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  AstroPay

  AstroPay is a global digital wallet that provides users with a way to pay, send, and receive money. The app provides online payments, virtual and physical debit cards, peer-to-peer money transfers, and more. == History == AstroPay was founded in Uruguay in 2009 as a payment processing company. Over time, it expanded its services across Latin America, EMEA, and APAC. A significant milestone occurred in 2016, when AstroPay spun off dLocal, focusing on cross-border payments for emerging markets. dLocal became Uruguay's first unicorn and eventually went public through a successful IPO. In 2020, AstroPay spun off its payment processing services into a new entity, D24, to focus on mobile wallet for cross border. Between 2023 and 2024 the Company brought new leadership to guide its transition towards becoming a fully focused global digital multicurrency wallet where users save, send, and spend globally. This shift introduced enhanced features, including loyalty prepaid cards and multicurrency accounts. == Services == AstroPay offers three main products: AstroPay Wallet, AstroPay check-out, and AstroPay Platform. AstroPay Wallet is a digital wallet for consumers, where they have multicurrency accounts, prepaid card and marketplace. With AstroPay check-out, businesses can tap into AstroPay's wallet user base by accepting AstroPay as a payment method in their check-out options. Lastly, AstroPay Platform enables other businesses to use the AstroPay network to launch their own global wallet. == Brand endorsements, partnerships == AstroPay's marketing strategy has included the development of co-branded products with sports teams and other brand. The company sponsored Burnley Football Club during the 2018–19 Premier League season, renewing the partnership for the 2021–22 Premier League season when it became the club's official payment service partner. In August 2021, AstroPay entered into a partnership with the Wolverhampton Wanderers for the 2021-22 Premier League season, and the following year, became the team's shirt sponsor. Later, in September 2021, AstroPay expanded its partnership with Wolverhampton Wanderers, which included becoming the team's official payment partner and later, in 2023, co-launching a co-branded card. Other partnerships include Newcastle United in 2021 in the English Premier League. AstroPay made arrangements to ensure that branding and logo would be visible on the pitch-side LED advertising during Premier League matches. Furthermore, in June 2022, the company renewed it's partnership with Wolverhampton Wanderers for the 2022-23 Premier League season and launched its Wolves debit card in February 2023. Some other notable partnerships include: Universidad de Chile in 2024, Tottenham Hotspurs in 2023-25, and even a collaboration with Lionel Messi across all of Latin America. == Recent developments == AstroPay has refocused its strategy since 2023, pivoting from payment processing to concentrate on its global digital wallet. This move reflects a broader effort to redefine the company's market positioning by emphasizing global user-friendly financial services, while separating its identity from previous operations managed by dLocal and D24.

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  Rule induction

  Rule induction is an area of machine learning in which formal rules are extracted from a set of observations. The rules extracted may represent a full scientific model of the data, or merely represent local patterns in the data. Data mining in general and rule induction in detail are trying to create algorithms without human programming but with analyzing existing data structures. In the easiest case, a rule is expressed with “if-then statements” and was created with the ID3 algorithm for decision tree learning. Rule learning algorithm are taking training data as input and creating rules by partitioning the table with cluster analysis. A possible alternative over the ID3 algorithm is genetic programming which evolves a program until it fits to the data. Creating different algorithm and testing them with input data can be realized in the WEKA software. Additional tools are machine learning libraries for Python, like scikit-learn. == Paradigms == Some major rule induction paradigms are: Association rule learning algorithms (e.g., Agrawal) Decision rule algorithms (e.g., Quinlan 1987) Hypothesis testing algorithms (e.g., RULEX) Horn clause induction Version spaces Rough set rules Inductive Logic Programming Boolean decomposition (Feldman) == Algorithms == Some rule induction algorithms are: Charade Rulex Progol CN2

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  Symbol level

  In knowledge-based systems, agents choose actions based on the principle of rationality to move closer to a desired goal. The agent is able to make decisions based on knowledge it has about the world (see knowledge level). But for the agent to actually change its state, it must use whatever means it has available. This level of description for the agent's behavior is the symbol level. The term was coined by Allen Newell in 1982. For example, in a computer program, the knowledge level consists of the information contained in its data structures that it uses to perform certain actions. The symbol level consists of the program's algorithms, the data structures themselves, and so on.

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  AI warfare

  AI warfare refers to the use of artificial intelligence technologies to automate military operation and enhance or bypass human decision-making in armed conflicts. AI is used to rapidly analyze large volumes of military intelligence data, including making recommendations or decisions on who and what to target. Abdul-Rahman al-Rawi, a 20-year-old student, was the first acknowledged civilian killed by AI-assisted airstrike in a U.S. strike in Iraq in 2024. In 2026, the U.S. declared it would become an 'AI-first' warfighting force. Husain et al (2018) coined the term hyperwar to refer to warfare which is algorithmic or controlled by artificial intelligence, with little to no human decision-making. == 2026 Iran war == The 2026 Iran war has been described as the "first AI war", although the Untied States and Israel have previously used AI to identify targets during the Gaza war. The U.S. has used AI tools to attack Iran. These tools have been used for military intelligence, targeting, and damage assessment in the war in Iran. Using the Maven smart system, the U.S. attacked 1,000 targets in the first 24 hours of the war and 5,000 targets over the course of 10 days. While the U.S. had used Maven in 2022 to share targeting information with Ukraine and strike against Iraq, Syria, and against the Houthis in 2024, Iran's attacks are its biggest. Authorities are looking into whether artificial intelligence was involved in the airstrike on an Iranian girls' school that killed 170 civilians, the majority of whom were female students. The United States Central Command emphasized that humans were making final targeting decisions. Per a White House tally released on April 8, the U.S. military hit over 13,000 targets in Iran during the war's first 38 days, including more than 2,000 command-and-control sites, 1,500 air defense targets, and 1,450 industrial infrastructure targets. == Gaza war == As part of the Gaza war, the Israel Defense Forces (IDF) have used artificial intelligence to rapidly and automatically perform much of the process of determining what to bomb. IDF's Unit 8200 developed AI systems, dubbed the Gospel and Lavender, to find targets for the Israeli Air Force to bomb. The Gospel automatically provides targeting recommendations to human analysts, who decide whether to approve strikes. Lavender identified 37,000 Hamas-linked individuals early in the war, and was used alongside the Gospel, which chooses buildings or structures as targets. According to a report by +972 Magazine and Local Call, strikes assisted by Lavender were routinely permitted to kill 5–20 civilians for each suspected Hamas militant, who were often bombed at home with their families. The IDF denies these claims, maintaining that every strike is assessed to minimize collateral damage, and that there is no policy "to kill tens of thousands of people in their homes." Israel deployed AI technologies during the Gaza war for audio analysis, facial recognition, and airstrike targeting. One such system was used to help identify the location of Hamas commander Ibrahim Biari through phone call analysis, leading to strikes that killed him as well as more than 125 civilians. == 2022 Russian Ukraine war == Kyiv launched a project with Palantir called Brave1 Dataroom to build AI systems using the extensive combat data Ukraine has gathered since Russia’s full-scale invasion in 2022. The country has also created tools for in-depth airstrike analysis, introduced AI to process large volumes of intelligence, and incorporated these technologies into the planning of long-range strike operations. == Involved companies == Maven Smart System is developed by Palantir. It integrates Anthropic's Claude as its large language model, and uses Amazon's AWS servers as its cloud infrastructure. Since Anthropic's refusal to support autonomous weapons development and domestic surveillance efforts. In its place, other AI firms, including OpenAI, have been brought in to take over that role. == Involved state actors == In 2024, the United States Department of Defense had 800-plus active AI-related projects and requested $1.8 billion in AI funding, with Project Maven and Project Artemis (AI-resistant drones developed together with Ukraine) being the main ones. The technology has been used in Iran, Iraq, Syria and Yemen to identify targets. China is pursuing intelligentized warfare, integrating AI across all combat domains—land, sea, air, space, and cyber—with military AI spending exceeding $1.6 billion annually. == International regulation == Since 2014, states meeting within the framework of the Convention on Certain Conventional Weapons have discussed lethal autonomous weapon systems. In 2016, the treaty's states parties established an open-ended Group of Governmental Experts on Lethal Autonomous Weapons Systems to continue those discussions. The discussions have addressed international humanitarian law, accountability, possible prohibitions and regulations, and the extent of human control required over AI-enabled weapons.

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  Diagnostically acceptable irreversible compression

  Diagnostically acceptable irreversible compression (DAIC) is the amount of lossy compression which can be used on a medical image to produce a result that does not prevent the reader from using the image to make a medical diagnosis. The term was first introduced at a workshop on irreversible compression convened by the European Society of Radiology (ESR) in Palma de Mallorca October 13, 2010, the results of which were reported in a subsequent position paper. == Determination == The "amount of compression" in irreversible compression used to be determined by the compression ratio, where the acceptable minimum is determined by the algorithm (typically JPEG or J2K) and the data type (body part and imaging method). Such a definition is easy to follow, and has been used by medical bodies in 2010 around the world. However, its downside is obvious: the compression ratio tells nothing about the real quality of the image, as different compressors can produce vastly different qualities under the same file size. For example, the JPEG format of 1992 can perform as well as many modern formats given newer techniques exploited in mozjpeg and ISO libjpeg, yet they would be lumped together with the legacy encoders in such a scheme. The image compression community has long used objective quality metrics like SSIM to measure the effects of compression. In the absence of good data regarding SSIM, the ESR review of 2010 concluded that it is still difficult to establish a criterion for whether a particular irreversible compression scheme applied with particular parameters to a particular individual image, or category of images, avoids the introduction of some quantifiable risk of a diagnostic error for any particular diagnostic task. A 2017 study showed that a SSIM variant called 4-G-r (4-component, gradient, structural component of SSIM) best reflects changes in images that affect the decision of radiologists out of 16 SSIM variants. A 2020 study shows that visual information fidelity (VIF), feature similarity index (FSIM), and noise quality metric (NQM) best reflect radiologist preferences out of ten metrics. It also mentions that the original version of SSIM works as poorly as a basic root-mean-square distance (RMSD) for this purpose, a result echoed by the 2017 study. The 4-G-r modification is not tested in the study.

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  CHAOS (chess)

  CHAOS (Chess Heuristics and Other Stuff) is a chess playing program that was developed by programmers working at the RCA Systems Programming division in the late 1960s. It played competitively in computer chess competitions in the 1970s and 1980s. It differed from other programs of that era in its look-ahead philosophy, choosing to use chess knowledge to evaluate fewer positions and continuations as opposed to simple evaluations that relied on deep look-ahead to avoid bad moves. == Introduction == CHAOS was originally developed by Ira Ruben, Fred Swartz, Victor Berman, Joe Winograd and William Toikka while working at RCA in Cinnaminson, NJ. Its name is an acronym for 'Chess Heuristics and Other Stuff.' Program development moved to the Computing Center of the University of Michigan when Swartz changed jobs, and Mike Alexander joined the development group. Swartz, Alexander and Berman were continuously group members from that point onward in CHAOS' evolution, as others of the original authors left and new members contributed episodically. Chess Senior Master Jack O'Keefe contributed to CHAOS' development from about 1980 onwards. CHAOS was written in Fortran, except for low-level board representation manipulations written in assembly language or C. Due to this portability, it ran on RCA, Univac and IBM-compatible mainframes in its lifetime. CHAOS heralds from the mainframe computing era when only machines of that capacity were able to play at a high level. Consequently, development and testing could only take place at off-peak times for production use of the machine. In a competition, CHAOS had to run on a dedicated mainframe with a telephone link to the match venue. In its later years, CHAOS ran on computers on the machine assembly floor of Amdahl Corporation on MTS. == Background == === Chess and artificial intelligence === Mathematicians Claude Shannon and Alan Turing, working separately, were the first to view playing chess as a challenge to machines. Working for AT&T / Bell Labs with its access to telephone switching equipment, Shannon built a relay-based machine that learned how to work its way through a two-dimensional, 5x5 cell maze in 1949. Shannon viewed this as an analogue of the way that organisms learn things about their natural environment. There is a random element to searching it, a memory element to benefit from the search outcome, and a reward element that reinforces learning when the global outcome is favorable to the organism. Soon afterward, Shannon wrote a mathematical analysis of the game of chess, published in 1950. Like with the maze, he broke down game play into the necessary elements for reinforcement learning. Associated with each board configuration a move will be made from, there is a numerical score. To decide what move to make, a player wants to maximize their own position's score after the move and to minimize their opponent's score (a minimax view). Since there are about 32 possible moves at each of the early stages of the game, and about 40 moves and responses in each game, then there are about 32 80 {\displaystyle 32^{80}} or about 10 120 {\displaystyle 10^{120}} possible games - an impossibly large set to evaluate completely. Therefore, there must be a way to limit the number of moves to look ahead for to find the best one. Reducing the game to these few key elements provided a way to think about human intelligence in general. Shannon became part of a wider group using computing machines to mimic aspects of human intelligence that grew into the general idea of artificial intelligence. (Other members of this group were John McCarthy, Herbert Simon, Allen Newell, Alan Kotok, Alex Bernstein and Richard Greenblatt.) The paradigm that evolved was that there was a quantification of the position on the board into a score, an evaluation method to find favorable outcomes (minimax, later alpha-beta pruning), and a strategy to manage the combinatorial explosion of the look-ahead possibilities. By the early 1960s, there were computer programs that played chess at a rudimentary level. They used very simple evaluation functions for each position and tried to search as far forward as was practical given the time constraints and available compute power. Naturally, programmers optimized their code to use the available computing resources. This led to a major philosophical divide among chess programs: those that tried to evaluate as many positions as possible, and those that tried to evaluate the most promising move sequences as deeply as possible. CHAOS was firmly in the camp believing only the most promising moves should be evaluated in depth. Said Swartz, "The 'brute force people' ... look at every (possible move) no matter what garbage it is. Most moves are just terrible, terrible moves, and most computing time is being spent on pure garbage." The program spent more time evaluating each board position in the expectation that it would find the most promising lines of play to explore in depth. In 1983, the then-fastest chess program (Belle) evaluated 110,000 positions per second, and typical programs 1000–50,000 per second, whereas CHAOS evaluated about 50-100 per second. === Machine learning and strategies to manage search === From about 1949 onward, Arthur Samuel began work for IBM on machine learning, culminating in a checkers-playing program in 1952 and publications on the topic. Concurrently, Christopher Strachey created Checkers, a program to play the board game of checkers in 1951, but it had no capacity to learn from its play. Checkers was chosen by both authors because it was simpler than chess yet contained the basic characteristics of an intellectual activity, and, in Samuel's view, was a test-bed in which heuristic procedures and learning processes could be evaluated quickly. Checker playing programs introduced the notion of the game tree and evaluating play to various depths to choose the best move. The complexity of chess, however, promoted it to the status of an analogue for human intelligence, and it attracted computer scientists' attention, who referred to it as research into artificial intelligence (AI). Like checkers, it required a numerical assessment of each arrangement of chess pieces on a board. It also required looking ahead to future moves to decide how to play the present position. Due to the enormous number of possible moves, there had to be a way to confine the look-ahead search to the most promising lines of play. From these factors, the notion of minimax score evaluation developed and, later, alpha-beta tree pruning to abandon looking at positions worse than any that have already been examined. === Chess search strategies === The AI community viewed artificial intelligence as comprising two parts: a way to symbolically quantify the knowledge in hand (a chess board position), and a set of heuristics to limit look-ahead to the consequences of a move. The early chess playing programs attempted to look forward as far as possible, perhaps to 3 moves ahead by each player, and to choose the best outcome. This led to the horizon effect, whereby a key move 4 or more moves ahead would be unexamined and therefore missed. Consequently, the programs were quite weak and heuristics to manage the search became important in their development. CHAOS used a selective search strategy with iterative widening. As chess programs evolved, they incorporated books of opening lines of play from historic sources. Nowadays, book moves are catalogued in machine-readable form, but originally programmers had to type them in. CHAOS had an extensive book for its time of around 10,000 moves that O'Keefe helped to develop. A problem with play from an opening book is the behavior of the program when the play leaves the book: the positional advantage may be so subtle that the evaluation scheme may be unable to understand it, leading to very wide and shallow searches to establish a line of play. The horizon effect again plagues move selection after leaving the book. CHAOS mitigated these problems by only using book lines that it could understand, and by relying on cached analyses of continuations out of the book made while the opponent's clock was running. == Game Play History == CHAOS played in twelve ACM computer chess tournaments and four World Computer Chess Championships (WCCC). Its debut was the ACM computer chess tournament in 1973, taking 2nd place. In 1974, it again won 2nd place in the WCCC, defeating the tournament favorite Chess 4.0 but losing to Kaissa. CHAOS was close to winning the 1980 WCCC, but lost to Belle in a playoff. The 1985 ACM computer chess tournament was CHAOS' last competition. One of CHAOS' notable victories was over Chess 4.0 at the 1974 WCCC tournament. Chess 4.0 was unbeaten by any other program up until then. Playing as white, CHAOS made a knight sacrifice (16 Nd4-e6!!) that traded material for open lines of attack and eventually won the game. CHAOS’ authors thought the move was due to a

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  Relational data mining

  Relational data mining is the data mining technique for relational databases. Unlike traditional data mining algorithms, which look for patterns in a single table (propositional patterns), relational data mining algorithms look for patterns among multiple tables (relational patterns). For most types of propositional patterns, there are corresponding relational patterns. For example, there are relational classification rules (relational classification), relational regression tree, and relational association rules. There are several approaches to relational data mining: Inductive Logic Programming (ILP) Statistical Relational Learning (SRL) Graph Mining Propositionalization Multi-view learning == Algorithms == Multi-Relation Association Rules: Multi-Relation Association Rules (MRAR) is a new class of association rules which in contrast to primitive, simple and even multi-relational association rules (that are usually extracted from multi-relational databases), each rule item consists of one entity but several relations. These relations indicate indirect relationship between the entities. Consider the following MRAR where the first item consists of three relations live in, nearby and humid: “Those who live in a place which is near by a city with humid climate type and also are younger than 20 -> their health condition is good”. Such association rules are extractable from RDBMS data or semantic web data. == Software == Safarii: a Data Mining environment for analysing large relational databases based on a multi-relational data mining engine. Dataconda: a software, free for research and teaching purposes, that helps mining relational databases without the use of SQL. == Datasets == Relational dataset repository: a collection of publicly available relational datasets.

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  EM algorithm and GMM model

  In statistics, EM (expectation maximization) algorithm handles latent variables, while GMM is the Gaussian mixture model. == Background == In the picture below, are shown the red blood cell hemoglobin concentration and the red blood cell volume data of two groups of people, the Anemia group and the control group (i.e. the group of people without Anemia). As expected, people with Anemia have lower red blood cell volume and lower red blood cell hemoglobin concentration than those without Anemia. x {\displaystyle x} is a random vector such as x := ( red blood cell volume , red blood cell hemoglobin concentration ) {\displaystyle x:={\big (}{\text{red blood cell volume}},{\text{red blood cell hemoglobin concentration}}{\big )}} , and from medical studies it is known that x {\displaystyle x} are normally distributed in each group, i.e. x ∼ N ( μ , Σ ) {\displaystyle x\sim {\mathcal {N}}(\mu ,\Sigma )} . z {\displaystyle z} is denoted as the group where x {\displaystyle x} belongs, with z i = 0 {\displaystyle z_{i}=0} when x i {\displaystyle x_{i}} belongs to the Anemia group and z i = 1 {\displaystyle z_{i}=1} when x i {\displaystyle x_{i}} belongs to the control group. Also z ∼ Categorical ⁡ ( k , ϕ ) {\displaystyle z\sim \operatorname {Categorical} (k,\phi )} where k = 2 {\displaystyle k=2} , ϕ j ≥ 0 , {\displaystyle \phi _{j}\geq 0,} and ∑ j = 1 k ϕ j = 1 {\displaystyle \sum _{j=1}^{k}\phi _{j}=1} . See Categorical distribution. The following procedure can be used to estimate ϕ , μ , Σ {\displaystyle \phi ,\mu ,\Sigma } . A maximum likelihood estimation can be applied: ℓ ( ϕ , μ , Σ ) = ∑ i = 1 m log ⁡ ( p ( x ( i ) ; ϕ , μ , Σ ) ) = ∑ i = 1 m log ⁡ ∑ z ( i ) = 1 k p ( x ( i ) ∣ z ( i ) ; μ , Σ ) p ( z ( i ) ; ϕ ) {\displaystyle \ell (\phi ,\mu ,\Sigma )=\sum _{i=1}^{m}\log(p(x^{(i)};\phi ,\mu ,\Sigma ))=\sum _{i=1}^{m}\log \sum _{z^{(i)}=1}^{k}p\left(x^{(i)}\mid z^{(i)};\mu ,\Sigma \right)p(z^{(i)};\phi )} As the z i {\displaystyle z_{i}} for each x i {\displaystyle x_{i}} are known, the log likelihood function can be simplified as below: ℓ ( ϕ , μ , Σ ) = ∑ i = 1 m log ⁡ p ( x ( i ) ∣ z ( i ) ; μ , Σ ) + log ⁡ p ( z ( i ) ; ϕ ) {\displaystyle \ell (\phi ,\mu ,\Sigma )=\sum _{i=1}^{m}\log p\left(x^{(i)}\mid z^{(i)};\mu ,\Sigma \right)+\log p\left(z^{(i)};\phi \right)} Now the likelihood function can be maximized by making partial derivative over μ , Σ , ϕ {\displaystyle \mu ,\Sigma ,\phi } , obtaining: ϕ j = 1 m ∑ i = 1 m 1 { z ( i ) = j } {\displaystyle \phi _{j}={\frac {1}{m}}\sum _{i=1}^{m}1\{z^{(i)}=j\}} μ j = ∑ i = 1 m 1 { z ( i ) = j } x ( i ) ∑ i = 1 m 1 { z ( i ) = j } {\displaystyle \mu _{j}={\frac {\sum _{i=1}^{m}1\{z^{(i)}=j\}x^{(i)}}{\sum _{i=1}^{m}1\left\{z^{(i)}=j\right\}}}} Σ j = ∑ i = 1 m 1 { z ( i ) = j } ( x ( i ) − μ j ) ( x ( i ) − μ j ) T ∑ i = 1 m 1 { z ( i ) = j } {\displaystyle \Sigma _{j}={\frac {\sum _{i=1}^{m}1\{z^{(i)}=j\}(x^{(i)}-\mu _{j})(x^{(i)}-\mu _{j})^{T}}{\sum _{i=1}^{m}1\{z^{(i)}=j\}}}} If z i {\displaystyle z_{i}} is known, the estimation of the parameters results to be quite simple with maximum likelihood estimation. But if z i {\displaystyle z_{i}} is unknown it is much more complicated. Being z {\displaystyle z} a latent variable (i.e. not observed), with unlabeled scenario, the expectation maximization algorithm is needed to estimate z {\displaystyle z} as well as other parameters. Generally, this problem is set as a GMM since the data in each group is normally distributed. In machine learning, the latent variable z {\displaystyle z} is considered as a latent pattern lying under the data, which the observer is not able to see very directly. x i {\displaystyle x_{i}} is the known data, while ϕ , μ , Σ {\displaystyle \phi ,\mu ,\Sigma } are the parameter of the model. With the EM algorithm, some underlying pattern z {\displaystyle z} in the data x i {\displaystyle x_{i}} can be found, along with the estimation of the parameters. The wide application of this circumstance in machine learning is what makes EM algorithm so important. == EM algorithm in GMM == The EM algorithm consists of two steps: the E-step and the M-step. Firstly, the model parameters and the z ( i ) {\displaystyle z^{(i)}} can be randomly initialized. In the E-step, the algorithm tries to guess the value of z ( i ) {\displaystyle z^{(i)}} based on the parameters, while in the M-step, the algorithm updates the value of the model parameters based on the guess of z ( i ) {\displaystyle z^{(i)}} of the E-step. These two steps are repeated until convergence is reached. The algorithm in GMM is: Repeat until convergence: 1. (E-step) For each i , j {\displaystyle i,j} , set w j ( i ) := p ( z ( i ) = j | x ( i ) ; ϕ , μ , Σ ) {\displaystyle w_{j}^{(i)}:=p\left(z^{(i)}=j|x^{(i)};\phi ,\mu ,\Sigma \right)} 2. (M-step) Update the parameters ϕ j := 1 m ∑ i = 1 m w j ( i ) {\displaystyle \phi _{j}:={\frac {1}{m}}\sum _{i=1}^{m}w_{j}^{(i)}} μ j := ∑ i = 1 m w j ( i ) x ( i ) ∑ i = 1 m w j ( i ) {\displaystyle \mu _{j}:={\frac {\sum _{i=1}^{m}w_{j}^{(i)}x^{(i)}}{\sum _{i=1}^{m}w_{j}^{(i)}}}} Σ j := ∑ i = 1 m w j ( i ) ( x ( i ) − μ j ) ( x ( i ) − μ j ) T ∑ i = 1 m w j ( i ) {\displaystyle \Sigma _{j}:={\frac {\sum _{i=1}^{m}w_{j}^{(i)}\left(x^{(i)}-\mu _{j}\right)\left(x^{(i)}-\mu _{j}\right)^{T}}{\sum _{i=1}^{m}w_{j}^{(i)}}}} With Bayes' rule, the following result is obtained by the E-step: p ( z ( i ) = j | x ( i ) ; ϕ , μ , Σ ) = p ( x ( i ) | z ( i ) = j ; μ , Σ ) p ( z ( i ) = j ; ϕ ) ∑ l = 1 k p ( x ( i ) | z ( i ) = l ; μ , Σ ) p ( z ( i ) = l ; ϕ ) {\displaystyle p\left(z^{(i)}=j|x^{(i)};\phi ,\mu ,\Sigma \right)={\frac {p\left(x^{(i)}|z^{(i)}=j;\mu ,\Sigma \right)p\left(z^{(i)}=j;\phi \right)}{\sum _{l=1}^{k}p\left(x^{(i)}|z^{(i)}=l;\mu ,\Sigma \right)p\left(z^{(i)}=l;\phi \right)}}} According to GMM setting, these following formulas are obtained: p ( x ( i ) | z ( i ) = j ; μ , Σ ) = 1 ( 2 π ) n / 2 | Σ j | 1 / 2 exp ⁡ ( − 1 2 ( x ( i ) − μ j ) T Σ j − 1 ( x ( i ) − μ j ) ) {\displaystyle p\left(x^{(i)}|z^{(i)}=j;\mu ,\Sigma \right)={\frac {1}{(2\pi )^{n/2}\left|\Sigma _{j}\right|^{1/2}}}\exp \left(-{\frac {1}{2}}\left(x^{(i)}-\mu _{j}\right)^{T}\Sigma _{j}^{-1}\left(x^{(i)}-\mu _{j}\right)\right)} p ( z ( i ) = j ; ϕ ) = ϕ j {\displaystyle p\left(z^{(i)}=j;\phi \right)=\phi _{j}} In this way, a switch between the E-step and the M-step is possible, according to the randomly initialized parameters.

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  Digistar

  Digistar is the first computer graphics-based planetarium projection and content system. It was designed by Evans & Sutherland and released in 1983. The technology originally focused on accurate and high quality display of stars, including for the first time showing stars from points of view other than Earth's surface, travelling through the stars, and accurately showing celestial bodies from different times in the past and future. Beginning with the Digistar 3 the system now projects full-dome video. == Projector == Unlike modern full-dome systems, which use LCD, DLP, SXRD, or laser projection technology, the Digistar projection system was designed for projecting bright pinpoints of light representing stars. This was accomplished using a calligraphic display, a form of vector graphics, rather than raster graphics. The heart of the Digistar projector is a large cathode-ray tube (CRT). A phosphor plate is mounted atop the tube, and light is then dispersed by a large lens with a 160 degree field of view to cover the planetarium dome. The original lens bore the inscription: "August 1979 mfg. by Lincoln Optical Corp., L.A., CA for Evans and Sutherland Computer Corp., SLC, UT, Digital planetarium CRT projection lens, 43mm, f2.8, 160 degree field of view". The coordinates of the stars and wire-frame models to be displayed by the projector were stored in computer RAM in a display list. The display would read each set of coordinates in turn and drive the CRT's electron beam directly to those coordinates. If the electron beam was enabled while being moved a line would be painted on the phosphor plate. Otherwise, the electron beam would be enabled once at its destination and a star would be painted. Once all coordinates in the display list had been processed, the display would repeat from the top of the display list. Thus, the shorter the display list the more frequently the electron beam would refresh the charge on a given point on the phosphor plate, making the projection of the points brighter. In this way, the stars projected by Digistar were substantially brighter than could be achieved using a raster display, which has to touch every point on the phosphor plate before repeating. Likewise, the calligraphic technology allowed Digistar to have a darker black-level than full-dome projectors, since the portions of the phosphor plate representing dark sky were never hit by the electron beam. As it is only one tube, with no pixelated color filter screen, the Digistar projector is monochromatic. The Digistar projects a bright, phosphorescent green, though many (including both visitors and planetarians) report they cannot distinguish between this green and white. Additionally, unlike a raster display, the calligraphic display is not discretized into pixels, so the displayed stars were a more realistic single spot of light, without the blocky or ropy artifacts that are hard to avoid with raster graphics. Due to the use of vector graphics, as opposed to raster imaging, the Digistar does not have the resolution issues that many full-dome systems have. Thanks to this, and the brightness of the CRT, only one projector is needed to project on the entire dome, whereas most full-dome systems require up to six raster projectors, depending on dome size. The projector in the original Digistar was housed in a square pyramid-shaped sheathing. When powered on, the four sides at the tip of the pyramid would recede into the housing, exposing the lens and appearing as a cut-off pyramid. As Digistar II was being developed, many planetaria were sold Digistar LEA projectors. The LEA, called Digistar 1.5 by many users, was effectively a prototype of the D2 projector, compatible with Digistar and upgradable to Digistar II. There are no significant differences in performance between the LEA and the true D2. == History == Digistar was the brainchild of Stephen McAllister and Brent Watson, both of whom were long-time amateur astronomers and computer graphics engineers. In 1977, E&S had been consulting with Johnson Space Center regarding training simulators for astronauts. McAllister had been writing proof-of-concept software for this consultation and in summer 1977 entered the data for 400 bright stars and wrote the software to display them. Steve and Brent both originally saw the system's purpose as celestial navigation training. Brent, who had until recently worked at Hansen planetarium, asked his planetarium coworkers what they thought of a potential digital planetarium system, and then Steve and Brent both targeted the system toward planetaria. The primary goal of the planetarium system was to use computer graphics to overcome the limitation of traditional star ball technology that only allowed display of star fields from the point of view of Earth's surface. By using computer graphics the stars could be displayed from viewpoints in space, including simulating the appearance of space flight. Likewise, planets and moons within the Solar System could be displayed accurately for any time in history, from any point of view. The system used the location of real stars from the Yale Bright Star Catalogue, as well as random stars. A laboratory prototype of Digistar was used to generate the star fields and tactical displays in the 1982 science fiction film Star Trek II: The Wrath of Khan. Filming was done directly from the Digistar display in the lab. ILM projected the effort would take two weeks, but in fact it took from late November 1981 until mid-February 1982. The last shot recorded was what became the first entirely computer generated feature film sequence. It was the opening scene of the film, a rotating forward translation through a star field that lasted 3.5 minutes. It was recorded in one take, at a rate of one frame every 3.5 seconds, taking four hours for the shoot. The Digistar team members are credited in the film. After prototyping in labs at Evans and Sutherland the team repeatedly used Salt Lake City's Hansen planetarium to beta test the system at the planetarium at night. The Digistar team performed one week of shows at the planetarium as a fund raiser to benefit the planetarium. The company also later gave the planetarium an improved prototype Digistar to replace "Jake", the planetarium's aging Spitz planetarium projector. The first customer installation was to the newly constructed Universe Planetarium at the Science Museum of Virginia in 1983, the largest planetarium dome in the world at the time, for $595,000. By September 1986 there were four installed Digistars. Even at this point the long-term success of the product was very much in doubt, but as of 2019 Digistar has an installed base of over 550 planetaria. === Versions === Digistar (1983) Digistar II (1995) Digistar 3 (2002) Digistar 4 (2010?) Digistar 5 (2012) Digistar 6 (2016) Digistar 7 (2021) == Hardware == Digistar was driven by a VAX-11/780 minicomputer, with custom graphics hardware related to the E&S Picture System 2. Later versions of Digistar 1 used a DEC MicroVAX 2, driving a custom version of a PS/300. The original Digistar and Digistar 2 had a physical control panel that was used for running the star shows. This control panel was approximately 3' x 4' and contained a keyboard, a 6 DOF joystick, and a large array of back-lit buttons. One button that was used for moving the viewpoint forward in space was labeled "Boldly Go". Later iterations of Digistar replaced the physical control panel with a common graphical user interface. Digistar 3 was the first Digistar system to offer full-dome video in 2002, using six projectors. Digistar 4 was able to cover the dome using only two projectors. == System limitations == Though technologically advanced in its day, and the closest system to true full-dome video at the time of its release, the original Digistar and Digistar 2 are limited to only projecting dots and lines—meaning only wireframe models can be projected. To compensate for this, the projector is capable of defocusing specific models, blurring lines and dots together. An example of this is in the Digistar 2's built-in Milky Way model. The model is a circle of parallel lines that, when defocused, appear as the continuous band of the Milky Way across the sky. On more complex models, especially three-dimensional ones, brightness and details may be lost in this process, so it is not useful in all situations. The Digistar and Digistar 2 also suffer focus limitations. Because they use a single lens to cover the entire dome, it is difficult to gain perfect focus across the dome. Coupled with this, stars greater than a certain brightness are "multihit" points, meaning the projector draws two dots at the given position to accommodate the brightness of the star. Errors in the projector can lead the second dot to be slightly out-of-place with the first one. These two issues together, along with other issues that can occur within the projector's focus system, give the stars a blobby look. Some p

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  Anna Becker

  Anna Becker is an Israeli researcher known in the field of artificial intelligence and computer science within the financial field. == Early life and education == Becker was born in Russia and immigrated to Israel at 16 after graduating from a school in Moscow. At 17, she began her studies at Technion – Israel Institute of Technology. During her master's degree in computer science, she taught first-year students of the same course, and at 27, Becker completed her PhD in Computer Science and Artificial Intelligence. == Career == While pursuing her PhD, Becker resolved an NP-complete approximation algorithm that had been unresolved for over twenty years. This made her a recognized scholar in the field. After completing her PhD, she developed an approximation technique by a factor of two. This technique is widely used today in operating systems, database systems, and VLSI chip designs. She then founded and sold Strategy Runner, a fintech software. After this, she founded EndoTech, an algorithmic trading platform based on artificial intelligence and machine learning. EndoTech's trading strategies have been operating in live cryptocurrency markets since 2017. The platform's BTC Alpha strategy has reported an average annual return of 163% on fixed capital over eight years of live operation, with a maximum drawdown of 14% and a trade accuracy rate of approximately 83%. In 2026, EndoTech entered a partnership with Bit1 Exchange to make its BTC Alpha and ETH Alpha copy trading strategies accessible to retail investors with no minimum deposit requirement, through a full-custody model in which user funds remain in their own exchange wallets at all times.As of 2023, Becker is working on Fianchetto Fund, an AI-based investing analysis platform. Becker has also co-authored a book on Bayesian networks, which has been published widely in the field of computer science and artificial intelligence.

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  Matrix regularization

  In the field of statistical learning theory, matrix regularization generalizes notions of vector regularization to cases where the object to be learned is a matrix. The purpose of regularization is to enforce conditions, for example sparsity or smoothness, that can produce stable predictive functions. For example, in the more common vector framework, Tikhonov regularization optimizes over min x ‖ A x − y ‖ 2 + λ ‖ x ‖ 2 {\displaystyle \min _{x}\left\|Ax-y\right\|^{2}+\lambda \left\|x\right\|^{2}} to find a vector x {\displaystyle x} that is a stable solution to the regression problem. When the system is described by a matrix rather than a vector, this problem can be written as min X ‖ A X − Y ‖ 2 + λ ‖ X ‖ 2 , {\displaystyle \min _{X}\left\|AX-Y\right\|^{2}+\lambda \left\|X\right\|^{2},} where the vector norm enforcing a regularization penalty on x {\displaystyle x} has been extended to a matrix norm on X {\displaystyle X} . Matrix regularization has applications in matrix completion, multivariate regression, and multi-task learning. Ideas of feature and group selection can also be extended to matrices, and these can be generalized to the nonparametric case of multiple kernel learning. == Basic definition == Consider a matrix W {\displaystyle W} to be learned from a set of examples, S = ( X i t , y i t ) {\displaystyle S=(X_{i}^{t},y_{i}^{t})} , where i {\displaystyle i} goes from 1 {\displaystyle 1} to n {\displaystyle n} , and t {\displaystyle t} goes from 1 {\displaystyle 1} to T {\displaystyle T} . Let each input matrix X i {\displaystyle X_{i}} be ∈ R D T {\displaystyle \in \mathbb {R} ^{DT}} , and let W {\displaystyle W} be of size D × T {\displaystyle D\times T} . A general model for the output y {\displaystyle y} can be posed as y i t = ⟨ W , X i t ⟩ F , {\displaystyle y_{i}^{t}=\left\langle W,X_{i}^{t}\right\rangle _{F},} where the inner product is the Frobenius inner product. For different applications the matrices X i {\displaystyle X_{i}} will have different forms, but for each of these the optimization problem to infer W {\displaystyle W} can be written as min W ∈ H E ( W ) + R ( W ) , {\displaystyle \min _{W\in {\mathcal {H}}}E(W)+R(W),} where E {\displaystyle E} defines the empirical error for a given W {\displaystyle W} , and R ( W ) {\displaystyle R(W)} is a matrix regularization penalty. The function R ( W ) {\displaystyle R(W)} is typically chosen to be convex and is often selected to enforce sparsity (using ℓ 1 {\displaystyle \ell ^{1}} -norms) and/or smoothness (using ℓ 2 {\displaystyle \ell ^{2}} -norms). Finally, W {\displaystyle W} is in the space of matrices H {\displaystyle {\mathcal {H}}} with Frobenius inner product ⟨ … ⟩ F {\displaystyle \langle \dots \rangle _{F}} . == General applications == === Matrix completion === In the problem of matrix completion, the matrix X i t {\displaystyle X_{i}^{t}} takes the form X i t = e t ⊗ e i ′ , {\displaystyle X_{i}^{t}=e_{t}\otimes e_{i}',} where ( e t ) t {\displaystyle (e_{t})_{t}} and ( e i ′ ) i {\displaystyle (e_{i}')_{i}} are the canonical basis in R T {\displaystyle \mathbb {R} ^{T}} and R D {\displaystyle \mathbb {R} ^{D}} . In this case the role of the Frobenius inner product is to select individual elements w i t {\displaystyle w_{i}^{t}} from the matrix W {\displaystyle W} . Thus, the output y {\displaystyle y} is a sampling of entries from the matrix W {\displaystyle W} . The problem of reconstructing W {\displaystyle W} from a small set of sampled entries is possible only under certain restrictions on the matrix, and these restrictions can be enforced by a regularization function. For example, it might be assumed that W {\displaystyle W} is low-rank, in which case the regularization penalty can take the form of a nuclear norm. R ( W ) = λ ‖ W ‖ ∗ = λ ∑ i | σ i | , {\displaystyle R(W)=\lambda \left\|W\right\|_{}=\lambda \sum _{i}\left|\sigma _{i}\right|,} where σ i {\displaystyle \sigma _{i}} , with i {\displaystyle i} from 1 {\displaystyle 1} to min D , T {\displaystyle \min D,T} , are the singular values of W {\displaystyle W} . === Multivariate regression === Models used in multivariate regression are parameterized by a matrix of coefficients. In the Frobenius inner product above, each matrix X {\displaystyle X} is X i t = e t ⊗ x i {\displaystyle X_{i}^{t}=e_{t}\otimes x_{i}} such that the output of the inner product is the dot product of one row of the input with one column of the coefficient matrix. The familiar form of such models is Y = X W + b {\displaystyle Y=XW+b} Many of the vector norms used in single variable regression can be extended to the multivariate case. One example is the squared Frobenius norm, which can be viewed as an ℓ 2 {\displaystyle \ell ^{2}} -norm acting either entrywise, or on the singular values of the matrix: R ( W ) = λ ‖ W ‖ F 2 = λ ∑ i ∑ j | w i j | 2 = λ Tr ⁡ ( W ∗ W ) = λ ∑ i σ i 2 . {\displaystyle R(W)=\lambda \left\|W\right\|_{F}^{2}=\lambda \sum _{i}\sum _{j}\left|w_{ij}\right|^{2}=\lambda \operatorname {Tr} \left(W^{}W\right)=\lambda \sum _{i}\sigma _{i}^{2}.} In the multivariate case the effect of regularizing with the Frobenius norm is the same as the vector case; very complex models will have larger norms, and, thus, will be penalized more. === Multi-task learning === The setup for multi-task learning is almost the same as the setup for multivariate regression. The primary difference is that the input variables are also indexed by task (columns of Y {\displaystyle Y} ). The representation with the Frobenius inner product is then X i t = e t ⊗ x i t . {\displaystyle X_{i}^{t}=e_{t}\otimes x_{i}^{t}.} The role of matrix regularization in this setting can be the same as in multivariate regression, but matrix norms can also be used to couple learning problems across tasks. In particular, note that for the optimization problem min W ‖ X W − Y ‖ 2 2 + λ ‖ W ‖ 2 2 {\displaystyle \min _{W}\left\|XW-Y\right\|_{2}^{2}+\lambda \left\|W\right\|_{2}^{2}} the solutions corresponding to each column of Y {\displaystyle Y} are decoupled. That is, the same solution can be found by solving the joint problem, or by solving an isolated regression problem for each column. The problems can be coupled by adding an additional regularization penalty on the covariance of solutions min W , Ω ‖ X W − Y ‖ 2 2 + λ 1 ‖ W ‖ 2 2 + λ 2 Tr ⁡ ( W T Ω − 1 W ) {\displaystyle \min _{W,\Omega }\left\|XW-Y\right\|_{2}^{2}+\lambda _{1}\left\|W\right\|_{2}^{2}+\lambda _{2}\operatorname {Tr} \left(W^{T}\Omega ^{-1}W\right)} where Ω {\displaystyle \Omega } models the relationship between tasks. This scheme can be used to both enforce similarity of solutions across tasks, and to learn the specific structure of task similarity by alternating between optimizations of W {\displaystyle W} and Ω {\displaystyle \Omega } . When the relationship between tasks is known to lie on a graph, the Laplacian matrix of the graph can be used to couple the learning problems. == Spectral regularization == Regularization by spectral filtering has been used to find stable solutions to problems such as those discussed above by addressing ill-posed matrix inversions (see for example Filter function for Tikhonov regularization). In many cases the regularization function acts on the input (or kernel) to ensure a bounded inverse by eliminating small singular values, but it can also be useful to have spectral norms that act on the matrix that is to be learned. There are a number of matrix norms that act on the singular values of the matrix. Frequently used examples include the Schatten p-norms, with p = 1 or 2. For example, matrix regularization with a Schatten 1-norm, also called the nuclear norm, can be used to enforce sparsity in the spectrum of a matrix. This has been used in the context of matrix completion when the matrix in question is believed to have a restricted rank. In this case the optimization problem becomes: min ‖ W ‖ ∗ subject to W i , j = Y i j . {\displaystyle \min \left\|W\right\|_{}~~{\text{ subject to }}~~W_{i,j}=Y_{ij}.} Spectral Regularization is also used to enforce a reduced rank coefficient matrix in multivariate regression. In this setting, a reduced rank coefficient matrix can be found by keeping just the top n {\displaystyle n} singular values, but this can be extended to keep any reduced set of singular values and vectors. == Structured sparsity == Sparse optimization has become the focus of much research interest as a way to find solutions that depend on a small number of variables (see e.g. the Lasso method). In principle, entry-wise sparsity can be enforced by penalizing the entry-wise ℓ 0 {\displaystyle \ell ^{0}} -norm of the matrix, but the ℓ 0 {\displaystyle \ell ^{0}} -norm is not convex. In practice this can be implemented by convex relaxation to the ℓ 1 {\displaystyle \ell ^{1}} -norm. While entry-wise regularization with an ℓ 1 {\displaystyle \ell ^{1}} -norm will find solutions with a small number of nonzero elements, applying an ℓ 1 {

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  Explanation-based learning

  Explanation-based learning (EBL) is a form of machine learning that exploits a very strong, or even perfect, domain theory (i.e. a formal theory of an application domain akin to a domain model in ontology engineering, not to be confused with Scott's domain theory) in order to make generalizations or form concepts from training examples. It is also linked with Encoding (memory) to help with Learning. == Details == An example of EBL using a perfect domain theory is a program that learns to play chess through example. A specific chess position that contains an important feature such as "Forced loss of black queen in two moves" includes many irrelevant features, such as the specific scattering of pawns on the board. EBL can take a single training example and determine what are the relevant features in order to form a generalization. A domain theory is perfect or complete if it contains, in principle, all information needed to decide any question about the domain. For example, the domain theory for chess is simply the rules of chess. Knowing the rules, in principle, it is possible to deduce the best move in any situation. However, actually making such a deduction is impossible in practice due to combinatoric explosion. EBL uses training examples to make searching for deductive consequences of a domain theory efficient in practice. In essence, an EBL system works by finding a way to deduce each training example from the system's existing database of domain theory. Having a short proof of the training example extends the domain-theory database, enabling the EBL system to find and classify future examples that are similar to the training example very quickly. The main drawback of the method—the cost of applying the learned proof macros, as these become numerous—was analyzed by Minton. === Basic formulation === EBL software takes four inputs: a hypothesis space (the set of all possible conclusions) a domain theory (axioms about a domain of interest) training examples (specific facts that rule out some possible hypothesis) operationality criteria (criteria for determining which features in the domain are efficiently recognizable, e.g. which features are directly detectable using sensors) == Application == An especially good application domain for an EBL is natural language processing (NLP). Here a rich domain theory, i.e., a natural language grammar—although neither perfect nor complete, is tuned to a particular application or particular language usage, using a treebank (training examples). Rayner pioneered this work. The first successful industrial application was to a commercial NL interface to relational databases. The method has been successfully applied to several large-scale natural language parsing systems, where the utility problem was solved by omitting the original grammar (domain theory) and using specialized LR-parsing techniques, resulting in huge speed-ups, at a cost in coverage, but with a gain in disambiguation. EBL-like techniques have also been applied to surface generation, the converse of parsing. When applying EBL to NLP, the operationality criteria can be hand-crafted, or can be inferred from the treebank using either the entropy of its or-nodes or a target coverage/disambiguation trade-off (= recall/precision trade-off = f-score). EBL can also be used to compile grammar-based language models for speech recognition, from general unification grammars. Note how the utility problem, first exposed by Minton, was solved by discarding the original grammar/domain theory, and that the quoted articles tend to contain the phrase grammar specialization—quite the opposite of the original term explanation-based generalization. Perhaps the best name for this technique would be data-driven search space reduction. Other people who worked on EBL for NLP include Guenther Neumann, Aravind Joshi, Srinivas Bangalore, and Khalil Sima'an.

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  Round-trip engineering

  Round-trip engineering (RTE) in the context of model-driven architecture is a functionality of software development tools that synchronizes two or more related software artifacts, such as, source code, models, configuration files, documentation, etc. between each other. The need for round-trip engineering arises when the same information is present in multiple artifacts and when an inconsistency may arise in case some artifacts are updated. For example, some piece of information was added to/changed in only one artifact (source code) and, as a result, it became missing in/inconsistent with the other artifacts (in models). == Overview == Round-trip engineering is closely related to traditional software engineering disciplines: forward engineering (creating software from specifications), reverse engineering (creating specifications from existing software), and reengineering (understanding existing software and modifying it). Round-trip engineering is often wrongly defined as simply supporting both forward and reverse engineering. In fact, the key characteristic of round-trip engineering that distinguishes it from forward and reverse engineering is the ability to synchronize existing artifacts that evolved concurrently by incrementally updating each artifact to reflect changes made to the other artifacts. Furthermore, forward engineering can be seen as a special instance of RTE in which only the specification is present and reverse engineering can be seen as a special instance of RTE in which only the software is present. Many reengineering activities can also be understood as RTE when the software is updated to reflect changes made to the previously reverse engineered specification. === Types === Various books describe two types of RTE: partial or uni-directional RTE: changes made to a higher level representation of a code and model are reflected in lower level, but not otherwise; the latter might be allowed, but with limitations that may not affect higher-level abstractions full or bi-directional RTE: regardless of changes, both higher and lower-level code and model representations are synchronized if any of them altered === Auto synchronization === Another characteristic of round-trip engineering is automatic update of the artifacts in response to automatically detected inconsistencies. In that sense, it is different from forward- and reverse engineering which can be both manual (traditionally) and automatic (via automatic generation or analysis of the artifacts). The automatic update can be either instantaneous or on-demand. In instantaneous RTE, all related artifacts are immediately updated after each change made to one of them. In on-demand RTE, authors of the artifacts may concurrently update the artifacts (even in a distributed setting) and at some point choose to execute matching to identify inconsistencies and choose to propagate some of them and reconcile potential conflicts. === Iterative approach === Round trip engineering may involve an iterative development process. After you have synchronized your model with revised code, you are still free to choose the best way to work – make further modifications to the code or make changes to your model. You can synchronize in either direction at any time and you can repeat the cycle as many times as necessary. == Software == Many commercial tools and research prototypes support this form of RTE; a 2007 book lists Rational Rose, Together, ESS-Model, BlueJ, and Fujaba among those capable, with Fujaba said to be capable to also identify design patterns. == Limitations == A 2005 book on Visual Studio notes for instance that a common problem in RTE tools is that the model reversed is not the same as the original one, unless the tools are aided by leaving laborious annotations in the source code. The behavioral parts of UML impose even more challenges for RTE. Usually, UML class diagrams are supported to some degree; however, certain UML concepts, such as associations and containment do not have straightforward representations in many programming languages which limits the usability of the created code and accuracy of code analysis/reverse engineering (e.g., containment is hard to recognize in the code). A more tractable form of round-trip engineering is implemented in the context of framework application programming interfaces (APIs), whereby a model describing the usage of a framework API by an application is synchronized with that application's code. In this setting, the API prescribes all correct ways the framework can be used in applications, which allows precise and complete detection of API usages in the code as well as creation of useful code implementing correct API usages. Two prominent RTE implementations in this category are framework-specific modeling languages and Spring Roo (Java). Round-trip engineering is critical for maintaining consistency among multiple models and between the models and the code in Object Management Group's (OMG) Model-driven architecture. OMG proposed the QVT (query/view/transformation) standard to handle model transformations required for MDA. To date, a few implementations of the standard have been created. (Need to present practical experiences with MDA in relation to RTE). == Controversies == === Code generation controversy === Code generation (forward-engineering) from models means that the user abstractly models solutions, which are connoted by some model data, and then an automated tool derives from the models parts or all of the source code for the software system. In some tools, the user can provide a skeleton of the program source code, in the form of a source code template where predefined tokens are then replaced with program source code parts during the code generation process. UML (if used for MDA) diagrams specification was criticized for lack the detail which is needed to contain the same information as is covered with the program source. Some developers even claim that "the Code is the design". == Disadvantages == There is a serious risk that the generated code will rapidly differ from the model or that the reverse-engineered model will lose its reflection on the code or a mix of these two problems as result of cycled reengineering efforts. Regarding behavioral/dynamic part of UML for features like statechart diagram there is no equivalents in programming languages. Their translation during code-generation will result in common programming statement (.e.g if,switch,enum) being either missing or misinterpreted. If edited and imported back may result in different or incomplete model. The same goes for code snippets used for code generation stage for the pattern-implementation and user-specific logic: intermixed they may not be easily reverse-engineered back. There is also general lack of advanced tooling for modelling that are comparable to that of modern IDEs (for testing, debugging, navigation, etc.) for general-purpose programming languages and domain-specific languages. == Examples in software engineering == Perhaps the most common form of round-trip engineering is synchronization between UML (Unified Modeling Language) models and the corresponding source code and entity–relationship diagrams in data modelling and database modelling. Round-trip engineering based on Unified Modeling Language (UML) needs three basic tools for software development: Source Code Editor; UML Editor for the Attributes and Methods; Visualisation of UML structure

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  Inductive bias

  The inductive bias (also known as learning bias) of a learning algorithm is the set of assumptions that the learner uses to predict outputs of given inputs that it has not encountered. Inductive bias is anything which makes the algorithm learn one pattern instead of another pattern (e.g., step-functions in decision trees instead of continuous functions in linear regression models). Learning involves searching a space of solutions for a solution that provides a good explanation of the data. However, in many cases, there may be multiple equally appropriate solutions. An inductive bias allows a learning algorithm to prioritize one solution (or interpretation) over another, independently of the observed data. In machine learning, the aim is to construct algorithms that are able to learn to predict a certain target output. To achieve this, the learning algorithm is presented some training examples that demonstrate the intended relation of input and output values. Then the learner is supposed to approximate the correct output, even for examples that have not been shown during training. Without any additional assumptions, this problem cannot be solved since unseen situations might have an arbitrary output value. The kind of necessary assumptions about the nature of the target function are subsumed in the phrase inductive bias. A classical example of an inductive bias is Occam's razor, assuming that the simplest consistent hypothesis about the target function is actually the best. Here, consistent means that the hypothesis of the learner yields correct outputs for all of the examples that have been given to the algorithm. Approaches to a more formal definition of inductive bias are based on mathematical logic. Here, the inductive bias is a logical formula that, together with the training data, logically entails the hypothesis generated by the learner. However, this strict formalism fails in many practical cases in which the inductive bias can only be given as a rough description (e.g., in the case of artificial neural networks), or not at all. == Types == The following is a list of common inductive biases in machine learning algorithms. Maximum conditional independence: if the hypothesis can be cast in a Bayesian framework, try to maximize conditional independence. This is the bias used in the Naive Bayes classifier. Minimum cross-validation error: when trying to choose among hypotheses, select the hypothesis with the lowest cross-validation error. Although cross-validation may seem to be free of bias, the "no free lunch" theorems show that cross-validation must be biased, for example assuming that there is no information encoded in the ordering of the data. Maximum margin: when drawing a boundary between two classes, attempt to maximize the width of the boundary. This is the bias used in support vector machines. The assumption is that distinct classes tend to be separated by wide boundaries. Minimum description length: when forming a hypothesis, attempt to minimize the length of the description of the hypothesis. Minimum features: unless there is good evidence that a feature is useful, it should be deleted. This is the assumption behind feature selection algorithms. Nearest neighbors: assume that most of the cases in a small neighborhood in feature space belong to the same class. Given a case for which the class is unknown, guess that it belongs to the same class as the majority in its immediate neighborhood. This is the bias used in the k-nearest neighbors algorithm. The assumption is that cases that are near each other tend to belong to the same class. == Shift of bias == Although most learning algorithms have a static bias, some algorithms are designed to shift their bias as they acquire more data. This does not avoid bias, since the bias shifting process itself must have a bias.

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  POP-11

  POP-11 is a reflective, incrementally compiled programming language with many of the features of an interpreted language. It is the core language of the Poplog programming environment developed originally by the University of Sussex, and recently in the School of Computer Science at the University of Birmingham, which hosts the main Poplog website. POP-11 is an evolution of the language POP-2, developed in Edinburgh University, and features an open stack model (like Forth, among others). It is mainly procedural, but supports declarative language constructs, including a pattern matcher, and is mostly used for research and teaching in artificial intelligence, although it has features sufficient for many other classes of problems. It is often used to introduce symbolic programming techniques to programmers of more conventional languages like Pascal, who find POP syntax more familiar than that of Lisp. One of POP-11's features is that it supports first-class functions. POP-11 is the core language of the Poplog system. The availability of the compiler and compiler subroutines at run-time (a requirement for incremental compiling) gives it the ability to support a far wider range of extensions (including run-time extensions, such as adding new data-types) than would be possible using only a macro facility. This made it possible for (optional) incremental compilers to be added for Prolog, Common Lisp and Standard ML, which could be added as required to support either mixed language development or development in the second language without using any POP-11 constructs. This made it possible for Poplog to be used by teachers, researchers, and developers who were interested in only one of the languages. The most successful product developed in POP-11 was the Clementine data mining system, developed by ISL. After SPSS bought ISL, they renamed Clementine to SPSS Modeler and decided to port it to C++ and Java, and eventually succeeded with great effort, and perhaps some loss of the flexibility provided by the use of an AI language. POP-11 was for a time available only as part of an expensive commercial package (Poplog), but since about 1999 it has been freely available as part of the open-source software version of Poplog, including various added packages and teaching libraries. An online version of ELIZA using POP-11 is available at Birmingham. At the University of Sussex, David Young used POP-11 in combination with C and Fortran to develop a suite of teaching and interactive development tools for image processing and vision, and has made them available in the Popvision extension to Poplog. == Simple code examples == Here is an example of a simple POP-11 program: define Double(Source) -> Result; Source2 -> Result; enddefine; Double(123) => That prints out: 246 This one includes some list processing: define RemoveElementsMatching(Element, Source) -> Result; lvars Index; [[% for Index in Source do unless Index = Element or Index matches Element then Index; endunless; endfor; %]] -> Result; enddefine; RemoveElementsMatching("the", [[the cat sat on the mat]]) => ;;; outputs [[cat sat on mat]] RemoveElementsMatching("the", [[the cat] [sat on] the mat]) => ;;; outputs [[the cat] [sat on] mat] RemoveElementsMatching([[= cat]], [[the cat]] is a [[big cat]]) => ;;; outputs [[is a]] Examples using the POP-11 pattern matcher, which makes it relatively easy for students to learn to develop sophisticated list-processing programs without having to treat patterns as tree structures accessed by 'head' and 'tail' functions (CAR and CDR in Lisp), can be found in the online introductory tutorial. The matcher is at the heart of the SimAgent (sim_agent) toolkit. Some of the powerful features of the toolkit, such as linking pattern variables to inline code variables, would have been very difficult to implement without the incremental compiler facilities.

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