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  Wrike

  Wrike, Inc. is an American project management application service provider based in San Jose, California. Wrike also has offices in India, Dallas, Tallinn, Nicosia, Dublin, Tokyo, Melbourne, and Prague. == History == Wrike was founded in 2006 by Andrew Filev. Currently CEO at Wrike is Thomas Scott. Filev initially self-funded the company before later obtaining investor funding. Wrike released the beta version of its software (also called Wrike) in December 2006. The company then launched a new "Enterprise" platform in December 2013. In June 2015, Wrike announced the opening of an office in Dublin, Ireland and in 2016, Wrike launched a datacenter there to host data in compliance with local privacy regulations. In July 2016, Wrike announced the launch of Wrike for Marketers. That same year, Wrike's headquarters moved from Mountain View to San Jose, California. In January 2021, Citrix Systems announced its intention to acquire Wrike for $2.25 billion. The acquisition closed in March 2021. On January 31, 2022, it was announced that Citrix had been acquired in a $16.5 billion deal by affiliates of Vista Equity Partners and Evergreen Coast Capital. Citrix would merge with TIBCO Software, a Vista portfolio company to form Cloud Software Group (CSG). In September 2022, Wrike separated from Citrix Systems. In July 2023, Vista transferred ownership to Symphony Technology Group. == Investments == Wrike received $1 million in Angel funding in 2012 from TMT Investments. In October, 2013, Wrike secured $10 million in investment funding from Bain Capital. In May 2015, the company secured $15 million in a new round of funding. Investors included Scale Venture Partners, DCM Ventures, and Bain Capital. At that time, Wrike had 8,000 customers, 200 employees, and 30,000 new users each month. On November 29, 2018, Wrike signed a definitive agreement to receive a majority investment by Vista Equity Partners (“Vista”), a firm focused on software, data and technology-enabled businesses. == Software == The Wrike project management software is a Software-as-a-Service (SaaS) product with tools for managing projects, deadlines, schedules, and workflow processes. It includes collaboration features. The application is available in English, French, Spanish, German, Portuguese, Italian, Japanese and Russian. Wrike has triggers for task automation in workflow management. === Features === Wrike features a multi-pane UI and consists of features in two categories: project management, and team collaboration. According to Wrike, project management features are designed to help teams track dates and dependencies associated with projects, manage assignments and resources, and track time. These include an interactive Gantt chart, a workload view, and a sortable table that can be customized to store project data. The software includes a co-editing tool, discussion threads on tasks, and tools for attaching documents, editing them, and tracking their changes. Wrike uses an "inbox" feature and browser notifications to alert users of updates from their colleagues and dashboards for quick overviews of pending tasks. These updates are also available in Wrike's mobile apps on iOS and Android. Wrike has an optional feature set called "Wrike for Marketers" which has several tools for managing marketing workflows. In May 2012, Wrike announced the launch of a freemium version of its software for teams of up to 5 users. That year also saw the integration of a live text coeditor into its workspace to unify collaboration and task management. In late 2013 Wrike released a new feature set called Wrike Enterprise which included advanced analytics and other tools targeted at large business customers. Since then it has released several major updates to Wrike Enterprise, including a customizable spreadsheet called "Dynamic Platform" in late 2014 and custom workflows for teams in 2015. In July 2016, Wrike was updated with a set of add-on features under the name "Wrike for Marketers," which includes integrations with Adobe Photoshop, a tool for submitting requests, and proofing and approval tools for creative assets like videos and images. Wrike is available as native Android and iOS apps. Mobile apps include an interactive Gantt chart that syncs across devices. The apps are available offline, and sync when connection is restored. === Criticism === Critics said new users may have a learning curve with complex features. Wrike has 2,710 customers for an estimated 0.04% market share. Competitors include Google Workspace, Slack (software), and Quip (software).

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  Models of DNA evolution

  A number of different Markov models of DNA sequence evolution have been proposed. These substitution models differ in terms of the parameters used to describe the rates at which one nucleotide replaces another during evolution. These models are frequently used in molecular phylogenetic analyses. In particular, they are used during the calculation of likelihood of a tree (in Bayesian and maximum likelihood approaches to tree estimation) and they are used to estimate the evolutionary distance between sequences from the observed differences between the sequences. == Introduction == These models are phenomenological descriptions of the evolution of DNA as a string of four discrete states. These Markov models do not explicitly depict the mechanism of mutation nor the action of natural selection. Rather they describe the relative rates of different changes. For example, mutational biases and purifying selection favoring conservative changes are probably both responsible for the relatively high rate of transitions compared to transversions in evolving sequences. However, the Kimura (K80) model described below only attempts to capture the effect of both forces in a parameter that reflects the relative rate of transitions to transversions. Evolutionary analyses of sequences are conducted on a wide variety of time scales. Thus, it is convenient to express these models in terms of the instantaneous rates of change between different states (the Q matrices below). If we are given a starting (ancestral) state at one position, the model's Q matrix and a branch length expressing the expected number of changes to have occurred since the ancestor, then we can derive the probability of the descendant sequence having each of the four states. The mathematical details of this transformation from rate-matrix to probability matrix are described in the mathematics of substitution models section of the substitution model page. By expressing models in terms of the instantaneous rates of change we can avoid estimating a large numbers of parameters for each branch on a phylogenetic tree (or each comparison if the analysis involves many pairwise sequence comparisons). The models described on this page describe the evolution of a single site within a set of sequences. They are often used for analyzing the evolution of an entire locus by making the simplifying assumption that different sites evolve independently and are identically distributed. This assumption may be justifiable if the sites can be assumed to be evolving neutrally. If the primary effect of natural selection on the evolution of the sequences is to constrain some sites, then models of among-site rate-heterogeneity can be used. This approach allows one to estimate only one matrix of relative rates of substitution, and another set of parameters describing the variance in the total rate of substitution across sites. == DNA evolution as a continuous-time Markov chain == === Continuous-time Markov chains === Continuous-time Markov chains have the usual transition matrices which are, in addition, parameterized by time, t {\displaystyle t} . Specifically, if E 1 , E 2 , E 3 , E 4 {\displaystyle E_{1},E_{2},E_{3},E_{4}} are the states, then the transition matrix P ( t ) = ( P i j ( t ) ) {\displaystyle P(t)={\big (}P_{ij}(t){\big )}} where each individual entry, P i j ( t ) {\displaystyle P_{ij}(t)} refers to the probability that state E i {\displaystyle E_{i}} will change to state E j {\displaystyle E_{j}} in time t {\displaystyle t} . Example: We would like to model the substitution process in DNA sequences (i.e. Jukes–Cantor, Kimura, etc.) in a continuous-time fashion. The corresponding transition matrices will look like: P ( t ) = ( p A A ( t ) p A G ( t ) p A C ( t ) p A T ( t ) p G A ( t ) p G G ( t ) p G C ( t ) p G T ( t ) p C A ( t ) p C G ( t ) p C C ( t ) p C T ( t ) p T A ( t ) p T G ( t ) p T C ( t ) p T T ( t ) ) {\displaystyle P(t)={\begin{pmatrix}p_{\mathrm {AA} }(t)&p_{\mathrm {AG} }(t)&p_{\mathrm {AC} }(t)&p_{\mathrm {AT} }(t)\\p_{\mathrm {GA} }(t)&p_{\mathrm {GG} }(t)&p_{\mathrm {GC} }(t)&p_{\mathrm {GT} }(t)\\p_{\mathrm {CA} }(t)&p_{\mathrm {CG} }(t)&p_{\mathrm {CC} }(t)&p_{\mathrm {CT} }(t)\\p_{\mathrm {TA} }(t)&p_{\mathrm {TG} }(t)&p_{\mathrm {TC} }(t)&p_{\mathrm {TT} }(t)\end{pmatrix}}} where the top-left and bottom-right 2 × 2 blocks correspond to transition probabilities and the top-right and bottom-left 2 × 2 blocks corresponds to transversion probabilities. Assumption: If at some time t 0 {\displaystyle t_{0}} , the Markov chain is in state E i {\displaystyle E_{i}} , then the probability that at time t 0 + t {\displaystyle t_{0}+t} , it will be in state E j {\displaystyle E_{j}} depends only upon i {\displaystyle i} , j {\displaystyle j} and t {\displaystyle t} . This then allows us to write that probability as p i j ( t ) {\displaystyle p_{ij}(t)} . Theorem: Continuous-time transition matrices satisfy: P ( t + τ ) = P ( t ) P ( τ ) {\displaystyle P(t+\tau )=P(t)P(\tau )} Note: There is here a possible confusion between two meanings of the word transition. (i) In the context of Markov chains, transition is the general term for the change between two states. (ii) In the context of nucleotide changes in DNA sequences, transition is a specific term for the exchange between either the two purines (A ↔ G) or the two pyrimidines (C ↔ T) (for additional details, see the article about transitions in genetics). By contrast, an exchange between one purine and one pyrimidine is called a transversion. === Deriving the dynamics of substitution === Consider a DNA sequence of fixed length m evolving in time by base replacement. Assume that the processes followed by the m sites are Markovian independent, identically distributed and that the process is constant over time. For a particular site, let E = { A , G , C , T } {\displaystyle {\mathcal {E}}=\{A,\,G,\,C,\,T\}} be the set of possible states for the site, and p ( t ) = ( p A ( t ) , p G ( t ) , p C ( t ) , p T ( t ) ) {\displaystyle \mathbf {p} (t)=(p_{A}(t),\,p_{G}(t),\,p_{C}(t),\,p_{T}(t))} their respective probabilities at time t {\displaystyle t} . For two distinct x , y ∈ E {\displaystyle x,y\in {\mathcal {E}}} , let μ x y {\displaystyle \mu _{xy}\ } be the transition rate from state x {\displaystyle x} to state y {\displaystyle y} . Similarly, for any x {\displaystyle x} , let the total rate of change from x {\displaystyle x} be μ x = ∑ y ≠ x μ x y . {\displaystyle \mu _{x}=\sum _{y\neq x}\mu _{xy}\,.} The changes in the probability distribution p A ( t ) {\displaystyle p_{A}(t)} for small increments of time Δ t {\displaystyle \Delta t} are given by p A ( t + Δ t ) = p A ( t ) − p A ( t ) μ A Δ t + ∑ x ≠ A p x ( t ) μ x A Δ t . {\displaystyle p_{A}(t+\Delta t)=p_{A}(t)-p_{A}(t)\mu _{A}\Delta t+\sum _{x\neq A}p_{x}(t)\mu _{xA}\Delta t\,.} In other words, (in frequentist language), the frequency of A {\displaystyle A} 's at time t + Δ t {\displaystyle t+\Delta t} is equal to the frequency at time t {\displaystyle t} minus the frequency of the lost A {\displaystyle A} 's plus the frequency of the newly created A {\displaystyle A} 's. Similarly for the probabilities p G ( t ) {\displaystyle p_{G}(t)} , p C ( t ) {\displaystyle p_{C}(t)} and p T ( t ) {\displaystyle p_{T}(t)} . These equations can be written compactly as p ( t + Δ t ) = p ( t ) + p ( t ) Q Δ t , {\displaystyle \mathbf {p} (t+\Delta t)=\mathbf {p} (t)+\mathbf {p} (t)Q\Delta t\,,} where Q = ( − μ A μ A G μ A C μ A T μ G A − μ G μ G C μ G T μ C A μ C G − μ C μ C T μ T A μ T G μ T C − μ T ) {\displaystyle Q={\begin{pmatrix}-\mu _{A}&\mu _{AG}&\mu _{AC}&\mu _{AT}\\\mu _{GA}&-\mu _{G}&\mu _{GC}&\mu _{GT}\\\mu _{CA}&\mu _{CG}&-\mu _{C}&\mu _{CT}\\\mu _{TA}&\mu _{TG}&\mu _{TC}&-\mu _{T}\end{pmatrix}}} is known as the rate matrix. Note that, by definition, the sum of the entries in each row of Q {\displaystyle Q} is equal to zero. It follows that p ′ ( t ) = p ( t ) Q . {\displaystyle \mathbf {p} '(t)=\mathbf {p} (t)Q\,.} For a stationary process, where Q {\displaystyle Q} does not depend on time t, this differential equation can be solved. First, P ( t ) = exp ⁡ ( t Q ) , {\displaystyle P(t)=\exp(tQ),} where exp ⁡ ( t Q ) {\displaystyle \exp(tQ)} denotes the exponential of the matrix t Q {\displaystyle tQ} . As a result, p ( t ) = p ( 0 ) P ( t ) = p ( 0 ) exp ⁡ ( t Q ) . {\displaystyle \mathbf {p} (t)=\mathbf {p} (0)P(t)=\mathbf {p} (0)\exp(tQ)\,.} === Ergodicity === If the Markov chain is irreducible, i.e. if it is always possible to go from a state x {\displaystyle x} to a state y {\displaystyle y} (possibly in several steps), then it is also ergodic. As a result, it has a unique stationary distribution π = { π x , x ∈ E } {\displaystyle {\boldsymbol {\pi }}=\{\pi _{x},\,x\in {\mathcal {E}}\}} , where π x {\displaystyle \pi _{x}} corresponds to the proportion of time spent in state x {\displaystyle x} after the Markov chain has run for an infinite amount of time. In DNA evo

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  PROMT

  ProMT is a lead Russian developer of language translation software for businesses and private users since 1991. The company provides on-premises software based on neural technologies. == History == On March 6, 1998, ProMT launched a free online translation services, which is now known as PROMT.One. In 1997, ProMT and the French company Softissimo developed a line of products for the European company Reverso. == Technology == Historically, ProMT systems used rule-based machine translation (RBMT) technology. In 2011 a hybrid approach which combined rule-based and statistical MT was implemented. In 2019, ProMT introduced its new neural technology and flagship solution - PROMT Neural Translation Server. Since then all MT systems developed by ProMT are based on neural machine translation. The software can run on Microsoft Windows, Linux, MacOS, iOS and Android and works in offline mode providing secure machine translation. As of 2025, it translates 62 languages from and to English, German, and Russian.

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  Gary B. Fogel

  Gary Bryce Fogel (born 1968) is an American biologist and computer scientist. He is the Chief Executive Officer of Natural Selection, Inc. He is most known for his applications of computational intelligence and machine learning to bioinformatics, computational biology, and industrial optimization. == Education and Research == Fogel was born and raised in La Jolla, California, graduating from La Jolla High School. He received a B.A. in biology with a minor in earth sciences from the University of California, Santa Cruz in 1991 and a Ph.D. in biology from the University of California, Los Angeles in 1998. Fogel has published over 150 peer-reviewed publications in conferences and journals, 2 edited books, and 11 patents. As CEO of Natural Selection, Inc., his research focuses on the application of computational intelligence, machine learning, and predictive analytics in areas not limited to: Viral evolution, cellular differentiation, drug discovery, RNA structure, cis-regulatory elements, cancer, and evolutionary game theory as well as the development of evolutionary algorithms and other approaches. == Service == Between 2008–2018 Gary Fogel was editor-in-chief of the Elsevier journal BioSystems. He has served previously as an associate editor for IEEE Transactions on Artificial Intelligence, IEEE Computational Intelligence Magazine (2005–2010), IEEE Transactions on Evolutionary Computation (2001–2013), IEEE Transactions on Emerging Topics in Computational Intelligence (2016–2018), IEEE/ACM Transactions on Computational Biology and Bioinformatics (2004–2008), International Journal of Bioinformatics Research and Applications (2004–2007), International Journal of Data Mining and Bioinformatics (2005–2007), as a consulting editor for the Journal of Computational Intelligence in Bioinformatics (2006–2007), and as an editorial board member of Ecological Informatics (2005–2009) and BMC Big Data Analytics (2015–2020). Within the IEEE Computational Intelligence Society, Fogel founded the Bioinformatics and Bioengineering Technical Committee and established the IEEE Computational Intelligence in Bioinformatics and Computational Biology conference series, chairing the first two meetings in 2004 and 2005 in San Diego. He co-founded the IEEE Conference on Artificial Intelligence in 2023. Fogel served on the IEEE Computational Intelligence Society Administrative Committee (2004–2009, 2014–2022) and served as IEEE CIS Vice President of Conferences (2010–2013, 2019). == Teaching == Gary Fogel also serves as adjunct faculty at San Diego State University in the department of aerospace engineering as well as in the Computational Science Research Center. He has authored four books and numerous articles on the history of early aviation focusing on motorless flight. He is an associate fellow of the American Institute of Aeronautics and Astronautics and serves on the AIAA History Committee. == Awards == 2023 – Outstanding Contribution to Aerospace Education Award, AIAA San Diego Section 2022 – Elected Fellow of the Asia-Pacific Artificial Intelligence Association 2019 – Top 100 AI Leaders in Drug Discovery and Advanced Healthcare by Deep Knowledge Analytics 2019 – Outstanding Contribution to Aerospace Education Award, AIAA San Diego Section 2016 – Meritorious Service Award, IEEE Computational Intelligence Society 2016 – Outstanding Contribution to the Community Award, AIAA San Diego Section 2015 – Outstanding Enhancement of the Image of the Aerospace Profession Award, AIAA San Diego Section 2012 – Medal for Significant Achievement, San Diego Chapter of Sigma Xi 2012 – Fellow of the Institute of Electrical and Electronics Engineers for contributions to computational intelligence and its application to biology, chemistry, and medicine. == Aeromodeling == Gary Fogel has established national and world records for model aircraft. He helped establish the National Model Aviation Heritage program for the Academy of Model Aeronautics. He is a leader member, contest director, and fellow of the Academy of Model Aeronautics, and was inducted into the Academy of Model Aeronautics Hall of Fame in 2025.

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  Video editing software

  Video editing software or a video editor is software used for performing the post-production video editing of digital video sequences on a non-linear editing system (NLE). It has replaced traditional flatbed celluloid film editing tools and analog video tape editing machines. Video editing software serves a lot of purposes, such as filmmaking, audio commentary, and general editing of video content. In NLE software, the user manipulates sections of video, images, and audio on a sequence. These clips can be trimmed, cut, and manipulated in many different ways. When editing is finished, the user exports the sequence as a video file. == Components == === Timeline === NLE software is typically based on a timeline interface where sections moving image video recordings, known as clips, are laid out in sequence and played back. The NLE offers a range of tools for trimming, splicing, cutting, and arranging clips across the timeline. Another kind of clip is a text clip, used to add text to a video, such as title screens or movie credits. Audio clips can additionally be mixed together, such as mixing a soundtrack with multiple sound effects. Typically, the timeline is divided into multiple rows on the y-axis for different clips playing simultaneously, whereas the x-axis represents the run time of the video. Effects such as transitions can be performed on each clip, such as a crossfade effect going from one scene to another. === Exporting === Since video editors represent a project with a file format specific to the program, one needs to export the video file in order to publish it. Once a project is complete, the editor can then export to movies in a variety of formats in a context that may range from broadcast tape formats to compressed video files for web publishing (such as on an online video platform or personal website), optical media, or saved to mobile devices. To facilitate editing, source video typically has a higher resolution than the desired output. Therefore, higher resolution video needs to be downscaled during exporting, or after exporting in a process known as transsizing. === Visual effects === As digital video editing advanced, visual effects became possible, and is part of the standard toolkit, usually found in prosumer and professional grade software. A common ability is to do compositing techniques such as chroma keying or luma keying, among others, which allow different objects to look as if they are in the same scene. A different kind of visual effects is motion capture. Software such as Blender can perform motion capture to make animated objects follow an actor's movements. === Additional features === Most professional video editors are able to do color grading, which is to manipulate visual attributes of a video such as contrast to enhance output, and improve emotional impact. Some video editors such as iMovie include stock footage available for use. == Hardware requirements == As video editing puts great demands on storage and graphics performance, especially at high resolutions such as 4K, and for videos with many visual effects, powerful hardware is often required. It is not uncommon for a computer built for video editing to have a lot of drive capacity, and a powerful graphics processing unit, which optimally has hardware accelerated video encoding. Having sufficient disk space is important since videos can take up large amounts of storage, depending on the resolution and compression format used. Each minute of a Full HD (1080p) video at 30 fps takes up 60MB of space. When visual effects are used, a server farm can be employed to speed up the rendering process. == Examples == Video editing software can be divided into consumer grade, which focuses on ease-of-use, along with professional grade software, which focuses on feature availability, and advanced editing techniques. The typical use case for the former is to edit personal videos on the go, when more advanced editing is not required. === Consumer grade === Photos (Apple) Google Photos YouTube Create === Prosumer grade === ==== Proprietary software ==== iMovie CyberLink PowerDirector === Professional grade === ==== Proprietary software ==== Final Cut Pro Adobe Premiere Pro DaVinci Resolve Vegas Pro Lightworks Camtasia Media Composer ==== Free and open source software ==== Avidemux Blender Cinelerra Flowblade Kdenlive OpenShot Shotcut While most video editing software has been separate from the operating systems, some operating systems have had a video editor installed by default, such as Windows Movie Maker in Windows XP, or as a component of the default photo viewer, such as the Photos app on iOS. Some social media platforms, such as TikTok and Instagram may include a rudimentary video editor to trim clips.

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  Conversational AI Platforms: Free vs Paid (2026)

  Comparing the best conversational AI platform? An conversational AI platform is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right conversational AI platform slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

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  Is an AI Sales Assistant Worth It in 2026?

  Shopping for the best AI sales assistant? An AI sales assistant 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 sales assistant slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

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  AI Copywriting Tools Reviews: What Actually Works in 2026

  Shopping for the best AI copywriting tool? An AI copywriting tool 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 copywriting tool slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

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  A Logical Calculus of the Ideas Immanent in Nervous Activity

  "A Logical Calculus of the Ideas Immanent in Nervous Activity" is a 1943 paper written by Warren Sturgis McCulloch and Walter Pitts, published in the journal The Bulletin of Mathematical Biophysics. The paper proposed a mathematical model of the nervous system as a network of simple logical elements, later known as artificial neurons, or McCulloch–Pitts neurons. These neurons receive inputs, perform a weighted sum, and fire an output signal based on a threshold function. By connecting these units in various configurations, McCulloch and Pitts demonstrated that their model could perform all logical functions. It is a seminal work in cognitive science, computational neuroscience, computer science, and artificial intelligence. It was a foundational result in automata theory. John von Neumann cited it as a significant result. == Mathematics == The artificial neuron used in the original paper is slightly different from the modern version. They considered neural networks that operate in discrete steps of time t = 0 , 1 , … {\displaystyle t=0,1,\dots } . The neural network contains a number of neurons. Let the state of a neuron i {\displaystyle i} at time t {\displaystyle t} be N i ( t ) {\displaystyle N_{i}(t)} . The state of a neuron can either be 0 or 1, standing for "not firing" and "firing". Each neuron also has a firing threshold θ {\displaystyle \theta } , such that it fires if the total input exceeds the threshold. Each neuron can connect to any other neuron (including itself) with positive synapses (excitatory) or negative synapses (inhibitory). That is, each neuron can connect to another neuron with a weight w {\displaystyle w} taking an integer value. A peripheral afferent is a neuron with no incoming synapses. We can regard each neural network as a directed graph, with the nodes being the neurons, and the directed edges being the synapses. A neural network has a circle or a circuit if there exists a directed circle in the graph. Let w i j ( t ) {\displaystyle w_{ij}(t)} be the connection weight from neuron j {\displaystyle j} to neuron i {\displaystyle i} at time t {\displaystyle t} , then its next state is N i ( t + 1 ) = H ( ∑ j = 1 n w i j ( t ) N j ( t ) − θ i ( t ) ) , {\displaystyle N_{i}(t+1)=H\left(\sum _{j=1}^{n}w_{ij}(t)N_{j}(t)-\theta _{i}(t)\right),} where H {\displaystyle H} is the Heaviside step function (outputting 1 if the input is greater than or equal to 0, and 0 otherwise). === Symbolic logic === The paper used, as a logical language for describing neural networks, "Language II" from The Logical Syntax of Language by Rudolf Carnap with some notations taken from Principia Mathematica by Alfred North Whitehead and Bertrand Russell. Language II covers substantial parts of classical mathematics, including real analysis and portions of set theory. To describe a neural network with peripheral afferents N 1 , N 2 , … , N p {\displaystyle N_{1},N_{2},\dots ,N_{p}} and non-peripheral afferents N p + 1 , N p + 2 , … , N n {\displaystyle N_{p+1},N_{p+2},\dots ,N_{n}} they considered logical predicate of form P r ( N 1 , N 2 , … , N p , t ) {\displaystyle Pr(N_{1},N_{2},\dots ,N_{p},t)} where P r {\displaystyle Pr} is a first-order logic predicate function (a function that outputs a boolean), N 1 , … , N p {\displaystyle N_{1},\dots ,N_{p}} are predicates that take t {\displaystyle t} as an argument, and t {\displaystyle t} is the only free variable in the predicate. Intuitively speaking, N 1 , … , N p {\displaystyle N_{1},\dots ,N_{p}} specifies the binary input patterns going into the neural network over all time, and P r ( N 1 , N 2 , … , N n , t ) {\displaystyle Pr(N_{1},N_{2},\dots ,N_{n},t)} is a function that takes some binary input patterns, and constructs an output binary pattern P r ( N 1 , N 2 , … , N n , 0 ) , P r ( N 1 , N 2 , … , N n , 1 ) , … {\displaystyle Pr(N_{1},N_{2},\dots ,N_{n},0),Pr(N_{1},N_{2},\dots ,N_{n},1),\dots } . A logical sentence P r ( N 1 , N 2 , … , N n , t ) {\displaystyle Pr(N_{1},N_{2},\dots ,N_{n},t)} is realized by a neural network iff there exists a time-delay T ≥ 0 {\displaystyle T\geq 0} , a neuron i {\displaystyle i} in the network, and an initial state for the non-peripheral neurons N p + 1 ( 0 ) , … , N n ( 0 ) {\displaystyle N_{p+1}(0),\dots ,N_{n}(0)} , such that for any time t {\displaystyle t} , the truth-value of the logical sentence is equal to the state of the neuron i {\displaystyle i} at time t + T {\displaystyle t+T} . That is, ∀ t = 0 , 1 , 2 , … , P r ( N 1 , N 2 , … , N p , t ) = N i ( t + T ) {\displaystyle \forall t=0,1,2,\dots ,\quad Pr(N_{1},N_{2},\dots ,N_{p},t)=N_{i}(t+T)} === Equivalence === In the paper, they considered some alternative definitions of artificial neural networks, and have shown them to be equivalent, that is, neural networks under one definition realizes precisely the same logical sentences as neural networks under another definition. They considered three forms of inhibition: relative inhibition, absolute inhibition, and extinction. The definition above is relative inhibition. By "absolute inhibition" they meant that if any negative synapse fires, then the neuron will not fire. By "extinction" they meant that if at time t {\displaystyle t} , any inhibitory synapse fires on a neuron i {\displaystyle i} , then θ i ( t + j ) = θ i ( 0 ) + b j {\displaystyle \theta _{i}(t+j)=\theta _{i}(0)+b_{j}} for j = 1 , 2 , 3 , … {\displaystyle j=1,2,3,\dots } , until the next time an inhibitory synapse fires on i {\displaystyle i} . It is required that b j = 0 {\displaystyle b_{j}=0} for all large j {\displaystyle j} . Theorem 4 and 5 state that these are equivalent. They considered three forms of excitation: spatial summation, temporal summation, and facilitation. The definition above is spatial summation (which they pictured as having multiple synapses placed close together, so that the effect of their firing sums up). By "temporal summation" they meant that the total incoming signal is ∑ τ = 0 T ∑ j = 1 n w i j ( t ) N j ( t − τ ) {\displaystyle \sum _{\tau =0}^{T}\sum _{j=1}^{n}w_{ij}(t)N_{j}(t-\tau )} for some T ≥ 1 {\displaystyle T\geq 1} . By "facilitation" they meant the same as extinction, except that b j ≤ 0 {\displaystyle b_{j}\leq 0} . Theorem 6 states that these are equivalent. They considered neural networks that do not change, and those that change by Hebbian learning. That is, they assume that at t = 0 {\displaystyle t=0} , some excitatory synaptic connections are not active. If at any t {\displaystyle t} , both N i ( t ) = 1 , N j ( t ) = 1 {\displaystyle N_{i}(t)=1,N_{j}(t)=1} , then any latent excitatory synapse between i , j {\displaystyle i,j} becomes active. Theorem 7 states that these are equivalent. === Logical expressivity === They considered "temporal propositional expressions" (TPE), which are propositional formulas with one free variable t {\displaystyle t} . For example, N 1 ( t ) ∨ N 2 ( t ) ∧ ¬ N 3 ( t ) {\displaystyle N_{1}(t)\vee N_{2}(t)\wedge \neg N_{3}(t)} is such an expression. Theorem 1 and 2 together showed that neural nets without circles are equivalent to TPE. For neural nets with loops, they noted that "realizable P r {\displaystyle Pr} may involve reference to past events of an indefinite degree of remoteness". These then encodes for sentences like "There was some x such that x was a ψ" or ( ∃ x ) ( ψ x ) {\displaystyle (\exists x)(\psi x)} . Theorems 8 to 10 showed that neural nets with loops can encode all first-order logic with equality and conversely, any looped neural networks is equivalent to a sentence in first-order logic with equality, thus showing that they are equivalent in logical expressiveness. As a remark, they noted that a neural network, if furnished with a tape, scanners, and write-heads, is equivalent to a Turing machine, and conversely, every Turing machine is equivalent to some such neural network. Thus, these neural networks are equivalent to Turing computability and Church's lambda-definability. == Context == === Previous work === The paper built upon several previous strands of work. In the symbolic logic side, it built on the previous work by Carnap, Whitehead, and Russell. This was contributed by Walter Pitts, who had a strong proficiency with symbolic logic. Pitts provided mathematical and logical rigor to McCulloch’s vague ideas on psychons (atoms of psychological events) and circular causality. In the neuroscience side, it built on previous work by the mathematical biology research group centered around Nicolas Rashevsky, of which McCulloch was a member. The paper was published in the Bulletin of Mathematical Biophysics, which was founded by Rashevsky in 1939. During the late 1930s, Rashevsky's research group was producing papers that had difficulty publishing in other journals at the time, so Rashevsky decided to found a new journal exclusively devoted to mathematical biophysics. Also in the Rashevsky's group was Alston Scott Householder, who in 1941 published an abstract model

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  Best AI Logo Makers in 2026

  Looking for the best AI logo maker? An AI logo maker 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 logo maker 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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  ISO 2033

  The ISO 2033:1983 standard ("Coding of machine readable characters (MICR and OCR)") defines character sets for use with Optical Character Recognition or Magnetic Ink Character Recognition systems. The Japanese standard JIS X 9010:1984 ("Coding of machine readable characters (OCR and MICR)", originally designated JIS C 6229-1984) is closely related. == Character set for OCR-A == The version of the encoding for the OCR-A font registered with the ISO-IR registry as ISO-IR-91 is the Japanese (JIS X 9010 / JIS C 6229) version, which differs from the encoding defined by ISO 2033 only in the addition of a Yen sign at 5C. == Character set for OCR-B == The version of the G0 set for the OCR-B font registered with the ISO-IR registry as ISO-IR-92 is the Japanese (JIS X 9010 / JIS C 6229) version, which differs from the encoding defined by ISO 2033 only in being based on JIS-Roman (with a dollar sign at 0x24 and a Yen sign at 0x5C) rather than on the ISO 646 IRV (with a backslash at 0x5C and, at the time, a universal currency sign (¤) at 0x24). Besides those code points, it differs from ASCII only in omitting the backtick (`) and tilde (~). An additional supplementary set registered as ISO-IR-93 assigns the pound sign (£), universal currency sign (¤) and section sign (§) to their ISO-8859-1 codepoints, and the backslash to the ISO-8859-1 codepoint for the Yen sign. == Character set for JIS X 9008 (JIS C 6257) == JIS X 9010 (JIS C 6229) also defines character sets for the JIS X 9008:1981 (formerly JIS C 6257-1981) "hand-printed" OCR font. These include subsets of the JIS X 0201 Roman set (registered as ISO-IR-94 and omitting the backtick (`), lowercase letters, curly braces ({, }) and overline (‾)), and kana set (registered as ISO-IR-96 and omitting the East Asian style comma (､) and full stop (｡), the interpunct (･) and the small kana), in addition to a set (registered as ISO-IR-95) containing only the backslash, which is assigned to the same code point as in ISO-IR-93. The JIS C 6527 font stylises the slash and backslash characters with a doubled appearance. The character names given are "Solidus" and "Reverse Solidus", matching the Unicode character names for the ASCII slash and backslash. However, the Unicode Optical Character Recognition block includes an additional code point for an "OCR Double Backslash" (⑊), although not for a double (forward) slash, although a double slash is available elsewhere, as U+2AFD ⫽ DOUBLE SOLIDUS OPERATOR. == Character set for E-13B == The ISO-IR-98 encoding defined by ISO 2033 encodes the character repertoire of the E13B font, as used with magnetic ink character recognition. Although ISO 2033 also specifies other encodings, the encoding for E-13B is the encoding referred to as ISO_2033_1983 by Perl libintl, and as ISO_2033-1983 or csISO2033 by the IANA. Other registered labels include iso-ir-98, its ISO-IR registration number, and simply e13b. The digits are preserved in their ASCII locations. Letters and symbols unavailable in the E13B font are omitted, while specialised punctuation for bank cheques included in the E13B font is added. The same symbols are available in Unicode in the Optical Character Recognition block.

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  Heng Ji

  Heng Ji is a computer scientist who works on information extraction and natural language processing. She is well known for her work on joined named entity recognition and relation extraction, as well as for her work on cross-document event extraction. She has been coordinating the popular NIST TAC Knowledge Base Population task since 2010. She has been recognised as one of AI's 10 to watch by IEEE Intelligent Systems in 2013, and has won multiple awards, including a NSF Career Award in 2009, Google Research awards in 2009 and 2014, and an IBM Watson Faculty Award in 2012. == Education == Heng Ji obtained a Bachelor's and master's degree in Computational Linguistics from Tsinghua University. She subsequently obtained a MSc, then PhD in Computer Science from New York University in 2008 under the supervision of Ralph Grishman. Her PhD thesis was on the topic of information extraction, with a particular focus on joint training of multiple components in the information extraction pipeline, as well as cross-lingual learning. == Career == Upon graduating with a PhD from New York University, Ji took up a position as assistant professor at Queens College, City University of New York, where she founded the BLENDER Lab, which focuses on research on cross-lingual, cross-documents, cross-media information extraction and fusion. In 2013, she joined Rensselaer Polytechnic Institute as an Edward P. Hamilton Development Chair and Tenured associate professor in Computer Science. Since 2019, she has been a full professor at the University of Illinois at Urbana–Champaign, as well as an Amazon Scholar. == Research == Heng Ji works in the area of natural language processing, machine learning and information extraction. She has published over 300 peer-reviewed research papers. Her work is published in the proceedings of computer science conferences, including the Annual Meeting of the Association for Computational Linguistics, The Web Conference, and the ACM Conference on Knowledge Discovery and Data Mining (KDD). Ji is a leading researcher in information extraction, having coordinated the popular NIST TAC Knowledge Base Population shared task since 2010. She is most recognised for her work on modelling interactions between subtasks in information extraction, which was also the topic of her PhD thesis, and for her work on event detection using cross-document signals. == Selected honors and distinctions == 2009 NSF Career Award 2009 Google Research Award 2012 IBM Watson Faculty Award 2013 IEEE AI's 10 to Watch 2014 Google Research Award 2016 World Economic Forum, 'Young Scientist' 2017 World Economic Forum, 'Young Scientist' 2020 Annual Meeting of the Association for Computational Linguistics, best demonstration paper

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  Adversarial stylometry

  Adversarial stylometry is the practice of altering writing style to reduce the potential for stylometry to discover the author's identity or their characteristics. This task is also known as authorship obfuscation or authorship anonymisation. Stylometry poses a significant privacy challenge in its ability to unmask anonymous authors or to link pseudonyms to an author's other identities, which, for example, creates difficulties for whistleblowers, activists, and hoaxers and fraudsters. The privacy risk is expected to grow as machine learning techniques and text corpora develop. All adversarial stylometry shares the core idea of faithfully paraphrasing the source text so that the meaning is unchanged but the stylistic signals are obscured. Such a faithful paraphrase is an adversarial example for a stylometric classifier. Several broad approaches to this exist, with some overlap: imitation, substituting the author's own style for another's; translation, applying machine translation with the hope that this eliminates characteristic style in the source text; and obfuscation, deliberately modifying a text's style to make it not resemble the author's own. Manually obscuring style is possible, but laborious; in some circumstances, it is preferable or necessary. Automated tooling, either semi- or fully-automatic, could assist an author. How best to perform the task and the design of such tools is an open research question. While some approaches have been shown to be able to defeat particular stylometric analyses, particularly those that do not account for the potential of adversariality, establishing safety in the face of unknown analyses is an issue. Ensuring the faithfulness of the paraphrase is a critical challenge for automated tools. It is uncertain if the practice of adversarial stylometry is detectable in itself. Some studies have found that particular methods produced signals in the output text, but a stylometrist who is uncertain of what methods may have been used may not be able to reliably detect them. == History == Rao & Rohatgi (2000), an early work in adversarial stylometry, identified machine translation as a possibility, but noted that the quality of translators available at the time presented severe challenges. Kacmarcik & Gamon (2006) is another early work. Brennan, Afroz & Greenstadt (2012) performed the first evaluation of adversarial stylometric methods on actual texts. Brennan & Greenstadt (2009) introduced the first corpus of adversarially authored texts specifically for evaluating stylometric methods; other corpora include the International Imitation Hemingway Competition, the Faux Faulkner contest, and the hoax blog A Gay Girl in Damascus. == Motivations == Rao & Rohatgi (2000) suggest that short, unattributed documents (i.e., anonymous posts) are not at risk of stylometric identification, but pseudonymous authors who have not practiced adversarial stylometry in producing corpuses of thousands of words may be vulnerable. Narayanan et al. (2012) attempted large-scale deanonymisation of 100,000 blog authors with mixed results: the identifications were significantly better than chance, but only accurately matched the blog and author a fifth of the time; identification improved with the number of posts written by the author in the corpus. Even if an author is not identified, some of their characteristics may still be deduced stylometrically, or stylometry may narrow the anonymity set of potential authors sufficiently for other information to complete the identification. Detecting author characteristics (e.g., gender or age) is often simpler than identifying an author from a large, possibly open, set of candidates. Modern machine learning techniques offer powerful tools for identification; further development of corpora and computational stylometric techniques are likely to raise further privacy issues. Gröndahl & Asokan (2020a) say that the general validity of the hypothesis underlying stylometry—that authors have invariant, content-independent 'style fingerprints'—is uncertain, but "the deanonymisation attack is a real privacy concern". Those interested in practicing adversarial stylometry and stylistic deception include whistleblowers avoiding retribution; journalists and activists; perpetrators of frauds and hoaxes; authors of fake reviews; literary forgers; criminals disguising their identity from investigators; and, generally, anyone with a desire for anonymity or pseudonymity. Authors, or agents acting on behalf of authors, may also attempt to remove stylistic clues to author characteristics (e.g., race or gender) so that knowledge of those characteristics cannot be used for discrimination (e.g., through algorithmic bias). Another possible use for adversarial stylometry is in disguising automatically generated text as human-authored. == Methods == With imitation, the author attempts to mislead stylometry by matching their style to another author's. An incomplete imitation, where some of the true author's unique characteristics appear alongside the imitated author's, can be a detectable signal for the use of adversarial stylometry. Imitation can be performed automatically with style transfer systems, though this typically requires a large corpus in the target style for the system to learn from. Another approach is translation, which employs machine translation of a source text to eliminate characteristic style, often through multiple translators in sequence to produce a round-trip translation. Such chained translation can lead to texts being significantly altered, even to the point of incomprehensibility; improved translation tools reduce this risk. More simply-structured texts can be easier to machine translate without losing the original meaning. Machine translation blurs into direct stylistic imitation or obfuscation achieved through automated style transfer, which can be viewed as a "translation" with the same language as input and output. With low-quality translation tools, an author can be required to manually correct major translation errors while avoiding the hazard of re-introducing stylistic characteristics. Wang, Juola & Riddell (2022) found that gross errors introduced by Google Translate were rare, but more common with several intermediate translations—however, occasional simple or short sentences and misspellings in the source text appeared verbatim in the output, potentially providing an identifying signal. Chain translation can leave characteristic traces of its application in a document, which may allow reconstruction of the intermediate languages used and the number of translation steps performed. Obfuscation involves deliberately changing the style of a text to reduce its similarity to other texts by some metric; this may be performed at the time of writing by conscious modification, or as part of a revision process with feedback from the metric being targeted as an input to decide when the text has been sufficiently obfuscated. In contrast to translation, complex texts can offer more opportunities for effective obfuscation without altering meaning, and likewise genres with more permissible variation allow more obfuscation. However, longer texts are harder to thoroughly obfuscate. Obfuscation can blend into imitation if the author develops a novel target style, distinct from their original style. With respect to masking author characteristics, obfuscation may aim to achieve a union (adding signals for imitated characteristics) or an intersection (removing signals and normalising) of other authors' styles. Avoiding the author's own idiosyncrasies and producing a "normalised" text is a critical obfuscatory step: an author may have a unique tendency to misspell certain words, use particular variants, or to format a document in a characteristic way. Stylometric signals vary in how simply they can be adversarially masked; an author may easily change their vocabulary by conscious choice, but altering the pattern of grammar or the letter frequency in their text may be harder to achieve, though Juola & Vescovi (2011) report that imitation typically succeeds at masking more characteristics than obfuscation. Automated obfuscation may require large amounts of training data written by the author. Concerning automated implementations of adversarial stylometry, two possible implementations are rule-based systems for paraphrasing; and encoder–decoder architectures, where the text passes through an intermediate format that is (intended to be) style-neutral. Another division in automated methods is whether there is feedback from an identification system or not. With such feedback, finding paraphrases for author masking has been characterised as a heuristic search problem, exploring textual variants until the result is stylistically sufficiently far (in the case of obfuscation) or near (in the case of imitation), which then constitutes an adversarial example for that identification system. == Evaluation == How

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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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  Joseph Keshet

  Joseph (Yossi) Keshet (Hebrew: יוסף (יוסי) קשת; born: 28 February 1973) is an Israeli professor in the Electrical and Computer Engineering Faculty of the Technion, where he is the director of the Speech, Language, and Deep Learning Lab. His research focuses on human speech processing and machine learning. == Early life and education == Keshet was born in Tel-Aviv. He graduated from the Amal School and began his academic studies at the Department of Electrical Engineering-Systems at Tel-Aviv University in 1991 and received his B.Sc. (Cum Laude) in 1994. Keshet served in the IDF Unit 8200 from 1995 to 2002 as the head of the speech processing research section in the R&D Center. During his service, he received a national award from the Administration for the Development of Weapons and Technological Infrastructure (Maf’at). Keshet was award his M.Sc. from the same department after he completed his Israel Defense Force service in 2002. His Dissertation was titled: Stop consonant spotting in continuous speech and was supervised by Dan Chazan from IBM Research Labs, Haifa. He continued his Ph.D. studies at the Hebrew University of Jerusalem until 2008. Prof. Yoram Singer supervised his thesis on Large Margin Algorithms for Discriminative Continuous Speech. == Career == Keshet was a Research Associate (postdoc) at IDIAP Research Institute, Martigny, Switzerland in 2007, and joined the TTI-Chicago and Department of Computer Science, University of Chicago, Chicago, IL in 2009 as Research Assistant Professor. In 2013, he returned to Israel and joined the Computer Science department at Bar-Ilan University as a senior lecturer and head of the Speech, Language, and Deep Learning Lab. In 2020, Keshet became a Founding Venture Partner at the Disruptive AI Venture Capital. In the same year, he also joined Amazon in Tel-Aviv as an Amazon Scholar. In 2022, Keshet joined the Faculty of Electrical and Computer Engineering at the Technion. == Research == Keshet's research work focuses on both machine learning and computational study of human speech and language. His work on speech and language concentrates on speech processing, speech recognition, acoustic phonetics, and pathological speech. In machine learning, Keshet is focused on deep learning and structured tasks. According to Google Scholar (September 2020), Keshet is one of the 15 most cited researchers in the field of spoken language processing. The algorithms that were developed in the Speech, Language, and Deep Learning Lab can analyze different pathological conditions in the throat and vocal cords based on the subject's voice. Other algorithms showed that the voice can be used to estimate physical and emotional state of the speaker. Another research led by Keshet suggested that it is possible to fool structured AI systems (like Google Voice). == Membership in professional societies == Keshet is the founder and chair of the Machine Learning for Speech and Language Processing Special Interest Group (SIGML) of the International Speech Communication Association (ISCA), from 2011. He is a senior member of the IEEE Signal Processing Society since 2018 and a member of ISCA since 2002. == Publications == Prof. Keshet has authored more than 70 scientific publications and edited one book. === Book === Joseph Keshet and Samy Bengio, Eds., Automatic Speech and Speaker Recognition: Large Margin and Kernel Methods, John Wiley & Sons, March 2009. === Selected articles === Jacob T. Cohen, Alma Cohen, Limor Benyamini, Yossi Adi, Joseph Keshet, Predicting glottal closure insufficiency using fundamental frequency contour analysis, Head & Neck, Journal of the Sciences and Specialities of the Head and Neck, Volume 41, Issue 7, pp. 2324–2331, July 2019. Yehoshua Dissen, Jacob Goldberger, and Joseph Keshet, Formant Estimation and Tracking: A Deep Learning Approach, Journal of the Acoustical Society of America, 145 (2), February 2019. Joseph Keshet, Automatic speech recognition: A primer for speech-language pathology researchers, International Journal of Speech-Language Pathology, Vol. 20 No. 6, pp. 599–609, 2018. Yossi Adi, Carsten Baum, Moustapha Cisse, Benny Pinkas, Joseph Keshet, Turning Your Weakness Into a Strength: Watermarking Deep Neural Networks by Backdooring, Usenix, 2018. Tzeviya Fuchs, Joseph Keshet, Spoken Term Detection Automatically Adjusted for a Given Threshold, IEEE Journal of Selected Topics in Signal Processing, Dec 2017, Volume 11, Issue 8, pp. 1–8. Moustapha Cisse, Yossi Adi, Natalia Neverova, Joseph Keshet, Houdini: Fooling Deep Structured Visual and Speech Recognition Models with Adversarial Examples, Neural Information and Processing Systems (NIPS), 2017. Joseph Keshet, Subhransu Maji, Tamir Hazan, and Tommi Jaakkola, Perturbation Models and PAC-Bayesian Generalization Bounds, in Perturbations, Optimization, and Statistics, Tamir Hazan, George Papandreou, and Daniel Tarlow, Eds., The MIT Press, 2016. Matthew Goldrick, Joseph Keshet, Erin Gustafson, Jordana Heller, and Jeremy Needle, Automatic Analysis of Slips of the Tongue: Insights into the Cognitive Architecture of Speech Production, Cognition, 149, 31–39, 2016. Joseph Keshet, Optimizing the Measure of Performance in Structured Prediction, in Advanced Structured Prediction, Sebastian Nowozin, Peter V. Gehler, Jeremy January, and Christoph H. Lampert, Eds., The MIT Press, 2014. Morgan Sonderegger and Joseph Keshet, Automatic Measurement of Voice Onset Time using Discriminative Structured Prediction, Journal of the Acoustical Society of America, Vol. 132, Issue 6, pp. 3965−3979, 2012. David McAllester, Tamir Hazan and Joseph Keshet, Direct Loss Minimization for Structured Prediction, The 24th Annual Conference on Neural Information Processing Systems (NIPS), 2010. Joseph Keshet, David Grangier and Samy Bengio, Discriminative Keyword Spotting, Speech Communication, Volume 51, Issue 4, pp. 317–329, April 2009. == Personal life == Keshet is married to Lital. They have three children.

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