In last trading session, Hyperfine Inc (NASDAQ:HYPR) saw 0.57 million shares changing hands with its beta currently measuring 0.85. Company’s recent per share price level of $1.17 trading at -$0.05 or -4.

Hyperfine Inc (NASDAQ:HYPR) Reduces -37.77% In A Week: What’s Lifting The Stock?

The 36-month beta value for HYPR is also noteworthy at 0.73. There are mixed opinions on the stock, with 2 analysts rating it as a “buy,” 0 rating it as “overweight,” 1 rating it as “hold,” and 0 rating it as “sell.

Analyzing the Price-to-Earnings Ratio of Hyperfine Inc (HYPR)

Hyperfine Inc (NASDAQ: HYPR) has experienced a rise in its stock price by 10.67 compared to its previous closing price of 1.78. However, the company has seen a gain of 0.51% in its stock price over the last five trading days.

Hyperfine Inc (HYPR) Shares Up Despite Recent Market Volatility

Welcome to this week's Chutes & Ladders, our roundup of hirings, firings and retirings throughout the industry.

Chutes & Ladders–Delta Dental of California promotes first female CEO

About two years after first introducing deep learning artificial intelligence technology capable of enhancing certain images captured by its MRI-on-wheels system, Hyperfine has now gotten the regul | The latest nod marks Hyperfine’s eighth FDA clearance in the span of three years for its MRI scanner-on-wheels.

Hyperfine wins FDA nod to expand MRI image-sharpening AI

Research by experts at King's and Evelina London Children's Hospital has found major advances for detecting brain conditions in babies using portable MRI scanners.

Major advance for detecting brain conditions in babies

October 10, 2023--(BUSINESS WIRE)--Hyperfine, Inc. (Nasdaq: HYPR), the groundbreaking medical device company that has redefined brain imaging with the world’s first FDA-cleared, portable ...

Hyperfine, Inc. Announces Promotions of Two Key Clinical Affairs Executives

October 09, 2023--(BUSINESS WIRE)--Hyperfine, Inc. (Nasdaq: HYPR), the groundbreaking medical device company that has redefined brain imaging with the world’s first FDA-cleared portable magnetic ...

Hyperfine, Inc. Receives FDA Clearance for Updated AI-powered Software with Improved Image Quality for All Swoop® System Sequences

“We have shown that our portable Hyperfine MRI can visualise brain health and pathology in the baby. “These results will inform our planned studies and new treatments of malnutrition ...

New bedside MRI scanning could pick up brain problems in sick babies

xperts have developed a method for using portable MRI scanners to pick up brain problems in babies at the bedside. A team from the Evelina London Children’s Hospital and King’s College London developed scanning techniques using a weakened magnetic field, instead of the stronger ones needed for traditional MRI machines.

Hyperfine

hyperfine

As developers, we spend a lot of our time in the terminal. Most of the developers I talked to use several tools in their console... yes, the console, that itchy thing that will only display letters and numbers. This tool is more powerful than you think. And there are very many nice handy tools to use. This post outlines my list of tools that every developer must have or has heard about ;). So let's get started! Utils - Auto-correct miss-typed commands thefuck is one of those utilities you won't be able to live without once you've tried it. Whenever you mis-type a command and get an error, just run and it'll auto-correct it. Use up/down to choose a correction, or just run to just execute the most likely immediately. thefuck fuck fuck --yeah - Community-maintained docs ) tldr (better man is a huge collection of community-maintained man pages. Unlike traditional man pages, they're summarized, contain useful usage examples and nicely colourized for easy reading tldr - Count lines of code ) scc (better cloc gives you a breakdown of number of lines of code written in each language for a specific directory. It also shows some fun stats, like estimated cost to develop and complexity info. It's incredibly fast, very accurate and has support for a wide range of languages scc - Listing Files ) exa (better ls is a modern Rust-based replacement for the command, for listing files. It can display file-type icons, colors, file/folder info and has several output formats - tree, grid or list exa ls - Disk Usage ) duf (better df is great for showing info about mounted disks and checking free space. It produces a clear and colorful output, and includes options for sorting and customizing results. duf - Download Utility ) aria2 (better wget is a lightweight, multi-protocol, resuming download utility for HTTP/HTTPS, FTP, SFTP, BitTorrent and Metalink, with support for controlling via an RPC interface. It's incredibly , and has tons of . There's also - a nice web interface companion. aria2 feature rich options ziahamza/webui-aria2 - Reading Files ) bat (better cat is a clone of with syntax highlighting and git integration. Written in Rust, it's very performant, and has several options for customizing output and theming. There's support for automatic piping and file concatenation bat cat - File Comparisons ) diff-so-fancy (better diff gives you better looking diffs for comparing strings, files, directories and git changes. The change highlighting makes spotting changes much easier, and you can customize the output layout and colors diff-so-fancy - Watch for changes entr lets you run an arbitrary command whenever file changes. You can pass a file, directory, symlink or regex to specify which files it should watch. It's really useful for automatically rebuilding projects, reacting to logs, automated testing, etc. Unlike similar projects, it uses kqueue(2) or inotify(7) to avoid polling, and improve performance entr - Reading + writing metadata exiftool ExifTool is handy utility for reading, writing, stripping and creating meta information for a wide variety of file types. Never accidentally leak your location when sharing a photo again! - Duplicate file finder fdupes is used for identifying and/or deleting duplicate files within specified directories. It's useful for freeing up disk space when you've got two or more identical files jdupes - Fuzzy file finder ) fzf (better find is an extremely powerful, and easy to use fuzzy file finder and filtering tool. It lets you search for a string or pattern across files. fzf also has available for most shells and IDEs, for showing instant results while searching. This by Alexey Samoshkin highlights some of it's use cases. fzf plugins post - Command benchmarking hyperfine makes it easy to accurately benchmark and compare arbitrary commands or scripts. It takes care of warm-up runs, clearing the cache for accurate results and preventing interference from other programs. It can also export results as raw data and generate charts. hyperfine - Process viewer procs (better ps) is an easy to navigate process viewer, it has colored highlighting, makes sorting and searching for processes easy, has tree view and updates in real-time procs - Search within files ) ripgrep (better grep is a line-oriented search tool that recursively searches the current directory for a regex pattern. It can ignore the contents of and skip binary files. It's able to search within compressed archives, or only search specific extension, and understands files using various encoding methods ripgrep .gitignore - Fast, incremental file transfer rsync lets you copy large files locally or to or from remote hosts or external drives. It can be used to keep files across multiple locations synced, and is perfect for creating, updating and restoring backups rsync - Find and replace ) sd (better sed is an easy, fast and intuitive find and replace tool, based on string literals. It can be executed on a file, an entire directory, or any piped text sd - Directory hierarchy ) tre (better tree outputs a tree stye list of files for your current or a specified directory, with colors. When running with the option, it numbers each item, and creates a temporary alias that you can use to quickly jump to that location tre -e CLI Monitoring and Performance Apps - Bandwidth utilization monitor bandwhich Show bandwidth usage, connection information, outgoing hosts and DNS queries in real-time - Container metrics and monitoring ctop Like , but for monitoring resource usage for running (Docker and runC) containers. It shows real-time CPU, memory and network bandwidth as well as the name, status and ID of each container. There's also a built-in log viewer, and options to manage (stop, start, exec, etc) containers top - Resource monitoring ) bpytop (better htop is a fast, interactive, visual resource monitor. It shows top running processes, recent CPU, mem, disk and network history. From the interface you can navigate, sort and search - there's also support for custom color themes bpytop - Resource monitor + web and API glances is another resource monitor, but with a different feature set. It includes a fully responsive web view, a REST API and historical monitoring. It's easily extendable, and can be integrated with other services glances - Interactive ping tool ) gping (better ping can run ping tests on multiple hosts, while showing results in real-time graph. It can also be used to monitor execution time, when used with the flag gping --cmd - Disk usage analyzer and monitor ) dua-cli (better du let's you interactively view used and available disk space for each mounted drive, and makes freeing up storage easy dua-cli - Command line speed test utility speedtest-cli just runs an internet speed test, via speedtest.net - but straight from the terminal :) speedtest-cli - DNS lookup client ) dog (better dig is an easy-to-use DNS lookup client, with support for DoT and DoH, nicely coloured outputs and the option to emit JSON dog CLI Productivity Apps Surf the web, play music, check emails, manage calendars, read the news and more, all without leaving the terminal! - CLI web browser browsh is a fully interactive, real-time, and modern text-based browser rendered to TTYs and browsers. It supports both mouse and keyboard navigation, and is surprisingly feature rich for a purely terminal based application. It also mitigates battery drain issues that plague modern browsers, and with support for MoSH, you can experience faster load times due to reduced bandwidth browsh - Bookmark manager buku is a terminal-based bookmark manager, with tons of configuration, storage and usage options. There's also an optional and , for accessing your bookmarks outside of the terminal buku web UI browser plugin - Music browser / player cmus is terminal music player, controlled with keyboard shortcuts. It has support for a wide range of audio formats and codecs, and allows organising tracks into playlists and applying playback settings cmus - Track crypto prices cointop show current crypto prices, and track the price history of your portfolio. Supports price alerts, historical charts, currency conversion, fuzzy searching, and much more. You can try the demo via the web at , or by running cointop cointop.sh ssh cointop.sh - Search the web from the terminal ddgr is like , but for DuckDuckGo. It's fast, clean and easy, with support for instant answers, search completion, search bangs, and advanced search. It respects your privacy by default, and also has HTTPS proxy support, and works with Tor ddgr googler - Code editor ) micro (better nano is an easy to use, fast and extendable code editor with mouse support. Since it's packaged into a single binary, installation is as simple as micro curl https://getmic.ro | bash - Calendar client khal is a terminal calendar app, which shows upcoming events, month and agenda views. You can sync it with any CalDAV calendar, and add, edit and remove events directly khal - Email client mutt is a classic, a terminal based mail client for sending, reading and managing emails. It supports all mainstream email protocols and mailbox formats, allows for attachments, BCC/CC, threads, mailing lists and delivery status notifications mut - RSS / ATOM news reader newsboat is an RSS feed reader and aggregator, for reading the news, blogs and following updates directly from the terminal newsboat - Todo + task management taskwarrior is a CLI task management/ todo app. It's both simple and unobtrusive, but also incredibly powerful and scalable, with advanced organisation and query features built in. There's also a lot (700+!) of extra for extending it's functionality and integrating with third-party services task plugins - Terminal UI for Reddit tuir is a great one if you want to look like you're working, while actually browsing Reddit! It's got intuitive keybindings, custom themes, and can render images and multi-media content too. There's also for hacker news tuir haxor CLI Dev Suits - HTTP / API testing testing client httpie is a HTTP client, for testing, debugging and using APIs. It supports everything you'd expect - HTTPS, proxies, authentication, custom headers, persistent sessions, JSON parsing. Usage is simple with an expressive syntax and colourized output. Like other HTTP clients (Postman, Hopscotch, Insomnia, etc) HTTPie also includes a web UI httpie - Full Docker management app lazydocker is a Docker management app, that lets you view all containers and images, manage their state, read logs, check resource usage, restart/ rebuild, analyse layers, prune unused containers, images and volumes, and so much more. It saves you from needing remember, type and chain multiple Docker commands. lazydocker - Full Git management app lazygit is a visual git client, on the command line. Easily add, commit and puch files, resolve conflicts, compare diffs, manage logs, and do complex operations like squashes and rewinds. There's keybindings for everything, colors, and it's easily configurable and extenable lazygit CLI External Sercvices - Reverse proxy for sharing localhost ngrok safely* exposes your localhost to the internet behind a unique URL. This lets you share what you're working on with you're remote colleagues, in real-time. Usage is , but it's also got a lot of advanced features for things like authentication, webhooks, firewalls, traffic inspection, custom/ wildcard domains and much more ngrok very simple - Fast file sharing transfer.sh makes uploading and sharing files really easy, directly from the command line. It's free, supports encryption, gives you a unique URL, and can also be self-hosted.I've written a Bash helper function to make usage a bit easier, you can or try it out by running transfer find it here bash <(curl -L -s https://alicia.url.lol/transfer) - Deploy a site in seconds surge is a free static hosting provider, that you can deploy to directly from the terminal in a single command, just run from within your directory! It supports custom domains, auto SSL certs, pushState support, cross-origin resource support - and it's free! surge surge dist - Check the weather wttr.in is a service that displays the weather in a format that's digestible in the command line. Just run or to try it out. There's URL parameters to customise what data is returned, as well as the format wttr.in curl wttr.in curl wttr.in/London CLI Fun - Have an ASCII cow say your message cowsay is a configurable talking cow. It's based off the by Tony Monroe cowsay original - Output text as big ASCII art text figlet outputs text as ASCII art figlet - Make console output raibow colored lolcat makes any text passed to it rainbow coloured lolcat - Show system data and ditstro info neofetch prints distro and system info (so you can flex that you use Arch btw on r/unixporn) neofetch As an example, I'm using , , and to create a custom time-based MOTD shown to the user when they first log in. It greets them by their name, shows server info and time, date, weather and IP. . cowsay figlet lolcat neofetch Here's the source code Conclusion I think there is at least one interesting tool for you and your productivity enlisted in this list. Hope you enjoy! Also published . here

Unleashing the Power of the Terminal: Essential Tools Every Developer Should Know

Introduction Reference counting (RC) has rather been a minor party to the other garbage collection (GC) algorithms in functional programming in the last decades as, for example, and use non-RC GC. However, several recent papers, such as and , showed the efficiency of highly optimized RC GC in functional languages with sacrifice or restriction of some language features like circular references. The latter paper introduced an efficient RC GC algorithm called Perceus which is basically RC. OCaml Haskell Counting Immutable Beans: Reference Counting Optimized for Purely Functional Programming Perceus: Garbage Free Reference Counting with Reuse all-in-one In this post, I describe my experience and some caveats about implementing and gaining benefits from the Perceus RC. I've been developing and implemented a large part of the Perceus RC there. I hope this post helps someone who is implementing the algorithm or even deciding if it's worth implementing it in their own languages. a programming language called Pen Overview of Perceus The Perceus reference counting algorithm is a thread-safe ownership-based reference counting algorithm with several optimizations: Heap reuse on data structure construction and deconstruction (pattern matching) Heap reuse specialization (in-place updates of data structures) Non-atomic operations or atomic operations with relaxed memory ordering for heap blocks not shared by multiple threads Borrow inference to reduce reference count operations By implementing all of those optimizations in , they achieved GC overhead much less and execution time faster than the other languages including OCaml, Haskell, and even C++ in several algorithms and data structures that frequently keep common sub-structures of them, such as red-black trees. For more information, see . the Koka programming language the latest version of the paper Implementing the algorithm What I've implemented so far in Pen are two core functionalities of the Perceus algorithm: In-place updates of records on heap This corresponds to heap reuse specialization described above. Relaxed atomic operations on references not shared by multiple threads Due to some differences in language features between Koka and Pen, I needed to make some modifications to the algorithm. First, Pen doesn't need any complex algorithm for in-place record updates with heap reuse specialization because it has , and its lowered directly into its mid-level intermediate representation (MIR) where the RC algorithm is applied. syntax for record updates Secondly, although I've also implemented generic reuse of heap blocks that matches their frees and allocations in functions initially, I've reverted it for now since I realized that it won't improve performance much in Pen because of the lack of pattern matching syntax with deconstruction and another optimization of small record unboxing planned to be implemented later. In addition, the implementation doesn't include borrow inference yet as it had the least contribution to the performance reported in a previous paper. The main part of the algorithm is implemented in the source files of a compiler itself and an FFI library in Rust listed below: https://github.com/pen-lang/pen/blob/d44df6d9cdcbe97fcdd5ac14c4de30f4897664ff/lib/mir-fmm/src/reference_count/pointer.rs https://github.com/pen-lang/pen/blob/d44df6d9cdcbe97fcdd5ac14c4de30f4897664ff/lib/ffi/src/arc/arc_block.rs Counting back synchronized references to 0 In this section, I use the term "synchronized" to mean "marked as shared by multiple threads." In Koka and Lean 4, they use the term "shared" to mean the same thing but I rephrased it to reduce confusion. In the Perceus reference counting GC, memory blocks have mainly two and states represented by positive and negative counts respectively. Heap blocks are before they get shared with other threads and are never reverted back to states once they get synchronized. But you may wonder if this is necessary or not. If we have a memory block with a reference count of 1, that also means it's not shared with any other threads anymore. So isn't it possible to use a common count value of 0 to represent unique references and reduce the overhead of some atomic operations potentially? un-synchronized synchronized synchronized un-synchronized The answer is no because in that case, we need to synchronize memory operations on those references back with drops of those references by the other threads with release memory ordering. For example, let's consider a situation where a thread shares a reference with the other thread: un-synchronized Thread A shares a reference with thread B. Some computation goes on... Thread B drops the reference. Thread A drops the reference frees its inner memory block. and Or, thread A reuses the memory block for heap reuse optimization mentioned in the earlier section. So if references can be back, we always need to use atomic operations with acquire memory ordering at the point (4) above to make all side effects performed by thread B at the point (3) visible for thread A. Otherwise, thread A might free or rewrite memory locations thread B is trying to read! So as a result, we are rather increasing the overhead of atomic operations for references never before. un-synchronized synchronized Benefitting from the algorithm In general, to get the most out of heap reuse in the Perceus algorithm, we need to write codes so that data structures filled with old data are updated with a small portion of new data. Pen's compiler previously had a performance bug where a relatively old data structure was merged into a new one of the same type. As a result, the code to merge two pieces of data was taking almost double in time although the logic was semantically correct. Recursive data types When your language has record types and syntax for record field access, things might be a little complex. Let's think about the following pseudo code where we want to update a recursive data structure of type in place (The code is written in but assume that we implemented it with Perceus.): A Elm type alias A =
  { x : Maybe A
  , y : Int
  }

f : A -> A

-- From here, assume that we are in a function scope rather than a module scope.
foo : A
foo = { x = Nothing, y = 42 }

bar : A
bar =
  -- Here, we want to reuse a memory block of `foo`...
  { foo |
    x = case foo.x of
      Nothing -> Nothing
      -- There are two references to `x` on evaluation of `f x` here!
      Just x -> f x
  } At the line of , the program applies a function to a field value which originates from . However, at this point of the function application, we are still keeping the record value itself and the value of has two references! Therefore, heap reuse specialization (i.e. in-place record update) cannot be applied there. In order to update the value of in place instead, we need to rather deconstruct into its inner values first as follows. Just x -> f x f x foo foo x x foo bar =
  let { x, y } = foo
  in
    { x =
      case x of
        Nothing -> Nothing
        Just x -> f x
    , y = y
    } Note that, even if languages do not support record deconstruction, for self-recursive types, dropping fields containing the types themselves is possible in most cases in practice because otherwise such types' values cannot exist at runtime unless they are dynamically generated in functions or thunks in those fields. When I look at , it seems to support record types but I couldn't find out how it handles this specific case yet. It's also an option to expose the compiler's details and allow annotations to enforce in-place updates for end-users while it might not be the best option in a long term. the Koka's documentation Benchmarking Here, I'm excited to show some benchmark results and their improvements. Details of their configurations are in a section later. Note that Pen still lacks some basic optimizations to reduce heap allocations (e.g. lambda lifting, unboxing small values on heap.) So the eventual performance improvements by Perceus would be lower than those results. Since I've never implemented the other GC methods like mark-and-sweep for Pen before, this is not a comparison of RC GC vs non-RC GC but rather a proof of how performant traditional thread-safe RC can be adopting Perceus on functional programming languages. Atomic RC (seconds) Perceus RC (seconds) Improvement (times) Conway's game of life 2.136 1.142 1.87 Hash map insertion 0.909 0.255 3.57 Hash map update 1.935 0.449 4.31 Configuration Conway's game of life The implementation uses lists to represent a field and lives so that it causes many allocations and deallocations of memory blocks on heap. Field size: 20 x 40 Iterations: 100 Implementation Hash map insertion/update The map update benchmark includes the time taken by insertion for map initialization as well. A number of entries: 100,000 Key type: 64-bit floating point number Data structure: Hash-Array Mapped Trie (HAMT) Implementation Insertion Update Conclusion In my experience so far, implementing the Perceus algorithm appears to be fairly straightforward compared with the other non-RC GC algorithms while there are a few stumbling blocks especially if you are not familiar with low-level concurrency and atomic instructions. I'm pretty happy having the algorithm implemented in my language and seeing it performing well despite its simple implementation. The Perceus RC can be a game changer in functional programming as it outperforms traditional GC on several common patterns in functional programming. However, it's definitely not for everyone and most likely affects language design. Finally, thanks for reading! I would appreciate your feedback on this post and . The language's new release has been blocked by but the ticket had some progress in the last few weeks. So I can probably release v0.4 of it soon... the Pen programming language LLVM 14 adoption in Homebrew Also, special thanks to the developers of for answering my questions on the algorithm! That was really helpful! Koka Appendix Raw benchmark results Environment: > uname -a
Linux xenon 5.13.0-1033-gcp #40~20.04.1-Ubuntu SMP Tue Jun 14 00:44:12 UTC 2022 x86_64 x86_64 x86_64 GNU/Linux

> lscpu
Architecture:            x86_64
  CPU op-mode(s):        32-bit, 64-bit
  Address sizes:         46 bits physical, 48 bits virtual
CPU(s):                  4
  On-line CPU(s) list:   0-3
Vendor ID:               GenuineIntel
  Model name:            Intel(R) Xeon(R) CPU @ 2.20GHz
Virtualization features:
  Hypervisor vendor:     KVM
Caches (sum of all):
  L1d:                   64 KiB (2 instances)
  L1i:                   64 KiB (2 instances)
  L2:                    512 KiB (2 instances)
  L3:                    55 MiB (1 instance)

> lsmem
Memory block size:       128M
Total online memory:       4G Conway's game of life > hyperfine -w 3 ./life-old ./life-new
Benchmark 1: ./life-old
  Time (mean ± σ):      2.136 s ±  0.033 s    [User: 1.699 s, System: 0.392 s]
  Range (min … max):    2.097 s …  2.206 s    10 runs

Benchmark 2: ./life-new
  Time (mean ± σ):      1.142 s ±  0.035 s    [User: 1.087 s, System: 0.009 s]
  Range (min … max):    1.102 s …  1.203 s    10 runs

Summary
  './life-new' ran
    1.87 ± 0.06 times faster than './life-old' Hash map insertion > hyperfine -w 3 ./insert-old ./insert-new
Benchmark 1: ./insert-old
  Time (mean ± σ):     909.0 ms ±  14.2 ms    [User: 605.7 ms, System: 250.6 ms]
  Range (min … max):   890.7 ms … 932.8 ms    10 runs

Benchmark 2: ./insert-new
  Time (mean ± σ):     254.8 ms ±   5.1 ms    [User: 189.1 ms, System: 15.0 ms]
  Range (min … max):   247.0 ms … 263.4 ms    12 runs

Summary
  './insert-new' ran
    3.57 ± 0.09 times faster than './insert-old' Hash map update > hyperfine -w 3 ./update-old ./update-new
Benchmark 1: ./update-old
  Time (mean ± σ):      1.935 s ±  0.032 s    [User: 1.405 s, System: 0.476 s]
  Range (min … max):    1.879 s …  1.976 s    10 runs

Benchmark 2: ./update-new
  Time (mean ± σ):     448.6 ms ±  14.4 ms    [User: 381.5 ms, System: 15.1 ms]
  Range (min … max):   430.9 ms … 484.3 ms    10 runs

Summary
  './update-new' ran
    4.31 ± 0.16 times faster than './update-old' Also Published Here

How to Implement the Perceus Reference Counting Garbage Collection

Crypto Crash? Not Really... 

Meet the Winners of Startups in North and Central America

We developed — a useful open-source tool for checking .env files. It helps to find problems in .env files that you may miss at first but later result in incorrect work of applications. Such problems commonly include key duplication, incorrect word delimiter, keys without value, and invalid first characters — just to name a few. We made the tool universal; it can be connected to any project regardless of the programming language. dotenv-linter What is a .env file? A .env file or dotenv file is a simple text file that contains all the environment variables of a project. Storing configuration in the environment variables is one of the tenets of the Manifesto of the Twelve-Factor App. The .env file has a simple key-value format, for example, FOO=BAR. Here's an overview of the key changes made in this new release of dotenv-linter — v3.0.0! API improvements In the previous version, dotenv-linter had several flags, which were essentially separate commands  --fix and --show-checks: This has been leading to a bit of confusion. In the new version, we have fixed this and moved the --fix and --show-checks flags into separate fix and list commands. Comparing .env files Also, in the new version, we added a new compare command, which allows you to compare keys in .env files. Displaying scanned files 👀 With multiple .env files, it was not always clear which ones were checked by dotenv-linter and which ones weren't. This could be happening due to a non-standard file name, or the absence of any problems in these files. In the new version, we have added the display of scanned files. You can disable this using the--quiet/-q flag. Colored output 🌈 To improve usability, we have added a colored warning display. You can disable color output using the --no-color flag. Support for multi-line values 💪 Multi-line values can be stored in .env files. Now, dotenv-linter does not display warnings for multiline values wrapped in quotes. Support for the export prefix 🔥 In the new version, we added support for the export prefix and now dotenv-linter does not display any warnings. Support for spaces 🙌 Another improvement is the support for spaces in values, wrapped in quotes. Now, for such values, dotenv-linter will not display warnings. Improved validation 👌 Also, we fixed an issue where dotenv-linter did not display all warnings at once. Performance improvements 🚀 Last but not least, we have improved the performance of the already fast dotenv-linter. The maximum start time has decreased from 9.3 ms to 4.3 ms (by more than 50%). To check this, we made a benchmark using the hyperfine utility. These are all the key changes that are included in the new v3.0.0 release. Thanks to everyone who contributed! You can support the project by starring or sponsoring it on GitHub. . Previously published at https://evrone.com/dotenv-linter-v300. The author of the story is the Chief Editor at Evrone

dotenv-linter v3.0.0: Identify Errors In .env Files

Author:
(1) Laurence Francis Lacey, Lacey Solutions Ltd, Skerries, County Dublin, Ireland. Editor's Note: This is Part 7 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Table of Links Abstract and 1 Introduction


Methods


2.1 Statistical Methodology
2.2 US Time Series Data
2.3 Hyperinflation Model


Results


3.1 Characterisation of Price Inflation
3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923)
4. Discussion
5. Conclusion, Supplementary materials, Acknowledgements, and References

Appendix 5. Conclusion The hypothesis that the annual rate of growth in the US consumer price index is a function of the annual growth in the US broad money supply minus the annual growth in US real GDP minus the annual growth in US savings, over the time period 2001 to 2019, has been shown to be the case. However, an exact relationship required the use of a non-zero residual term. A mathematical statistical formulation of a hyperinflationary process has been provided and used to quantify the period of hyperinflation in the Weimar Republic from July 1922 until the end of November 1923. The main mathematical difference between inflation and hyperinflation is that the former is a process with a constant rate of increase, at a constant acceleration, whereas the latter is a process with a constant rate of acceleration. Supplementary materials There is an Appendix providing the mathematical statistical characterization of a hyperinflationary process. Acknowledgements No financial support was received for any aspect of this research. References [1] “Monetary inflation”. Accessed on 11 August 2021 from Wikipedia.com. url: https://en.wikipedia.org/wiki/Monetary_inflation [2] “Consumer Price Index (CPI)”. Accessed on 11 August 2021 from Investopedia.com. url: https://www.investopedia.com/terms/c/consumerpriceindex.asp [3] “Hyperinflation”. Accessed on 11 August 2021 from Investopedia.com. url: https://www.investopedia.com/terms/h/hyperinflation.asp [4] “Broad Money”. Accessed on 11 August 2021 from Investopedia. url: https://www.investopedia.com/terms/b/broad-money.asp [5] Lacey, LF. Characterization of the probability and information entropy of a statistical process with an exponentially increasing sample space. arXiv:2105.14193, 2021. Accessed on 10 August 2021 from arxiv.org. url: https://arxiv.org/abs/2105.14193 [6] Lacey LF. Characterization of the probability and information entropy of a process with an increasing sample space by different functional forms of expansion, with an application to hyperinflation. arXiv:2107.05483, 2021. Accessed on 10 August 2021 from arxiv.org. url: https://arxiv.org/abs/2107.05483 [7] Lacey LF. The relationship between the US broad money supply and US GDP for the time period 2001 to 2019 with that of the corresponding time series for US national property and stock market indices, using an information entropy methodology. arXiv:2106.07354, 2021. Accessed on 10 August 2021 from arxiv.org. url: https://arxiv.org/abs/2106.07354 [8] “The broad money supply of US$ from 2001 to 2019”. Monetary, Broad Money, US Dollars, International Financial Statistics (IFS). Accessed on 13 April 2021 from International Monetary Fund (IMF). url: https://data.imf.org/?sk=B83F71E8-61E3-4CF1-8CF3- 6D7FE04D0930&sId=1393552803658 [9] “Gross Domestic Product for United States, Percent Change, Annual, Not Seasonally Adjusted”. Accessed on 15 April 2021 from Federal Reserve Bank of St. Louis. url: https://fred.stlouisfed.org/series/USANGDPRPCH [10] “US Consumer Price Index (CPI) From 1903”. Federal Reserve Bank of Minneapolis. Accessed on 15 April 2021 from url: https://www.minneapolisfed.org/about-us/monetarypolicy/inflation-calculator/consumer-price-index-1913- [11] Perez, L. “Average U.S. Savings Account Balance 2021: A Demographic Breakdown”. Accessed on 07 August 2021 from valuepenguin.com. url: https://www.valuepenguin.com/banking/average-savings-account-balance [12] Seabold, Skipper, and Josef Perktold. “statsmodels: Econometric and statistical modeling with python.” Proceedings of the 9th Python in Science Conference. 2010. [13] Mizunoa, T; Takayasub, M; Takayasu H. The mechanism of double exponential growth in hyper-inflation. Physica A: Statistical Mechanics and its Applications. 2002, 308, Issues 1–4, 411-419. Accessed on 18 May 2021. url: https://doi.org/10.1016/S0378- 4371(02)00598-8 [14] “Hyperinflation in the Weimar Republic”. Accessed on 18 May 2021 from Wikipedia.com. url: https://en.wikipedia.org/wiki/Hyperinflation_in_the_Weimar_Republic [15] “Velocity of Money”. Accessed on 13 April 2021 from Investopedia. url: https://www.investopedia.com/terms/v/velocity.asp Appendix: Characterization of a hyperinflationary process – one with an initial exponential expansion of the sample space followed a subsequent second exponential expansion of the sample space A process with an exponentially increasing sample space (s) has been characterised [5]. When the exponential expansion occurs with time (t), it has been shown [5] that: s(t) = exp(λ 𝑥 t) H(t) = λ 𝑥 t where, s(t) is the size of the sample space with time, H(t) is the information entropy of the expansionary process with time, and λ is exponential rate constant. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Author: (1) Laurence Francis Lacey, Lacey Solutions Ltd, Skerries, County Dublin, Ireland. Author: Author: (1) Laurence Francis Lacey, Lacey Solutions Ltd, Skerries, County Dublin, Ireland. Editor's Note: This is Part 7 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Editor's Note: This is Part 7 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Editor's Note: This is Part 7 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Editor's Note: This is Part 7 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Table of Links Abstract and 1 Introduction Methods 2.1 Statistical Methodology 2.2 US Time Series Data 2.3 Hyperinflation Model Results 3.1 Characterisation of Price Inflation 3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923) 4. Discussion 5. Conclusion, Supplementary materials, Acknowledgements, and References

Appendix Abstract and 1 Introduction Abstract and 1 Introduction Methods Methods Methods 2.1 Statistical Methodology 2.1 Statistical Methodology 2.2 US Time Series Data 2.2 US Time Series Data 2.3 Hyperinflation Model 2.3 Hyperinflation Model Results Results Results 3.1 Characterisation of Price Inflation 3.1 Characterisation of Price Inflation 3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923) 3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923) 4. Discussion 4. Discussion 5. Conclusion, Supplementary materials, Acknowledgements, and References Appendix 5. Conclusion, Supplementary materials, Acknowledgements, and References Appendix Appendix 5. Conclusion The hypothesis that the annual rate of growth in the US consumer price index is a function of the annual growth in the US broad money supply minus the annual growth in US real GDP minus the annual growth in US savings, over the time period 2001 to 2019, has been shown to be the case. However, an exact relationship required the use of a non-zero residual term. A mathematical statistical formulation of a hyperinflationary process has been provided and used to quantify the period of hyperinflation in the Weimar Republic from July 1922 until the end of November 1923. The main mathematical difference between inflation and hyperinflation is that the former is a process with a constant rate of increase, at a constant acceleration, whereas the latter is a process with a constant rate of acceleration. Supplementary materials There is an Appendix providing the mathematical statistical characterization of a hyperinflationary process. Acknowledgements No financial support was received for any aspect of this research. References [1] “Monetary inflation”. Accessed on 11 August 2021 from Wikipedia.com. url: https://en.wikipedia.org/wiki/Monetary_inflation [2] “Consumer Price Index (CPI)”. Accessed on 11 August 2021 from Investopedia.com. url: https://www.investopedia.com/terms/c/consumerpriceindex.asp [3] “Hyperinflation”. Accessed on 11 August 2021 from Investopedia.com. url: https://www.investopedia.com/terms/h/hyperinflation.asp [4] “Broad Money”. Accessed on 11 August 2021 from Investopedia. url: https://www.investopedia.com/terms/b/broad-money.asp [5] Lacey, LF. Characterization of the probability and information entropy of a statistical process with an exponentially increasing sample space. arXiv:2105.14193, 2021. Accessed on 10 August 2021 from arxiv.org. url: https://arxiv.org/abs/2105.14193 [6] Lacey LF. Characterization of the probability and information entropy of a process with an increasing sample space by different functional forms of expansion, with an application to hyperinflation. arXiv:2107.05483, 2021. Accessed on 10 August 2021 from arxiv.org. url: https://arxiv.org/abs/2107.05483 [7] Lacey LF. The relationship between the US broad money supply and US GDP for the time period 2001 to 2019 with that of the corresponding time series for US national property and stock market indices, using an information entropy methodology. arXiv:2106.07354, 2021. Accessed on 10 August 2021 from arxiv.org. url: https://arxiv.org/abs/2106.07354 [8] “The broad money supply of US$ from 2001 to 2019”. Monetary, Broad Money, US Dollars, International Financial Statistics (IFS). Accessed on 13 April 2021 from International Monetary Fund (IMF). url: https://data.imf.org/?sk=B83F71E8-61E3-4CF1-8CF3- 6D7FE04D0930&sId=1393552803658 [9] “Gross Domestic Product for United States, Percent Change, Annual, Not Seasonally Adjusted”. Accessed on 15 April 2021 from Federal Reserve Bank of St. Louis. url: https://fred.stlouisfed.org/series/USANGDPRPCH [10] “US Consumer Price Index (CPI) From 1903”. Federal Reserve Bank of Minneapolis. Accessed on 15 April 2021 from url: https://www.minneapolisfed.org/about-us/monetarypolicy/inflation-calculator/consumer-price-index-1913- [11] Perez, L. “Average U.S. Savings Account Balance 2021: A Demographic Breakdown”. Accessed on 07 August 2021 from valuepenguin.com. url: https://www.valuepenguin.com/banking/average-savings-account-balance [12] Seabold, Skipper, and Josef Perktold. “statsmodels: Econometric and statistical modeling with python.” Proceedings of the 9th Python in Science Conference. 2010. [13] Mizunoa, T; Takayasub, M; Takayasu H. The mechanism of double exponential growth in hyper-inflation. Physica A: Statistical Mechanics and its Applications. 2002, 308, Issues 1–4, 411-419. Accessed on 18 May 2021. url: https://doi.org/10.1016/S0378- 4371(02)00598-8 [14] “Hyperinflation in the Weimar Republic”. Accessed on 18 May 2021 from Wikipedia.com. url: https://en.wikipedia.org/wiki/Hyperinflation_in_the_Weimar_Republic [15] “Velocity of Money”. Accessed on 13 April 2021 from Investopedia. url: https://www.investopedia.com/terms/v/velocity.asp Appendix: Characterization of a hyperinflationary process – one with an initial exponential expansion of the sample space followed a subsequent second exponential expansion of the sample space A process with an exponentially increasing sample space (s) has been characterised [5]. When the exponential expansion occurs with time (t), it has been shown [5] that: s(t) = exp(λ 𝑥 t) H(t) = λ 𝑥 t where, s(t) is the size of the sample space with time, H(t) is the information entropy of the expansionary process with time, and λ is exponential rate constant. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv

On The Nature of Monetary and Price Inflation and Hyperinflation

Author:
(1) Laurence Francis Lacey, Lacey Solutions Ltd, Skerries, County Dublin, Ireland. Editor's Note: This is Part 6 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Table of Links Abstract and 1 Introduction


Methods


2.1 Statistical Methodology
2.2 US Time Series Data
2.3 Hyperinflation Model


Results


3.1 Characterisation of Price Inflation
3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923)
4. Discussion
5. Conclusion, Supplementary materials, Acknowledgements, and References

Appendix 4. Discussion The consumer price inflation model described is intended to investigate the consumer price index (CPI), over a period of years and not over a period of months, in order to investigate the longer-term relationships involved. In contrast, the hyperinflation model described is intended to investigate the increase in nominal prices, over a period of months, because of the accelerating nature of the decline in the purchasing power of the fiat currency being studied. Unlike in the case of hyperinflation, under “ordinary” circumstances, the growth in price inflation has a velocity, but the acceleration can be ignored because it is approximately constant, i.e., price inflation increases at an approximate constant rate with time. The hypothesis that the annual rate of growth in the US CPI is a function of the annual growth in the US broad money supply minus the annual growth in US real GDP minus the annual growth in US savings, over the time period 2001 to 2019, has been shown to be the case. However, an exact relationship required the use of a non-zero residual term, RES(t): 𝑣𝐶𝑃𝐼(𝑡) = 𝑣𝐵𝑀𝑆(𝑡) − 𝑣𝐺𝐷𝑃(𝑡) − 𝑣𝑆𝐴𝑉(𝑡) − 𝑅𝐸𝑆(𝑡) This may be the case for a couple of reasons: (1) The measure of savings used was the estimated average annual American household savings [11]. While, this might be expected to be technically challenging to calculate accurately, it only pertains to households. It might be expected that in addition to average annual American household savings, there should also exist annual American non-household savings. Therefore, a limitation of this paper is that American household savings were used as a measure of overall savings in the US economy. (2) There may be an additional factor that needed to be included in the model, other than savings. Savings were included in the model because savings can be used, if required / desired to purchase goods and/or services, or not, as the case might be, and as a result might be expected to influence the CPI. An alternative approach might be to use another broad measure of the money supply that excludes savings. The model includes the terms, BMS and GDP. So also does the concept of the “velocity of money” [15], in which: "𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑚𝑜𝑛𝑒𝑦" = 𝐺𝐷𝑃/𝑀𝑜𝑛𝑒𝑦 𝑆𝑢𝑝𝑝𝑙𝑦 This equation can be rearranged as follow: However, for the concept of the “velocity of money” to be relevant to this paper, it would need to be expressed in terms of its constant rate of change with time, as follows: Should the CPI model be valid (subject to the caveat discussed above in relation to savings) such that: 𝑣𝐶𝑃𝐼(𝑡) = 𝑣𝐵𝑀𝑆(𝑡) − 𝑣𝐺𝐷𝑃(𝑡) − 𝑣𝑆𝐴𝑉(𝑡) this would predict a few different economic scenarios: (1) When there is no (or very little) growth in GDP or savings (“stagflation scenario”): 𝑣𝐶𝑃𝐼(𝑡) = 𝑣𝐵𝑀𝑆(𝑡) (2) When the growth in savings is sufficiently high, the growth in CPI could turn negative (“deflation scenario”). (3) When there is negative growth in GDP (“recession scenario”), the growth in CPI could be greater than the growth in BMS, should there be no “rebalancing” change in the growth of BMS. A mathematical statistical formulation of a hyperinflationary process has been provided and used to quantify the period of hyperinflation in the Weimar Republic from July 1922 until the end of November 1923. Why did this hyperinflationary happen and why was it allowed to occur by the Government and central bankers of the Weimar Republic? As outlined in [14], following World War 1 and the Treaty of Versailles (which came into effect on January 10, 1920), the strategy that Germany used to pay war reparations was the mass printing of bank notes to buy foreign currency, which was then used to pay reparations, but which also caused inflation of the paper mark. After Germany failed to pay France an instalment of reparations on time in late 1922, French and Belgian troops occupied the Ruhr valley, Germany's main industrial region, in January 1923. The German government's response was to order a policy of passive resistance in the Ruhr, akin to a general strike, to protest the occupation, while providing financial assistance to the striking workers by printing more and more banknotes, with the result that the paper mark became increasing worthless throughout 1923. The mathematical statistical formulation of a hyperinflationary process could be extended beyond two sequential exponential expansions to include any arbitrary number (n) of sequential exponential expansions. However, while this may have theoretical interest, it is not a phenomenon that has yet occurred in real-world economics, to the knowledge of the author. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Author: (1) Laurence Francis Lacey, Lacey Solutions Ltd, Skerries, County Dublin, Ireland. Author: Author: (1) Laurence Francis Lacey, Lacey Solutions Ltd, Skerries, County Dublin, Ireland. Editor's Note: This is Part 6 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Editor's Note: This is Part 6 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Editor's Note: This is Part 6 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Editor's Note: This is Part 6 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Table of Links Abstract and 1 Introduction Methods 2.1 Statistical Methodology 2.2 US Time Series Data 2.3 Hyperinflation Model Results 3.1 Characterisation of Price Inflation 3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923) 4. Discussion 5. Conclusion, Supplementary materials, Acknowledgements, and References

Appendix Abstract and 1 Introduction Abstract and 1 Introduction Methods Methods Methods 2.1 Statistical Methodology 2.1 Statistical Methodology 2.2 US Time Series Data 2.2 US Time Series Data 2.3 Hyperinflation Model 2.3 Hyperinflation Model Results Results Results 3.1 Characterisation of Price Inflation 3.1 Characterisation of Price Inflation 3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923) 3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923) 4. Discussion 4. Discussion 5. Conclusion, Supplementary materials, Acknowledgements, and References Appendix 5. Conclusion, Supplementary materials, Acknowledgements, and References Appendix Appendix 4. Discussion The consumer price inflation model described is intended to investigate the consumer price index (CPI), over a period of years and not over a period of months, in order to investigate the longer-term relationships involved. In contrast, the hyperinflation model described is intended to investigate the increase in nominal prices, over a period of months, because of the accelerating nature of the decline in the purchasing power of the fiat currency being studied. Unlike in the case of hyperinflation, under “ordinary” circumstances, the growth in price inflation has a velocity, but the acceleration can be ignored because it is approximately constant, i.e., price inflation increases at an approximate constant rate with time. The hypothesis that the annual rate of growth in the US CPI is a function of the annual growth in the US broad money supply minus the annual growth in US real GDP minus the annual growth in US savings, over the time period 2001 to 2019, has been shown to be the case. However, an exact relationship required the use of a non-zero residual term, RES(t): 𝑣𝐶𝑃𝐼(𝑡) = 𝑣𝐵𝑀𝑆(𝑡) − 𝑣𝐺𝐷𝑃(𝑡) − 𝑣𝑆𝐴𝑉(𝑡) − 𝑅𝐸𝑆(𝑡) This may be the case for a couple of reasons: (1) The measure of savings used was the estimated average annual American household savings [11]. While, this might be expected to be technically challenging to calculate accurately, it only pertains to households. It might be expected that in addition to average annual American household savings, there should also exist annual American non-household savings. Therefore, a limitation of this paper is that American household savings were used as a measure of overall savings in the US economy. (2) There may be an additional factor that needed to be included in the model, other than savings. Savings were included in the model because savings can be used, if required / desired to purchase goods and/or services, or not, as the case might be, and as a result might be expected to influence the CPI. An alternative approach might be to use another broad measure of the money supply that excludes savings. The model includes the terms, BMS and GDP. So also does the concept of the “velocity of money” [15], in which: "𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑚𝑜𝑛𝑒𝑦" = 𝐺𝐷𝑃/𝑀𝑜𝑛𝑒𝑦 𝑆𝑢𝑝𝑝𝑙𝑦 This equation can be rearranged as follow: However, for the concept of the “velocity of money” to be relevant to this paper, it would need to be expressed in terms of its constant rate of change with time, as follows: Should the CPI model be valid (subject to the caveat discussed above in relation to savings) such that: 𝑣𝐶𝑃𝐼(𝑡) = 𝑣𝐵𝑀𝑆(𝑡) − 𝑣𝐺𝐷𝑃(𝑡) − 𝑣𝑆𝐴𝑉(𝑡) this would predict a few different economic scenarios: (1) When there is no (or very little) growth in GDP or savings (“stagflation scenario”): 𝑣𝐶𝑃𝐼(𝑡) = 𝑣𝐵𝑀𝑆(𝑡) (2) When the growth in savings is sufficiently high, the growth in CPI could turn negative (“deflation scenario”). (3) When there is negative growth in GDP (“recession scenario”), the growth in CPI could be greater than the growth in BMS, should there be no “rebalancing” change in the growth of BMS. A mathematical statistical formulation of a hyperinflationary process has been provided and used to quantify the period of hyperinflation in the Weimar Republic from July 1922 until the end of November 1923. Why did this hyperinflationary happen and why was it allowed to occur by the Government and central bankers of the Weimar Republic? As outlined in [14], following World War 1 and the Treaty of Versailles (which came into effect on January 10, 1920), the strategy that Germany used to pay war reparations was the mass printing of bank notes to buy foreign currency, which was then used to pay reparations, but which also caused inflation of the paper mark. After Germany failed to pay France an instalment of reparations on time in late 1922, French and Belgian troops occupied the Ruhr valley, Germany's main industrial region, in January 1923. The German government's response was to order a policy of passive resistance in the Ruhr, akin to a general strike, to protest the occupation, while providing financial assistance to the striking workers by printing more and more banknotes, with the result that the paper mark became increasing worthless throughout 1923. The mathematical statistical formulation of a hyperinflationary process could be extended beyond two sequential exponential expansions to include any arbitrary number (n) of sequential exponential expansions. However, while this may have theoretical interest, it is not a phenomenon that has yet occurred in real-world economics, to the knowledge of the author. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv

Hyperinflation Model Successfully Explains Rapid Inflation Escalation

Author:
(1) Laurence Francis Lacey, Lacey Solutions Ltd, Skerries, County Dublin, Ireland. Editor's Note: This is Part 5 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Table of Links Abstract and 1 Introduction


Methods


2.1 Statistical Methodology
2.2 US Time Series Data
2.3 Hyperinflation Model


Results


3.1 Characterisation of Price Inflation
3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923)
4. Discussion
5. Conclusion, Supplementary materials, Acknowledgements, and References

Appendix 3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923) The monetary and price hyperinflation of in the Weimar Republic between the middle of 1920 to the end of November 2023 is investigated in this paper and the data analysed are based on the value of one gold Mark in paper Marks over this time period (obtained from [14]) and are plotted in Figure 6 (semi-log plot). When t < 23, where, PI(t) is price inflation, with a growth rate of 10.4% per month (inflation velocity), and where 10 is the value of PI(t) at t = 0. When t ≥ 23, During this period of hyperinflation, the acceleration in price inflation was 11.8% per month. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Author: (1) Laurence Francis Lacey, Lacey Solutions Ltd, Skerries, County Dublin, Ireland. Author: Author: (1) Laurence Francis Lacey, Lacey Solutions Ltd, Skerries, County Dublin, Ireland. Editor's Note: This is Part 5 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Editor's Note: This is Part 5 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Editor's Note: This is Part 5 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Editor's Note: This is Part 5 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Table of Links Abstract and 1 Introduction Methods 2.1 Statistical Methodology 2.2 US Time Series Data 2.3 Hyperinflation Model Results 3.1 Characterisation of Price Inflation 3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923) 4. Discussion 5. Conclusion, Supplementary materials, Acknowledgements, and References

Appendix Abstract and 1 Introduction Abstract and 1 Introduction Methods Methods Methods 2.1 Statistical Methodology 2.1 Statistical Methodology 2.2 US Time Series Data 2.2 US Time Series Data 2.3 Hyperinflation Model 2.3 Hyperinflation Model Results Results Results 3.1 Characterisation of Price Inflation 3.1 Characterisation of Price Inflation 3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923) 3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923) 4. Discussion 4. Discussion 5. Conclusion, Supplementary materials, Acknowledgements, and References Appendix 5. Conclusion, Supplementary materials, Acknowledgements, and References Appendix Appendix 3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923) The monetary and price hyperinflation of in the Weimar Republic between the middle of 1920 to the end of November 2023 is investigated in this paper and the data analysed are based on the value of one gold Mark in paper Marks over this time period (obtained from [14]) and are plotted in Figure 6 (semi-log plot). When t < 23, where, PI(t) is price inflation, with a growth rate of 10.4% per month (inflation velocity), and where 10 is the value of PI(t) at t = 0. When t ≥ 23, During this period of hyperinflation, the acceleration in price inflation was 11.8% per month. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv

Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923)

Author:
(1) Laurence Francis Lacey, Lacey Solutions Ltd, Skerries, County Dublin, Ireland. Editor's Note: This is Part 4 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Table of Links Abstract and 1 Introduction


Methods


2.1 Statistical Methodology
2.2 US Time Series Data
2.3 Hyperinflation Model


Results


3.1 Characterisation of Price Inflation
3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923)
4. Discussion
5. Conclusion, Supplementary materials, Acknowledgements, and References

AppendixLaurence Francis Lacey 2.3 Hyperinflation Model A mathematical statistical characterisation of a hyperinflation process is given in the Supplementary Appendix, building on the original characterisation of a process with a monoexponentially increasing sample space [5]. As is shown in the Supplementary Appendix, an exponential growth process becomes a double exponential growth process, when a second exponential growth process occurs, at some point in time (t*), on top of the initial exponential growth process. When t < t*, When t ≥ t*, While the information entropy of an expansionary process can be considered to be related to the “velocity” of the expansion, the natural log of the information entropy of an expansionary process can be considered to be related to the “acceleration” of the expansion. The double exponential nature of some cases of monetary hyperinflation has been investigated [13] and there has been an exploratory investigation of a double exponential hyperinflationary process, using the information entropy methodology [6]. All plots of the data analysis given below were obtained using Microsoft Excel 2019, 32- bit version. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Author: (1) Laurence Francis Lacey, Lacey Solutions Ltd, Skerries, County Dublin, Ireland. Author: Author: (1) Laurence Francis Lacey, Lacey Solutions Ltd, Skerries, County Dublin, Ireland. Editor's Note: This is Part 4 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Editor's Note: This is Part 4 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Editor's Note: This is Part 4 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Editor's Note: This is Part 4 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Table of Links Abstract and 1 Introduction Methods 2.1 Statistical Methodology 2.2 US Time Series Data 2.3 Hyperinflation Model Results 3.1 Characterisation of Price Inflation 3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923) 4. Discussion 5. Conclusion, Supplementary materials, Acknowledgements, and References

AppendixLaurence Francis Lacey Abstract and 1 Introduction Abstract and 1 Introduction Methods Methods Methods 2.1 Statistical Methodology 2.1 Statistical Methodology 2.2 US Time Series Data 2.2 US Time Series Data 2.3 Hyperinflation Model 2.3 Hyperinflation Model Results Results Results 3.1 Characterisation of Price Inflation 3.1 Characterisation of Price Inflation 3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923) 3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923) 4. Discussion 4. Discussion 5. Conclusion, Supplementary materials, Acknowledgements, and References AppendixLaurence Francis Lacey 5. Conclusion, Supplementary materials, Acknowledgements, and References AppendixLaurence Francis Lacey AppendixLaurence Francis Lacey 2.3 Hyperinflation Model A mathematical statistical characterisation of a hyperinflation process is given in the Supplementary Appendix, building on the original characterisation of a process with a monoexponentially increasing sample space [5]. As is shown in the Supplementary Appendix, an exponential growth process becomes a double exponential growth process, when a second exponential growth process occurs, at some point in time (t*), on top of the initial exponential growth process. When t < t*, When t ≥ t*, While the information entropy of an expansionary process can be considered to be related to the “velocity” of the expansion, the natural log of the information entropy of an expansionary process can be considered to be related to the “acceleration” of the expansion. The double exponential nature of some cases of monetary hyperinflation has been investigated [13] and there has been an exploratory investigation of a double exponential hyperinflationary process, using the information entropy methodology [6]. All plots of the data analysis given below were obtained using Microsoft Excel 2019, 32- bit version. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv

The Mathematical Formula to Hyperinflation

HyperRing introduced its second-generation payment ring on December 4, which operates in multiple countries through Visa and Mastercard networks. The device functions without batteries and processes transactions through NFC technology. The ring connects to credit cards, debit cards, or prepaid accounts through the HyperRing Pay application. Users can make purchases in North America, Europe, Asia, the Middle East, North Africa, and South America where contactless payments are accepted. The device includes security measures that limit transaction authorization to within 3 centimeters of payment terminals. Users can disable payment capabilities through the HyperRing Pay application if the ring is lost. The ring uses NFC technology for power during transactions, which eliminates the need for charging. The construction makes it resistant to water and dust exposure. The company manufactures the ring in several materials: 14-karat gold, sterling silver, titanium, and ceramic. The ceramic versions come in white and black. The device measures smaller in width compared to the previous version. Customers who purchase during the pre-order period receive lifetime access to HyperRing software, which costs $20 per year. The company states the pre-order quantities remain limited. HyperRing plans to increase banking partnerships and add cryptocurrency payment features in future updates, according to company statements. The release represents the first payment ring available for purchase in the United States with international usage capabilities. The device processes transactions through proximity-based authentication technology. The product targets users seeking alternatives to traditional payment methods. The ring processes payments at terminals that accept contactless transactions from Visa and Mastercard. Final Thoughts HyperRing operates as a technology company producing wearable payment devices. The company focuses on creating payment rings that work with existing financial systems. The HyperRing Pay platform enables businesses to process transactions while providing customers with a payment method that does not require cards or phones. The company maintains operations across multiple continents and continues developing partnerships with financial institutions. The second-generation release expands their product line into new markets while building on their existing payment technology infrastructure. The launch indicates growing development in wearable payment technology. As consumers seek new transaction methods, companies continue creating alternatives to traditional payment cards. The expansion of contactless payment acceptance provides opportunities for devices that can interact with existing payment systems. Don’t forget to like and share the story! Vested Interest Disclosure: This author is an independent contributor publishing via our business blogging program. HackerNoon has reviewed the report for quality, but the claims herein belong to the author. #DYOR HyperRing introduced its second-generation payment ring on December 4, which operates in multiple countries through Visa and Mastercard networks. The device functions without batteries and processes transactions through NFC technology. The ring connects to credit cards, debit cards, or prepaid accounts through the HyperRing Pay application. Users can make purchases in North America, Europe, Asia, the Middle East, North Africa, and South America where contactless payments are accepted. HyperRing The device includes security measures that limit transaction authorization to within 3 centimeters of payment terminals. Users can disable payment capabilities through the HyperRing Pay application if the ring is lost. The ring uses NFC technology for power during transactions, which eliminates the need for charging. The construction makes it resistant to water and dust exposure. The company manufactures the ring in several materials: 14-karat gold, sterling silver, titanium, and ceramic. The ceramic versions come in white and black. The device measures smaller in width compared to the previous version. Customers who purchase during the pre-order period receive lifetime access to HyperRing software, which costs $20 per year. The company states the pre-order quantities remain limited. HyperRing plans to increase banking partnerships and add cryptocurrency payment features in future updates, according to company statements. The release represents the first payment ring available for purchase in the United States with international usage capabilities. The device processes transactions through proximity-based authentication technology. The product targets users seeking alternatives to traditional payment methods. The ring processes payments at terminals that accept contactless transactions from Visa and Mastercard. Final Thoughts HyperRing operates as a technology company producing wearable payment devices. The company focuses on creating payment rings that work with existing financial systems. The HyperRing Pay platform enables businesses to process transactions while providing customers with a payment method that does not require cards or phones. The company maintains operations across multiple continents and continues developing partnerships with financial institutions. The second-generation release expands their product line into new markets while building on their existing payment technology infrastructure. The launch indicates growing development in wearable payment technology. As consumers seek new transaction methods, companies continue creating alternatives to traditional payment cards. The expansion of contactless payment acceptance provides opportunities for devices that can interact with existing payment systems. Don’t forget to like and share the story! Vested Interest Disclosure: This author is an independent contributor publishing via our business blogging program. HackerNoon has reviewed the report for quality, but the claims herein belong to the author. #DYOR Vested Interest Disclosure: This author is an independent contributor publishing via our business blogging program . HackerNoon has reviewed the report for quality, but the claims herein belong to the author. #DYOR Vested Interest Disclosure: business blogging program business blogging program

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