The Level-set method (LSM) is a conceptual framework for using level sets as a tool for numerical analysis of surfaces and shapes. LSM can perform numerical computations involving curves and surfaces on a fixed Cartesian grid without having to parameterize these objects. LSM makes it easier to perform computations on shapes with sharp corners and shapes that change topology (such as by splitting in two or developing holes). These characteristics make LSM effective for modeling objects that vary in time, such as an airbag inflating or a drop of oil floating in water. == Overview == The figure on the right illustrates several ideas about LSM. In the upper left corner is a bounded region with a well-behaved boundary. Below it, the red surface is the graph of a level set function φ {\displaystyle \varphi } determining this shape, and the flat blue region represents the X-Y plane. The boundary of the shape is then the zero-level set of φ {\displaystyle \varphi } , while the shape itself is the set of points in the plane for which φ {\displaystyle \varphi } is positive (interior of the shape) or zero (at the boundary). In the top row, the shape's topology changes as it is split in two. It is challenging to describe this transformation numerically by parameterizing the boundary of the shape and following its evolution. An algorithm can be used to detect the moment the shape splits in two and then construct parameterizations for the two newly obtained curves. On the bottom row, however, the plane at which the level set function is sampled is translated upwards, on which the shape's change in topology is described. It is less challenging to work with a shape through its level-set function rather than with itself directly, in which a method would need to consider all the possible deformations the shape might undergo. Thus, in two dimensions, the level-set method amounts to representing a closed curve Γ {\displaystyle \Gamma } (such as the shape boundary in our example) using an auxiliary function φ {\displaystyle \varphi } , called the level-set function. The curve Γ {\displaystyle \Gamma } is represented as the zero-level set of φ {\displaystyle \varphi } by Γ = { ( x , y ) ∣ φ ( x , y ) = 0 } , {\displaystyle \Gamma =\{(x,y)\mid \varphi (x,y)=0\},} and the level-set method manipulates Γ {\displaystyle \Gamma } implicitly through the function φ {\displaystyle \varphi } . This function φ {\displaystyle \varphi } is assumed to take positive values inside the region delimited by the curve Γ {\displaystyle \Gamma } and negative values outside. == The level-set equation == If the curve Γ {\displaystyle \Gamma } moves in the normal direction with a speed v {\displaystyle v} , then by chain rule and implicit differentiation, it can be determined that the level-set function φ {\displaystyle \varphi } satisfies the level-set equation ∂ φ ∂ t = v | ∇ φ | . {\displaystyle {\frac {\partial \varphi }{\partial t}}=v|\nabla \varphi |.} Here, | ⋅ | {\displaystyle |\cdot |} is the Euclidean norm (denoted customarily by single bars in partial differential equations), and t {\displaystyle t} is time. This is a partial differential equation, in particular a Hamilton–Jacobi equation, and can be solved numerically, for example, by using finite differences on a Cartesian grid. However, the numerical solution of the level set equation may require advanced techniques. Simple finite difference methods fail quickly. Upwinding methods such as the Godunov method are considered better; however, the level set method does not guarantee preservation of the volume and shape of the set level in an advection field that maintains shape and size, for example, a uniform or rotational velocity field. Instead, the shape of the level set may become distorted, and the level set may disappear over a few time steps. Therefore, high-order finite difference schemes, such as high-order essentially non-oscillatory (ENO) schemes, are often required, and even then, the feasibility of long-term simulations is questionable. More advanced methods have been developed to overcome this; for example, combinations of the leveling method with tracking marker particles suggested by the velocity field. == Example == Consider a unit circle in R 2 {\textstyle \mathbb {R} ^{2}} , shrinking in on itself at a constant rate, i.e. each point on the boundary of the circle moves along its inwards pointing normally at some fixed speed. The circle will shrink and eventually collapse down to a point. If an initial distance field is constructed (i.e. a function whose value is the signed Euclidean distance to the boundary, positive interior, negative exterior) on the initial circle, the normalized gradient of this field will be the circle normal. If the field has a constant value subtracted from it in time, the zero level (which was the initial boundary) of the new fields will also be circular and will similarly collapse to a point. This is due to this being effectively the temporal integration of the Eikonal equation with a fixed front velocity. == Applications == In mathematical modeling of combustion, LSM is used to describe the instantaneous flame surface, known as the G equation. Level-set data structures have been developed to facilitate the use of the level-set method in computer applications. Computational fluid dynamics Trajectory planning Optimization Image processing Computational biophysics Discrete complex dynamics (visualization of the parameter plane and the dynamic plane) == History == The level-set method was developed in 1979 by Alain Dervieux, and subsequently popularized by Stanley Osher and James Sethian. It has since become popular in many disciplines, such as image processing, computer graphics, computational geometry, optimization, computational fluid dynamics, and computational biology.
Sprite multiplexing
Sprite multiplexing is a computer graphics technique where additional sprites (moving images) can be drawn on the screen, beyond the nominal maximum. It is largely historical, applicable principally to older hardware, where limited resources (such as CPU speed and memory) meant only a relatively small number of sprites were supported. On the other hand, it is also true that without multiplexing, the sprite circuitry would be idle much of the time, and limited resources were wasted. == Description == The sprite multiplexing technique is based on the idea that while the hardware may only support a finite number of sprites, it is sometimes possible to re-use the same sprite "slots" more than once per frame or scan line. The program will first use the hardware to draw one or more sprite(s), as normal. Before the next frame (or next scanline) needs to be drawn, the software reprograms the hardware to display additional sprites, in other positions. For example, the Nintendo Entertainment System explicitly supports hardware sprite multiplexing, where it has 64 hardware sprites, but is only capable of rendering 8 of them per scanline. On the older Atari 2600, sprite multiplexing was not intentionally designed in, but programmers discovered they could reset the TIA graphics chip to draw additional sprites on the same scanline. The sprite multiplexing technique relies on the program being able to identify what part of the video screen is being drawn at the moment, or being triggered by the video hardware to run a subroutine at the crucial moment. The programmer must carefully consider the layout of the screen. If the video graphics hardware is not reprogrammed in time for the extra sprites to be displayed, they will not appear, or will be drawn incorrectly. Modern video graphics hardware typically does not use hardware sprites, since modern computer systems do not have the kind of limitations that sprite hardware is designed to circumvent. == Implementations == Systems that allow the programmer to employ the sprite multiplexing technique include: Atari 2600 Atari 8-bit computers Amiga Commodore 64 MSX Nintendo Entertainment System Super Nintendo Entertainment System Master System Sega Genesis/Mega Drive
Artificial intelligence industry in China
The roots of the development of artificial intelligence in the People's Republic of China started in the late 1970s following Deng Xiaoping's reform and opening up emphasizing science and technology as the country's primary productive force. The initial stages of China's AI development were slow and encountered significant challenges due to lack of resources and talent. At the beginning China was behind most Western countries in terms of AI development. A majority of the research was led by scientists who had received higher education abroad. Since 2006, the Chinese government has steadily developed a national agenda for artificial intelligence development and emerged as one of the leading nations in artificial intelligence research and development. In 2016, the Chinese Communist Party (CCP) released its 13th Five-Year Plan in which it aimed to become a global AI leader by 2030. As of 2025, China is considered to be a world leader in AI technology along with the United States. The State Council has a list of "national AI teams" including fifteen China-based companies, including Baidu, Tencent, Alibaba, SenseTime, and iFlytek. Each company should lead the development of a designated specialized AI sector in China, such as facial recognition, software/hardware, and speech recognition. China's rapid AI development has significantly impacted Chinese society in many areas, including the socio-economic, military, intelligence, and political spheres. Agriculture, transportation, accommodation and food services, and manufacturing are the top industries that would be the most impacted by further AI deployment. The private sector, university laboratories, and the military are working collaboratively in many aspects as there are few current existing boundaries. In 2021, China published the Data Security Law of the People's Republic of China, its first national law addressing AI-related ethical concerns. In October 2022, the United States federal government announced a series of export controls and trade restrictions intended to restrict China's access to advanced computer chips for AI applications. In 2023, the Cyberspace Administration of China issued guidelines requiring that AI content upholds the ideology of the CCP including Core Socialist Values, avoids discrimination, respects intellectual property rights, and safeguards user data. In 2025, the Chinese government issued a document regarding training data, requiring companies to use as little as data deemed "unsafe" as possible, as well as requiring companies to test models regularly. Concerns have been raised about the effects of the Chinese government's censorship regime on the development of generative artificial intelligence and long-term talent acquisition with state of the country's demographics. Others have noted that official notions of AI safety require following the priorities of the CCP and are antithetical to standards in democratic societies and raised concerns about the extension of China's system of mass surveillance and censorship abroad. == History == The Chinese term for artificial intelligence (réngōngzhìnéng 人工智能) connotes "humanmade" intelligence. The term developed as mid-20th century localisation of the Japanese term jinko chino. The research and development of artificial intelligence in China started in the 1980s, with the announcement by Deng Xiaoping of the importance of science and technology for China's economic growth. === Late 1970s to early 2010s === Chinese artificial intelligence research and development began in late 1970s after Deng Xiaoping's reform and opening up. China's first national conference on AI occurred in 1979. Academic journals in the late 1970s began publishing literature reviews of Western research on AI topics. In the 1980s, a group of Chinese scientists launched AI research led by Qian Xuesen and Wu Wenjun. However, during the time, China's society still had a generally conservative view towards AI. In the early 1980s, Science Press published translated versions of Western textbooks such as Patrick Winston's Artificial Intelligence and Nils John Nilsson's Principles of Artificial Intelligence. In 1980, a journal of the Chinese Academy of Sciences convened its first annual National Symposium on Artificial Intelligence, which included national and international scholars like Herbert A. Simon. The Chinese Association for Artificial Intelligence (CAAI) was founded in September 1981 and was authorized by the Ministry of Civil Affairs. CAAI has continued to be the largest AI association in China as of 2025. In 1982, CAAI began publishing the Artificial Intelligence Journal, which published early AI research by Chinese academics. In the 1980s, Chinese research on AI was influenced by the field of cybernetics, particularly the work of Norbert Weiner and his text Cybernetics: Or Control and Communication in the Animal and the Machine. Chinese researchers at the time sought to situate AI as part of a broader "Intelligence Science" field which would include disciplines like mathematics, computer science, cognitive science, social sciences, and philosophy. In 1987, Tsinghua University began a research publication on AI. Beginning in 1993, smart automation and intelligence have been part of China's national technology plan. Since the 2000s, the Chinese government has further expanded its research and development funds for AI and the number of government-sponsored research projects has dramatically increased. In 2006, China announced a policy priority for the development of artificial intelligence, which was included in the National Medium and Long Term Plan for the Development of Science and Technology (2006–2020), released by the State Council. In the same year, artificial intelligence was also mentioned in the 11th Five-Year Plan. In 2011, the Association for the Advancement of Artificial Intelligence (AAAI) established a branch in Beijing, China. At same year, the Wu Wenjun Artificial Intelligence Science and Technology Award was founded in honor of Chinese mathematician Wu Wenjun, and it became the highest award for Chinese achievements in the field of artificial intelligence. The first award ceremony was held on May 14, 2012. In 2013, the International Joint Conferences on Artificial Intelligence (IJCAI) was held in Beijing, marking the first time the conference was held in China. This event coincided with the Chinese government's announcement of the "Chinese Intelligence Year," a significant milestone in China's development of artificial intelligence. === Late 2010s to early 2020s === AI became a major issue of commercial, public, and political focus in China in the latter half of the 2010s. Various interpretations of the primary cause for this increased focus exist, with some analyses focusing on the 2016 Go match between Google's AlphaGo and Lee Sedol, others emphasising the U.S. increasing trade restrictions on China's technology industries and the desire to achieve national technological self-sufficiency. The State Council of China issued "A Next Generation Artificial Intelligence Development Plan" (State Council Document [2017] No. 35) on 20 July 2017. In the document, the CCP Central Committee and the State Council urged governing bodies in China to promote the development of artificial intelligence. Specifically, the plan described AI as a strategic technology that has become a "focus of international competition".:2 The document urged significant investment in a number of strategic areas related to AI and called for close cooperation between the state and private sectors. It set the goal of China becoming the preeminent country for AI research and application by 2030. During the general secretaryship of Xi Jinping, artificial intelligence has been a focus of the CCP's military-civil fusion efforts. On the occasion of Xi's speech at the first plenary meeting of the Central Military-Civil Fusion Development Committee (CMCFDC), scholars from the National Defense University wrote in the PLA Daily that the "transferability of social resources" between economic and military ends is an essential component to being a great power. During the Two Sessions 2017,"artificial intelligence plus" was proposed to be elevated to a strategic level. The same year witnessed the emergence of multiple application-level usages in the medical field according to reports. In 2018, Xinhua News Agency, in partnership with Tencent's subsidiary Sogou, launched its first artificial intelligence-generated news anchor. In 2018, the State Council budgeted $2.1 billion for an AI industrial park in Mentougou district. In order to achieve this the State Council stated the need for massive talent acquisition, theoretical and practical developments, as well as public and private investments. Some of the stated motivations that the State Council gave for pursuing its AI strategy include the potential of artificial intelligence for industrial transformation, better social
Metadata management
Metadata management involves managing metadata about other data, whereby this "other data" is generally referred to as content data. The term is used most often in relation to digital media, but older forms of metadata are catalogs, dictionaries, and taxonomies. For example, the Dewey Decimal Classification is a metadata management system developed in 1876 for libraries. == Metadata schema == Metadata management goes by the end-to-end process and governance framework for creating, controlling, enhancing, attributing, defining and managing a metadata schema, model or other structured aggregation system, either independently or within a repository and the associated supporting processes (often to enable the management of content). For web-based systems, URLs, images, video etc. may be referenced from a triples table of object, attribute and value. == Scope == With specific knowledge domains, the boundaries of the metadata for each must be managed, since a general ontology is not useful to experts in one field whose language is knowledge-domain specific. == Metadata Manager == In the process of developing a knowledge management solution, creating a metadata schema, and a system in which metadata is managed, a dedicated resource may be appointed to maintain adherence to metadata standards as defined by data owners as well as general best practice. This person is responsible for curation of the business and technical layers of the metadata schema, and commonly involved with strategy and implementation. A metadata manager is not required to master all aspects, or be involved with everything concerning the solution, but an understanding of as much of the process as possible to ensure a relevant schema is developed. == Metadata management over time == Managing the metadata in a knowledge management solution is an important step in a metadata strategy. It is part of the strategy to make sure that the metadata are complete, current and correct at any given time. Managing a metadata project is also about making sure that users of the system are aware of the possibilities allowed by a well-designed metadata system and how to maximize the benefits of metadata. Regularly monitoring the metadata to ensure that the schema remains relevant is advised. === Wikipedia metadata === Wikipedia is a project that actively manages metadata for its articles and files. For example, volunteer editors carefully curate new biographical articles based on the notability (claim to fame), name, birth, and/or death dates. Similarly, volunteer editors carefully curate new architectural articles based on name, municipality, or geo coordinates. When new articles with a valid alternate spelling are added to Wikipedia that match up to existing articles based on metadata, these are then manually checked and if needed, tagged for merging. When new articles are added that are considered out of scope or otherwise unfit for Wikipedia, these are nominated for deletion. To help keep track of metadata on Wikipedia, the new Wikimedia project Wikidata was established in 2012. Click on the pictures to view more metadata about these images:
Zassenhaus algorithm
In mathematics, the Zassenhaus algorithm is a method to calculate a basis for the intersection and sum of two subspaces of a vector space. It is named after Hans Zassenhaus, but no publication of this algorithm by him is known. It is used in computer algebra systems. == Algorithm == === Input === Let V be a vector space and U, W two finite-dimensional subspaces of V with the following spanning sets: U = ⟨ u 1 , … , u n ⟩ {\displaystyle U=\langle u_{1},\ldots ,u_{n}\rangle } and W = ⟨ w 1 , … , w k ⟩ . {\displaystyle W=\langle w_{1},\ldots ,w_{k}\rangle .} Finally, let B 1 , … , B m {\displaystyle B_{1},\ldots ,B_{m}} be linearly independent vectors so that u i {\displaystyle u_{i}} and w i {\displaystyle w_{i}} can be written as u i = ∑ j = 1 m a i , j B j {\displaystyle u_{i}=\sum _{j=1}^{m}a_{i,j}B_{j}} and w i = ∑ j = 1 m b i , j B j . {\displaystyle w_{i}=\sum _{j=1}^{m}b_{i,j}B_{j}.} === Output === The algorithm computes the base of the sum U + W {\displaystyle U+W} and a base of the intersection U ∩ W {\displaystyle U\cap W} . === Algorithm === The algorithm creates the following block matrix of size ( ( n + k ) × ( 2 m ) ) {\displaystyle ((n+k)\times (2m))} : ( a 1 , 1 a 1 , 2 ⋯ a 1 , m a 1 , 1 a 1 , 2 ⋯ a 1 , m ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ a n , 1 a n , 2 ⋯ a n , m a n , 1 a n , 2 ⋯ a n , m b 1 , 1 b 1 , 2 ⋯ b 1 , m 0 0 ⋯ 0 ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ b k , 1 b k , 2 ⋯ b k , m 0 0 ⋯ 0 ) {\displaystyle {\begin{pmatrix}a_{1,1}&a_{1,2}&\cdots &a_{1,m}&a_{1,1}&a_{1,2}&\cdots &a_{1,m}\\\vdots &\vdots &&\vdots &\vdots &\vdots &&\vdots \\a_{n,1}&a_{n,2}&\cdots &a_{n,m}&a_{n,1}&a_{n,2}&\cdots &a_{n,m}\\b_{1,1}&b_{1,2}&\cdots &b_{1,m}&0&0&\cdots &0\\\vdots &\vdots &&\vdots &\vdots &\vdots &&\vdots \\b_{k,1}&b_{k,2}&\cdots &b_{k,m}&0&0&\cdots &0\end{pmatrix}}} Using elementary row operations, this matrix is transformed to the row echelon form. Then, it has the following shape: ( c 1 , 1 c 1 , 2 ⋯ c 1 , m ∙ ∙ ⋯ ∙ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ c q , 1 c q , 2 ⋯ c q , m ∙ ∙ ⋯ ∙ 0 0 ⋯ 0 d 1 , 1 d 1 , 2 ⋯ d 1 , m ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ 0 0 ⋯ 0 d ℓ , 1 d ℓ , 2 ⋯ d ℓ , m 0 0 ⋯ 0 0 0 ⋯ 0 ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ 0 0 ⋯ 0 0 0 ⋯ 0 ) {\displaystyle {\begin{pmatrix}c_{1,1}&c_{1,2}&\cdots &c_{1,m}&\bullet &\bullet &\cdots &\bullet \\\vdots &\vdots &&\vdots &\vdots &\vdots &&\vdots \\c_{q,1}&c_{q,2}&\cdots &c_{q,m}&\bullet &\bullet &\cdots &\bullet \\0&0&\cdots &0&d_{1,1}&d_{1,2}&\cdots &d_{1,m}\\\vdots &\vdots &&\vdots &\vdots &\vdots &&\vdots \\0&0&\cdots &0&d_{\ell ,1}&d_{\ell ,2}&\cdots &d_{\ell ,m}\\0&0&\cdots &0&0&0&\cdots &0\\\vdots &\vdots &&\vdots &\vdots &\vdots &&\vdots \\0&0&\cdots &0&0&0&\cdots &0\end{pmatrix}}} Here, ∙ {\displaystyle \bullet } stands for arbitrary numbers, and the vectors ( c p , 1 , c p , 2 , … , c p , m ) {\displaystyle (c_{p,1},c_{p,2},\ldots ,c_{p,m})} for every p ∈ { 1 , … , q } {\displaystyle p\in \{1,\ldots ,q\}} and ( d p , 1 , … , d p , m ) {\displaystyle (d_{p,1},\ldots ,d_{p,m})} for every p ∈ { 1 , … , ℓ } {\displaystyle p\in \{1,\ldots ,\ell \}} are nonzero. Then ( y 1 , … , y q ) {\displaystyle (y_{1},\ldots ,y_{q})} with y i := ∑ j = 1 m c i , j B j {\displaystyle y_{i}:=\sum _{j=1}^{m}c_{i,j}B_{j}} is a basis of U + W {\displaystyle U+W} and ( z 1 , … , z ℓ ) {\displaystyle (z_{1},\ldots ,z_{\ell })} with z i := ∑ j = 1 m d i , j B j {\displaystyle z_{i}:=\sum _{j=1}^{m}d_{i,j}B_{j}} is a basis of U ∩ W {\displaystyle U\cap W} . === Proof of correctness === First, we define π 1 : V × V → V , ( a , b ) ↦ a {\displaystyle \pi _{1}:V\times V\to V,(a,b)\mapsto a} to be the projection to the first component. Let H := { ( u , u ) ∣ u ∈ U } + { ( w , 0 ) ∣ w ∈ W } ⊆ V × V . {\displaystyle H:=\{(u,u)\mid u\in U\}+\{(w,0)\mid w\in W\}\subseteq V\times V.} Then π 1 ( H ) = U + W {\displaystyle \pi _{1}(H)=U+W} and H ∩ ( 0 × V ) = 0 × ( U ∩ W ) {\displaystyle H\cap (0\times V)=0\times (U\cap W)} . Also, H ∩ ( 0 × V ) {\displaystyle H\cap (0\times V)} is the kernel of π 1 | H {\displaystyle {\pi _{1}|}_{H}} , the projection restricted to H. Therefore, dim ( H ) = dim ( U + W ) + dim ( U ∩ W ) {\displaystyle \dim(H)=\dim(U+W)+\dim(U\cap W)} . The Zassenhaus algorithm calculates a basis of H. In the first m columns of this matrix, there is a basis y i {\displaystyle y_{i}} of U + W {\displaystyle U+W} . The rows of the form ( 0 , z i ) {\displaystyle (0,z_{i})} (with z i ≠ 0 {\displaystyle z_{i}\neq 0} ) are obviously in H ∩ ( 0 × V ) {\displaystyle H\cap (0\times V)} . Because the matrix is in row echelon form, they are also linearly independent. All rows which are different from zero ( ( y i , ∙ ) {\displaystyle (y_{i},\bullet )} and ( 0 , z i ) {\displaystyle (0,z_{i})} ) are a basis of H, so there are dim ( U ∩ W ) {\displaystyle \dim(U\cap W)} such z i {\displaystyle z_{i}} s. Therefore, the z i {\displaystyle z_{i}} s form a basis of U ∩ W {\displaystyle U\cap W} . == Example == Consider the two subspaces U = ⟨ ( 1 − 1 0 1 ) , ( 0 0 1 − 1 ) ⟩ {\displaystyle U=\left\langle \left({\begin{array}{r}1\\-1\\0\\1\end{array}}\right),\left({\begin{array}{r}0\\0\\1\\-1\end{array}}\right)\right\rangle } and W = ⟨ ( 5 0 − 3 3 ) , ( 0 5 − 3 − 2 ) ⟩ {\displaystyle W=\left\langle \left({\begin{array}{r}5\\0\\-3\\3\end{array}}\right),\left({\begin{array}{r}0\\5\\-3\\-2\end{array}}\right)\right\rangle } of the vector space R 4 {\displaystyle \mathbb {R} ^{4}} . Using the standard basis, we create the following matrix of dimension ( 2 + 2 ) × ( 2 ⋅ 4 ) {\displaystyle (2+2)\times (2\cdot 4)} : ( 1 − 1 0 1 1 − 1 0 1 0 0 1 − 1 0 0 1 − 1 5 0 − 3 3 0 0 0 0 0 5 − 3 − 2 0 0 0 0 ) . {\displaystyle \left({\begin{array}{rrrrrrrr}1&-1&0&1&&1&-1&0&1\\0&0&1&-1&&0&0&1&-1\\\\5&0&-3&3&&0&0&0&0\\0&5&-3&-2&&0&0&0&0\end{array}}\right).} Using elementary row operations, we transform this matrix into the following matrix: ( 1 0 0 0 ∙ ∙ ∙ ∙ 0 1 0 − 1 ∙ ∙ ∙ ∙ 0 0 1 − 1 ∙ ∙ ∙ ∙ 0 0 0 0 1 − 1 0 1 ) {\displaystyle \left({\begin{array}{rrrrrrrrr}1&0&0&0&&\bullet &\bullet &\bullet &\bullet \\0&1&0&-1&&\bullet &\bullet &\bullet &\bullet \\0&0&1&-1&&\bullet &\bullet &\bullet &\bullet \\\\0&0&0&0&&1&-1&0&1\end{array}}\right)} (Some entries have been replaced by " ∙ {\displaystyle \bullet } " because they are irrelevant to the result.) Therefore ( ( 1 0 0 0 ) , ( 0 1 0 − 1 ) , ( 0 0 1 − 1 ) ) {\displaystyle \left(\left({\begin{array}{r}1\\0\\0\\0\end{array}}\right),\left({\begin{array}{r}0\\1\\0\\-1\end{array}}\right),\left({\begin{array}{r}0\\0\\1\\-1\end{array}}\right)\right)} is a basis of U + W {\displaystyle U+W} , and ( ( 1 − 1 0 1 ) ) {\displaystyle \left(\left({\begin{array}{r}1\\-1\\0\\1\end{array}}\right)\right)} is a basis of U ∩ W {\displaystyle U\cap W} .
H2O (software)
H2O is an open-source, in-memory, distributed machine learning and predictive analytics platform developed by the company H2O.ai (previously 0xdata). The software uses a distributed architecture for parallel processing on standard hardware. It supports algorithms for large-scale data analysis and model deployment. H2O is primarily used by data scientists and developers for statistical modeling and data-driven decision-making. The platform is designed to handle in-memory computations across a distributed computing environment. It offers implementations for numerous statistical and machine learning algorithms, which are accessible through various programming interfaces. The software is released under the Apache License 2.0. == Functionality and features == H2O provides a suite of supervised and unsupervised machine learning algorithms. Its core functions include: Supervised learning: algorithms in the field of statistics, data mining and machine learning such as generalized linear models, random forests, gradient boosting and deep learning are implemented for classification and regression tasks. Unsupervised learning: including K-Means clustering and principal component analysis. Automated machine learning: a features designed to automate the processes of model selection, tuning, and ensemble creation. The software can ingest data from various sources, including the Hadoop Distributed File System, Amazon S3, SQL databases, as well as local file systems. It operates natively on Apache Spark clusters through Sparkling Water. Proponents claim that improved performance is achieved compared to other analysis tools. The software is distributed free of charge, under a business model based on the development of individual applications and support. == Architecture == H2O is primarily written in Java. It uses a distributed architecture that allows the platform to cluster nodes for parallel processing and in-memory storage of data and models. Users interact with the H2O platform through several primary interfaces: Programming language interfaces: APIs are provided for the R and Python programming languages, and various Apache offerings (Apache Hadoop and Spark, as well as Maven). H2O Flow: a graphical web-based interactive computational environment that functions as a notebook interface for data exploration, model building, and scripting. REST-API: allows for integration with other applications and frameworks such as Microsoft Excel or RStudio. With the H2O Machine Learning Integration Nodes, KNIME offers algorithmic workflows. While the algorithm executes, approximate results are displayed, so that users can track the progress and intervene if needed. == History, influences, and extensions == The software project was initiated by the company 0xdata, which later changed its name to H2O.ai. The three Stanford professors Stephen P. Boyd, Robert Tibshirani and Trevor Hastie form a panel that advises H2O on scientific issues. Since its inception, H2O provides open-source machine learning libraries for enterprise use. The core H2O platform is often complemented by offerings from H2O.ai, such as H2O Driverless AI. == Reception == H2O is referenced in peer-reviewed literature regarding automated machine learning (AutoML). The platform has been categorized as a "Leader" and a "Strong Performer" in industry reports by Forrester Research. H2O (the open-source platform) and the associated commercial platform Driverless AI have been recurring winners of InfoWorld's most prestigious awards, including both the Best of Open Source Software ("Bossies") and the Technology of the Year awards.
Manufacture Modules Technologies
Manufacture Modules Technologies Sarl (MMT) is a Swiss company established in Geneva in 2015 which originally specialised in the development and commercialization of "Horological Smartwatch modules", firmware, apps and cloud. Located at Geneva's Skylab high-tech hub, it expanded into the development and manufacturing of "E-Straps" operated with a mobile application. Philippe Fraboulet is the CEO. == History == In June 2015, Fullpower Technologies and Union Horlogère Suisse (Swiss Watchmakers Corporation) formed MMT as a joint venture, which then launched the MotionX Horological Smartwatch Open Platform for the Swiss watch industry. The initial licensees were Frederique Constant, Alpina and Mondaine, brands owned by Union Horlogère Suisse. Fullpower created and managed the circuit design, firmware, smartphone applications (including sleep activity), as well as the cloud Infrastructure. MMT managed the Swiss watch movement development and production as well as licensing and support. In July 2016, Union Horlogere Holding and MMT were spun-out of the Frédérique Constant Group. Fullpower Technologies' 19.99% share was acquired by Union Horlogere Holding BV, giving it 100% of MMT's shares. == Business == The company offers firmware, a cloud, manufacturing, service and over-the-air facilities for upgrades. The company also offers its own apps, which bear the label “Swiss Made software”.