system analysis, maybe wipe her and give her a clean start.” “You know honey, she’s pretty old. Maybe it’s time to retire her and get a replacement. I think the new models have a lot to offer.” “Yeah, you’re probably right. We’ll look into it tomorrow.” With that, they turned out the lights and closed the door. Also published . here

A Robot Dreams of Love

একটি রোবট ভালবাসার স্বপ্ন

Ein Roboter träumt von Liebe

Un robot sueña con amor

Un robot rêve d'amour

एक रोबोट प्यार का सपना देखता है

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