AI Headshot Generator For Linkedin

AI Headshot Generator For Linkedin — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Jaggies

  Jaggies are visual artifacts in raster images, most frequently from aliasing, which in turn is often caused by non-linear mixing effects producing high-frequency components, or missing or poor anti-aliasing filtering prior to sampling. Jaggies are stair-like lines that appear where there should be "smooth" straight lines or curves. For example, when a nominally straight, un-aliased line steps across one pixel either horizontally or vertically, a "dogleg" occurs halfway through the line, where it crosses the threshold from one pixel to the other. Jaggies should not be confused with most compression artifacts, which are a different phenomenon. == Causes == Jaggies occur due to the "staircase effect". This is because a line represented in raster mode is approximated by a sequence of pixels. Jaggies can occur for a variety of reasons, the most common being that the output device (display monitor or printer) does not have sufficient resolution to portray a smooth line. In addition, jaggies often occur when a bit-mapped image is scaled to a higher resolution. This is one of the advantages that vector graphics have over bitmapped graphics – a vector image can be losslessly scaled to any arbitrary resolution or stretched infinitely in either axis without introducing jaggies. == Solutions == The effect of jaggies can be reduced by a graphics technique known as spatial anti-aliasing. Anti-aliasing smooths out jagged lines by surrounding them with transparent pixels to simulate the appearance of fractionally-filled pixels when viewed at a distance. The downside of anti-aliasing is that it reduces contrast – rather than sharp black/white transitions, there are shades of gray – and the resulting image can appear fuzzy. This is an inescapable trade-off: if the resolution is insufficient to display the desired detail, the output will either be jagged, fuzzy, or some combination thereof. While machine learning-based upscaling techniques such as DLSS can be used to infer this missing information, other types of artifacts may be introduced in the process. In real-time 3D rendering such as in video games, various anti-aliasing techniques are used to remove jaggies created by the edges of polygons and other contrasting lines. Since anti-aliasing can impose a significant performance overhead, games for home computers often allow users to choose the level and type of anti-aliasing in use in order to optimize their experience, whereas on consoles this setting is typically fixed for each title to ensure a consistent experience. While anti-aliasing is generally implemented through graphics APIs like DirectX and Vulkan, some consoles such as the Xbox 360 and PlayStation 3 are also capable of anti-aliasing to little direct performance cost by way of dedicated hardware which performs anti-aliasing on the contents of the framebuffer once it has been rendered by the GPU. Jaggies in bitmaps, such as sprites and surface materials, are most often dealt with by separate texture filtering routines, which are far easier to perform than anti-aliasing filtering. Texture filtering became ubiquitous on PCs after the introduction of 3Dfx's Voodoo GPU. == Notable uses of the term == In the 1985 game Rescue on Fractalus! for the Atari 8-bit computers, the graphics depicting the cockpit of the player's spacecraft contains two window struts, which are not anti-aliased and are therefore very "jagged". The developers made fun of this and named the in-game enemies "Jaggi", and also initially titled the game Behind Jaggi Lines!. The latter idea was scrapped by the marketing department before release.

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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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  Is an AI Voice Assistant Worth It in 2026?

  Trying to pick the best AI voice assistant? An AI voice assistant is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI voice assistant slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.

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  AI Subtitle Generators: Free vs Paid (2026)

  Looking for the best AI subtitle generator? An AI subtitle generator 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 subtitle generator 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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  Soterml

  SoTerML (Soil and Terrain Markup Language) is a XML-based markup language for storing and exchanging soil and terrain related data. SoTerML development is being done within The e-SoTer Platform. GEOSS plans a global Earth Observation System and, within this framework, the e-SOTER project addresses the felt need for a global soil and terrain database. The Centre for Geospatial Science (Currently Nottingham Geospatial Institute) at the University of Nottingham has initiated the development since January 2009. Further development and maintenance is currently handled in National Soil Resources Institute (NSRI) at Cranfield University, UK. The role of CGS is within the development of the e-SOTER dissemination platform, which is based on INSPIRE principles. The SoTerML development included: 1. Development of a data dictionary for nomenclatures and various data sources (data and metadata). 2. Development of an exchange format/procedures from the World Reference Base 2006.

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  Bob Coecke

  Bob Coecke (born 23 July 1968) is a Belgian theoretical physicist and logician. He was Professor of Quantum foundations, Logics, and Structures at Oxford University until 2020. He was Chief Scientist at quantum computing company Quantinuum, until 2025 and founded a startup called Relational Intelligence in 2026. He is also Distinguished Visiting Research Chair at the Perimeter Institute for Theoretical Physics, and Emeritus Fellow at Wolfson College, Oxford. He pioneered categorical quantum mechanics (entry 18M40 in Mathematics Subject Classification 2020), Quantum Picturalism, ZX-calculus, DisCoCat model for natural language,, quantum natural language processing (QNLP) and quantum education through the book Quantum in Pictures. He is a founder of the Quantum Physics and Logic community and the Applied Category Theory communities and conference series, and of the journal Compositionality. Coecke is also a composer and musician, who has been called a pioneer of industrial music, and is also one of the pioneers of employing quantum computers in music. == Education and career == Coecke obtained his doctorate in sciences at the Vrije Universiteit Brussel in 1996, and performed postdoctoral work in the Theoretical Physics Group of Imperial College, London in the Category Theory Group of the Mathematics and Statistics Department at McGill University in Montreal, in the Department of Pure Mathematics and Mathematical Statistics of Cambridge University, and in the Department of Computer Science, University of Oxford. He was an EPSRC Advanced Research Fellow at the Department of Computer Science, University of Oxford, where he became Lecturer in Quantum Computer Science in 2007, and jointly with Samson Abramsky built and headed the Quantum Group. In July 2011, he was nominated professor of Quantum Foundations, Logics and Structures at Oxford University, with retroactive effect as of October 2010. He was a Governing Body Fellow of Wolfson College, Oxford since 2007, where he now is an Emeritus Fellow. In January 2019, Coecke became Senior Scientific Advisor of Cambridge Quantum Computing, and in January 2021 he resigned from his Professorship at Oxford, to become Chief Scientist of Cambridge Quantum Computing. After the merger of Cambridge Quantum Computing with Honeywell Quantum Systems, he stayed on as Chief Scientist of the joint entity Quantinuum until 2025. In January 2023 he also became Distinguished Visiting Research Chair at the Perimeter Institute for Theoretical Physics. == Work == Coecke's research focuses on the foundations of physics, more particularly category theory, logic, and diagrammatic reasoning, with application to quantum informatics, quantum gravity, and NLP. He has pioneered categorical quantum mechanics together with Samson Abramsky, and spearheaded the development of a diagrammatic quantum formalism based on Penrose graphical notation, on which he wrote a textbook entitled Picturing Quantum Processes with Aleks Kissinger. With Ross Duncan he pioneered ZX-calculus. He pioneered the DisCoCat model for natural language, with Stephen Clark and Mehrnoosh Sadrzadeh. He also pioneered quantum natural language processing (QNLP), with Will Zeng, and colleagues at Cambridge Quantum Computing. == Music == Coecke is also a musician, performing and recording since the eighties. He retrospectively has been named a pioneer of industrial music. His band, Black Tish, "used cutting edge sampling techniques for the time, a host of synth and sound loops and metal-style guitars to create a heavy rock/electronica fusion unlike anything heard before", and "bridge the gap between the pure experimental nature of bands like Throbbing Gristle and Einstürzende Neubauten and the (comparatively) more radio accessible Ministry or Nine Inch Nails". Coecke is also one of the pioneers of employing quantum computers in music. == Selected publications == Textbooks Bob Coecke, Aleks Kissinger:Picturing Quantum Processes. A First Course in Quantum Theory and Diagrammatic Reasoning, Cambridge University Press, 2017, ISBN 978-1316219317 Bob Coecke, Stefano Gogioso:Quantum in Pictures, Quantinuum, 2022, ISBN 978-1-7392147-1-5 Books (as editor) Bob Coecke, David Moore, Alexander Wilce (eds.): Current Research in Operational Quantum Logic: Algebras, Categories, Languages, Fundamental Theories of Physics, Kluwer Academic, 2010, ISBN 978-9048154371 Bob Coecke (ed.): New Structures for Physics, Lecture Notes in Physics 813, Springer, 2011, ISBN 978-3642128202 Articles Bob Coecke: Kindergarten quantum mechanics, arXiv:quant-ph/0510032 Samson Abramsky, Bob Coecke: A categorical semantics of quantum protocols, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004, pp. 415–425 Bob Coecke, Ross Duncan: Interacting quantum observables, Automata, Languages and Programming, pp. 298–310, 2008 Konstantinos Meichanetzidis, Alexis Toumi, Giovanni de Felice, Bob Coecke: Grammar-Aware Question-Answering on Quantum Computers, arXiv:2012.03756 Bob Coecke: The Mathematics of Text Structure, arXiv:1904.03478 Will Zeng, Bob Coecke: Quantum Algorithms for Compositional Natural Language Processing, arXiv:1608.01406 Bob Coecke, Tobias Fritz, Robert Spekkens: A mathematical theory of resources, arXiv:1409.5531 Bob Coecke: An Alternative Gospel of structure: order, composition, processes, arxiv:1307.4038 Bob Coecke, Mehrnoosh Sadrzadeh, Steven Clark: Mathematical Foundations for a Compositional Distributional Model of Meaning, arXiv:1003.4394 Bob Coecke: Quantum Picturalism, arXiv:0908.1787 Software articles Eduardo Reck Miranda, Richie Yeung, Anna Pearson, Konstantinos Meichanetzidis, Bob Coecke: A quantum natural language processing approach to musical intelligence, arXiv:2111.06741 Dimitri Kartsaklis, Ian Fan, Richie Yeung, Anna Pearson, Robin Lorenz, Alexis Toumi, Giovanni de Felice, Konstantinos Meichanetzidis, Stephen Clark, Bob Coecke: lambeq: An efficient high-level python library for quantum NLP, arXiv:2110.04236 Giovanni de Felice, Alexis Toumi, Bob Coecke: Discopy: monoidal categories in Python, arXiv:2111.06741

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  Sepp Hochreiter

  Josef "Sepp" Hochreiter (born 14 February 1967) is a German computer scientist. Since 2018 he has led the Institute for Machine Learning at the Johannes Kepler University of Linz after having led the Institute of Bioinformatics from 2006 to 2018. In 2017 he became the head of the Linz Institute of Technology (LIT) AI Lab. Hochreiter is also a founding director of the Institute of Advanced Research in Artificial Intelligence (IARAI). Previously, he was at Technische Universität Berlin, at University of Colorado Boulder, and at the Technical University of Munich. He is a chair of the Critical Assessment of Massive Data Analysis (CAMDA) conference. Hochreiter has made contributions in the fields of machine learning, deep learning and bioinformatics, most notably the development of the long short-term memory (LSTM) neural network architecture, but also in meta-learning, reinforcement learning and biclustering with application to bioinformatics data. == Scientific career == === Long short-term memory (LSTM) === Hochreiter developed the long short-term memory (LSTM) neural network architecture in his diploma thesis in 1991 leading to the main publication in 1997. LSTM overcomes the problem of numerical instability in training recurrent neural networks (RNNs) that prevents them from learning from long sequences (vanishing or exploding gradient). In 2007, Hochreiter and others successfully applied LSTM with an optimized architecture to very fast protein homology detection without requiring a sequence alignment. LSTM networks have also been used in Google Voice for transcription and search, and in the Google Allo chat app for generating response suggestion with low latency. === Other machine learning contributions === Beyond LSTM, Hochreiter has developed "Flat Minimum Search" to increase the generalization of neural networks and introduced rectified factor networks (RFNs) for sparse coding which have been applied in bioinformatics and genetics. Hochreiter introduced modern Hopfield networks with continuous states and applied them to the task of immune repertoire classification. Hochreiter worked with Jürgen Schmidhuber in the field of reinforcement learning on actor-critic systems that learn by "backpropagation through a model". Hochreiter has been involved in the development of factor analysis methods with application to bioinformatics, including FABIA for biclustering, HapFABIA for detecting short segments of identity by descent and FARMS for preprocessing and summarizing high-density oligonucleotide DNA microarrays to analyze RNA gene expression. In 2006, Hochreiter and others proposed an extension of the support vector machine (SVM), the "Potential Support Vector Machine" (PSVM), which can be applied to non-square kernel matrices and can be used with kernels that are not positive definite. Hochreiter and his collaborators have applied PSVM to feature selection, including gene selection for microarray data. == Awards == Hochreiter was awarded the IEEE CIS Neural Networks Pioneer Prize in 2021 for his work on LSTM.

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  Model inversion attack

  Model inversion attack is a type of adversarial machine learning attack where an attacker tries to reconstruct or infer sensitive information about a model's training data by analyzing the outputs of a trained machine learning model. Instead of directly querying the underlying dataset, attackers query the model (usually via APIs or prediction interfaces), and leverage patterns in the model responses to infer properties of the original inputs. These attacks leverage the fact that machine learning models encode statistical information about their training data in their parameters and outputs, which can unintentionally leak private or proprietary information. Depending on the access level to the target model, model inversion attacks can be performed in both black-box and white-box settings. In a generic attack, an adversary makes several queries to a model and leverages the responses (e.g. confidence scores, predictions) to train a surrogate or inversion model that learns to approximate the inverse mapping from outputs to inputs. This process may enable the reconstruction of sensitive attributes, e.g., facial features, medical data, or user behavior patterns, from models trained on such data. The technique has been demonstrated against various models like deep neural networks, classification systems etc. The technique has significant privacy risks in areas like healthcare, finance, biometric identification etc. Mitigation strategies include restricting model access, reducing output granularity, using differential privacy and monitoring anomalous query patterns.

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  SEMAT

  SEMAT (Software Engineering Method and Theory) is an initiative to reshape software engineering such that software engineering qualifies as a rigorous discipline. The initiative was launched in December 2009 by Ivar Jacobson, Bertrand Meyer, and Richard Soley with a call for action statement and a vision statement. The initiative was envisioned as a multi-year effort for bridging the gap between the developer community and the academic community and for creating a community giving value to the whole software community. The work is now structured in four different but strongly related areas: Practice, Education, Theory, and Community. The Practice area primarily addresses practices. The Education area is concerned with all issues related to training for both the developers and the academics including students. The Theory area is primarily addressing the search for a General Theory in Software Engineering. Finally, the Community area works with setting up legal entities, creating websites and community growth. It was expected that the Practice area, the Education area and the Theory area would at some point in time integrate in a way of value to all of them: the Practice area would be a "customer" of the Theory area, and direct the research to useful results for the developer community. The Theory area would give a solid and practical platform for the Practice area. And, the Education area would communicate the results in proper ways. == Practice area == The first step was here to develop a common ground or a kernel including the essence of software engineering – things we always have, always do, always produce when developing software. The second step was envisioned to add value on top of this kernel in the form of a library of practices to be composed to become specific methods, specific for all kinds of reasons such as the preferences of the team using it, kind of software being built, etc. The first step is as of this writing just about to be concluded. The results are a kernel including universal elements for software development – called the Essence Kernel, and a language – called the Essence Language - to describe these elements (and elements built on top of the kernel (practices, methods, and more). Essence, including both the kernel and language, has been published as an OMG standard in beta status in July 2013 and is expected to become a formally adopted standard in early 2014. The second step has just started, and the Practice area will be divided into a number of separate but interconnected tracks: the practice (library track), the tool track are so far identified and work has started or is about to get started. The practice track is currently working on a Users Guide. == Education area == The area focuses on leveraging the work of SEMAT in software engineering education, both within academia and industry. It promotes global education based on a common ground called Essence. The area's target groups are instructors such as university professors and industrial coaches as well as their students and learning practitioners. The goal of the area is to create educational courses and course materials that are internationally viable, identify pedagogical approaches that are appropriate and effective for specific target groups and disseminate experience and lessons learned. The area includes members from a number of universities and institutes worldwide. Most members have already been involved in leveraging aspects of SEMAT in the context of their software engineering courses. They are gathering their resources and starting a common venture towards defining a new generation of SEMAT-powered software engineering curricula. As of 2018, some studies of utilizing Essence in educational settings exist. One example of the use of Essence in university education was a software engineering course carried out in Norwegian University of Science and Technology. A study was conducted by introducing Essence into a project-based software engineering course, with the aim of understanding what difficulties the students faced in using Essence, and whether they considered it to have been useful. The results indicated that Essence could also be useful for novice software engineers by (1) encouraging them to look up and study new practices and methods in order to create their own, (2) encouraging them to adjust their way-of-working reflectively and in a situation-specific manner, (3) helping them structure their way of working. The findings of another study introducing students to Essence through a digital game supported these findings: the students felt that Essence will be useful to them in future, real-world projects, and that they wish to utilize it in them. == Theory area == An important part of SEMAT is that a general theory of software engineering is planned to emerge with significant benefits. A series of workshops held under the title SEMAT Workshop on a General Theory of Software Engineering (GTSE) are a key component in awareness building around general theories. In addition to community awareness building, SEMAT also aims to contribute with a specific general theory of software engineering. This theory should be solidly based on the SEMAT Essence language and kernel, and should support software engineering practitioners' goal-oriented decision making. As argued elsewhere, such support is predicated on the predictive capabilities of the theory. Thus, the SEMAT Essence should be augmented to allow the prediction of critical software engineering phenomena. The GTSE workshop series assists in the development of the SEMAT general software engineering theory by engaging a larger community in the search for, development of, and evaluation of promising theories, which may be used as a base for the SEMAT theory. == Organizational structure == === Main organization === SEMAT is chaired by Sumeet S. Malhotra of Tata Consultancy Services. The CEO of the organization is Ste Nadin of Fujitsu. The Executive Management Committee of SEMAT are Ivar Jacobson, Ste Nadin, Sumeet S. Malhotra, Paul E. McMahon, Michael Goedicke and Cecile Peraire. === Japan Chapter === Japan Chapter was established in April 2013, and it has more than 250 members as of November 2013. Member activities include carrying out seminars about SEMAT, considering utilization of SEMAT Essence for integrating different requirements engineering techniques and body of knowledges (BoKs), and translating articles into Japanese. === Korea Chapter === The chapter was inaugurated with about 50 members in October 2013. Member activities include: 2e Consulting started rewriting their IT service engagement methods using the Essence kernel, and uEngine Solutions started developing a tool to orchestrate Essence-kernel based practices into a project method. Korean government supported KAIST to conduct research in Essence. === Latin American Chapter === Semat Latin American Chapter was created in August 2011 in Medellin (Colombia) by Ivar Jacobson during the Latin American Software Engineering Symposium. This Chapter has 9 Executive Committee members from Colombia, Venezuela, Peru, Brazil, Argentina, Chile, and Mexico, chaired by Dr. Carlos Zapata from Colombia. More than 80 people signed the initial declaration of the Chapter and nowadays the Chapter members are in charge of disseminating the Semat ideas in all Latin America. Chapter members have participated in various Latin American conferences, including the Latin American Conference on Informatics (CLEI), the Ibero American Software Engineering and Knowledge Engineering Journeys (JIISIC), the Colombian Computing Conference (CCC), and the Chilean Computing Meeting (ECC). The Chapter contributed in the submission sent in response to the OMG call for proposals and currently studies didactic strategies for teaching the Semat kernel by games, theoretical studies about some kernel elements, and practical representations of several software development and quality methods by using the Semat kernel. Some of the members also translated the Essence book and some other Semat materials and papers into Spanish. === Russia Chapter === Russian Chapter has about 20 members. A few universities have incorporated SEMAT in their training courses , including Moscow State University, Moscow Institute of Physics and Technology, Higher School of Economics, Moscow State University of Economics, Statistics, and Informatics. The chapter and some commercial companies are carrying out seminars about SEMAT. INCOSE Russian Chapter is working on an extension of SEMAT to systems engineering. EC-leasing is working on an extension of the Kernel for Software Life Cycle. Russian Chapter attended in two conferences: Actual Problems of System and Software Engineering and SECR with SEMAT section and articles. Translation of the Essence book into Russian is in progress. == Practical Applications of SEMAT == Ideas developed by the SEMAT community have been applied by both industry and ac

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  Markov property

  In probability theory and statistics, the Markov property is the memoryless property of a stochastic process, which means that its future evolution is independent of its history. It is named after the Russian mathematician Andrey Markov. The term strong Markov property is similar to the Markov property, except that the meaning of "present" is defined in terms of a random variable known as a stopping time. The term Markov assumption is used to describe a model where the Markov property is assumed to hold, such as a hidden Markov model. A Markov random field extends this property to two or more dimensions or to random variables defined for an interconnected network of items. An example of a model for such a field is the Ising model. A discrete-time stochastic process satisfying the Markov property is known as a Markov chain. == Introduction == A stochastic process has the Markov property if the conditional probability distribution of future states of the process (conditional on both past and present values) depends only upon the present state; that is, given the present, the future does not depend on the past. A process with this property is said to be Markov or Markovian and known as a Markov process. Two famous classes of Markov process are the Markov chain and Brownian motion. Note that there is a subtle, often overlooked and very important point that is often missed in the plain English statement of the definition: the statespace of the process is constant through time. The conditional description involves a fixed "bandwidth". For example, without this restriction we could augment any process to one which includes the complete history from a given initial condition and it would be made to be Markovian. But the state space would be of increasing dimensionality over time and does not meet the definition. == History == == Definition == Let ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} be a probability space with a filtration ( F s , s ∈ I ) {\displaystyle ({\mathcal {F}}_{s},\ s\in I)} , for some (totally ordered) index set I {\displaystyle I} ; and let ( S , Σ ) {\displaystyle (S,\Sigma )} be a measurable space. An ( S , Σ ) {\displaystyle (S,\Sigma )} -valued stochastic process X = { X t : Ω → S } t ∈ I {\displaystyle X=\{X_{t}:\Omega \to S\}_{t\in I}} adapted to the filtration is said to possess the Markov property if, for each A ∈ Σ {\displaystyle A\in \Sigma } and each s , t ∈ I {\displaystyle s,t\in I} with s < t {\displaystyle s Read more →

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  Regular language

  In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to many modern regular expression engines, which are augmented with features that allow the recognition of non-regular languages). Alternatively, a regular language can be defined as a language recognised by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene's theorem (after American mathematician Stephen Cole Kleene). In the Chomsky hierarchy, regular languages are the languages generated by Type-3 grammars. == Formal definition == The collection of regular languages over an alphabet Σ is defined recursively as follows: The empty language ∅ is a regular language. For each a ∈ Σ (a belongs to Σ), the singleton language {a} is a regular language. If A is a regular language, A (Kleene star) is a regular language. Due to this, the empty string language {ε} is also regular. If A and B are regular languages, then A ∪ B (union) and A • B (concatenation) are regular languages. No other languages over Σ are regular. See Regular expression § Formal language theory for syntax and semantics of regular expressions. == Examples == All finite languages are regular; in particular the empty string language {ε} = ∅ is regular. Other typical examples include the language consisting of all strings over the alphabet {a, b} which contain an even number of as, or the language consisting of all strings of the form: several as followed by several bs. A simple example of a language that is not regular is the set of strings {anbn | n ≥ 0}. Intuitively, it cannot be recognized with a finite automaton, since a finite automaton has finite memory and it cannot remember the exact number of a's. Techniques to prove this fact rigorously are given below. == Equivalent formalisms == A regular language satisfies the following equivalent properties: it is the language of a regular expression (by the above definition) it is the language accepted by a nondeterministic finite automaton (NFA) it is the language accepted by a deterministic finite automaton (DFA) it can be generated by a regular grammar it is the language accepted by an alternating finite automaton it is the language accepted by a two-way finite automaton it can be generated by a prefix grammar it can be accepted by a read-only Turing machine it can be defined in monadic second-order logic (Büchi–Elgot–Trakhtenbrot theorem) it is recognized by some finite syntactic monoid M, meaning it is the preimage {w ∈ Σ | f(w) ∈ S} of a subset S of a finite monoid M under a monoid homomorphism f : Σ → M from the free monoid on its alphabet the number of equivalence classes of its syntactic congruence is finite. (This number equals the number of states of the minimal deterministic finite automaton accepting L.) Properties 10. and 11. are purely algebraic approaches to define regular languages; a similar set of statements can be formulated for a monoid M ⊆ Σ. In this case, equivalence over M leads to the concept of a recognizable language. Some authors use one of the above properties different from "1." as an alternative definition of regular languages. Some of the equivalences above, particularly those among the first four formalisms, are called Kleene's theorem in textbooks. Precisely which one (or which subset) is called such varies between authors. One textbook calls the equivalence of regular expressions and NFAs ("1." and "2." above) "Kleene's theorem". Another textbook calls the equivalence of regular expressions and DFAs ("1." and "3." above) "Kleene's theorem". Two other textbooks first prove the expressive equivalence of NFAs and DFAs ("2." and "3.") and then state "Kleene's theorem" as the equivalence between regular expressions and finite automata (the latter said to describe "recognizable languages"). A linguistically oriented text first equates regular grammars ("4." above) with DFAs and NFAs, calls the languages generated by (any of) these "regular", after which it introduces regular expressions which it terms to describe "rational languages", and finally states "Kleene's theorem" as the coincidence of regular and rational languages. Other authors simply define "rational expression" and "regular expressions" as synonymous and do the same with "rational languages" and "regular languages". Apparently, the term regular originates from a 1951 technical report where Kleene introduced regular events and explicitly welcomed "any suggestions as to a more descriptive term". Noam Chomsky, in his 1959 seminal article, used the term regular in a different meaning at first (referring to what is called Chomsky normal form today), but noticed that his finite state languages were equivalent to Kleene's regular events. == Closure properties == The regular languages are closed under various operations, that is, if the languages K and L are regular, so is the result of the following operations: the set-theoretic Boolean operations: union K ∪ L, intersection K ∩ L, and complement L, hence also relative complement K − L. the regular operations: K ∪ L, concatenation ⁠ K ∘ L {\displaystyle K\circ L} ⁠, and Kleene star L. the trio operations: string homomorphism, inverse string homomorphism, and intersection with regular languages. As a consequence they are closed under arbitrary finite state transductions, like quotient K / L with a regular language. Even more, regular languages are closed under quotients with arbitrary languages: If L is regular then L / K is regular for any K. the reverse (or mirror image) LR. Given a nondeterministic finite automaton to recognize L, an automaton for LR can be obtained by reversing all transitions and interchanging starting and finishing states. This may result in multiple starting states; ε-transitions can be used to join them. == Decidability properties == Given two deterministic finite automata A and B, it is decidable whether they accept the same language. As a consequence, using the above closure properties, the following problems are also decidable for arbitrarily given deterministic finite automata A and B, with accepted languages LA and LB, respectively: Containment: is LA ⊆ LB ? Disjointness: is LA ∩ LB = {} ? Emptiness: is LA = {} ? Universality: is LA = Σ ? Membership: given a ∈ Σ, is a ∈ LB ? For regular expressions, the universality problem is NP-complete already for a singleton alphabet. For larger alphabets, that problem is PSPACE-complete. If regular expressions are extended to allow also a squaring operator, with "A2" denoting the same as "AA", still just regular languages can be described, but the universality problem has an exponential space lower bound, and is in fact complete for exponential space with respect to polynomial-time reduction. For a fixed finite alphabet, the theory of the set of all languages – together with strings, membership of a string in a language, and for each character, a function to append the character to a string (and no other operations) – is decidable, and its minimal elementary substructure consists precisely of regular languages. For a binary alphabet, the theory is called S2S. == Complexity results == In computational complexity theory, the complexity class of all regular languages is sometimes referred to as REGULAR or REG and equals DSPACE(O(1)), the decision problems that can be solved in constant space (the space used is independent of the input size). REGULAR ≠ AC0, since it (trivially) contains the parity problem of determining whether the number of 1 bits in the input is even or odd and this problem is not in AC0. On the other hand, REGULAR does not contain AC0, because the nonregular language of palindromes, or the nonregular language { 0 n 1 n : n ∈ N } {\displaystyle \{0^{n}1^{n}:n\in \mathbb {N} \}} can both be recognized in AC0. If a language is not regular, it requires a machine with at least Ω(log log n) space to recognize (where n is the input size). In other words, DSPACE(o(log log n)) equals the class of regular languages. In practice, most nonregular problems are studied in a setting with at least logarithmic space, as this is the amount of space required to store a pointer into the input tape. == Location in the Chomsky hierarchy == To locate the regular languages in the Chomsky hierarchy, one notices that every regular language is context-free. The converse is not true: for example, the language consisting of all strings having the same number of as as bs is context-free but not regular. To prove that a language is not regular, one often uses the Myhill–Nerode theorem and the pumping lemma. Other approaches include using the closure properties of regular languages or quantifying Kolmogorov complexity. Important subclasses of regular languages include: Finite languages, those containing only a finite number of words. These are regular la

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  Ali Farhadi

  Ali Farhadi is a professor of computer science and currently serves as the CEO of the Allen Institute for Artificial Intelligence (AI2). == Career == Farhadi is an AI professor in the Paul G. Allen School of Computer Science & Engineering at the University of Washington in Seattle. == Recognitions == Among other awards and recognitions, Farhadi was one of the winners of the 2017 Sloan Research Fellowship granted by the Alfred P. Sloan Foundation. == Personal life == Farhadi is married to Hanna Hajishirzi, a computer science professor at the University of Washington and senior director at the Allen Institute who studies natural language processing.

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  Continuum robot

  A continuum robot is a type of robot that is characterised by infinite degrees of freedom and number of joints. These characteristics allow continuum manipulators to adjust and modify their shape at any point along their length, granting them the possibility to work in confined spaces and complex environments where standard rigid-link robots cannot operate. In particular, we can define a continuum robot as an actuatable structure whose constitutive material forms curves with continuous tangent vectors. This is a fundamental definition that allows to distinguish between continuum robots and snake-arm robots or hyper-redundant manipulators: the presence of rigid links and joints allows them to only approximately perform curves with continuous tangent vectors. The design of continuum robots is bioinspired, as the intent is to resemble biological trunks, snakes and tentacles. Several concepts of continuum robots have been commercialised and can be found in many different domains of application, ranging from the medical field to undersea exploration. == Classification == Continuum robots can be categorised according to two main criteria: structure and actuation. === Structure === The main characteristic of the design of continuum robots is the presence of a continuously curving core structure, named backbone, whose shape can be actuated. The backbone must also be compliant, meaning that the backbone yields smoothly to external loads. According to the design principles chosen for the continuum manipulator, we can distinguish between: single-backbone: these continuum manipulators have one central elastic backbone through which actuation/transmission elements can run. multi-backbone: the structure of these continuum robots has two or more elastic elements (either rods or tubes) parallel to each other and constrained with one another in some way. concentric-tube: the backbone is made of concentric tubes that are free to rotate and translate between each other, depending on the actuation happening at the base of the robot. === Actuation === The actuation strategy of continuum manipulators can be distinguished between extrinsic or intrinsic actuation, depending on where the actuation happens: extrinsic actuation: the actuation happens outside the main structure of the robot and the forces are transmitted via mechanical transmission; among these techniques, there are cable/tendon driven actuators and multi-backbone strategies. intrinsic actuation: the actuation mechanism operates within the structure of the robot; these strategies include pneumatic or hydraulic chambers and the shape memory effect. The Actuated Flexible Manifold (AFM), introduced by Medina, Shapiro, and Shvalb (2016), models flexible grid-based robots that approximate smooth manifolds using discrete segments, each contributing one degree of freedom. Their work provides forward and inverse kinematics for planar and spatial configurations, bridging hyper-redundant and continuum robotics. == Advantages == The particular design of continuum robots offers several advantages with respect to rigid-link robots. First of all, as already said, continuum robots can more easily operate in environments that require a high level of dexterity, adaptability and flexibility. Moreover, the simplicity of their structure makes continuum robots more prone to miniaturisation. The rise of continuum robots has also paved the way for the development of soft continuum manipulators. These continuum manipulators are made of highly compliant materials that are flexible and can adapt and deform according to the surrounding environment. The "softness" of their material grants higher safety in human-robot interactions. == Disadvantages == The particular design of continuum robots also introduces many challenges. To properly and safely use continuum robots, it is crucial to have an accurate force and shape sensing system. Traditionally, this is done using cameras that are not suitable for some of the applications of continuum robots (e.g. minimally invasive surgery), or using electromagnetic sensors that are however disturbed by the presence of magnetic objects in the environment. To solve this issue, in the last years fiber-Bragg-grating sensors have been proposed as a possible alternative and have shown promising results. It is also necessary to notice that while the mechanical properties of rigid-link robots are fully understood, the comprehension of the behaviour and properties of continuum robots is still subject of study and debate. This poses new challenges in developing accurate models and control algorithms for this kind of robots. == Modelling == Creating an accurate model that can predict the shape of a continuum robot allows to properly control the robot's shape. There are three main approaches to model continuum robots: Cosserat rod theory: this approach is an exact solution to the static of a continuum robot, as it is not subject to any assumption. It solves a set of equilibrium equations between position, orientation, internal force and torque of the robot. This method requires to be solved numerically and it is therefore computationally expensive, due to its high complexity. Constant curvature: this technique assumes the backbone to be made of a series of mutually tangent sections that can be approximated as arcs with constant curvature. This approach is also known as piecewise constant-curvature. This assumption can be applied to the entire segment of the backbone or to its subsegments. This model has shown promising results, however it must be taken into account that the segment/subsegments of the backbone may not comply to the constant curvature assumption and therefore the model's behaviour may not entirely reflect the behaviour of the robot. Rigid-link model: this approach is based on the assumption that the continuum robot can be divided in small segments with rigid links. This is a strong assumption, since if the number of segments is too low, the model hardly behaves like the continuum robot, while increasing the number of segments means increasing the number of variables, and thus complexity. Despite this limitation, rigid-link modelling allows the use of the standard control techniques that are well known for rigid-link robots. It has been proven that this model can be coupled with shape and force sensing to mitigate its inaccuracy and can lead to promising results. == Sensing == To develop accurate control algorithms, it is necessary to complement the presented modelling techniques with real time shape sensing. The following options are currently available: Electromagnetic (EM) sensing: shape is reconstructed thanks to the mutual induction between a magnetic field generator and a magnetic field sensor. The most common external EM tracking system is the commercially available NDI Aurora: small sensors can be placed on the robot and their position is tracked in an external generated magnetic field. The validity of this method has been extensively assessed, however its performance is hindered by the limited workspace, whose dimension depends on the magnetic field. Another alternative is to embed the sensors internally in the continuum robot, combining magnetic sensors with Hall effect sensors: the magnetic field is measured at the level of the Hall effect sensors in order to estimate the deflection of the robot. However, it has been noticed that the higher the bending of the manipulator, the higher is the estimation error, due to crosstalk between sensors and magnets. Optical sensing: fiber Bragg grating sensors incorporated in an optical fiber can be embedded into the backbone of the continuum robot to estimate its shape; these sensors can only reflect a small range of the input light spectrum depending on their strain; therefore, by measuring the strain on each sensor it is possible to obtain the shape of the robot. This type of sensor is however expensive and is more prone to breaking in case of excessive strain, and this can happen in robots that can perform high deflections. == Control strategies == The control strategies can be distinguished in static and dynamic; the first one is based on the steady-state assumption, while the latter also considers the dynamic behaviour of the continuum robot. We can also differentiate between model-based controllers, that depend on a model of the robot, and model-free, that learn the robot's behaviour from data. Model-based static controllers: they rely on one of the modelling approaches presented above; once the model is defined, the kinematics must be inverted to obtain the desired actuator or configuration space variables. There are several ways to do this, like differential inverse kinematics, direct inversion or optimization. Model-free static controllers: these approaches learn directly, via machine learning techniques (e.g. regression methods and neural networks), the inverse kinematic or the direct kinematic representation of the con

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  The Best Free AI Chatbot for Beginners

  Trying to pick the best AI chatbot? An AI chatbot is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI chatbot 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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  Noisy channel model

  The noisy channel model is a framework used in spell checkers, question answering, speech recognition, and machine translation. In this model, the goal is to find the intended word given a word where the letters have been scrambled in some manner. == In spell-checking == See Chapter B of. Given an alphabet Σ {\displaystyle \Sigma } , let Σ ∗ {\displaystyle \Sigma ^{}} be the set of all finite strings over Σ {\displaystyle \Sigma } . Let the dictionary D {\displaystyle D} of valid words be some subset of Σ ∗ {\displaystyle \Sigma ^{}} , i.e., D ⊆ Σ ∗ {\displaystyle D\subseteq \Sigma ^{}} . The noisy channel is the matrix Γ w s = Pr ( s | w ) {\displaystyle \Gamma _{ws}=\Pr(s|w)} , where w ∈ D {\displaystyle w\in D} is the intended word and s ∈ Σ ∗ {\displaystyle s\in \Sigma ^{}} is the scrambled word that was actually received. The goal of the noisy channel model is to find the intended word given the scrambled word that was received. The decision function σ : Σ ∗ → D {\displaystyle \sigma :\Sigma ^{}\to D} is a function that, given a scrambled word, returns the intended word. Methods of constructing a decision function include the maximum likelihood rule, the maximum a posteriori rule, and the minimum distance rule. In some cases, it may be better to accept the scrambled word as the intended word rather than attempt to find an intended word in the dictionary. For example, the word schönfinkeling may not be in the dictionary, but might in fact be the intended word. === Example === Consider the English alphabet Σ = { a , b , c , . . . , y , z , A , B , . . . , Z , . . . } {\displaystyle \Sigma =\{a,b,c,...,y,z,A,B,...,Z,...\}} . Some subset D ⊆ Σ ∗ {\displaystyle D\subseteq \Sigma ^{}} makes up the dictionary of valid English words. There are several mistakes that may occur while typing, including: Missing letters, e.g., leter instead of letter Accidental letter additions, e.g., misstake instead of mistake Swapping letters, e.g., recieved instead of received Replacing letters, e.g., fimite instead of finite To construct the noisy channel matrix Γ {\displaystyle \Gamma } , we must consider the probability of each mistake, given the intended word ( Pr ( s | w ) {\displaystyle \Pr(s|w)} for all w ∈ D {\displaystyle w\in D} and s ∈ Σ ∗ {\displaystyle s\in \Sigma ^{}} ). These probabilities may be gathered, for example, by considering the Damerau–Levenshtein distance between s {\displaystyle s} and w {\displaystyle w} or by comparing the draft of an essay with one that has been manually edited for spelling. == In machine translation == One naturally wonders if the problem of translation could conceivably be treated as a problem in cryptography. When I look at an article in Russian, I say: 'This is really written in English, but it has been coded in some strange symbols. I will now proceed to decode. See chapter 1, and chapter 25 of. Suppose we want to translate a foreign language to English, we could model P ( E | F ) {\displaystyle P(E|F)} directly: the probability that we have English sentence E given foreign sentence F, then we pick the most likely one E ^ = arg ⁡ max E P ( E | F ) {\displaystyle {\hat {E}}=\arg \max _{E}P(E|F)} . However, by Bayes law, we have the equivalent equation: E ^ = argmax E ∈ English P ( F ∣ E ) ⏞ translation model P ( E ) ⏞ language model {\displaystyle {\hat {E}}={\underset {E\in {\text{ English }}}{\operatorname {argmax} }}\overbrace {P(F\mid E)} ^{\text{translation model }}\overbrace {P(E)} ^{\text{language model}}} The benefit of the noisy-channel model is in terms of data: If collecting a parallel corpus is costly, then we would have only a small parallel corpus, so we can only train a moderately good English-to-foreign translation model, and a moderately good foreign-to-English translation model. However, we can collect a large corpus in the foreign language only, and a large corpus in the English language only, to train two good language models. Combining these four models, we immediately get a good English-to-foreign translator and a good foreign-to-English translator. The cost of noisy-channel model is that using Bayesian inference is more costly than using a translation model directly. Instead of reading out the most likely translation by arg ⁡ max E P ( E | F ) {\displaystyle \arg \max _{E}P(E|F)} , it would have to read out predictions by both the translation model and the language model, multiply them, and search for the highest number. == In speech recognition == Speech recognition can be thought of as translating from a sound-language to a text-language. Consequently, we have T ^ = argmax T ∈ Text P ( S ∣ T ) ⏞ speech model P ( T ) ⏞ language model {\displaystyle {\hat {T}}={\underset {T\in {\text{ Text }}}{\operatorname {argmax} }}\overbrace {P(S\mid T)} ^{\text{speech model }}\overbrace {P(T)} ^{\text{language model}}} where P ( S | T ) {\displaystyle P(S|T)} is the probability that a speech sound S is produced if the speaker is intending to say text T. Intuitively, this equation states that the most likely text is a text that's both a likely text in the language, and produces the speech sound with high probability. The utility of the noisy-channel model is not in capacity. Theoretically, any noisy-channel model can be replicated by a direct P ( T | S ) {\displaystyle P(T|S)} model. However, the noisy-channel model factors the model into two parts which are appropriate for the situation, and consequently it is generally more well-behaved. When a human speaks, it does not produce the sound directly, but first produces the text it wants to speak in the language centers of the brain, then the text is translated into sound by the motor cortex, vocal cords, and other parts of the body. The noisy-channel model matches this model of the human, and so it is appropriate. This is justified in the practical success of noisy-channel model in speech recognition. === Example === Consider the sound-language sentence (written in IPA for English) S = aɪ wʊd laɪk wʌn tuː. There are three possible texts T 1 , T 2 , T 3 {\displaystyle T_{1},T_{2},T_{3}} : T 1 = {\displaystyle T_{1}=} I would like one to. T 2 = {\displaystyle T_{2}=} I would like one too. T 3 = {\displaystyle T_{3}=} I would like one two. that are equally likely, in the sense that P ( S | T 1 ) = P ( S | T 2 ) = P ( S | T 3 ) {\displaystyle P(S|T_{1})=P(S|T_{2})=P(S|T_{3})} . With a good English language model, we would have P ( T 2 ) > P ( T 1 ) > P ( T 3 ) {\displaystyle P(T_{2})>P(T_{1})>P(T_{3})} , since the second sentence is grammatical, the first is not quite, but close to a grammatical one (such as "I would like one to [go]."), while the third one is far from grammatical. Consequently, the noisy-channel model would output T 2 {\displaystyle T_{2}} as the best transcription.

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