AI Assistant Vs AI Agent

AI Assistant Vs AI Agent — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  JBoss Tools

  JBoss Tools is a set of Eclipse plugins and features designed to help JBoss and JavaEE developers develop applications. It is an umbrella project for the JBoss developed plugins that will make it into JBoss Developer Studio. == Modules == JBoss Tools includes the following modules: Visual Page Editor (VPE). The visual editor contributed by Exadel supports visual editing of HTML and JSF (JSP and Facelets) pages. VPE also includes visual support for JSF component libraries including JBoss RichFaces. Seam Tools. Includes support for (for example) seam-gen, RichFaces VE integration, Seam related code completion and refactoring. Hibernate Tools. Supporting mapping files, annotations and JPA with reverse engineering, code completion, project wizards, refactoring, interactive HQL/JPA-QL/Criteria execution and more. In short a merger of Hibernate Tools and Exadel ORM features. JBoss AS Tools. Easy start, stop and debug of JBoss AS 4+ servers from within Eclipse. Also includes features for packaging and deployment of any type of Eclipse project. Drools IDE. Rules file editing, Rete View, working memory debugging/inspection and more. jBPM Tools. jBPM workflow editing, deployment, etc. JBossWS Tools. Inspecting, invoking, developing and functional/load/compliance testing of web services over HTTP, base tooling provided by soapUI with the addition of JBossWS specific features/support. JBoss ESB Tools. The structured xml editor for the jboss-esb.xml file used in JBoss ESB. Birt Tools. Hibernate and Seam extensions for Eclipse BIRT. Portal Tools. JBoss Tools supports the JSR-168 Portlet Specification (Portlet 1.0), JSR-286 Portlet Specification (Portlet 2.0) and works with PortletBridge for supporting Portlets in JSF/Seam applications. To enable these features, add the JBoss Portlet facet to a new or an existing web project. Core/General Tools. To reduce the UI clutter, most of the "configure project" menu items move into the Configure menu introduced in Eclipse 3.5 instead of always having a static JBoss Tools menu entry show up even in projects unrelated to JBoss Tools. Smooks Tools. The editor for Smooks configuration files. JBoss ESB Tools. The ESB project Wizard, which creates a project that can be deployed as an .esb archive to a JBoss AS-based server with JBoss ESB installed. JMX Tools. JMX Tools allows establishing multiple JMX connections and provides views for exploring the JMX tree and execute operations directly from Eclipse. The JMX Tools replaces the JMX node previously available in the JBoss Server View. JST/JSF Tools. RichFaces Support, Code Assists, Web XML/JSP/XHTML Editors, CSS Style Editing, web.xml validation, Faceleted taglib in taglib.xml is supported with XSD schema location. Project Examples. The experimental feature called Project Example wizard aims to allow users to download example projects from a remote site and have them working out-of-the-box. AS/Project Archives Tools. To deploy projects compressed, configurable in the server editor. If enabled, all projects deployed to that server will be compressed instead of in an exploded folder. Maven Tools. The optional integration with m2eclipse to provide Maven support for projects created by JBoss Tools and to some extent core WTP projects. BPEL Tools. A BPEL Editor based on the Eclipse BPEL project has been added to JBoss Tools. This means that users can create, edit and deploy BPEL artifacts for the Riftsaw BPEL Runtime. CDI (JSR-299) Tools. Support of the Contexts and Dependency Injection annotations; it works on any Eclipse Java project (via the Configure menu with CDI enabled).

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  James F. Allen (computer scientist)

  James Frederick Allen (born 1950) is an American computational linguist recognized for his contributions to temporal logic, in particular Allen's interval algebra. He is interested in knowledge representation, commonsense reasoning, and natural language understanding, believing that "deep language understanding can only currently be achieved by significant hand-engineering of semantically-rich formalisms coupled with statistical preferences". He is the John H. Dessaurer Professor of Computer Science at the University of Rochester. == Biography == Allen received his Ph.D. from the University of Toronto in 1979, under the supervision of C. Raymond Perrault, after which he joined the faculty at Rochester. At Rochester, he was department chair from 1987 to 1990, directed the Cognitive Science Program from 1992 to 1996, and co-directed the Center for the Sciences of Language from 1996 to 1998. He served as the Editor-in-Chief of Computational Linguistics from 1983–1993. Since 2006 he has also been associate director of the Florida Institute for Human and Machine Cognition. == Academic life == === TRIPS project === The TRIPS project is a long-term research to build generic technology for dialogue (both spoken and 'chat') systems, which includes natural language processing, collaborative problem solving, and dynamic context-sensitive language modeling. This is contrast with the data driven approaches by machine learning, which requires to collect and annotate corpora, i.e. training data, firstly. === PLOW agent === PLOW agent is a system that learns executable task models from a single collaborative learning session, which integrates wide AI technologies including deep natural language understanding, knowledge representation and reasoning, dialogue systems, planning/agent-based systems, and machine learning. This paper won the outstanding paper award at AAAI in 2007. == Selected works == === Books === Allen is the author of the textbook Natural Language Understanding (Benjamin-Cummings, 1987; 2nd ed., 1995). He is also the co-author with Henry Kautz, Richard Pelavin, and Josh Tenenberg of Reasoning About Plans (Morgan Kaufmann, 1991). === Articles === 2007. PLOW: A Collaborative Task Learning Agent. (with Nathanael Chambers et al) AAAI'07 won the outstanding paper award at AAAI in 2007. 2006. Chester: Towards a Personal Medication Advisor. (with N. Blaylock, et al) Biomedical informatics 39(5) 1998. TRIPS: An Integrated Intelligent Problem-Solving Assistant. (with George Ferguson) AAAI'98 1983. Maintaining Knowledge about Temporal Intervals. CACM 26, 11, 832-843 == Awards and honors == In 1991 he was elected as a fellow of the Association for the Advancement of Artificial Intelligence (1990, founding fellow). In 1992 he became the Dessaurer Professor at Rochester.

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  Black in AI

  Black in AI, formally called the Black in AI Workshop, is a technology research organization and affinity group, founded by computer scientists Timnit Gebru and Rediet Abebe in 2017. It started as a conference workshop, later pivoting into an organization. Black in AI increases the presence and inclusion of Black people in the field of artificial intelligence (AI) by creating space for sharing ideas, fostering collaborations, mentorship, and advocacy. == History == Black in AI was created in 2017 to address issues of lack of diversity in AI workshops, and was started as its own workshop within the Conference on Neural Information Processing Systems (NeurIPS) conference. Because of algorithmic bias, ethical issues, and underrepresentation of Black people in AI roles; there has been an ongoing need for unity within the AI community to have focus on these issues. Black in AI has strived to continue the progress of improving the presence of people of color in the field of artificial intelligence. In 2018 and 2019, the Black in AI workshop had many immigration visa issues to Canada, which spurred the conference to be planned for 2020 in Addis Ababa, Ethiopia. On December 7, 2020, Black in AI held its fourth annual workshop and first virtual workshop (due to the COVID-19 pandemic). In 2021, Black in AI, alongside the groups Queer in AI and Widening NLP, released a public statement refusing funding from Google in an act of protest of Google's treatment of Timnit Gebru, Margaret Mitchell, and April Christina Curley in the events that occurred in December 2020. == Founders == Rediet Abebe is an Ethiopian computer scientist who specializes in algorithms and artificial intelligence. She is a Computer Science Assistant Professor at the University of California, Berkeley. She was previously a Junior Fellow at Harvard's Society of Fellows. She was the first Black woman to receive a Ph.D. in computer science at Cornell University. She "designs and analyzes algorithms, discrete optimizations, network-based, [and] computational strategies to increase access to opportunity for historically disadvantaged populations," according to her web bio. Timnit Gebru was born in Ethiopia and moved to the United States at the age of fifteen. She got her B.S. and M.S. in electrical engineering from Stanford University, as well as a PhD from the Stanford Artificial Intelligence Laboratory, where she studied computer vision under Fei-Fei Li. She formerly worked as a postdoctoral researcher at Microsoft Research in the Fairness Accountability Transparency, and Ethics (FATE) division. She's also worked with Apple, where she assisted in the development of signal-processing algorithms for the original iPad. == Grants == Black in AI received grants and support from private foundations like MacArthur Foundation and Rockefeller Foundation. The organization received $10,000 in 2018 for its annual workshop and $150,000 in 2019 for its long-term organizational planning. In 2020, during the pandemic, the organization received a grant of $300,000 by MacArthur Foundation in order to provide broad organizational support. In 2022, Rockefeller Foundation announced $300,000 to fight prejudice in artificial intelligence (AI) across the globe and incorporate equity into this rapidly expanding field. == Programs == "Black in AI works in academics, advocacy, entrepreneurship, financial support, and summer research programs." The Black in AI Academic Program is a resource for Black junior researchers applying to graduate schools, navigating graduate school, and transitioning into the postgraduate employment market. They provide online education sessions, offer scholarships to cover application fees, pair participants with peer and senior mentors, and distribute crowdsourced papers that simplify the application process. They also undertake research projects to investigate and highlight the difficulties that Black young researchers face, as well as push for structural reforms to eliminate these barriers and build equitable research settings. Moses Namara is a Facebook Research Fellow at Clemson University and a PhD candidate in Human-Centered Computing (HCC). He is the mentor for the new Black in AI Academic Program. During the graduate school admissions season in 2021, Black in AI served more than 200 potential graduate program candidates in some capacity. Furthermore, the organization's study identified greater problems encountered by Black graduate school candidates, such as the high cost of graduate school admissions examinations (GREs), which are known to be biased against those from low-income backgrounds. Black in AI's attempts to encourage institutions to eliminate the obstacles were supported by the findings. Black in AI is also developing a program to help and connect Black tech startups with investors. Black in AI also mentors early-career Black AI academics and is forming relationships with Historically Black Colleges and Universities to extend its academic program. In 2021, Black in AI launched two summer research programs, one for undergraduate internships and another for unconstrained research mentorship, including one aimed explicitly at empowering Black women's AI research projects. == Conferences and workshops == At NeurIPS 2017, the first Black in AI event took place in December 8, 2017 in Long Beach, California. The goal was to bring together experts in the area to share ideas and debate efforts aimed at increasing the participation of Black people in artificial intelligence, both for diversity and to avoid data bias. Black AI researchers had the opportunity to share their work at the workshop's oral and poster sessions. The second workshop was hosted in Montréal, Canada, on December 7, 2018. According to AI experts, visa issues stymie efforts to make their area more inclusive, making technology that discriminates or disadvantages individuals who aren't white or Western less likely. Hundreds of participants who were supposed to attend or present work at the Black in AI session on Friday were unable to fly to Canada; many of the participants were from African countries. The third workshop was held in NeurIPS 2019, one of the premier machine learning conferences Vancouver, Canada. The workshop was able to give travel scholarships and visa support to hundreds of academics who would not have been able to attend NeurIPS without the help of sponsors. For instance, Ramon Vilarino of the University of Sao Paulo, who presented a poster at the conference on his study of geographical and racial prejudice in credit scoring in Brazil, would not have been able to attend NeurIPS without the help of Black in AI. Twenty-four academics from Africa and South America were denied visas to attend this session during the conference, according to Victor Silva, the workshop organizer. He noted that, less than a month before the conference, 40 applicants from both continents had been given visas but that more than 70 applications were still waiting. For the second year in a row, visa restrictions have stopped several African scholars from attending the 2018 meeting in Montreal. The AAAI announced the first Black in AI lunch, which was held in conjunction with AAAI-19. The lunch was hosted on Tuesday, January 29, 2019. This event was intended to promote networking, discussion of various AI career options, and the exchange of ideas in order to boost the number of Black researchers in the area. The fourth Black in AI workshop, which was held in conjunction with NeurIPS 2020, took place the week of December 7, 2020. The workshop was scheduled to take place in Vancouver, British Columbia. Due to the pandemic, the session was held for the first time in a virtual format. Victor Silva, an AI4Society student, served as the event's chair. The fifth annual Black in AI workshop was also held virtually in 2021. Oral presentations, guest keynote speakers, a combined poster session with other affinity groups, sponsored sessions, and startup showcases was all featured. The goal of the session was to raise the visibility of black scholars at NeurIPS.

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  Michael L. Littman

  Michael Lederman Littman (born August 30, 1966) is a computer scientist, researcher, educator, and author. His research interests focus on reinforcement learning. He is currently a University Professor of Computer Science at Brown University, where he has taught since 2012. As of July 2025, he is also the university’s inaugural Associate Provost for Artificial Intelligence. == Career == Before graduate school, Littman worked with Thomas Landauer at Bellcore and was granted a patent for one of the earliest systems for cross-language information retrieval. Littman received his Ph.D. in computer science from Brown University in 1996. From 1996 to 1999, he was a professor at Duke University. During his time at Duke, he worked on an automated crossword solver PROVERB, which won an Outstanding Paper Award in 1999 from AAAI and competed in the American Crossword Puzzle Tournament. From 2000 to 2002, he worked at AT&T. From 2002 to 2012, he was a professor at Rutgers University; he chaired the department from 2009-12. In Summer 2012 he returned to Brown University as a full professor. He has also taught at Georgia Institute of Technology, where he was listed as an adjunct professor. Littman served as the Division Director for Information and Intelligent Systems (the AI division) at the National Science Foundation from 2022-2025. After serving a term, he returned to Brown University as their first Associate Provost for Artificial Intelligence where he coordinates the intersection of AI with research, teaching, operations, policy, and communication at the university level. == Research == Littman's research interests are varied but have focused mostly on reinforcement learning and related fields, particularly, in machine learning more generally, game theory, computer networking, partially observable Markov decision process solving, computer solving of analogy problems and other areas. He is also interested in computing education more broadly and has authored a book on programming for everyone. == Leadership and Service == Littman has chaired the panel for The One Hundred‑Year Study on Artificial Intelligence (AI100) 2021 Report and will chair the standing committee for the 2026 report. During his time at the National Science Foundation, he co-led the development of the 2023 National Strategic Artificial Intelligence Research and Development Strategic Plan. == Personal Notes == Littman is also known for his playful approach to communication. He has produced multiple education and parody videos (for example a machine-learning version of Michael Jackson’s Thriller with his oft-collaborator Charles Lee Isbell, Jr.) as part of his teaching outreach. Among his hobbies, he has been noted riding an electric unicycle to his office at the NSF. == Awards == Elected as an ACM Fellow in 2018 for "contributions to the design and analysis of sequential decision-making algorithms in artificial intelligence". Winner of the IFAAMAS Influential Paper Award (2014) Winner of the AAAI “Shakey” Award for Overfitting: Machine Learning Music Video (2014) Elected as a AAAI Fellow in 2010 for "significant contributions to the fields of reinforcement learning, decision making under uncertainty, and statistical language applications". Winner of the AAAI “Shakey” Award for Short Video for Aibo Ingenuity (2007) Winner of the Warren I. Susman Award for Excellence in Teaching at Rutgers (2011) Winner of the Robert B. Cox Award at Duke (1999) Winner of the AAAI Outstanding Paper Award (1999)

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  Reparameterization trick

  The reparameterization trick (aka "reparameterization gradient estimator") is a technique used in statistical machine learning, particularly in variational inference, variational autoencoders, and stochastic optimization. It allows for the efficient computation of gradients through random variables, enabling the optimization of parametric probability models using stochastic gradient descent, and the variance reduction of estimators. It was developed in the 1980s in operations research, under the name of "pathwise gradients", or "stochastic gradients". Its use in variational inference was proposed in 2013. == Mathematics == Let z {\displaystyle z} be a random variable with distribution q ϕ ( z ) {\displaystyle q_{\phi }(z)} , where ϕ {\displaystyle \phi } is a vector containing the parameters of the distribution. === REINFORCE estimator === Consider an objective function of the form: L ( ϕ ) = E z ∼ q ϕ ( z ) [ f ( z ) ] {\displaystyle L(\phi )=\mathbb {E} _{z\sim q_{\phi }(z)}[f(z)]} Without the reparameterization trick, estimating the gradient ∇ ϕ L ( ϕ ) {\displaystyle \nabla _{\phi }L(\phi )} can be challenging, because the parameter appears in the random variable itself. In more detail, we have to statistically estimate: ∇ ϕ L ( ϕ ) = ∇ ϕ ∫ d z q ϕ ( z ) f ( z ) {\displaystyle \nabla _{\phi }L(\phi )=\nabla _{\phi }\int dz\;q_{\phi }(z)f(z)} The REINFORCE estimator, widely used in reinforcement learning and especially policy gradient, uses the following equality: ∇ ϕ L ( ϕ ) = ∫ d z q ϕ ( z ) ∇ ϕ ( ln ⁡ q ϕ ( z ) ) f ( z ) = E z ∼ q ϕ ( z ) [ ∇ ϕ ( ln ⁡ q ϕ ( z ) ) f ( z ) ] {\displaystyle \nabla _{\phi }L(\phi )=\int dz\;q_{\phi }(z)\nabla _{\phi }(\ln q_{\phi }(z))f(z)=\mathbb {E} _{z\sim q_{\phi }(z)}[\nabla _{\phi }(\ln q_{\phi }(z))f(z)]} This allows the gradient to be estimated: ∇ ϕ L ( ϕ ) ≈ 1 N ∑ i = 1 N ∇ ϕ ( ln ⁡ q ϕ ( z i ) ) f ( z i ) {\displaystyle \nabla _{\phi }L(\phi )\approx {\frac {1}{N}}\sum _{i=1}^{N}\nabla _{\phi }(\ln q_{\phi }(z_{i}))f(z_{i})} The REINFORCE estimator has high variance, and many methods were developed to reduce its variance. === Reparameterization estimator === The reparameterization trick expresses z {\displaystyle z} as: z = g ϕ ( ϵ ) , ϵ ∼ p ( ϵ ) {\displaystyle z=g_{\phi }(\epsilon ),\quad \epsilon \sim p(\epsilon )} Here, g ϕ {\displaystyle g_{\phi }} is a deterministic function parameterized by ϕ {\displaystyle \phi } , and ϵ {\displaystyle \epsilon } is a noise variable drawn from a fixed distribution p ( ϵ ) {\displaystyle p(\epsilon )} . This gives: L ( ϕ ) = E ϵ ∼ p ( ϵ ) [ f ( g ϕ ( ϵ ) ) ] {\displaystyle L(\phi )=\mathbb {E} _{\epsilon \sim p(\epsilon )}[f(g_{\phi }(\epsilon ))]} Now, the gradient can be estimated as: ∇ ϕ L ( ϕ ) = E ϵ ∼ p ( ϵ ) [ ∇ ϕ f ( g ϕ ( ϵ ) ) ] ≈ 1 N ∑ i = 1 N ∇ ϕ f ( g ϕ ( ϵ i ) ) {\displaystyle \nabla _{\phi }L(\phi )=\mathbb {E} _{\epsilon \sim p(\epsilon )}[\nabla _{\phi }f(g_{\phi }(\epsilon ))]\approx {\frac {1}{N}}\sum _{i=1}^{N}\nabla _{\phi }f(g_{\phi }(\epsilon _{i}))} == Examples == For some common distributions, the reparameterization trick takes specific forms: Normal distribution: For z ∼ N ( μ , σ 2 ) {\displaystyle z\sim {\mathcal {N}}(\mu ,\sigma ^{2})} , we can use: z = μ + σ ϵ , ϵ ∼ N ( 0 , 1 ) {\displaystyle z=\mu +\sigma \epsilon ,\quad \epsilon \sim {\mathcal {N}}(0,1)} Exponential distribution: For z ∼ Exp ( λ ) {\displaystyle z\sim {\text{Exp}}(\lambda )} , we can use: z = − 1 λ log ⁡ ( ϵ ) , ϵ ∼ Uniform ( 0 , 1 ) {\displaystyle z=-{\frac {1}{\lambda }}\log(\epsilon ),\quad \epsilon \sim {\text{Uniform}}(0,1)} Discrete distribution can be reparameterized by the Gumbel distribution (Gumbel-softmax trick or "concrete distribution") and diffusion models. In general, any distribution that is differentiable with respect to its parameters can be reparameterized by inverting the multivariable CDF function, then apply the implicit method. See for an exposition and application to the Gamma, Beta, Dirichlet, and von Mises distributions. == Applications == === Variational autoencoder === In Variational Autoencoders (VAEs), the VAE objective function, known as the Evidence Lower Bound (ELBO), is given by: ELBO ( ϕ , θ ) = E z ∼ q ϕ ( z | x ) [ log ⁡ p θ ( x | z ) ] − D KL ( q ϕ ( z | x ) | | p ( z ) ) {\displaystyle {\text{ELBO}}(\phi ,\theta )=\mathbb {E} _{z\sim q_{\phi }(z|x)}[\log p_{\theta }(x|z)]-D_{\text{KL}}(q_{\phi }(z|x)||p(z))} where q ϕ ( z | x ) {\displaystyle q_{\phi }(z|x)} is the encoder (recognition model), p θ ( x | z ) {\displaystyle p_{\theta }(x|z)} is the decoder (generative model), and p ( z ) {\displaystyle p(z)} is the prior distribution over latent variables. The gradient of ELBO with respect to θ {\displaystyle \theta } is simply E z ∼ q ϕ ( z | x ) [ ∇ θ log ⁡ p θ ( x | z ) ] ≈ 1 L ∑ l = 1 L ∇ θ log ⁡ p θ ( x | z l ) {\displaystyle \mathbb {E} _{z\sim q_{\phi }(z|x)}[\nabla _{\theta }\log p_{\theta }(x|z)]\approx {\frac {1}{L}}\sum _{l=1}^{L}\nabla _{\theta }\log p_{\theta }(x|z_{l})} but the gradient with respect to ϕ {\displaystyle \phi } requires the trick. Express the sampling operation z ∼ q ϕ ( z | x ) {\displaystyle z\sim q_{\phi }(z|x)} as: z = μ ϕ ( x ) + σ ϕ ( x ) ⊙ ϵ , ϵ ∼ N ( 0 , I ) {\displaystyle z=\mu _{\phi }(x)+\sigma _{\phi }(x)\odot \epsilon ,\quad \epsilon \sim {\mathcal {N}}(0,I)} where μ ϕ ( x ) {\displaystyle \mu _{\phi }(x)} and σ ϕ ( x ) {\displaystyle \sigma _{\phi }(x)} are the outputs of the encoder network, and ⊙ {\displaystyle \odot } denotes element-wise multiplication. Then we have ∇ ϕ ELBO ( ϕ , θ ) = E ϵ ∼ N ( 0 , I ) [ ∇ ϕ log ⁡ p θ ( x | z ) + ∇ ϕ log ⁡ q ϕ ( z | x ) − ∇ ϕ log ⁡ p ( z ) ] {\displaystyle \nabla _{\phi }{\text{ELBO}}(\phi ,\theta )=\mathbb {E} _{\epsilon \sim {\mathcal {N}}(0,I)}[\nabla _{\phi }\log p_{\theta }(x|z)+\nabla _{\phi }\log q_{\phi }(z|x)-\nabla _{\phi }\log p(z)]} where z = μ ϕ ( x ) + σ ϕ ( x ) ⊙ ϵ {\displaystyle z=\mu _{\phi }(x)+\sigma _{\phi }(x)\odot \epsilon } . This allows us to estimate the gradient using Monte Carlo sampling: ∇ ϕ ELBO ( ϕ , θ ) ≈ 1 L ∑ l = 1 L [ ∇ ϕ log ⁡ p θ ( x | z l ) + ∇ ϕ log ⁡ q ϕ ( z l | x ) − ∇ ϕ log ⁡ p ( z l ) ] {\displaystyle \nabla _{\phi }{\text{ELBO}}(\phi ,\theta )\approx {\frac {1}{L}}\sum _{l=1}^{L}[\nabla _{\phi }\log p_{\theta }(x|z_{l})+\nabla _{\phi }\log q_{\phi }(z_{l}|x)-\nabla _{\phi }\log p(z_{l})]} where z l = μ ϕ ( x ) + σ ϕ ( x ) ⊙ ϵ l {\displaystyle z_{l}=\mu _{\phi }(x)+\sigma _{\phi }(x)\odot \epsilon _{l}} and ϵ l ∼ N ( 0 , I ) {\displaystyle \epsilon _{l}\sim {\mathcal {N}}(0,I)} for l = 1 , … , L {\displaystyle l=1,\ldots ,L} . This formulation enables backpropagation through the sampling process, allowing for end-to-end training of the VAE model using stochastic gradient descent or its variants. === Variational inference === More generally, the trick allows using stochastic gradient descent for variational inference. Let the variational objective (ELBO) be of the form: ELBO ( ϕ ) = E z ∼ q ϕ ( z ) [ log ⁡ p ( x , z ) − log ⁡ q ϕ ( z ) ] {\displaystyle {\text{ELBO}}(\phi )=\mathbb {E} _{z\sim q_{\phi }(z)}[\log p(x,z)-\log q_{\phi }(z)]} Using the reparameterization trick, we can estimate the gradient of this objective with respect to ϕ {\displaystyle \phi } : ∇ ϕ ELBO ( ϕ ) ≈ 1 L ∑ l = 1 L ∇ ϕ [ log ⁡ p ( x , g ϕ ( ϵ l ) ) − log ⁡ q ϕ ( g ϕ ( ϵ l ) ) ] , ϵ l ∼ p ( ϵ ) {\displaystyle \nabla _{\phi }{\text{ELBO}}(\phi )\approx {\frac {1}{L}}\sum _{l=1}^{L}\nabla _{\phi }[\log p(x,g_{\phi }(\epsilon _{l}))-\log q_{\phi }(g_{\phi }(\epsilon _{l}))],\quad \epsilon _{l}\sim p(\epsilon )} === Dropout === The reparameterization trick has been applied to reduce the variance in dropout, a regularization technique in neural networks. The original dropout can be reparameterized with Bernoulli distributions: y = ( W ⊙ ϵ ) x , ϵ i j ∼ Bernoulli ( α i j ) {\displaystyle y=(W\odot \epsilon )x,\quad \epsilon _{ij}\sim {\text{Bernoulli}}(\alpha _{ij})} where W {\displaystyle W} is the weight matrix, x {\displaystyle x} is the input, and α i j {\displaystyle \alpha _{ij}} are the (fixed) dropout rates. More generally, other distributions can be used than the Bernoulli distribution, such as the gaussian noise: y i = μ i + σ i ⊙ ϵ i , ϵ i ∼ N ( 0 , I ) {\displaystyle y_{i}=\mu _{i}+\sigma _{i}\odot \epsilon _{i},\quad \epsilon _{i}\sim {\mathcal {N}}(0,I)} where μ i = m i ⊤ x {\displaystyle \mu _{i}=\mathbf {m} _{i}^{\top }x} and σ i 2 = v i ⊤ x 2 {\displaystyle \sigma _{i}^{2}=\mathbf {v} _{i}^{\top }x^{2}} , with m i {\displaystyle \mathbf {m} _{i}} and v i {\displaystyle \mathbf {v} _{i}} being the mean and variance of the i {\displaystyle i} -th output neuron. The reparameterization trick can be applied to all such cases, resulting in the variational dropout method.

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  AI Video Generators: Free vs Paid (2026)

  In search of the best AI video generator? An AI video generator is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI video generator 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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  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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  Frederick Jelinek

  Frederick Jelinek (18 November 1932 – 14 September 2010) was a Czech-American researcher in information theory, automatic speech recognition, and natural language processing. He is well known for his oft-quoted statement, "Every time I fire a linguist, the performance of the speech recognizer goes up". Jelinek was born in Czechoslovakia before World War II and emigrated with his family to the United States in the early years of the communist regime. He studied engineering at the Massachusetts Institute of Technology and taught for 10 years at Cornell University before accepting a job at IBM Research. In 1961, he married Czech screenwriter Milena Jelinek. At IBM, his team advanced approaches to computer speech recognition and machine translation. After IBM, he went to head the Center for Language and Speech Processing at Johns Hopkins University for 17 years, where he was still working on the day he died. == Personal life == Jelinek was born on November 18, 1932, as Bedřich Jelínek in Kladno to Vilém and Trude Jelínek. His father was Jewish; his mother was born in Switzerland to Czech Catholic parents and had converted to Judaism. Jelínek senior, a dentist, had planned early to escape Nazi occupation and flee to England; he arranged for a passport, visa, and the shipping of his dentistry materials. The couple planned to send their son to an English private school. However, Vilém decided to stay at the last minute and was eventually sent to the Theresienstadt concentration camp, where he died in 1945. The family was forced to move to Prague in 1941, but Frederick, his sister and mother—thanks to the latter's background—escaped the concentration camps. After the war, Jelinek entered in the gymnasium, despite having missed several years of schooling because education of Jewish children had been forbidden since 1942. His mother, anxious that her son should get a good education, made great efforts for their emigration, especially when it became clear he would not be allowed to even attempt the graduation examination. His mother hoped her son would become a physician, but Jelinek dreamed of being a lawyer. He studied engineering in evening classes at the City College of New York and received stipends from the National Committee for a Free Europe that allowed him to study at the Massachusetts Institute of Technology. About his choice of specialty, he said: "Fortunately, to electrical engineering there belonged a discipline whose aim was not the construction of physical systems: the theory of information". He obtained his Ph.D. in 1962, with Robert Fano as his adviser. In 1957, Jelinek paid an unexpected visit to Prague. He had been in Vienna and applied for a visa, hoping to see his former acquaintances again. He met with his old friend Miloš Forman, who introduced him to film student Milena Tobolová—whose screenplay had been the basis for the movie Easy Life (Snadný život). His flight back to the U.S. had a stopover in Munich, during which he called her to propose. Tobolová was considered a dissident and the authorities were not happy with her film. Jelinek asked for help from Jerome Wiesner and Cyrus Eaton, the latter who lobbied Nikita Khrushchev. Following the inauguration of John F. Kennedy, a group of Czech dissidents were allowed to emigrate in January 1961. Thanks to the lobbying, the future Milena Jelinek was one of them. After completing his graduate studies, Jelinek, who had developed an interest in linguistics, had plans to work with Charles F. Hockett at Cornell University. However these fell through and during the next ten years he continued to study information theory. Having previously worked at IBM during a sabbatical, he began full-time work there in 1972—at first on leave for Cornell, but permanently from 1974. He remained there for over twenty years. Although at first he had been offered a regular research job, upon his arrival he learned that Josef Raviv had recently been promoted to head of the newly opened IBM Haifa Research Laboratory, and became head of the Continuous Speech Recognition group at the Thomas J. Watson Research Center. Despite his team's successes in this area, Jelinek's work remained little known in his home country because Czech scientists were not allowed to participate in key conferences. After the 1989 fall of communism, Jelinek helped establish scientific relationships, regularly visiting to lecture and helping to persuade IBM to establish a computing centre at Charles University. In 1993, he retired from IBM and went to Johns Hopkins University's Center for Language and Speech Processing, where he was director and Julian Sinclair Smith Professor of Electrical and Computer Engineering. He was still working there at the time of his death; Jelinek died of a heart attack at the close of an otherwise normal workday in mid-September 2010. He was survived by his wife, daughter and son, sister, stepsister, and three grandchildren, including Sophie Gold Jelinek. == Research and legacy == Information theory was a fashionable scientific approach in the mid '50s. However, pioneer Claude Shannon wrote in 1956 that this trendiness was dangerous. He said, "Our fellow scientists in many different fields, attracted by the fanfare and by the new avenues opened to scientific analysis, are using these ideas in their own problems ... It will be all too easy for our somewhat artificial prosperity to collapse overnight when it is realized that the use of a few exciting words like information, entropy, redundancy, do not solve all our problems." During the next decade, a combination of factors shut down the application of information theory to natural language processing (NLP) problems—in particular machine translation. One factor was the 1957 publication of Noam Chomsky's Syntactic Structures, which stated, "probabilistic models give no insight into the basic problems of syntactic structure". This accorded well with the philosophy of the artificial intelligence research of the time, which promoted rule-based approaches. The other factor was the 1966 ALPAC report, which recommended that the government should stop funding research into machine translation. ALPAC chairman John Pierce later said that the field was filled with "mad inventors or untrustworthy engineers". He said that the underlying linguistic problems must be solved before attempts at NLP could be reasonably made. These elements essentially halted research in the field. Jelinek had begun to develop an interest in linguistics after the immigration of his wife, who initially enrolled in the MIT linguistics program with the help of Roman Jakobson. Jelinek often accompanied her to Chomsky's lectures, and even discussed the possibility of changing orientation with his adviser. Fano was "really upset", and after the failure of his project with Hockett at Cornell, he did not return to this field of research until starting work at IBM. The scope of research at IBM was considerably different from that of most other teams. According to Mark Liberman, "While [Jelinek] was leading IBM's effort to solve the general dictation problem during the decade or so following 1972, most other U.S. companies and academic researchers were working on very limited problems ... or were staying out of the field entirely". Jelinek regarded speech recognition as an information theory problem—a noisy channel, in this case the acoustic signal—which some observers considered a daring approach. The concept of perplexity was introduced in their first model, New Raleigh Grammar, which was published in 1976 as the paper "Continuous Speech Recognition by Statistical Methods" in the journal Proceedings of the IEEE. According to Young, the basic noisy channel approach "reduced the speech recognition problem to one of producing two statistical models". Whereas New Raleigh Grammar was a hidden Markov model, their next model, called Tangora, was broader and involved n-grams, specifically trigrams. Even though "it was obvious to everyone that this model was hopelessly impoverished", it was not improved upon until Jelinek presented another paper in 1999. The same trigram approach was applied to phones in single words. Although the identification of parts of speech turned out not to be very useful for speech recognition, tagging methods developed during these projects are now used in various NLP applications. The incremental research techniques developed at IBM eventually became dominant in the field after DARPA, in the mid-80s, returned to NLP research and imposed that methodology to participating teams, shared common goals, data, and precise evaluation metrics. The Continuous Speech Recognition Group's research, which required large amounts of data to train the algorithms, eventually led to the creation of the Linguistic Data Consortium. In the 1980s, although the broader problem of speech recognition remained unsolved, they sought to apply the methods developed to other problems; machine translat

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  Leakage (machine learning)

  In statistics and machine learning, leakage (also known as data leakage or target leakage) refers to the use of information during model training that would not be available at prediction time. This results in overly optimistic performance estimates, as the model appears to perform better during evaluation than it actually would in a production environment. Leakage is often subtle and indirect, making it difficult to detect and eliminate. It can lead a statistician or modeler to select a suboptimal model, which may be outperformed by a leakage-free alternative. == Leakage modes == Leakage can occur at multiple stages of the machine learning workflow. Broadly, its sources can be divided into two categories: those arising from features and those arising from training examples. === Feature leakage === Feature or column-wise leakage is caused by the inclusion of columns which are one of the following: a duplicate label, a proxy for the label, or the label itself. These features, known as anachronisms, will not be available when the model is used for predictions, and result in leakage if included when the model is trained. For example, including a "MonthlySalary" column when predicting "YearlySalary"; or "MinutesLate" when predicting "IsLate". === Training example leakage === Row-wise leakage is caused by improper sharing of information between rows of data. Types of row-wise leakage include: Premature featurization; leaking from premature featurization before Cross-validation/Train/Test split (must fit MinMax/ngrams/etc on only the train split, then transform the test set) Duplicate rows between train/validation/test (for example, oversampling a dataset to pad its size before splitting; or, different rotations/augmentations of a single image; bootstrap sampling before splitting; or duplicating rows to up sample the minority class) Non-independent and identically distributed random (non-IID) data Time leakage (for example, splitting a time-series dataset randomly instead of newer data in test set using a train/test split or rolling-origin cross-validation) Group leakage—not including a grouping split column (for example, Andrew Ng's group had 100k x-rays of 30k patients, meaning ~3 images per patient. The paper used random splitting instead of ensuring that all images of a patient were in the same split. Hence the model partially memorized the patients instead of learning to recognize pneumonia in chest x-rays.) A 2023 review found data leakage to be "a widespread failure mode in machine-learning (ML)-based science", having affected at least 294 academic publications across 17 disciplines, and causing a potential reproducibility crisis. == Detection == Data leakage in machine learning can be detected through various methods, focusing on performance analysis, feature examination, data auditing, and model behavior analysis. Performance-wise, unusually high accuracy or significant discrepancies between training and test results often indicate leakage. Inconsistent cross-validation outcomes may also signal issues. Feature examination involves scrutinizing feature importance rankings and ensuring temporal integrity in time series data. A thorough audit of the data pipeline is crucial, reviewing pre-processing steps, feature engineering, and data splitting processes. Detecting duplicate entries across dataset splits is also important. For language models, the Min-K% method can detect the presence of data in a pretraining dataset. It presents a sentence suspected to be present in the pretraining dataset, and computes the log-likelihood of each token, then compute the average of the lowest K of these. If this exceeds a threshold, then the sentence is likely present. This method is improved by comparing against a baseline of the mean and variance. Analyzing model behavior can reveal leakage. Models relying heavily on counter-intuitive features or showing unexpected prediction patterns warrant investigation. Performance degradation over time when tested on new data may suggest earlier inflated metrics due to leakage. Advanced techniques include backward feature elimination, where suspicious features are temporarily removed to observe performance changes. Using a separate hold-out dataset for final validation before deployment is advisable.

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  Evaluation of machine translation

  Various methods for the evaluation for machine translation have been employed. This article focuses on the evaluation of the output of machine translation, rather than on performance or usability evaluation. == Round-trip translation == A typical way for lay people to assess machine translation quality is to translate from a source language to a target language and back to the source language with the same engine. Though intuitively this may seem like a good method of evaluation, it has been shown that round-trip translation is a "poor predictor of quality". The reason why it is such a poor predictor of quality is reasonably intuitive. A round-trip translation is not testing one system, but two systems: the language pair of the engine for translating into the target language, and the language pair translating back from the target language. Consider the following examples of round-trip translation performed from English to Italian and Portuguese from Somers (2005): In the first example, where the text is translated into Italian then back into English—the English text is significantly garbled, but the Italian is a serviceable translation. In the second example, the text translated back into English is perfect, but the Portuguese translation is meaningless; the program thought "tit" was a reference to a tit (bird), which was intended for a "tat", a word it did not understand. While round-trip translation may be useful to generate a "surplus of fun," the methodology is deficient for serious study of machine translation quality. == Human evaluation == This section covers two of the large scale evaluation studies that have had significant impact on the field—the ALPAC 1966 study and the ARPA study. === Automatic Language Processing Advisory Committee (ALPAC) === One of the constituent parts of the ALPAC report was a study comparing different levels of human translation with machine translation output, using human subjects as judges. The human judges were specially trained for the purpose. The evaluation study compared an MT system translating from Russian into English with human translators, on two variables. The variables studied were "intelligibility" and "fidelity". Intelligibility was a measure of how "understandable" the sentence was, and was measured on a scale of 1–9. Fidelity was a measure of how much information the translated sentence retained compared to the original, and was measured on a scale of 0–9. Each point on the scale was associated with a textual description. For example, 3 on the intelligibility scale was described as "Generally unintelligible; it tends to read like nonsense but, with a considerable amount of reflection and study, one can at least hypothesize the idea intended by the sentence". Intelligibility was measured without reference to the original, while fidelity was measured indirectly. The translated sentence was presented, and after reading it and absorbing the content, the original sentence was presented. The judges were asked to rate the original sentence on informativeness. So, the more informative the original sentence, the lower the quality of the translation. The study showed that the variables were highly correlated when the human judgment was averaged per sentence. The variation among raters was small, but the researchers recommended that at the very least, three or four raters should be used. The evaluation methodology managed to separate translations by humans from translations by machines with ease. The study concluded that, "highly reliable assessments can be made of the quality of human and machine translations". === Advanced Research Projects Agency (ARPA) === As part of the Human Language Technologies Program, the Advanced Research Projects Agency (ARPA) created a methodology to evaluate machine translation systems, and continues to perform evaluations based on this methodology. The evaluation programme was instigated in 1991, and continues to this day. Details of the programme can be found in White et al. (1994) and White (1995). The evaluation programme involved testing several systems based on different theoretical approaches; statistical, rule-based and human-assisted. A number of methods for the evaluation of the output from these systems were tested in 1992 and the most recent suitable methods were selected for inclusion in the programmes for subsequent years. The methods were; comprehension evaluation, quality panel evaluation, and evaluation based on adequacy and fluency. Comprehension evaluation aimed to directly compare systems based on the results from multiple choice comprehension tests, as in Church et al. (1993). The texts chosen were a set of articles in English on the subject of financial news. These articles were translated by professional translators into a series of language pairs, and then translated back into English using the machine translation systems. It was decided that this was not adequate for a standalone method of comparing systems and as such abandoned due to issues with the modification of meaning in the process of translating from English. The idea of quality panel evaluation was to submit translations to a panel of expert native English speakers who were professional translators and get them to evaluate them. The evaluations were done on the basis of a metric, modelled on a standard US government metric used to rate human translations. This was good from the point of view that the metric was "externally motivated", since it was not specifically developed for machine translation. However, the quality panel evaluation was very difficult to set up logistically, as it necessitated having a number of experts together in one place for a week or more, and furthermore for them to reach consensus. This method was also abandoned. Along with a modified form of the comprehension evaluation (re-styled as informativeness evaluation), the most popular method was to obtain ratings from monolingual judges for segments of a document. The judges were presented with a segment, and asked to rate it for two variables, adequacy and fluency. Adequacy is a rating of how much information is transferred between the original and the translation, and fluency is a rating of how good the English is. This technique was found to cover the relevant parts of the quality panel evaluation, while at the same time being easier to deploy, as it didn't require expert judgment. Measuring systems based on adequacy and fluency, along with informativeness is now the standard methodology for the ARPA evaluation program. == Automatic evaluation == In the context of this article, a metric is a measurement. A metric that evaluates machine translation output represents the quality of the output. The quality of a translation is inherently subjective, there is no objective or quantifiable "good." Therefore, any metric must assign quality scores so they correlate with the human judgment of quality. That is, a metric should score highly translations that humans score highly, and give low scores to those humans give low scores. Human judgment is the benchmark for assessing automatic metrics, as humans are the end-users of any translation output. The measure of evaluation for metrics is correlation with human judgment. This is generally done at two levels, at the sentence level, where scores are calculated by the metric for a set of translated sentences, and then correlated against human judgment for the same sentences. And at the corpus level, where scores over the sentences are aggregated for both human judgments and metric judgments, and these aggregate scores are then correlated. Figures for correlation at the sentence level are rarely reported, although Banerjee et al. (2005) do give correlation figures that show that, at least for their metric, sentence-level correlation is substantially worse than corpus level correlation. While not widely reported, it has been noted that the genre, or domain, of a text has an effect on the correlation obtained when using metrics. Coughlin (2003) reports that comparing the candidate text against a single reference translation does not adversely affect the correlation of metrics when working in a restricted domain text. Even if a metric correlates well with human judgment in one study on one corpus, this successful correlation may not carry over to another corpus. Good metric performance, across text types or domains, is important for the reusability of the metric. A metric that only works for text in a specific domain is useful, but less useful than one that works across many domains—because creating a new metric for every new evaluation or domain is undesirable. Another important factor in the usefulness of an evaluation metric is to have a good correlation, even when working with small amounts of data, that is candidate sentences and reference translations. Turian et al. (2003) point out that, "Any MT evaluation measure is less reliable on shorter translations", and

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  Android Auto

  Android Auto is a mobile app developed by Google to mirror features of a smartphone (or other Android device) on a car's dashboard information and entertainment head unit. Once an Android device is paired with the car's head unit, the system can mirror some apps on the vehicle's display. Supported apps include GPS mapping and navigation, music playback, SMS, telephone, and Web search. The system supports both touchscreen and button-controlled head units. Hands-free operation through voice commands is available and recommended to reduce driver distraction. Android Auto is part of the Open Automotive Alliance, a joint effort of 28 automobile manufacturers, with Nvidia as tech supplier, available in 36 countries. == History == Android Auto was revealed at Google I/O 2014. The app was released to the public on March 19, 2015. In November 2016, Google implemented an app that would run the Android Auto UI on the mobile device. In July 2019, Android Auto received its first major UI rework, which among other changes, brought an app drawer to Android Auto for the first time. Google also announced that the app's ability to be used on a phone would be discontinued in favor of Google Assistant's drive mode. In December 2020, Google announced the expansion of Android Auto to 36 additional countries in Europe, Indonesia, and more. In April 2021, Android Auto launched in Belgium, Denmark, Netherlands, Norway, Portugal, and Sweden. Google announced in May 2022 a user interface redesign for Android Auto, codenamed CoolWalk, which aims to simplify the app's usage, and make it more adaptable to screens of different orientations and aspect ratios. The redesign incorporates a new split-screen layout, where Google Maps can be displayed alongside a music player. CoolWalk was originally slated to launch in Q3 2022. In June 2022, Android Auto no longer ran directly on a mobile device; the app permitting this was decommissioned, in favor of a Driving Mode built into the Google Assistant app for a similar purpose. In November 2022, the CoolWalk user interface was released in Android Auto's beta program. == Functionality == Android Auto is software that can be utilized from an Android mobile device, acting as a vehicle's dashboard head unit. Once the user's Android device is connected to the vehicle, the head unit will serve as an external display for the Android device, presenting supported software in a car-specific user interface provided by the Android Auto app. In Android Auto's first iterations, the device was required to be connected via USB to the car. For some time, starting in November 2016, Google added the option to run Android Auto as a regular app on an Android device, allowing users to choose whether to use Android Auto on a personal phone or tablet, rather than on a compatible automotive head unit. This app was decommissioned in June 2022 in favor of a Driving Mode built into the Google Assistant app. At CES 2018, Google confirmed that the Google Assistant would be coming to Android Auto later in the year. An Android Auto SDK has been released, allowing third parties to modify their apps to work with Android Auto; initially, only APIs for music and messaging apps were available. == Head unit support == In May 2015, Hyundai became the first manufacturer to offer Android Auto support, making it first available in the 2015 Hyundai Sonata. Automobile manufacturers that will offer Android Auto support in their cars include Abarth, Acura, Alfa Romeo, Aston Martin, Audi, Bentley, Buick, BMW, BYD, Cadillac, Chevrolet, Chrysler, Citroën, Dodge, Ferrari, Fiat, Ford, GMC, Genesis, Holden, Honda, Hyundai, Infiniti, Jaguar Land Rover, Jeep, Kia, Lamborghini, Lexus, Lincoln, Mahindra and Mahindra, Maserati, Maybach, Mazda, Mercedes-Benz, Mitsubishi, Nissan, Opel, Peugeot, Porsche, RAM, Renault, SEAT, Škoda, SsangYong, Subaru, Suzuki, Tata Motors Cars, Toyota, Volkswagen and Volvo. Additionally, aftermarket car-audio systems supporting Android Auto add the technology into host vehicles, including Pioneer, Kenwood, Panasonic, and Sony. == Criticism == In May 2019, Italy filed an antitrust complaint targeting Android Auto, citing a Google policy of allowing third-parties to only offer media and messaging apps on the platform, preventing Enel from offering an app for locating vehicle charging stations. Google announced a new SDK, to be released to select partners in August 2020 and made generally available by the end of the year. == Availability == As of December 2025, Android Auto is available in 46 countries:

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  DFA minimization

  In automata theory (a branch of theoretical computer science), DFA minimization is the task of transforming a given deterministic finite automaton (DFA) into an equivalent DFA that has a minimum number of states. Here, two DFAs are called equivalent if they recognize the same regular language. Several different algorithms accomplishing this task are known and described in standard textbooks on automata theory. == Minimal DFA == For each regular language, there also exists a minimal automaton that accepts it, that is, a DFA with a minimum number of states and this DFA is unique (except that states can be given different names). The minimal DFA ensures minimal computational cost for tasks such as pattern matching. There are three classes of states that can be removed or merged from the original DFA without affecting the language it accepts. Unreachable states are the states that are not reachable from the initial state of the DFA, for any input string. These states can be removed. Dead states are the states from which no final state is reachable. These states can be removed unless the automaton is required to be complete. Nondistinguishable states are those that cannot be distinguished from one another for any input string. These states can be merged. DFA minimization is usually done in three steps: remove dead and unreachable states (this will accelerate the following step), merge nondistinguishable states, optionally, re-create a single dead state ("sink" state) if the resulting DFA is required to be complete. == Unreachable states == The state p {\displaystyle p} of a deterministic finite automaton M = ( Q , Σ , δ , q 0 , F ) {\displaystyle M=(Q,\Sigma ,\delta ,q_{0},F)} is unreachable if no string w {\displaystyle w} in Σ ∗ {\displaystyle \Sigma ^{}} exists for which p = δ ∗ ( q 0 , w ) {\displaystyle p=\delta ^{}(q_{0},w)} . In this definition, Q {\displaystyle Q} is the set of states, Σ {\displaystyle \Sigma } is the set of input symbols, δ {\displaystyle \delta } is the transition function (mapping a state and an input symbol to a set of states), δ ∗ {\displaystyle \delta ^{}} is its extension to strings (also known as extended transition function), q 0 {\displaystyle q_{0}} is the initial state, and F {\displaystyle F} is the set of accepting (also known as final) states. Reachable states can be obtained with the following algorithm: Assuming an efficient implementation of the state sets (e.g. new_states) and operations on them (such as adding a state or checking whether it is present), this algorithm can be implemented with time complexity O ( n + m ) {\displaystyle O(n+m)} , where n {\displaystyle n} is the number of states and m {\displaystyle m} is the number of transitions of the input automaton. Unreachable states can be removed from the DFA without affecting the language that it accepts. == Nondistinguishable states == The following algorithms present various approaches to merging nondistinguishable states. === Hopcroft's algorithm === One algorithm for merging the nondistinguishable states of a DFA, due to Hopcroft (1971), is based on partition refinement, partitioning the DFA states into groups by their behavior. These groups represent equivalence classes of the Nerode congruence, whereby every two states are equivalent if they have the same behavior for every input sequence. That is, for every two states p1 and p2 that belong to the same block of the partition P, and every input word w, the transitions determined by w should always take states p1 and p2 to either states that both accept or states that both reject. It should not be possible for w to take p1 to an accepting state and p2 to a rejecting state or vice versa. The following pseudocode describes the form of the algorithm as given by Xu. Alternative forms have also been presented. The algorithm starts with a partition that is too coarse: every pair of states that are equivalent according to the Nerode congruence belong to the same set in the partition, but pairs that are inequivalent might also belong to the same set. It gradually refines the partition into a larger number of smaller sets, at each step splitting sets of states into pairs of subsets that are necessarily inequivalent. The initial partition is a separation of the states into two subsets of states that clearly do not have the same behavior as each other: the accepting states and the rejecting states. The algorithm then repeatedly chooses a set A from the current partition and an input symbol c, and splits each of the sets of the partition into two (possibly empty) subsets: the subset of states that lead to A on input symbol c, and the subset of states that do not lead to A. Since A is already known to have different behavior than the other sets of the partition, the subsets that lead to A also have different behavior than the subsets that do not lead to A. When no more splits of this type can be found, the algorithm terminates. Lemma. Given a fixed character c and an equivalence class Y that splits into equivalence classes B and C, only one of B or C is necessary to refine the whole partition. Example: Suppose we have an equivalence class Y that splits into equivalence classes B and C. Suppose we also have classes D, E, and F; D and E have states with transitions into B on character c, while F has transitions into C on character c. By the Lemma, we can choose either B or C as the distinguisher, let's say B. Then the states of D and E are split by their transitions into B. But F, which doesn't point into B, simply doesn't split during the current iteration of the algorithm; it will be refined by other distinguisher(s). Observation. All of B or C is necessary to split referring classes like D, E, and F correctly—subsets won't do. The purpose of the outermost if statement (if Y is in W) is to patch up W, the set of distinguishers. We see in the previous statement in the algorithm that Y has just been split. If Y is in W, it has just become obsolete as a means to split classes in future iterations. So Y must be replaced by both splits because of the Observation above. If Y is not in W, however, only one of the two splits, not both, needs to be added to W because of the Lemma above. Choosing the smaller of the two splits guarantees that the new addition to W is no more than half the size of Y; this is the core of the Hopcroft algorithm: how it gets its speed, as explained in the next paragraph. The worst case running time of this algorithm is O(ns log n), where n is the number of states and s is the size of the alphabet. This bound follows from the fact that, for each of the ns transitions of the automaton, the sets drawn from Q that contain the target state of the transition have sizes that decrease relative to each other by a factor of two or more, so each transition participates in O(log n) of the splitting steps in the algorithm. The partition refinement data structure allows each splitting step to be performed in time proportional to the number of transitions that participate in it. This remains the most efficient algorithm known for solving the problem, and for certain distributions of inputs its average-case complexity is even better, O(n log log n). Once Hopcroft's algorithm has been used to group the states of the input DFA into equivalence classes, the minimum DFA can be constructed by forming one state for each equivalence class. If S is a set of states in P, s is a state in S, and c is an input character, then the transition in the minimum DFA from the state for S, on input c, goes to the set containing the state that the input automaton would go to from state s on input c. The initial state of the minimum DFA is the one containing the initial state of the input DFA, and the accepting states of the minimum DFA are the ones whose members are accepting states of the input DFA. === Moore's algorithm === Moore's algorithm for DFA minimization is due to Edward F. Moore (1956). Like Hopcroft's algorithm, it maintains a partition that starts off separating the accepting from the rejecting states, and repeatedly refines the partition until no more refinements can be made. At each step, it replaces the current partition with the coarsest common refinement of s + 1 partitions, one of which is the current one and the rest of which are the preimages of the current partition under the transition functions for each of the input symbols. The algorithm terminates when this replacement does not change the current partition. Its worst-case time complexity is O(n2s): each step of the algorithm may be performed in time O(ns) using a variant of radix sort to reorder the states so that states in the same set of the new partition are consecutive in the ordering, and there are at most n steps since each one but the last increases the number of sets in the partition. The instances of the DFA minimization problem that cause the worst-case behavior are the same as for Hopcroft's algorithm. The number of steps th

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  Circular thresholding

  Circular thresholding is an algorithm for automatic image threshold selection in image processing. Most threshold selection algorithms assume that the values (e.g. intensities) lie on a linear scale. However, some quantities such as hue and orientation are a circular quantity, and therefore require circular thresholding algorithms. The example shows that the standard linear version of Otsu's method when applied to the hue channel of an image of blood cells fails to correctly segment the large white blood cells (leukocytes). In contrast the white blood cells are correctly segmented by the circular version of Otsu's method. == Methods == There are a relatively small number of circular image threshold selection algorithms. The following examples are all based on Otsu's method for linear histograms: (Tseng, Li and Tung 1995) smooth the circular histogram, and apply Otsu's method. The histogram is cyclically rotated so that the selected threshold is shifted to zero. Otsu's method and histogram rotation are applied iteratively until several heuristics involving class size, threshold location, and class variance are satisfied. (Wu et al. 2006) smooth the circular histogram until it contains only two peaks. The histogram is cyclically rotated so that the midpoint between the peaks is shifted to zero. Otsu's method and histogram rotation are applied iteratively until convergence of the threshold. (Lai and Rosin 2014) applied Otsu's method to the circular histogram. For the two class circular thresholding task they showed that, for a histogram with an even number of bins, the optimal solution for Otsu's criterion of within-class variance is obtained when the histogram is split into two halves. Therefore the optimal solution can be efficiently obtained in linear rather than quadratic time. == References and further reading == D.-C. Tseng, Y.-F. Li, and C.-T. Tung, Circular histogram thresholding for color image segmentation in Proc. Int. Conf. Document Anal. Recognit., 1995, pp. 673–676. J. Wu, P. Zeng, Y. Zhou, and C. Olivier, A novel color image segmentation method and its application to white blood cell image analysis in Proc. Int. Conf. Signal Process., vol. 2. 2006, pp. 16–20. Y.K. Lai, P.L. Rosin, Efficient Circular Thresholding, IEEE Trans. on Image Processing 23(3), 992–1001 (2014). doi:10.1109/TIP.2013.2297014

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  General Regionally Annotated Corpus of Ukrainian

  General Regionally Annotated Corpus of the Ukrainian Language (GRAC, Ukrainian: Генеральний регіонально анотований корпус української мови, romanized: Heneralnyi rehionalno anotovanyi korpus ukrainskoi movy, ГРАК, Ukrainian грак for rook) is a text corpus of the Ukrainian language comprising more than 2 billion tokens, intended for linguistic research in grammar, vocabulary, and the history of the Ukrainian literary language, as well as for use in compiling dictionaries and grammars. The corpus can be used for language study and also for preparing teaching materials, textbooks, learner’s dictionaries, and exercises using examples from real texts, taking into account frequency and collocational patterns, and so on. The corpus is not a model of standard Ukrainian: it may contain words and combinations that do not match current norms of the literary language. The corpus covers the period from 1816 to 2025, and as of 29 November 2025 it contains more than 812,000 texts by about 35,000 authors. == Composition of the corpus == In the 10th version of the corpus, available for searching from 20 October 2020, 35% consists of fiction. Some fiction genres are highlighted separately: children’s literature, folklore, dramatic works, and scripts. Among non-fiction texts: journalistic writing, including newspaper collections from 1888–1893, 1905, 1913–1918, 1919–1943, modern newspapers from different regions, and texts from online news/information sites; memoirs, letters, and diaries, including a sizeable corpus of Facebook texts representing blogs by people from all regions of Ukraine and the diaspora; scholarly and educational texts: monographs, dissertations, academic articles, textbooks; large subcorpora of academic literature in history, ethnography, philosophy, and law are singled out separately; religious texts, including two Ukrainian translations of the Bible; speeches and interviews. Some dictionaries that include phrasal examples and phraseology have also been incorporated, including the Ukrainian dictionary by Borys Hrinchenko and the Russian-Ukrainian idiomatic dictionary by I. Vyrhan and M. Pylynska. Using the corpus tools, these dictionaries can be searched not only for words, but also for lexico-grammatical patterns within examples and phraseological expressions. About 20% of the texts in the corpus are translations. The corpus includes translations from more than 80 languages, most of all from English and Russian. == Dating == Texts in the corpus are dated by the year of writing, or by the latest year in which a work could have been written; translated texts are dated by the year the translation was produced. A publication year may also be indicated, corresponding to the edition from which the text is taken. == Regional annotation == The corpus’s regional annotation is based on the modern administrative division of Ukraine. The corpus includes texts from all oblasts of Ukraine and from Crimea. A single text may belong to several regional subcorpora (if the author or translator was born, studied, or lived for a long time in different regions). In addition to regional subcorpora, there are subcorpora of works by authors of the Ukrainian diaspora (USA, Canada, Poland, Germany, the United Kingdom, France, etc.). These are mostly texts by emigrants of the 1940s, and to a lesser extent of 1917–1920s. == Morphological annotation == GRAC is based on the morphological analysis system nlp_uk, developed by specialists from the r2u group. The program analyzes the text and, for each word form, determines the lemma (lexeme) and tags (grammatical features). == Research based on the corpus == Research on the Ukrainian language has been carried out using the corpus, including studies of the historical dynamics of language norms, and letter and letter-combination frequencies for font development.

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  Janyce Wiebe

  Janyce Marbury Wiebe (1959–2018) was an American computer science specializing in natural language processing and known for her work on subjectivity, sentiment analysis, opinion mining, discourse processing, and word-sense disambiguation. == Early life and education == Wiebe was born in 1959, in Albany, New York. She majored in English at the Binghamton University, graduating in 1981, and completed a Ph.D. in computer science in 1990, at the University at Buffalo. Her dissertation, Recognizing Subjective Sentences: A Computational Investigation of Narrative Text, was supervised by philosopher William J. Rapaport. == Career == After postdoctoral research at the University of Toronto, she became an assistant professor at New Mexico State University in 1992. In 2000, she moved to the University of Pittsburgh, where she became a professor of computer science and director of the Intelligent Systems Program. == Recognition == Wiebe was named a Fellow of the Association for Computational Linguistics in 2015. == Death == She died of leukemia on December 10, 2018.

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