Sparse identification of non-linear dynamics

Sparse identification of non-linear dynamics

Sparse identification of nonlinear dynamics (SINDy) is a data-driven algorithm for obtaining dynamical systems from data. Given a series of snapshots of a dynamical system and its corresponding time derivatives, SINDy performs a sparsity-promoting regression (such as LASSO and sparse Bayesian inference) on a library of nonlinear candidate functions of the snapshots against the derivatives to find the governing equations. This procedure relies on the assumption that most physical systems only have a few dominant terms which dictate the dynamics, given an appropriately selected coordinate system and quality training data. It has been applied to identify the dynamics of fluids, based on proper orthogonal decomposition, as well as other complex dynamical systems, such as biological networks. == Mathematical Overview == First, consider a dynamical system of the form x ˙ = d d t x ( t ) = f ( x ( t ) ) , {\displaystyle {\dot {\textbf {x}}}={\frac {d}{dt}}{\textbf {x}}(t)={\textbf {f}}({\textbf {x}}(t)),} where x ( t ) ∈ R n {\displaystyle {\textbf {x}}(t)\in \mathbb {R} ^{n}} is a state vector (snapshot) of the system at time t {\displaystyle t} and the function f ( x ( t ) ) {\displaystyle {\textbf {f}}({\textbf {x}}(t))} defines the equations of motion and constraints of the system. The time derivative may be either prescribed or numerically approximated from the snapshots. With x {\displaystyle {\textbf {x}}} and x ˙ {\displaystyle {\dot {\textbf {x}}}} sampled at m {\displaystyle m} equidistant points in time ( t 1 , t 2 , ⋯ , t m {\displaystyle t_{1},t_{2},\cdots ,t_{m}} ), these can be arranged into matrices of the form X = [ x T ( t 1 ) x T ( t 2 ) ⋮ x T ( t m ) ] = [ x 1 ( t 1 ) x 2 ( t 1 ) ⋯ x n ( t 1 ) x 1 ( t 2 ) x 2 ( t 2 ) ⋯ x n ( t 2 ) ⋮ ⋮ ⋱ ⋮ x 1 ( t m ) x 2 ( t m ) ⋯ x n ( t m ) ] , {\displaystyle {\bf {{X}={\begin{bmatrix}\mathbf {x} ^{\mathsf {T}}(t_{1})\\\mathbf {x} ^{\mathsf {T}}(t_{2})\\\vdots \\\mathbf {x} ^{\mathsf {T}}(t_{m})\end{bmatrix}}={\begin{bmatrix}x_{1}(t_{1})&x_{2}(t_{1})&\cdots &x_{n}(t_{1})\\x_{1}(t_{2})&x_{2}(t_{2})&\cdots &x_{n}(t_{2})\\\vdots &\vdots &\ddots &\vdots \\x_{1}(t_{m})&x_{2}(t_{m})&\cdots &x_{n}(t_{m})\end{bmatrix}},}}} and similarly for X ˙ {\displaystyle {\dot {\mathbf {X} }}} . Next, a library Θ ( X ) {\displaystyle \mathbf {\Theta } (\mathbf {X} )} of nonlinear candidate functions of the columns of X {\displaystyle {\textbf {X}}} is constructed, which may be constant, polynomial, or more exotic functions (like trigonometric and rational terms, and so on): Θ ( X ) = [ | | | | | | 1 X X 2 X 3 ⋯ sin ⁡ ( X ) cos ⁡ ( X ) ⋯ | | | | | | ] {\displaystyle \ \ \ {\bf {{\Theta }({\bf {{X})={\begin{bmatrix}\vline &\vline &\vline &\vline &&\vline &\vline &\\1&{\bf {X}}&{\bf {{X}^{2}}}&{\bf {{X}^{3}}}&\cdots &\sin({\bf {{X})}}&\cos({\bf {{X})}}&\cdots \\\vline &\vline &\vline &\vline &&\vline &\vline &\end{bmatrix}}}}}}} The number of possible model structures from this library is combinatorially high. f ( x ( t ) ) {\displaystyle {\textbf {f}}({\textbf {x}}(t))} is then substituted by Θ ( X ) {\displaystyle {\bf {{\Theta }({\textbf {X}})}}} and a vector of coefficients Ξ = [ ξ 1 ξ 2 ⋯ ξ n ] {\displaystyle {\bf {{\Xi }=\left[{\bf {{\xi }_{1}{\bf {{\xi }_{2}\cdots {\bf {{\xi }_{n}}}}}}}\right]}}} determining the active terms in f ( x ( t ) ) {\displaystyle {\textbf {f}}({\textbf {x}}(t))} : X ˙ = Θ ( X ) Ξ {\displaystyle {\dot {\bf {X}}}={\bf {{\Theta }({\bf {{X}){\bf {\Xi }}}}}}} Because only a few terms are expected to be active at each point in time, an assumption is made that f ( x ( t ) ) {\displaystyle {\textbf {f}}({\textbf {x}}(t))} admits a sparse representation in Θ ( X ) {\displaystyle {\bf {{\Theta }({\textbf {X}})}}} . This then becomes an optimization problem in finding a sparse Ξ {\displaystyle {\bf {\Xi }}} which optimally embeds X ˙ {\displaystyle {\dot {\textbf {X}}}} . In other words, a parsimonious model is obtained by performing least squares regression on the system (4) with sparsity-promoting ( L 1 {\displaystyle L_{1}} ) regularization ξ k = arg ⁡ min ξ k ′ | | X ˙ k − Θ ( X ) ξ k ′ | | 2 + λ | | ξ k ′ | | 1 , {\displaystyle {\bf {{\xi }_{k}={\underset {\bf {{\xi }'_{k}}}{\arg \min }}\left|\left|{\dot {\bf {X}}}_{k}-{\bf {{\Theta }({\bf {{X}){\bf {{\xi }'_{k}}}}}}}\right|\right|_{2}+\lambda \left|\left|{\bf {{\xi }'_{k}}}\right|\right|_{1},}}} where λ {\displaystyle \lambda } is a regularization parameter. Finally, the sparse set of ξ k {\displaystyle {\bf {{\xi }_{k}}}} can be used to reconstruct the dynamical system: x ˙ k = Θ ( x ) ξ k {\displaystyle {\dot {x}}_{k}={\bf {{\Theta }({\bf {{x}){\bf {{\xi }_{k}}}}}}}}

Calais (Reuters product)

Calais is a service created by Thomson Reuters that automatically extracts semantic information from web pages in a format that can be used on the semantic web. Calais was launched in January 2008, and is free to use. The technology is now available via the website of Refinitiv, a provider of financial market data and infrastructure founded in 2018, that is a subsidiary of London Stock Exchange Group. The Calais Web service reads unstructured text and returns Resource Description Framework formatted results identifying entities, facts and events within the text. The service appears to be based on technology acquired when Reuters purchased ClearForest in 2007. The technology has also been used to automatically tag blog articles, and organize museum collections. Calais uses natural language processing technologies delivered via a web service interface.

BitClout

BitClout was an open source blockchain-based social media platform. On the platform, users could post short-form writings and photos, award money to posts they particularly like by clicking a diamond icon, as well as buy and sell "creator coins" (personalized tokens whose value depends on people's reputations). BitClout ran on a custom proof of work blockchain, and was a prototype of what can be built on DeSo (short for "Decentralized Social"). BitClout's founder and primary leader is Nader al-Naji, known pseudonymously as "Diamondhands". Under development since 2019, BitClout's blockchain created its first block in January 2021, and BitClout itself launched publicly in March 2021. The platform launched with 15,000 "reserved" accounts — a move intended to prevent impersonation, but which backfired as some people with reserved accounts tried to actively distance themselves. Later, in September 2021, BitClout was revealed to be the flagship product of the DeSo blockchain. == History == === Origins (2019 - March 2021) === In early 2019, Nader al-Naji became interested in "mixing investing and social media". He started creating a custom blockchain in May 2019, but didn't tell anyone else until November 2020. However, in the fall of 2020, al-Naji pitched BitClout's own investors under his real name and began posting job listings for a "new operation". Although BitClout was not originally intended to launch until mid-2021, its development was sped up due to "zeitgeist about decentralized social media" in January 2021. BitClout's first block was mined on 18 January 2021. Its next block was mined on 1 March 2021. === As BitClout (March - September 2021) === In early March 2021, about fifty investors received links to a password-protected website with the BitClout white paper. They were encouraged to explore the site and send the same link to "two or three other 'trusted contacts'". Within weeks users were spending millions of dollars per day on the platform. The platform's founders said they were "completely unprepared", having planned to have a "soft-launch". The leader went by the name "diamondhands" on the platform. On 24 March 2021, BitClout launched out of private beta. Investors include Sequoia Capital, Andreessen Horowitz, the venture capital firm Social Capital, Coinbase Ventures, Winklevoss Capital Management, Alexis Ohanian, Polychain, Pantera, and Digital Currency Group (CoinDesk's parent company). During its initial launch, BitClout's currency could be bought with bitcoin, but not sold except on Discord servers or Twitter threads. A single bitcoin wallet related to BitClout received more than $165M worth of deposits. In March 2021, law firm Anderson Kill P.C. sent Nader al-Naji, the presumed leader of the BitClout platform, a cease-and-desist letter, demanding the removal of Brandon Curtis's account and alleging that BitClout violated sections 1798 and 3344 of the California Civil Code by using Curtis's name and likeness without his consent. Curtis also tweeted, "Adopting Bitcoin's aesthetic to raise VC funding to carry out unethical and blatantly illegal schemes like BitClout: not cool". (However, Curtis's coin, despite not being listed on the official website, can still be bought by users searching for the original username.) Additionally, in April 2021, Lee Hsien Loong asked for his name and photograph to be removed from the site, stating that he has "nothing to do with the platform" and that "it is misleading and done without [his] permission". On 18 May 2021, diamondhands announced that 100% of the BitClout code went public. On 12 June 2021, the supply of BitClout was capped at around 11 million coins. On 18 July 2021, BitClout added the ability for users to mint and purchase NFTs within the platform. === As part of DeSo (September 2021 - July 2024) === On 21 September 2021, it was revealed that BitClout was a prototype built on DeSo, short for "Decentralized Social". As a part of this revelation, diamondhands confirmed his identity as Nader al-Naji. (As early as April 2021, it had been believed that diamondhands indeed was that person.)The Bitclout project raised $200M in funding, which went to setting up the DeSo Foundation. === End and aftermath (July 2024 - present) === In July 2024, al-Naji was arrested by the FBI and charged with wire fraud involving BitClout. He also faced civil charges of securities fraud and unregistered offers and sales of securities from the Securities and Exchange Commission. In response, the official "deso" account posted that al-Naji was "safe and at home" and "that this experience has only reinforced [his] commitment to DeSo". In February 2025, the Justice Department dropped its case against al-Naji. In March 2026, the SEC voluntarily dismissed the enforcement case with prejudice. == Design == BitClout is a social media platform. Its users can post short-form writings and photos (similarly to Twitter). They can award money to posts they particularly like by clicking a diamond icon (similarly to Twitch Bits). The prices of each account's "creator coin" goes up and down with the popularity of the celebrity behind it. For example, if someone says something negative, the value of their corresponding account may go down. This price is computed automatically according to the formula p r i c e _ i n _ b i t c l o u t = .003 ∗ c r e a t o r _ c o i n s _ i n _ c i r c u l a t i o n 2 {\displaystyle price\_in\_bitclout=.003creator\_coins\_in\_circulation^{2}} . At launch time, BitClout scraped 15,000 profiles of celebrities from Twitter to create "reserved" accounts in their names. To claim a reserved account, the account holder would need to tweet about it (which also serves as a marketing strategy). At least 80 such reserved profiles have been claimed. Proof of stake was introduced in March 2024.

Gaumina

Gaumina is the largest interactive agency in the Baltics, providing services of web design, web development, online advertising, video, multimedia, mobile and viral. The company works on projects for Procter & Gamble, Nokia, Nissan, Unilever, YX Energi, 7 Up, Vodafone, MTV, Dunnes Stores, Philip Morris, FIBA Europe as well as Irish public sector. == History == Founded in 1998, Gaumina accounts for 39 percent of the Lithuanian interactive market and has completed more than 2,000 online projects. Since 2004 the company has been operating in the UK and Ireland as Gaumina.co.uk. In 2007 Gaumina gained wide media coverage for winning three awards in three days. A website developed by Gaumina won the Best Social Networking website award at the same the Irish Golden Spiders awards. A website developed by Gaumina was named among the 21 best European multimedia projects of 2007 in the final of Europrix Top Talent Award in Austria. The company was also named one of the winners of the national Innovation Prize 2007, awarding the Lithuania's most innovative companies, in the category of Innovative Enterprise. The agency was named "Digital Agency of the Year" by International advertising festival Golden Hammer in September 2008. The agency also won the main prize at the best at Best Use of Film, Digital Animation or Motion Graphics category by the Irish Golden Spider awards in November 2008. Gaumina is currently managed by CEO Darius Bagdžiūnas.

Open Sound Control

Open Sound Control (OSC) is a protocol for networking sound synthesizers, computers, and other multimedia devices for purposes such as musical performance or show control. OSC's advantages include interoperability, accuracy, flexibility and enhanced organization and documentation. Its disadvantages include higher bandwidth requirements, increased load on embedded processors, and lack of standardized messages/interoperability. The first specification was released in March 2002. == Motivation == OSC is a content format developed at CNMAT by Adrian Freed and Matt Wright comparable to XML, WDDX, or JSON. It was originally intended for sharing music performance data (gestures, parameters and note sequences) between musical instruments (especially electronic musical instruments such as synthesizers), computers, and other multimedia devices. OSC is sometimes used as an alternative to the 1983 MIDI standard, when higher resolution and a richer parameter space is desired. OSC messages are transported across the internet and within local subnets using UDP/IP and Ethernet. OSC messages between gestural controllers are usually transmitted over serial endpoints of USB wrapped in the SLIP protocol. == Features == OSC's main features, compared to MIDI, include: Open-ended, dynamic, URI-style symbolic naming scheme Symbolic and high-resolution numeric data Pattern matching language to specify multiple recipients of a single message High resolution time tags "Bundles" of messages whose effects must occur simultaneously == Applications == There are dozens of OSC applications, including real-time sound and media processing environments, web interactivity tools, software synthesizers, programming languages and hardware devices. OSC has achieved wide use in fields including musical expression, robotics, video performance interfaces, distributed music systems and inter-process communication. The TUIO community standard for tangible interfaces such as multitouch is built on top of OSC. Similarly the GDIF system for representing gestures integrates OSC. OSC is used extensively in experimental musical controllers, and has been built into several open source and commercial products. The Open Sound World (OSW) music programming language is designed around OSC messaging. OSC is the heart of the DSSI plugin API, an evolution of the LADSPA API, in order to make the eventual GUI interact with the core of the plugin via messaging the plugin host. LADSPA and DSSI are APIs dedicated to audio effects and synthesizers. In 2007, a standardized namespace within OSC called SYN, for communication between controllers, synthesizers and hosts, was proposed. == Design == OSC messages consist of an address pattern (such as /oscillator/4/frequency), a type tag string (such as ,fi for a float32 argument followed by an int32 argument), and the arguments themselves (which may include a time tag). Address patterns form a hierarchical name space, reminiscent of a Unix filesystem path, or a URL, and refer to "Methods" inside the server, which are invoked with the attached arguments. Type tag strings are a compact string representation of the argument types. Arguments are represented in binary form with four-byte alignment. The core types supported are 32-bit two's complement signed integers 32-bit IEEE floating point numbers Null-terminated arrays of eight-bit encoded data (C-style strings) arbitrary sized blob (e.g. audio data, or a video frame) An example message is included in the spec (with null padding bytes represented by ␀): /oscillator/4/frequency␀,f␀␀, Followed by the 4-byte float32 representation of 440.0: 0x43dc0000. Messages may be combined into bundles, which themselves may be combined into bundles, etc. Each bundle contains a timestamp, which determines whether the server should respond immediately or at some point in the future. Applications commonly employ extensions to this core set. More recently some of these extensions such as a compact Boolean type were integrated into the required core types of OSC 1.1. The advantages of OSC over MIDI are primarily internet connectivity; data type resolution; and the comparative ease of specifying a symbolic path, as opposed to specifying all connections as seven-bit numbers with seven-bit or fourteen-bit data types. This human-readability has the disadvantage of being inefficient to transmit and more difficult to parse by embedded firmware, however. The spec does not define any particular OSC Methods or OSC Containers. All messages are implementation-defined and vary from server to server.

Israeli cybersecurity industry

The Israeli cybersecurity industry is a rapidly growing sector within Israel's technology and innovation ecosystem. Israel is internationally recognized as a powerhouse in the cybersecurity domain, with numerous cybersecurity startups, established companies, research institutions, and government initiatives. Tel Aviv itself is being ranked 7th in annual list of best global tech ecosystems, as reported by the Jerusalem Post. == History == The roots of Israel's cybersecurity industry can be traced back to the country's strong focus on national security and intelligence. The establishment of elite military units such as Unit 8200, the Israeli Intelligence Corps unit responsible for signals intelligence and code decryption, played a significant role in the development of cybersecurity expertise in the country. Many former members of Unit 8200 have gone on to establish successful cybersecurity companies or join existing organizations, bringing their unique skill sets and experience to the private sector. == Market overview == As of 2024, Israel housed more than 450 cybersecurity startups and companies. In 2023, the value of exits by Israeli tech companies reached $7.5 billion. Israel's cybersecurity industry is characterized by a high concentration of startups develop new technologies in areas such as network security, endpoint protection, data security, cloud security, and threat intelligence. In recent years, the sector has attracted significant investment from both local and international venture capital firms, as well as major technology companies such as Microsoft, Google, and IBM. Several Israeli cybersecurity companies have gained global recognition and success, with some being acquired by major corporations or conducting successful initial public offerings (IPOs). === Key Israeli cybersecurity companies === Some key Israeli cybersecurity companies include: Check Point Software Technologies CyberArk Cato Networks Radware Wiz === Financial activity === Israel’s cybersecurity sector has seen significant financial activity. As of 2023, mergers and acquisitions in the cybersecurity sector totaled $2.8 billion. In the first quarter of 2024, the sector secured $846 million in private funding. == Background == The military experience helped much. Israel's mandatory military service, combined with the expertise developed within elite units such as Unit 8200, has fostered a strong talent pool with practical experience in cybersecurity. Israel's thriving startup ecosystem, often referred to as the "Startup Nation," has fostered an environment of innovation and collaboration that has contributed to the growth of the cybersecurity industry. Israeli cybersecurity companies often collaborate with international partners, both in the private and public sectors, to share knowledge and develop joint solutions. === Government Initiatives and Support === The government also supported well through various initiatives, such as the Israel National Cyber Directorate (INCD), which works to strengthen cybersecurity defenses and promote the development of the sector. === Academic institutions === Israeli universities and research centers are involved in cybersecurity research and education, contributing to the development of new technologies and training the next generation of cybersecurity professionals. Academic Tech transfer offices in Israel also facilitate the commercialization of cybersecurity technologies. Some academic institutions with cybersecurity laboratories include: Tel Aviv University Technion Ben-Gurion University

Packard Bell Statesman

The Packard Bell Statesman was an economy line of notebook-sized laptops introduced in 1993 by Packard Bell. They were slower in performance and lacked features compared to most competitor products, but they were lower in price. It was created in a collaboration between Packard Bell and Zenith Data Systems. The Statesman series was essentially a rebrand of Zenith Data Systems Z-Star 433 series, with the only notable difference of the logo in the middle and text on the front bezel. == History == In June 1993 Zenith Data Systems announced an alliance with Packard Bell. Zenith acquired about 20% of Packard Bell and they would both now work together to design and build PC's. Zenith would also provide Packard Bell with private-label versions of their portable PC's. The Packard Bell Statesman was a rebrand of the Zenith Z-Star notebook computer series. While the Statesman was being advertised by Packard Bell, the Z-Star series was also still being sold by Zenith. The Statesman was first introduced on October 4, 1993. Prices started at $1,500 for a monochrome or color DSTN model with a 33 MHz Cyrix Cx486SLC, 4 MB of RAM, 200 MB hard disk drive, internal 1.44 MB floppy disk drive, and MS-DOS 6.0 with Windows 3.1 for the included software. A "J mouse" pointing device was included, similar to the TrackPoint. The Statesman was expected to begin shipping within the next few weeks. == Specifications == === Hardware === CPU The first two models, the 200M and 200C, used the Cyrix Cx486SLC. This was Cyrix's first processor, which was a 386SX pin-compatible chip with on-board L1 cache and 486 instructions, being known as a "hybrid chip". The processor was clocked at 33 MHz and had 1 KB of L1 cache. It was a 16-bit processor and was pin compatible with the Intel 80386SX. On the bottom of the unit, the motherboard had an empty socket for a Cyrix FasMath co-processor, which could improve floating-point math performance. The 200M and 200C plus models had a Cyrix Cx486SLC2 clocked at 50 MHz, which was 50% faster than the original 486SLC. The SLC2 similarly had 1 KB of on-board cache and was pin compatible with the previous model. Graphics & Display For video all models used three versions of the Chips & Technologies 655xx, the CT65520, 65525, and 65530. The 65520 was first introduced in early 1992 as the first controller with Super VGA resolution. It supported resolutions up to 1024x768 in 16 colors or shades of gray. If in 800x600 resolution, it can display up to 256 colors. All 3 chips were the same, with the CT65525 identifying as a CT65530. The CT65530 had an ability of 5V and 3.3V mixed operation and linear video memory addressing. All models used a 9.5in 800x600 resolution DSTN LCD. The 200M and 200M Plus had a monochrome display, while the 200C and 200C Plus had a color display. Audio All models had only basic audio available, with just a piezo speaker soldered onto the motherboard and no sound controller. Memory Standard RAM included was 4-8 MB of EDO RAM. The RAM was on a proprietary SIPP package that could only be upgraded to 12 MB maximum if the user had compatible modules. Storage For storage all models used a hard drive with a size of 100 or 200 MB, and all models had an internal 1.44 MB floppy disk drive located on the side of the unit. The maximum capacity hard drive compatible if the user wanted to upgrade was 500 MB.Ports & Expansion For ports all models had 1x serial, 1x parallel, 1x VGA output, and 1x PS/2 keyboard/mouse input. For expansion all models only had one PCMCIA type II slot. Keyboard & Mouse All models used a small-scale keyboard with control keys. One interesting feature of the keyboard is that the J key also acted as a mouse, working similar to IBM's ThinkPad TrackPoint. On some models additional keys such as S, D, F, G and space let you do other mouse actions such as right click, left click, double click, and middle mouse click. === Software === The series shipped with MS-DOS and Windows 3.1 as the included operating system. == Model Comparison == Statesman 200M — The first Statesman model, it came with a DSTN monochrome screen, and a Nickel-cadmium battery pack which could last up to 4 hours. It weighed 7.4 lb and was $1500. Statesman 200C — The second Statesman model, it was the same as the 200M with the only notable differences of a DSTN color display rather than monochrome and a slightly decreased battery life of about 3 hours. It cost $700 more than the 200M at $2200. Statesman 200M/200C Plus — The 200M/200C Plus were both identical to their previous base models, with the only difference of them having a Cx486SLC2 running at 50 MHz. In 1994 it cost around $2,295 for the 200C plus with 4 MB of ram, with 8 MB costing an extra $400. == Reception == The Statesman received fair reception, with most reviewers giving positivity for the low price and high battery life, but mainly criticizing the performance and screen quality of the model line. A review by PC World writer Rex Farrance and Owen Linderholm said the 200M had a good price, being only $1500, and a good battery life which lasted about 4 hours. In benchmarks however, the 200M performed "noticeably below the average". It was noted that the 200M's worst feature was its monochrome display, being "cloudy and a bit dim for our tastes". The J mouse was considered a decent choice, and was said to be "highly usable" after some practice. The 200M was listed as number 3 on PC World's top 20 budget PC list. PC World also reviewed the 200C, saying the color display is only a "marginal, although an improvement on the monochrome version". The 200C placed 9 on the PC World top 20 budget PC list. Compute! Magazine reviewed the 200C Plus in September 1994 stating it "lagged far behind the others, especially the DXs, but then speed isn't everything". It was given pros for low cost and good display, but criticized for its low performance, not having a trackball, and poor external monitor support.