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  Direct voice input

  Direct voice input (DVI), sometimes called voice input control (VIC), is a style of human–machine interaction "HMI" in which the user makes voice commands to issue instructions to the machine through speech recognition. In the field of military aviation, DVI has been introduced into the cockpits of several modern military aircraft, such as the Eurofighter Typhoon, the Lockheed Martin F-35 Lightning II, the Dassault Rafale, the KF-21 Boramae and the Saab JAS 39 Gripen. Such systems have also been used for various other purposes, including industry control systems and speech recognition assistance for impaired individuals. == Overview == DVI systems can be divided into two major categories of functionality: "user-dependent" or "user-independent". A user-dependent system requires that a personal voice template to be generated for a specific person; the template for this individual has to be loaded onto their assigned machine prior to use of the DVI system for it to function properly. In contrast, a user-independent system does not require any personal voice template, being intended to respond correctly to the voice of any user. They can also be categorised between "discrete recognition" and "continuous recognition". Users of a discrete recognition system must pause between each word so that the DVI system can identify the separations between each word, while a continuous speech recognition system is capable of understanding a normal rate of speech. During the mid-2000s, researchers at the National Aerospace Laboratory in the Netherlands examined the use of DVI in the "GRACE" simulator; a total of twelve pilots participated in the ensuing experiment. The tests performed reportedly revealed that, while the hardware itself functioned well, several improvements were desirable prior to real-world deployment on aircraft since DVI operations actually consumed more time in comparison to traditional existing methods. Recommendations for improvements included the adoption of simpler syntax, the achievement of a greater recognition rate, and a decrease in response times; all of the issues encountered were determined to be of a technological nature, and were deemed feasible to resolve. The researchers concluded that in cockpits, especially during emergencies where pilots have to operate entirely on their own, a DVI system could be highly relevant, but that it was not of crucial importance during most other conceivable scenarios. Around the same time, evaluations of DVI systems for civil aviation purposes were conducted within the framework of Project SafeSound, coordinated by the European Union. It involved the observation of pilot workloads in real-world cockpits and contrasting them against pilot activity in flight simulators using both conventional systems and DVI assistance. The project aimed to enhance aviation safety and to decrease the workload in both ground and flight operations via the application of enhanced audio functions. == Applications == === Aviation === Prior to its widespread deployment, a handful of conventional military aircraft were converted to trial DVI systems; examples include the Harrier AV-8B and F-16 VISTA. In another case, a General Dynamics F-16 Fighting Falcon simulator was modified with DVI for a voice control study that was undertaken by the Royal Netherlands Air Force. DVI trials have also been conducted on helicopters, including the Boeing AH-64 Apache, showing the potential to improve flight safety and mission effectiveness. Numerous modern fighter aircraft have been outfitted with DVI systems, often in combination with various other man-machine interface schemes, such as HOTAS-compliant controls and other advanced control technologies. The combination of Voice and HOTAS control schemes has sometimes been referred to as the "V-TAS" concept. A prominent fighter aircraft to be furnished with a V-TAS cockpit is the Eurofighter Typhoon. The Lockheed Martin F-35 Lightning II also features a DVI system, which was developed by Adacel. Other examples includes the Dassault Rafale and the Saab JAS 39 Gripen. Numerous aircraft have been planned to use DVI. At one stage, the United States Air Force had sought to integrate DVI upon the Lockheed Martin F-22 Raptor; however, the technology was eventually judged to pose too many technical risks at that point in time, and thus such efforts were abandoned. === Personal === By 1990, working prototypes of speech recognition systems were being demonstrated; these were being promoted for the purpose of providing an effective man-machine interface for individuals with impaired speech. Techniques employed included time-encoded digital speech and automatic token set selection. Investigations of these early DVI systems reportedly included the use of automatic diagnostic routines and limited-scale trials using volunteers. During the 2010s, various companies were offering voice recognition systems to the general public in the form of personal digital assistants. One example is the Google Voice service, which allows users to pose questions via a DVI package installed on either a personal computer, tablet, or mobile phone. Numerous digital assistants have been developed, such as Amazon Echo, Siri, and Cortana, that use DVI to interact with users. === Commercial === DVI technology has enabled automated telephone systems to be widely deployed. Many companies commonly use centralised phone systems that route callers to the correct department via such methods. Various car manufacturers have also furnished their road vehicles with DVI systems; these typically allow drivers to control infotainment systems and interact with mobile phones with more convenience than legacy methods. During the late 1980s, investigations into the use of DVI systems for controlling CNC machines and other manufacturing apparatus were underway. During the 2010s, such systems were being used for logistics and warehouse management purposes.

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  Theano (software)

  Theano is a Python library and optimizing compiler for manipulating and evaluating mathematical expressions, especially matrix-valued ones. In Theano, computations are expressed using a NumPy-esque syntax and compiled to run efficiently on either CPU or GPU architectures. == History == Theano is an open source project primarily developed by the Montreal Institute for Learning Algorithms (MILA) at the Université de Montréal. The name of the software references the ancient philosopher Theano, long associated with the development of the golden mean. On 28 September 2017, Pascal Lamblin posted a message from Yoshua Bengio, Head of MILA: major development would cease after the 1.0 release due to competing offerings by strong industrial players. Theano 1.0.0 was then released on 15 November 2017. On 17 May 2018, Chris Fonnesbeck wrote on behalf of the PyMC development team that the PyMC developers will officially assume control of Theano maintenance once the MILA development team steps down. On 29 January 2021, they started using the name Aesara for their fork of Theano. On 29 Nov 2022, the PyMC development team announced that the PyMC developers will fork the Aesara project under the name PyTensor. == Sample code == The following code is the original Theano's example. It defines a computational graph with 2 scalars a and b of type double and an operation between them (addition) and then creates a Python function f that does the actual computation. == Examples == === Matrix Multiplication (Dot Product) === The following code demonstrates how to perform matrix multiplication using Theano, which is essential for linear algebra operations in many machine learning tasks. === Gradient Calculation === The following code uses Theano to compute the gradient of a simple operation (like a neuron) with respect to its input. This is useful in training machine learning models (backpropagation). === Building a Simple Neural Network === The following code shows how to start building a simple neural network. This is a very basic neural network with one hidden layer. === Broadcasting in Theano === The following code demonstrates how broadcasting works in Theano. Broadcasting allows operations between arrays of different shapes without needing to explicitly reshape them.

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  Geoffrey J. Gordon

  Geoffrey J. Gordon is a professor at the Machine Learning Department at Carnegie Mellon University in Pittsburgh and director of research at the Microsoft Montréal lab. He is known for his research in statistical relational learning (a subdiscipline of artificial intelligence and machine learning) and on anytime dynamic variants of the A search algorithm. His research interests include multi-agent planning, reinforcement learning, decision-theoretic planning, statistical models of difficult data (e.g. maps, video, text), computational learning theory, and game theory. Gordon received a B.A. in computer science from Cornell University in 1991, and a PhD at Carnegie Mellon in 1999.

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  Nathalie Japkowicz

  Nathalie Japkowicz is a Canadian computer scientist specializing in machine learning. She is a professor and department chair of computer science at the American University College of Arts and Sciences. == Life == Nathalie Japkowicz completed a B.Sc. at McGill University in 1988. She earned an M.Sc. from the University of Toronto in 1990. She completed a Ph.D. at Rutgers University in 1999. Her dissertation was titled Concept-learning in the absence of counter-examples: an autoassociation-based approach to classification. Stephen José Hanson and Casimir Alexander Kulikowski were her doctoral advisors. Japkowicz worked at the University of Ottawa in the school of electrical engineering and computer science. She was the lead of its laboratory for research on machine learning for defense security. From 2003 to 2005, Japkowicz was the secretary of the Canadian Artificial Intelligence Association (CAIAC). She was CAIAC vice president from 2009 to 2014 and president from 2013 to 2015, and part-president from 2015 to 2017. Japkowicz is a professor and department chair of computer science at the American University College of Arts and Sciences. She researches artificial intelligence, machine learning, data mining, and big data analysis. == Selected works == Gao, Yong; Japkowicz, Nathalie, eds. (2009). Advances in Artificial Intelligence: 22nd Canadian Conference on Artificial Intelligence, Canadian AI 2009 Kelowna, Canada, May 25–27, 2009 Proceedings. Lecture Notes in Computer Science. Vol. 5549. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-642-01818-3. ISBN 978-3-642-01817-6. S2CID 27083226. Japkowicz, Nathalie; Shah, Mohak (2011). Evaluating Learning Algorithms: A Classification Perspective (1 ed.). Cambridge University Press. doi:10.1017/cbo9780511921803. ISBN 978-0-511-92180-3. Japkowicz, Nathalie; Matwin, Stan, eds. (2015). Discovery Science: 18th International Conference, DS 2015, Banff, AB, Canada, October 4–6, 2015. Proceedings. Lecture Notes in Computer Science. Vol. 9356. Cham: Springer International Publishing. doi:10.1007/978-3-319-24282-8. ISBN 978-3-319-24281-1. S2CID 1302223. Japkowicz, Nathalie; Stefanowski, Jerzy, eds. (2016). Big Data Analysis: New Algorithms for a New Society. Studies in Big Data. Vol. 16. Cham: Springer International Publishing. doi:10.1007/978-3-319-26989-4. ISBN 978-3-319-26987-0. Ceci, Michelangelo; Japkowicz, Nathalie; Liu, Jiming; Papadopoulos, George A.; Raś, Zbigniew W., eds. (2018). Foundations of Intelligent Systems: 24th International Symposium, ISMIS 2018, Limassol, Cyprus, October 29–31, 2018, Proceedings. Lecture Notes in Computer Science. Vol. 11177. Cham: Springer International Publishing. doi:10.1007/978-3-030-01851-1. ISBN 978-3-030-01850-4. S2CID 53038780.

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  Domain adaptation

  Domain adaptation is a field associated with machine learning and transfer learning. It addresses the challenge of training a model on one data distribution (the source domain) and applying it to a related but different data distribution (the target domain). A common example is spam filtering, where a model trained on emails from one user (source domain) is adapted to handle emails for another user with significantly different patterns (target domain). Domain adaptation techniques can also leverage unrelated data sources to improve learning. When multiple source distributions are involved, the problem extends to multi-source domain adaptation. Domain adaptation is a specific type of transfer learning. According to the taxonomy laid out by Pan and Yang (2010), it falls into the category of transductive transfer learning. In this setting, the source and target tasks are the same (e.g., both are object recognition), but the domains differ (different marginal distributions). This distinguishes it from inductive transfer learning (where labeled data is available for the target task) and unsupervised transfer learning (where labels are unavailable in both domains). == Classification of domain adaptation problems == Domain adaptation setups are classified in two different ways: according to the distribution shift between the domains, and according to the available data from the target domain. === Distribution shifts === Common distribution shifts are classified as follows: Covariate Shift occurs when the input distributions of the source and destination change, but the relationship between inputs and labels remains unchanged. The above-mentioned spam filtering example typically falls in this category. Namely, the distributions (patterns) of emails may differ between the domains, but emails labeled as spam in the one domain should similarly be labeled in another. Prior Shift (Label Shift) occurs when the label distribution differs between the source and target datasets, while the conditional distribution of features given labels remains the same. An example is a classifier of hair color in images from Italy (source domain) and Norway (target domain). The proportions of hair colors (labels) differ, but images within classes like blond and black-haired populations remain consistent across domains. A classifier for the Norway population can exploit this prior knowledge of class proportions to improve its estimates. Concept Shift (Conditional Shift) refers to changes in the relationship between features and labels, even if the input distribution remains the same. For instance, in medical diagnosis, the same symptoms (inputs) may indicate entirely different diseases (labels) in different populations (domains). === Data available during training === Domain adaptation problems typically assume that some data from the target domain is available during training. Problems can be classified according to the type of this available data: Unsupervised: Unlabeled data from the target domain is available, but no labeled data. In the above-mentioned example of spam filtering, this corresponds to the case where emails from the target domain (user) are available, but they are not labeled as spam. Domain adaptation methods can benefit from such unlabeled data, by comparing its distribution (patterns) with the labeled source domain data. Semi-supervised: Most data that is available from the target domain is unlabelled, but some labeled data is also available. In the above-mentioned case of spam filter design, this corresponds to the case that the target user has labeled some emails as being spam or not. Supervised: All data that is available from the target domain is labeled. In this case, domain adaptation reduces to refinement of the source domain predictor. In the above-mentioned example classification of hair-color from images, this could correspond to the refinement of a network already trained on a large dataset of labeled images from Italy, using newly available labeled images from Norway. == Formalization == Let X {\displaystyle X} be the input space (or description space) and let Y {\displaystyle Y} be the output space (or label space). The objective of a machine learning algorithm is to learn a mathematical model (a hypothesis) h : X → Y {\displaystyle h:X\to Y} able to attach a label from Y {\displaystyle Y} to an example from X {\displaystyle X} . This model is learned from a learning sample S = { ( x i , y i ) ∈ ( X × Y ) } i = 1 m {\displaystyle S=\{(x_{i},y_{i})\in (X\times Y)\}_{i=1}^{m}} . Usually in supervised learning (without domain adaptation), we suppose that the examples ( x i , y i ) ∈ S {\displaystyle (x_{i},y_{i})\in S} are drawn i.i.d. from a distribution D S {\displaystyle D_{S}} of support X × Y {\displaystyle X\times Y} (unknown and fixed). The objective is then to learn h {\displaystyle h} (from S {\displaystyle S} ) such that it commits the least error possible for labelling new examples coming from the distribution D S {\displaystyle D_{S}} . The main difference between supervised learning and domain adaptation is that in the latter situation we study two different (but related) distributions D S {\displaystyle D_{S}} and D T {\displaystyle D_{T}} on X × Y {\displaystyle X\times Y} . The domain adaptation task then consists of the transfer of knowledge from the source domain D S {\displaystyle D_{S}} to the target one D T {\displaystyle D_{T}} . The goal is then to learn h {\displaystyle h} (from labeled or unlabelled samples coming from the two domains) such that it commits as little error as possible on the target domain D T {\displaystyle D_{T}} . The major issue is the following: if a model is learned from a source domain, what is its capacity to correctly label data coming from the target domain? == Four algorithmic principles == === Reweighting algorithms === The objective is to reweight the source labeled sample such that it "looks like" the target sample (in terms of the error measure considered). === Iterative algorithms === A method for adapting consists in iteratively "auto-labeling" the target examples. The principle is simple: a model h {\displaystyle h} is learned from the labeled examples; h {\displaystyle h} automatically labels some target examples; a new model is learned from the new labeled examples. Note that there exist other iterative approaches, but they usually need target labeled examples. === Search of a common representation space === The goal is to find or construct a common representation space for the two domains. The objective is to obtain a space in which the domains are close to each other while keeping good performances on the source labeling task. This can be achieved through the use of Adversarial machine learning techniques where feature representations from samples in different domains are encouraged to be indistinguishable. === Hierarchical Bayesian Model === The goal is to construct a Bayesian hierarchical model p ( n ) {\displaystyle p(n)} , which is essentially a factorization model for counts n {\displaystyle n} , to derive domain-dependent latent representations allowing both domain-specific and globally shared latent factors. == Software packages == Several compilations of domain adaptation and transfer learning algorithms have been implemented over the past decades: SKADA (Python) ADAPT (Python) TLlib (Python) Domain-Adaptation-Toolbox (MATLAB)

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  Samer Hassan

  Samer Hassan is a computer scientist, social scientist, activist and researcher, focused on the study of the collaborative economy, online communities and decentralized technologies. He is an associate professor at Universidad Complutense de Madrid (Spain) and Faculty Associate at the Berkman Klein Center for Internet & Society at Harvard University. He is the recipient of an ERC Grant of 1.5M€ with the P2P Models project, to research blockchain-based decentralized autonomous organizations for the collaborative economy. == Education and career == Hassan is a Spanish/Lebanese scholar with an interdisciplinary background, which combines computer sciences with social sciences and activism. He received a degree in Computer Science and MSc in Artificial Intelligence from the Universidad Complutense de Madrid (UCM) in Spain. He also studied three years of Political Science at the distance learning university UNED. He then pursued a PhD in Social Simulation at the department of Software Engineering and Artificial Intelligence of UCM, supervised by the computer scientist Juan Pavón and the sociologist Millán Arroyo-Menéndez. He has been researching in several institutions, funded by several scholarships and awards, most notably Harvard's Real Colegio Complutense, and the Spanish postdoctoral grants Juan de la Cierva and José Castillejo. Thus, he was a visiting researcher at the Centre for Research in Social Simulation, in the Department of Sociology at the University of Surrey in the UK, working under the supervision of Nigel Gilbert (2007-2008), and a lecturer at the American University of Science and Technology in Lebanon (2010–11). He was selected as Fellow at the Berkman Klein Center for Internet & Society at Harvard University (2015-2017) and is presently a Faculty Associate at the same structure. Starting in 2024, he joined, as affiliate faculty, the Institute for Digital Cooperative Economy (The New School), part of the Platform Cooperativism Consortium. == Activism and social engagement == As an activist, Hassan has been engaged in both offline (La Tabacalera de Lavapiés, Medialab-Prado) and online (Ourproject.org, Barrapunto, Wikipedia) initiatives. He was accredited as a grassroots facilitator by the Altekio Cooperative. He co-founded the Comunes Nonprofit in 2009 and the Move Commons webtool project in 2010. He has co-organized practitioner-oriented workshops on platform co-ops and free/open source decentralized tools for communities, and has presented his work in non-academic conferences of Mozilla, the Internet Archive, and others. As a privacy advocate, he co-created a course on cyber-ethics which has been teaching since 2013 (as of 2021). He was co-founder of the Sci-Fdi Spanish science-fiction magazine. His gender is non-binary and uses he/they pronouns. == Work == Hassan's interdisciplinary research spans multiple fields, including online communities, online governance, online collaboration, decentralized technologies, blockchain-based decentralized autonomous organizations, free/libre/open source software, Commons-based peer production, agent-based social simulation, social movements and cyberethics. He has published more than 60 works in these fields. Hassan's PhD thesis focused on the methodological challenges for building data-driven social simulation models. The main model built simulated the transition from modern values to postmodern values in Spain. His methodological work also explored the combination of different artificial intelligence technologies, i.e. software agents with fuzzy logic, data mining, natural language processing, and microsimulation. In his postdoctoral period, he focused on experimenting with multiple software systems to facilitate the collaborative economy, e.g. semantic-web labelling for commons-based initiatives, distribution of value in peer production communities, agent-supported online assemblies, decentralized real-time collaborative software, decentralized blockchain based reputation, or blockchain-enabled commons governance. Hassan was Principal Investigator of the UCM partner in the EU-funded P2Pvalue project on building decentralized web-tools for collaborative communities. As such, he led the team that created SwellRT, a federated backend-as-a-service focused to ease development of apps featuring real-time collaboration. Intellectual Property of this project was transferred to the Apache Software Foundation in 2017. As part of this research line, Hassan's team also develop two SwellRT-based apps, "Teem" for management of social collectives and Jetpad, a federated real time editor. He presented the innovations concerning these software at Harvard's Berkman Klein Center and Harvard's Center for Research on Computation and Society. Other research lines offered outcomes beyond publications. "Wikichron", coled by Javier Arroyo, is a web tool to visualize MediaWiki community metrics, currently in production and available for third-parties. "Decentralized Science", led by Hassan's PhD student Ámbar Tenorio-Fornés, is a framework to facilitate decentralized infrastructure and open peer review in the scientific publication process, which has been selected by the European Commission to receive funding as a spin-off social enterprise. His research on blockchain and crowdfunding models awarded him with a commission from Triple Canopy. His team pushed forward a mapping of the ecosystem of blockchain for social good, led by the Joint Research Centre and published by the European Commission. As part of his ERC project P2P Models, Hassan and his team –including Silvia Semenzin– are investigating whether blockchain technology and Decentralized Autonomous Organizations could contribute to improving the governance of commons-oriented communities, both online and offline. Their work has been showcased for tackling the impact of blockchain on governance, proposing alternatives to the current sharing economy, emerging forms of techno-social systems like NFTs or prediction markets, or giving relevance to gender issues in the field. Hassan was invited to present the project achievements in Harvard Kennedy School, MIT Media Lab, Harvard's Data Privacy Lab, Harvard's Center for Research on Computation and Society, and Harvard's SEAS EconCS. British MP and Opposition Leader Ed Miliband showcased his research and its potential impact on policy. The project made public its way of organizing and its core values. In particular, it has shown a commitment to diversity as a core value in hiring, or choosing case studies. == Selected works == Arroyo, Javier; Davó, David; Martínez-Vicente, Elena; Faqir-Rhazoui, Youssef; Hassan, Samer (8 November 2022). "DAO-Analyzer: Exploring Activity and Participation in Blockchain Organizations" (PDF). Companion Publication of the 2022 Conference on Computer Supported Cooperative Work and Social Computing. CSCW'22 Companion. New York, NY, USA: Association for Computing Machinery. pp. 193–196. doi:10.1145/3500868.3559707. ISBN 978-1-4503-9190-0. Rozas, David; Tenorio-Fornés, Antonio; Díaz-Molina, Silvia; Hassan, Samer (2021). "When Ostrom Meets Blockchain: Exploring the Potentials of Blockchain for Commons Governance". SAGE Open. 11 (1): 215824402110025. doi:10.1177/21582440211002526. ISSN 2158-2440. Faqir-Rhazoui, Youssef; Ariza-Garzón, Miller-Janny; Arroyo, Javier; Hassan, Samer (8 May 2021). "Effect of the Gas Price Surges on User Activity in the DAOs of the Ethereum Blockchain" (PDF). Extended Abstracts of the 2021 CHI Conference on Human Factors in Computing Systems. CHI EA '21. New York, NY, USA: Association for Computing Machinery. pp. 1–7. doi:10.1145/3411763.3451755. ISBN 978-1-4503-8095-9. Hassan, Samer; Filippi, Primavera De (20 April 2021). "Decentralized Autonomous Organization". Internet Policy Review. 10 (2). doi:10.14763/2021.2.1556. hdl:10419/235960. ISSN 2197-6775. Joint Research Centre (European Commission); Hassan, Samer; Hakami, Anna; Brekke, Jaya Klara; De Filippi, Primavera; Lopéz Morales, Genoveva; Pólvora, Alexandre; Orgaz Alonso, Christian; Bodó, Balázs (2020). Scanning the European ecosystem of distributed ledger technologies for social and public good: what, why, where, how, and ways to move forward. LU: Publications Office of the European Union. doi:10.2760/300796. ISBN 978-92-76-21578-3. Filippi, Primavera De; Hassan, Samer (14 November 2016). "Blockchain technology as a regulatory technology: From code is law to law is code". First Monday. arXiv:1801.02507. doi:10.5210/fm.v21i12.7113. ISSN 1396-0466.

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  Max Welling

  Max Welling (born 1968) is a Dutch computer scientist in machine learning at the University of Amsterdam. In August 2017, the university spin-off Scyfer BV, co-founded by Welling, was acquired by Qualcomm. He has since then served as a Vice President of Technology at Qualcomm Netherlands. He is also a Distinguished Scientist at Microsoft Research AI4Science, based in Amsterdam. Welling received his PhD in physics with a thesis on quantum gravity under the supervision of Nobel laureate Gerard 't Hooft (1998) at the Utrecht University. He has published over 250 peer-reviewed articles in machine learning, computer vision, statistics and physics, and has most notably invented variational autoencoders (VAEs), together with Diederik P Kingma. In 2025 Welling was elected member of the Royal Netherlands Academy of Arts and Sciences.

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  Magnetic ink character recognition

  Magnetic ink character recognition code, known in short as MICR code, is a character recognition technology used mainly by the banking industry to streamline the processing and clearance of cheques and other documents. MICR encoding, called the MICR line, is at the bottom of cheques and other vouchers and typically includes the document-type indicator, bank code, bank account number, cheque number, cheque amount (usually added after a cheque is presented for payment), and a control indicator. The format for the bank code and bank account number is country-specific. The technology allows MICR readers to scan and read the information directly into a data-collection device. Unlike barcode and similar technologies, MICR characters can be read easily by humans. MICR encoded documents can be processed much faster and more accurately than conventional OCR encoded documents. == Pre-Unicode standard representation == The ISO standard ISO 2033:1983, and the corresponding Japanese Industrial Standard JIS X 9010:1984 (originally JIS C 6229–1984), define character encodings for OCR-A, OCR-B and E-13B. == International spread == There are two major MICR fonts in use: E-13B and CMC-7. There is no particular international agreement on which countries use which font. In practice, this does not create particular problems as cheques and other vouchers do not usually flow out of a particular jurisdiction. The E-13B font has been adopted as an international standard in ISO 1004-1:2013, and is the standard in Australia, Canada, the United Kingdom, the United States, as well as Central America and much of Asia, besides other countries. The CMC-7 font has been adopted as an international standard in ISO 1004-2:2013, and is widely used in Europe, including France and Italy, Mexico, and South America, including Argentina, Brazil, Chile, besides other countries. Israel is the only country that can use both fonts simultaneously, though the practice makes the system significantly less efficient. This situation is the product of the Israelis adopting CMC-7, while the Palestinians opted for E-13B. == Fonts == === E-13B === E-13B is a 14-character set, comprising the 10 decimal digits, and the following symbols: ⑆ (transit: used to delimit a bank code); ⑈ (on-us: used to delimit a customer account number); ⑇ (amount: used to delimit a transaction amount); ⑉ (dash: used to delimit parts of numbers—e.g., routing numbers or account numbers). In the check printing and banking industries the E-13B MICR line is also commonly referred to as the TOAD line. This reference comes from the 4 characters: Transit, On-us, Amount, and Dash. Compared to CMC-7, some pairs of E-13B characters (notably 2 and 5) can produce relatively similar results when magnetically scanned; however, as a fallback if magnetic reading fails, E-13B also performs well under optical character recognition. The E-13B repertoire can be represented in Unicode (see below). The official Unicode names contain misnomers. For example, the ⑈ on-us symbol is official titled "OCR Dash". Prior to Unicode, it could be encoded according to ISO 2033:1983, which encodes digits in their usual ASCII locations, transit as 0x3A, on-us as 0x3C, amount as 0x3B, and dash as 0x3D. For EBCDIC, IBM code page 1001 encodes digits in their usual EBCDIC locations, transit as 0xDB, on-us as 0xEB, amount as 0xCB, and dash as 0xFB. IBM code page 1032 extends code page 1001 by adding alternative encodings for transit at 0x5C, 0x7A and 0xC1, on-us at 0x4C, 0x61 and 0xC3, amount at 0x5B, 0x5E and 0xC2 and dash at 0x60, 0x7E and 0xC4, in addition to a zero-width space at 0x5A. These alternative representations were added for interoperability with Siemens and Océ printers. === CMC-7 === CMC-7 includes 10 numeric digits, 26 capital letters, and 5 control characters: S I (internal), S II (terminator), S III (amount), S IV (an unused character), and S V (routing). CMC-7 has a barcode format, with every character having two distinct large gaps in different places, as well as distinct patterns in between, to minimize any chance for character confusion while reading magnetically; however, these bars are too close and narrow to be reliably recognised at a typical scan resolution if falling back to optical scanning. CMC-7 can also produce superficially successful, but incorrect, scans of upside-down MICR lines. Unicode does not include support for the CMC-7 control symbols. IBM code page 1033 encodes: Digits and capitals in their usual EBCDIC locations S I (internal) as 0x5E, 0x61 or 0xCB; S II (terminator) as 0x4C, 0x5B or 0xEB; S III (amount) as 0x60, 0x7E or 0xFB; S IV as 0x50, 0x7A or 0xDB; S V (routing) as 0x5C, 0x6E or 0xBB. == MICR reader == MICR characters are printed on documents in one of the two MICR fonts, using magnetizable (commonly known as magnetic) ink or toner, usually containing iron oxide. In scanning, the document is passed through a MICR reader, which performs two functions: magnetization of the ink, and detection of the characters. The characters are read by a MICR reader head, a device similar to the playback head of a tape recorder. As each character passes over the head, it produces a unique waveform that can be easily identified by the system. MICR readers are the primary tool for cheque sorting and are used across the cheque distribution network at multiple stages. For example, a merchant will use a MICR reader to sort cheques by bank and send the sorted cheques to a clearing house for redistribution to those banks. Upon receipt, the banks perform another MICR sort to determine which customer's account is charged and to which branch the cheque should be sent on its way back to the customer. However, many banks no longer offer this last step of returning the cheque to the customer. Instead, cheques are scanned and stored digitally. Sorting of cheques is done as per the geographical coverage of banks in a nation. == Unicode == OCR and MICR characters have been included in the Unicode Standard since at least version 1.1 (June 1993). Since the Unicode Character Database only tracks characters starting with version 1.1, they may also have been present in Unicode 1.0 or 1.0.1. The Unicode block that includes OCR and MICR characters is called Optical Character Recognition and covers U+2440–U+245F. Of the characters in this block, four are from the MICR E-13B font: U+2446 ⑆ OCR BRANCH BANK IDENTIFICATION U+2447 ⑇ OCR AMOUNT OF CHECK U+2448 ⑈ OCR DASH (corrected alias MICR ON US SYMBOL) U+2449 ⑉ OCR CUSTOMER ACCOUNT NUMBER (corrected alias MICR DASH SYMBOL) The names of the latter two characters were inadvertently switched when they were named in ISO/IEC 10646:1993, and they have been assigned accurate names as formal aliases. Per the Unicode Stability Policy, the existing names remain, allowing their use as stable identifiers. Additionally, all four characters have informative (non-formal) aliases in the Unicode charts: "transit", "amount", "on-us", and "dash" respectively. Prior to Unicode, these symbols had been encoded by the ISO-IR-98 encoding defined by ISO 2033:1983, in which they were simply named SYMBOL ONE through SYMBOL FOUR. They were encoded immediately following the digits, which were encoded at their ASCII locations. Although ISO 2033 also specifies encoding for OCR-A and OCR-B, its encoding for E-13B is known simply as ISO_2033-1983 by the IANA. == History == Before the mid-1940s, cheques were processed manually using the Sort-A-Matic or Top Tab Key method. The processing and cheque clearing was very time-consuming and was a significant cost in cheque clearance and bank operations. As the number of cheques increased, ways were sought for automating the process. Standards were developed to ensure uniformity in financial institutions. By the mid-1950s, the Stanford Research Institute and General Electric Computer Laboratory had developed the first automated system to process cheques using MICR. The same team also developed the E-13B MICR font. "E" refers to the font being the fifth considered, and "B" to the fact that it was the second version. The "13" refers to the 0.013-inch character grid. The trial of MICR E-13B font was shown to the American Bankers Association (ABA) in July 1956, which adopted it in 1958 as the MICR standard for negotiable documents in the United States. ABA adopted MICR as its standard because machines could read MICR accurately, and MICR could be printed using existing technology. In addition, MICR remained machine readable, even through overstamping, marking, mutilation and more. The first cheques using MICR were printed by the end of 1959. Although compliance with MICR standards was voluntary in the United States, it had been almost universally adopted in the United States by 1963. In 1963, ANSI adopted the ABA's E-13B font as the American standard for MICR printing, and E-13B was also standardized as ISO 1004:1995. Other countries set their own standards, though the MICR readers and m

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  Confused deputy problem

  In information security, a confused deputy is a computer program that is tricked by another program (with fewer privileges or less rights) into misusing its authority on the system. It is a specific type of privilege escalation. The confused deputy problem is often cited as an example of why capability-based security is important. Capability systems protect against the confused deputy problem, whereas access-control list–based systems do not. Such systems can mitigate the confused deputy problem by eliminating ambient authority, allowing programs to act only on resources for which they hold explicit capabilities, whereas access-control list–based systems are more susceptible to it. However, this protection depends on correct implementation; in formally verified capability systems such as seL4, it can be shown that the kernel enforces capability constraints correctly, preventing such behavior at the system level. == Example == In the original example of a confused deputy, there was a compiler program provided on a commercial timesharing service. Users could run the compiler and optionally specify a filename where it would write debugging output, and the compiler would be able to write to that file if the user had permission to write there. The compiler also collected statistics about language feature usage. Those statistics were stored in a file called "(SYSX)STAT", in the directory "SYSX". To make this possible, the compiler program was given permission to write to files in SYSX. But there were other files in SYSX: in particular, the system's billing information was stored in a file "(SYSX)BILL". A user ran the compiler and named "(SYSX)BILL" as the desired debugging output file. This produced a confused deputy problem. The compiler made a request to the operating system to open (SYSX)BILL. Even though the user did not have access to that file, the compiler did, so the open succeeded. The compiler wrote the compilation output to the file (here "(SYSX)BILL") as normal, overwriting it, and the billing information was destroyed. === The confused deputy === In this example, the compiler program is the deputy because it is acting at the request of the user. The program is seen as 'confused' because it was tricked into overwriting the system's billing file. Whenever a program tries to access a file, the operating system needs to know two things: which file the program is asking for, and whether the program has permission to access the file. In the example, the file is designated by its name, “(SYSX)BILL”. The program receives the file name from the user, but does not know whether the user had permission to write the file. When the program opens the file, the system uses the program's permission, not the user's. When the file name was passed from the user to the program, the permission did not go along with it; the permission was increased by the system silently and automatically. It is not essential to the attack that the billing file be designated by a name represented as a string. The essential points are that: the designator for the file does not carry the full authority needed to access the file; the program's own permission to access the file is used implicitly. == Other examples == A cross-site request forgery (CSRF) is an example of a confused deputy attack that uses the web browser to perform sensitive actions against a web application. A common form of this attack occurs when a web application uses a cookie to authenticate all requests transmitted by a browser. Using JavaScript, an attacker can force a browser into transmitting authenticated HTTP requests. The Samy computer worm used cross-site scripting (XSS) to turn the browser's authenticated MySpace session into a confused deputy. Using XSS the worm forced the browser into posting an executable copy of the worm as a MySpace message which was then viewed and executed by friends of the infected user. Clickjacking is an attack where the user acts as the confused deputy. In this attack a user thinks they are harmlessly browsing a website (an attacker-controlled website) but they are in fact tricked into performing sensitive actions on another website. An FTP bounce attack can allow an attacker to connect indirectly to TCP ports to which the attacker's machine has no access, using a remote FTP server as the confused deputy. Another example relates to personal firewall software. It can restrict Internet access for specific applications. Some applications circumvent this by starting a browser with instructions to access a specific URL. The browser has authority to open a network connection, even though the application does not. Firewall software can attempt to address this by prompting the user in cases where one program starts another which then accesses the network. However, the user frequently does not have sufficient information to determine whether such an access is legitimate—false positives are common, and there is a substantial risk that even sophisticated users will become habituated to clicking "OK" to these prompts. Not every program that misuses authority is a confused deputy. Sometimes misuse of authority is simply a result of a program error. The confused deputy problem occurs when the designation of an object is passed from one program to another, and the associated permission changes unintentionally, without any explicit action by either party. It is insidious because neither party did anything explicit to change the authority. Another example is when an administrator authorizes an AI agent to act on their behalf, and that AI subsequently delegates authority to another AI agent neither vetted nor authorized by the original administrator. The unvetted AI can then act without permissions or oversight from the original developer. == Solutions == In some systems it is possible to ask the operating system to open a file using the permissions of another client. This solution has some drawbacks: It requires explicit attention to security by the server. A naive or careless server might not take this extra step. It becomes more difficult to identify the correct permission if the server is in turn the client of another service and wants to pass along access to the file. It requires the client to trust the server to not abuse the borrowed permissions. Note that intersecting the server and client's permissions does not solve the problem either, because the server may then have to be given very wide permissions (all of the time, rather than those needed for a given request) in order to act for arbitrary clients. The simplest way to solve the confused deputy problem is to bundle together the designation of an object and the permission to access that object. This is exactly what a capability is. Using capability security in the compiler example, the client would pass to the server a capability to the output file, such as a file descriptor, rather than the name of the file. Since it lacks a capability to the billing file, it cannot designate that file for output. In the cross-site request forgery example, a URL supplied "cross"-site would include its own authority independent of that of the client of the web browser.

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  AI Resume Builders Reviews: What Actually Works in 2026

  Shopping for the best AI resume builder? An AI resume builder is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI resume builder slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  Radford M. Neal

  Radford M. Neal (born September 12, 1956) is a professor emeritus at the Department of Statistics and Department of Computer Science at the University of Toronto, where he held a Canada research chair in statistics and machine learning. == Education and career == Neal studied computer science at the University of Calgary, where he received his B.Sc. in 1977 and M.Sc. in 1980, with thesis work supervised by David Hill. He worked for several years as a sessional instructor at the University of Calgary and as a statistical consultant in the industry before coming back to the academia. Neal continued his study at the University of Toronto, where he received his Ph.D. in 1995 under the supervision of Geoffrey Hinton. Neal became an assistant professor at the University of Toronto in 1995, an associated professor in 1999 and a full professor since 2001. He was the Canada Research Chair in Statistics and Machine Learning from 2003 to 2016 and retired in 2017. Neal has made great contributions in the area of machine learning and statistics, where he is particularly well known for his work on Markov chain Monte Carlo, error correcting codes and Bayesian learning for neural networks. He is also known for his blog and as the developer of pqR: a new version of the R interpreter.

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  The Best Free AI Text-to-image Tool for Beginners

  Looking for the best AI text-to-image tool? An AI text-to-image tool is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI text-to-image tool slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.

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  Depth peeling

  In computer graphics, depth peeling is an exact multipass method of order-independent transparency that extracts transparent fragments into depth layers and composites those layers in depth order. Depth peeling has the advantage of being able to generate correct results even for complex images containing intersecting transparent objects. == Method == Depth peeling works by rendering the image multiple times. Depth peeling uses two Z buffers, one that works conventionally, and one that is not modified, and sets the minimum distance at which a fragment can be drawn without being discarded. For each pass, the previous pass' conventional Z-buffer is used as the minimal Z-buffer, so each pass removes already-captured nearer fragments and draws the next depth layer behind them. The resulting images can then be composited in depth order to form a single image. A major drawback of classical depth peeling is performance: it requires one geometry pass per peeled layer, so scenes with high depth complexity require many passes that each re-rasterize the transparent geometry. Later variants reduce the number of passes by peeling multiple layers or both front and back layers in a pass. Dual depth peeling reduces the geometry-pass count from N to N/2+1 by peeling one layer from the front and one from the back in each pass, while multi-layer depth peeling peels several layers per pass and reported up to an 8x speed-up in RGBA8 settings.

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  Pascale Fung

  Pascale Fung (馮雁) (born in Shanghai, China) is a co-founder and Chief Research and Innovation Officer of AMI Labs, an artificial intelligence research company focused on world models. She is a professor in the Department of Electronic & Computer Engineering and the Department of Computer Science & Engineering at the Hong Kong University of Science & Technology(HKUST). She is the director of the Centre for AI Research (CAiRE) at HKUST. She is an elected Fellow of the Institute of Electrical and Electronics Engineers (IEEE) for her “contributions to human-machine interactions”, an elected Fellow of the International Speech Communication Association for “fundamental contributions to the interdisciplinary area of spoken language human-machine interactions” and an elected Fellow of the Association for Computational Linguistics (ACL) for her “significant contributions toward statistical NLP, comparable corpora, and building intelligent systems that can understand and empathize with humans”. She is a member of the Global Future Council on Artificial Intelligence and Robotics, a think tank of the World Economic Forum, and blogs for the Forum's online publication Agenda. She is a member of the Partnership on AI. She has been invited as an AI expert to different government initiatives in China, Japan, the UAE, India, the European Union and the United Nations. Fung's publication topics include spoken language systems, natural language processing, and empathetic human-robot interaction. She co-founded the Human Language Technology Center (HLTC) and is an affiliated faculty with the Robotics Institute and the Big Data Institute, both at HKUST. Additionally, she is the founding chair of the Women Faculty Association at HKUST. She is actively involved in encouraging young women into careers in engineering and science. == Career and research interests == Fung's work is focused on building systems that try to understand and empathize with humans. She has authored and co-authored hundreds of publications, along with many journal listings and book chapters. Fung is often found in the media, among others as a writer for Scientific American, the World Economic Forum, and the London School of Economics, and the Design Society. She was a pioneer in using statistical models for natural language understanding. Her PhD thesis proposed unsupervised methods for aligning texts and mining dictionary translations in different languages by distributional properties. She is an expert in spoken language understanding and computer emotional intelligence, and is a strong proponent of technology transfer. Fung has applied many of her research group's results in the fields of, among others, robotics, IoT, and financial analytics. Her efforts led to the launch of the world's first Chinese natural language search engine in 2001, the first Chinese virtual assistant for smartphones in 2010, and the first emotional intelligent speaker in 2017. == Honors == Elected Fellow, Association for the Advancement of Artificial Intelligence (AAAI), for “significant contributions to the field of Conversational AI and to the development of ethical AI principles and algorithms” Elected Fellow, Association for Computational Linguistics (ACL), for “significant contributions toward statistical NLP, comparable corpora, and building intelligent systems that can understand and empathize with humans” Nominee, the VentureBeat AI Innovation Awards at Transform 2020, for "AI for Good" Awardee, 2017 Outstanding Women Professionals & Entrepreneurs Award, Hong Kong Women Professionals & Entrepreneurs Association Elected Fellow, Institute of Electrical and Electronics Engineers (IEEE), for “contributions to human-machine interactions” Elected Fellow, International Speech Communication Association (ISCA), for “fundamental contributions to the interdisciplinary area of spoken language human-machine interactions" Member, Global Future Council on AI and Robotics, World Economic Forum (2016–) One of the Top 50 Women of Hope, selected by List Magazine in 2014 Selected as “My Favorite Teacher” by top engineering students in 2007 and in 2009 == Affiliations == Fung is affiliated with the following institutions and organizations: Hong Kong University of Science and Technology World Economic Forum Institute of Electrical and Electronics Engineers Association for Computational Linguistics International Speech Communication Association Association for Computing Machinery Association for the Advancement of Artificial Intelligence

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  Hebbian theory

  Hebbian theory is a neuropsychological theory claiming that an increase in synaptic efficacy arises from a presynaptic cell's repeated and persistent stimulation of a postsynaptic cell. It is an attempt to explain synaptic plasticity, the adaptation of neurons during the learning process. Hebbian theory was introduced by Donald Hebb in his 1949 book The Organization of Behavior. The theory is also called Hebb's rule, Hebb's law, Hebb's postulate, and cell assembly theory. Hebb states it as follows: Let us assume that the persistence or repetition of a reverberatory activity (or "trace") tends to induce lasting cellular changes that add to its stability. ... When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A's efficiency, as one of the cells firing B, is increased. The theory is often summarized as "Neurons that fire together, wire together." However, Hebb emphasized that cell A needs to "take part in firing" cell B, and such causality can occur only if cell A fires just before, not at the same time as, cell B. This aspect of causation in Hebb's work foreshadowed what is now known about spike-timing-dependent plasticity, which requires temporal precedence. Hebbian theory attempts to explain associative or Hebbian learning, in which simultaneous activation of cells leads to pronounced increases in synaptic strength between those cells. It also provides a biological basis for errorless learning methods for education and memory rehabilitation. In the study of neural networks in cognitive function, it is often regarded as the neuronal basis of unsupervised learning. == Engrams, cell assembly theory, and learning == Hebbian theory provides an explanation for how neurons might connect to become engrams, which may be stored in overlapping cell assemblies, or groups of neurons that encode specific information. Initially created as a way to explain recurrent activity in specific groups of cortical neurons, Hebb's theories on the form and function of cell assemblies can be understood from the following: The general idea is an old one, that any two cells or systems of cells that are repeatedly active at the same time will tend to become 'associated' so that activity in one facilitates activity in the other. Hebb also wrote: When one cell repeatedly assists in firing another, the axon of the first cell develops synaptic knobs (or enlarges them if they already exist) in contact with the soma of the second cell. D. Alan Allport posits additional ideas regarding cell assembly theory and its role in forming engrams using the concept of auto-association, or the brain's ability to retrieve information based on a partial cue, described as follows: If the inputs to a system cause the same pattern of activity to occur repeatedly, the set of active elements constituting that pattern will become increasingly strongly inter-associated. That is, each element will tend to turn on every other element and (with negative weights) to turn off the elements that do not form part of the pattern. To put it another way, the pattern as a whole will become 'auto-associated'. We may call a learned (auto-associated) pattern an engram. Research conducted in the laboratory of Nobel laureate Eric Kandel has provided evidence supporting the role of Hebbian learning mechanisms at synapses in the marine gastropod Aplysia californica. Because synapses in the peripheral nervous system of marine invertebrates are much easier to control in experiments, Kandel's research found that Hebbian long-term potentiation along with activity-dependent presynaptic facilitation are both necessary for synaptic plasticity and classical conditioning in Aplysia californica. While research on invertebrates has established fundamental mechanisms of learning and memory, much of the work on long-lasting synaptic changes between vertebrate neurons involves the use of non-physiological experimental stimulation of brain cells. However, some of the physiologically relevant synapse modification mechanisms that have been studied in vertebrate brains do seem to be examples of Hebbian processes. One such review indicates that long-lasting changes in synaptic strengths can be induced by physiologically relevant synaptic activity using both Hebbian and non-Hebbian mechanisms. == Principles == In artificial neurons and artificial neural networks, Hebb's principle can be described as a method of determining how to alter the weights between model neurons. The weight between two neurons increases if the two neurons activate simultaneously, and reduces if they activate separately. Nodes that tend to be either both positive or both negative at the same time have strong positive weights, while those that tend to be opposite have strong negative weights. The following is a formulaic description of Hebbian learning (many other descriptions are possible): w i j = x i x j , {\displaystyle \,w_{ij}=x_{i}x_{j},} where w i j {\displaystyle w_{ij}} is the weight of the connection from neuron j {\displaystyle j} to neuron i {\displaystyle i} , and x i {\displaystyle x_{i}} is the input for neuron i {\displaystyle i} . This is an example of pattern learning, where weights are updated after every training example. In a Hopfield network, connections w i j {\displaystyle w_{ij}} are set to zero if i = j {\displaystyle i=j} (no reflexive connections allowed). With binary neurons (activations either 0 or 1), connections would be set to 1 if the connected neurons have the same activation for a pattern. When several training patterns are used, the expression becomes an average of the individuals: w i j = 1 p ∑ k = 1 p x i k x j k , {\displaystyle w_{ij}={\frac {1}{p}}\sum _{k=1}^{p}x_{i}^{k}x_{j}^{k},} where w i j {\displaystyle w_{ij}} is the weight of the connection from neuron j {\displaystyle j} to neuron i {\displaystyle i} , p {\displaystyle p} is the number of training patterns and x i k {\displaystyle x_{i}^{k}} the k {\displaystyle k} -th input for neuron i {\displaystyle i} . This is learning by epoch, with weights updated after all the training examples are presented and is last term applicable to both discrete and continuous training sets. Again, in a Hopfield network, connections w i j {\displaystyle w_{ij}} are set to zero if i = j {\displaystyle i=j} (no reflexive connections). A variation of Hebbian learning that takes into account phenomena such as blocking and other neural learning phenomena is the mathematical model of Harry Klopf. Klopf's model assumes that parts of a system with simple adaptive mechanisms can underlie more complex systems with more advanced adaptive behavior, such as neural networks. == Relationship to unsupervised learning, stability, and generalization == Because of the simple nature of Hebbian learning, based only on the coincidence of pre- and post-synaptic activity, it may not be intuitively clear why this form of plasticity leads to meaningful learning. However, it can be shown that Hebbian plasticity does pick up the statistical properties of the input in a way that can be categorized as unsupervised learning. This can be mathematically shown in a simplified example. Let us work under the simplifying assumption of a single rate-based neuron of rate y ( t ) {\displaystyle y(t)} , whose inputs have rates x 1 ( t ) . . . x N ( t ) {\displaystyle x_{1}(t)...x_{N}(t)} . The response of the neuron y ( t ) {\displaystyle y(t)} is usually described as a linear combination of its input, ∑ i w i x i {\displaystyle \sum _{i}w_{i}x_{i}} , followed by a response function f {\displaystyle f} : y = f ( ∑ i = 1 N w i x i ) . {\displaystyle y=f\left(\sum _{i=1}^{N}w_{i}x_{i}\right).} As defined in the previous sections, Hebbian plasticity describes the evolution in time of the synaptic weight w {\displaystyle w} : d w i d t = η x i y . {\displaystyle {\frac {dw_{i}}{dt}}=\eta x_{i}y.} Assuming, for simplicity, an identity response function f ( a ) = a {\displaystyle f(a)=a} , we can write d w i d t = η x i ∑ j = 1 N w j x j {\displaystyle {\frac {dw_{i}}{dt}}=\eta x_{i}\sum _{j=1}^{N}w_{j}x_{j}} or in matrix form: d w d t = η x x T w . {\displaystyle {\frac {d\mathbf {w} }{dt}}=\eta \mathbf {x} \mathbf {x} ^{T}\mathbf {w} .} As in the previous chapter, if training by epoch is done an average ⟨ … ⟩ {\displaystyle \langle \dots \rangle } over discrete or continuous (time) training set of x {\displaystyle \mathbf {x} } can be done: d w d t = ⟨ η x x T w ⟩ = η ⟨ x x T ⟩ w = η C w . {\displaystyle {\frac {d\mathbf {w} }{dt}}=\langle \eta \mathbf {x} \mathbf {x} ^{T}\mathbf {w} \rangle =\eta \langle \mathbf {x} \mathbf {x} ^{T}\rangle \mathbf {w} =\eta C\mathbf {w} .} where C = ⟨ x x T ⟩ {\displaystyle C=\langle \,\mathbf {x} \mathbf {x} ^{T}\rangle } is the correlation matrix of the input under the additional assumption that ⟨ x ⟩ = 0 {\displaystyle \langle \mathbf

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