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JAUS Tool Set

The JAUS Tool Set (JTS) is a software engineering tool for the design of software services used in a distributed computing environment. JTS provides a graphical user interface (GUI) and supporting tools for the rapid design, documentation, and implementation of service interfaces that adhere to the Society of Automotive Engineers' standard AS5684A, the JAUS Service Interface Design Language (JSIDL). JTS is designed to support the modeling, analysis, implementation, and testing of the protocol for an entire distributed system. == Overview == The JAUS Tool Set (JTS) is a set of open source software specification and development tools accompanied by an open source software framework to develop Joint Architecture for Unmanned Systems (JAUS) designs and compliant interface implementations for simulations and control of robotic components per SAE-AS4 standards. JTS consists of the components: GUI based Service Editor: The Service Editor (referred to as the GUI in this document) provides a user friendly interface with which a system designer can specify and analyze formal specifications of Components and Services defined using the JAUS Service Interface Definition Language (JSIDL). Validator: A syntactic and semantic validator provides on-the-fly validation of specifications entered (or imported) by the user with respect to JSIDL syntax and semantics is integrated into the GUI. Specification Repository: A repository (or database) that is integrated into the GUI that allows for the storage of and encourages the reuse of existing formal specifications. C++ Code Generator: The Code Generator automatically generates C++ code that has a 1:1 mapping to the formal specifications. The generated code includes all aspects of the service, including the implementations of marshallers and unmarshallers for messages, and implementations of finite-state machines for protocol behavior that are effectively decoupled from application behavior. Document Generator: The Document Generator automatically generates documentation for sets of Service Definitions. Documents may be generated in several formats. Software Framework: The software framework implements the transport layer specification AS5669A, and provides the interfaces necessary to integrate the auto-generated C++ code with the transport layer implementation. Present transport options include UDP and TCP in wired or wireless networks, as well as serial connections. The transport layer itself is modular, and allows end-users to add additional support as needed. Wireshark Plugin: The Wireshark plugin implements a plugin to the popular network protocol analyzer called Wireshark. This plugin allows for the live capture and offline analysis of JAUS message-based communication at runtime. A built-in repository facilitates easy reuse of service interfaces and implementations traffic across the wire. The JAUS Tool Set can be downloaded from www.jaustoolset.org User documentation and community forum are also available at the site. == Release history == Following a successful Beta test, Version 1.0 of the JAUS Tool Set was released in July 2010. The initial offering focused on core areas of User Interface, HTML document generation, C++ code generation, and the software framework. The Version 1.1 update was released in October 2010. In addition to bug fixes and UI improvements, this version offered several important upgrades including enhancement to the Validator, Wireshark plug-in, and generated code. The JTS 2.0 release is scheduled for the second quarter of 2011 and further refines the Tool Set functionality: Protocol Validation: Currently, JTS provides validation for message creation, to ensure users cannot create invalid messages specifications. That capability does not currently exist for protocol definitions, but is being added. This will help ensure that users create all necessary elements of a service definition, and reduce user error. C# and Java Code Generation: Currently, JTS generates cross-platform C++ code. However, other languages including Java and C# are seeing a dramatic increase in their use in distributed systems, particularly in the development of graphical clients to embedded services. MS Word Document Generation: HTML and JSIDL output is supported, but native Office-Open-XML (OOXML) based MS Word generation has advantages in terms of output presentation, and ease of use for integration with other documents. Therefore, we plan to integrate MS Word service document generation. In addition, the development team has several additional goals that are not-yet-scheduled for a particular release window: Protocol Verification: This involves converting the JSIDL definition of a service into a PROMELA model, for validation by the SPIN model checking tool. Using PROMELA to model client and server interfaces will allow developers to formally validate JAUS services. End User Experience: We plan to conduct formal User Interface testing. This involves defining a set of tasks and use cases, asking users with various levels of JAUS experience to accomplish those tasks, and measuring performance and collecting feedback, to look for areas where the overall user experience can be improved. Improved Service Re-Use: JSIDL allows for inheritance of protocol descriptions, much like object-oriented programming languages allow child classes to re-use and extend behaviors defined by the parent class. At present, the generated code 'flattens' these state machines into a series of nested states which gives the correct interface behavior, but only if each single leaf (child) service is generated within its own component. This limits service re-use and can lead to a copy-and-paste of the same implementation across multiple components. The team is evaluating other inheritance solutions that would allow for multiple leaf (child) services to share access to a common parent, but at present the approach is sufficient to address the requirements of the JAUS Core Service Set. == Domains and application == The JAUS Tool Set is based on the JAUS Service Interface Definition Language (JSIDL), which was originally developed for application within the unmanned systems, or robotics, communities. As such, JTS has quickly gained acceptance as a tool for generation of services and interfaces compliant with the SAE AS-4 "JAUS" publications. Although usage statistics are not available, the Tool Set has been downloaded by representatives of US Army, Navy, Marines, and numerous defense contractors. It was also used in a commercial product called the JAUS Expansion Module sold by DeVivo AST, Inc. Since the JSIDL schema is independent of the data being exchanged, however, the Tool Set can be used for the design and implementation of a Service Oriented Architecture for any distributed systems environment that uses binary encoded message exchange. JSIDL is built on a two-layered architecture that separates the application layer and the transport layer, effectively decoupling the data being exchanges from the details of how that data moves from component to component. Furthermore, since the schema itself is widely generic, it's possible to define messages for any number of domains including but not limited to industrial control systems, remote monitoring and diagnostics, and web-based applications. == Licensing == JTS is released under the open source BSD license. The JSIDL Standard is available from the SAE. The Jr Middleware on which the Software Framework (Transport Layer) is based is open source under LGPL. Other packages distributed with JTS may have different licenses. == Sponsors == Development of the JAUS Tool Set was sponsored by several United States Department of Defense organizations: Office of Under Secretary of Defense for Acquisition, Technology & Logistics / Unmanned Warfare. Navy Program Executive Officer Littoral and Mine Navy Program Executive Officer Unmanned Aviation and Strike Weapons Office of Naval Research Air Force Research Lab
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HFST

Helsinki Finite-State Technology (HFST) is a computer programming library and set of utilities for natural language processing with finite-state automata and finite-state transducers. It is free and open-source software, released under a mix of the GNU General Public License version 3 (GPLv3) and the Apache License. == Features == The library functions as an interchanging interface to multiple backends, such as OpenFST, foma and SFST. The utilities comprise various compilers, such as hfst-twolc (a compiler for morphological two-level rules), hfst-lexc (a compiler for lexicon definitions) and hfst-regexp2fst (a regular expression compiler). Functions from Xerox's proprietary scripting language xfst is duplicated in hfst-xfst, and the pattern matching utility pmatch in hfst-pmatch, which goes beyond the finite-state formalism in having recursive transition networks (RTNs). The library and utilities are written in C++, with an interface to the library in Python and a utility for looking up results from transducers ported to Java and Python. Transducers in HFST may incorporate weights depending on the backend. For performing FST operations, this is currently only possible via the OpenFST backend. HFST provides two native backends, one designed for fast lookup (hfst-optimized-lookup), the other for format interchange. Both of them can be weighted. == Uses == HFST has been used for writing various linguistic tools, such as spell-checkers, hyphenators, and morphologies. Morphological dictionaries written in other formalisms have also been converted to HFST's formats.
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Lorien Pratt

Lorien Pratt is an American computer scientist known for contributions to transfer learning and for her work in promoting and developing the concept of decision intelligence. She is chief scientist and founder of Quantellia. Since 1988, she has conducted research on the use of machine learning as an academic, professor, industry analyst, and practicing data scientist. Pratt received her AB degree in computer science from Dartmouth College and her master's and doctorate degrees in computer science from Rutgers University. == Learning to Learn == She is best known for her book "Learning to Learn," co-edited with Sebastian Thrun, which provided an overview on how to use machine learning to better understand bias and generalization of discrete subjects. This approach, still largely theoretical when the book was published in 1998, is also called metalearning and is now a foundational underpinning of machine learning algorithms such as GPT-3 and DALL-E. == Research == === Transfer learning === Pratt's research includes early work in transfer learning where she developed the discriminability-based transfer (DBT) algorithm in 1993 during her tenure as a professor of computer science at Colorado School of Mines. This paper is considered one of the earliest academic works referring to the use of transfer in machine learning and has been cited over 400 times as foundational research for deep neural networks. === Decision intelligence === Since then, Pratt's research has continued to explore the relationships between machine learning and human cognition with the concept of decision intelligence, an emerging field of machine learning guided analytics designed to support human decision. Pratt introduced this concept in 2008, and this term has since been used by a number of vendors providing machine learning-guided analytics including Diwo, Peak AI, Sisu, and Tellius as the technologies used to support machine learning at scale have become easier to deploy, manage, and embed into software platforms. Pratt's work is cited as a core starting point for defining modern aspects of decision intelligence. Pratt's work at Quantellia since 2020 has focused on the use of decision intelligence to improve COVID-19-based outcomes.
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Top 10 AI Chatbots Compared (2026)

Shopping for the best AI chatbot? An AI chatbot 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 chatbot 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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Mentimeter

Mentimeter (or Menti for short) is a Swedish company based in Stockholm that develops and maintains an eponymous app used to create presentations with real-time feedback. == Foundation and background == Based in Stockholm, Sweden, the Mentimeter app was started by Swedish entrepreneur Johnny Warström and Niklas Ingvar as a response to unproductive meetings. The initial start-up budget was $500,000 raised by a group of prominent investors, including Per Appelgren in 2014, following the market's tendency to invest in Scandinavia. The app also focuses on online collaboration for the education sector, allowing students or public members to answer questions anonymously. The app enables users to share knowledge and real-time feedback on mobile devices with presentations, polls or brainstorming sessions in classes, meetings, gatherings, conferences and other group activities. == Achievements == By 2021, Mentimeter had over 270 million users and was one of Sweden's fastest-growing startups. The company also ranked #10 on 20 Fastest Growing 500 Startups Batch 16 Companies. It was ranked Stockholm's fastest growing company of the 2018 edition of the DI Gasell Award. Mentimeter has a freemium business model.
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Emma Brunskill

Emma Patricia Brunskill is an American computer scientist. Her research combines machine learning with human–computer interaction by studying the effects of AI systems in human-centered applications including educational software and healthcare, and the theory of reinforcement learning in situations where mistakes impose high risks or costs. She is an associate professor of computer science at Stanford University, where she also holds a courtesy appointment in the Stanford Graduate School of Education and is an affiliate of the King Center on Global Development. == Education and career == Brunskill grew up in Seattle and Edmonds, Washington, and entered the University of Washington at age 15. She graduated magna cum laude in 2000, with a bachelor's degree in computer engineering and physics. A Rhodes Scholarship took her to Magdalen College, Oxford in England, where she received a master's degree in neuroscience in 2002. After a summer working in Rwanda, she became a graduate student of computer science at the Massachusetts Institute of Technology, where she completed her Ph.D. in 2009. Her doctoral dissertation, Compact parametric models for efficient sequential decision making in high-dimensional, uncertain domains, was supervised by Nicholas Roy. After working as an NSF Postdoctoral Research Fellow at the University of California, Berkeley, she joined Carnegie Mellon University (CMU) in 2011 as an assistant professor of computer science. She moved from CMU to Stanford University in 2017. == Recognition == Brunskill was a 2014 recipient of the National Science Foundation CAREER Award and a 2015 recipient of the Office of Naval Research Young Investigator Award. She was one of two alumni of the University of Washington's Paul G. Allen School of Computer Science and Engineering to be honored in 2020 by the school's Alumni Impact Awards. She was elected as a Fellow of the Association for the Advancement of Artificial Intelligence in 2025, "for significant contributions to the field of reinforcement learning, and applications for societal benefit, in particular AI for education".
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How to Choose an AI Copywriting Tool

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

Round-trip translation (RTT), also known as back-and-forth translation, recursive translation and bi-directional translation, is the process of translating a word, phrase or text into another language (forward translation), then translating the result back into the original language (back translation), using machine translation (MT) software. It is often used by laypeople to evaluate a machine translation system, or to test whether a text is suitable for MT when they are unfamiliar with the target language. Because the resulting text can often differ substantially from the original, RTT can also be a source of entertainment. == Software quality == To compare the quality of different machine translation systems, users perform RTT and compare the resulting text to the original. The theory is that the closer the result of the RTT is to the original text, the higher the quality of the machine translation system. One of the problems with this technique is that if there is a problem with the resulting text it is impossible to know whether the error occurred in the forward translation, in the back translation, or in both. In addition, it is possible to get a good back translation from a bad forward translation. A study using the automatic evaluation methods BLEU and F-score compared five different free online translation programs, evaluating the quality of both the forward translation and the back translation, and found no correlation between the quality of the forward translation and the quality of the back translation (i.e., a high quality forward translation did not always correspond to a high quality back translation). The author concluded that RTT was a poor method of predicting the quality of machine translation software. This conclusion was reinforced by a more in-depth study also using automatic evaluation methods. A subsequent study which included human evaluation of the back translation in addition to automatic evaluation methods found that RTT might have some ability to predict the quality of a machine translation system not on a sentence-by-sentence basis but for larger texts. == Suitability of text for machine translation == It is also suggested that RTT can be used to determine whether a text is suitable for machine translation. The idea being that if RTT results in a text that is close to the original, the text is suitable for MT. If after using RTT, the resulting text is inaccurate, the source text can then be edited until a satisfactory result is achieved. One of the studies looking at RTT as a means of measuring MT system quality also looked at its ability to predict whether a text was suitable for machine translation. It found that using different types of text also did not result in any correlation between the quality of the forward translation and the quality of the back translation. In contrast another study using human evaluation found that there was a correlation between the quality of the forward translation and the back translation and that this correlation could be used to estimate the quality of the forward translation. This correlation could be used to estimate the quality of the forward translation and by simplifying the source text, improve the quality of the forward translation. == Entertainment == Although the use of RTT for assessing MT system quality or the suitability of a text for MT is in doubt, it is a way to have fun with machine translation. The text produced from an RTT can be comically bad. At one time websites existed for the sole purpose of performing RTT for fun. Other variations send the text through several languages before translating it back into the original or continue translating the text back and forth until it reaches equilibrium (i.e., the result of the back translation is identical to the text used for the forward translation). RTT as entertainment appeared in Philip K. Dick's novel Galactic Pot-Healer. The main character runs book titles and sayings through RTT then has his friends try to guess the original. The Australian television show Spicks and Specks had a contest called "Turning Japanese" which used RTT on song lyrics. Contestants needed to correctly guess the title of the song from which the lyrics were taken.
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Euratlas

Euratlas is a Switzerland-based software company dedicated to elaborate digital history maps of Europe. Founded in 2001, Euratlas has created a collection of history maps of Europe from year 1 AD to year 2000 AD that present the evolution of every country from the Roman Empire to present times. The evolution includes sovereign states and their administrative subdivisions, but also unorganized peoples and dependent territories. The maps show European country borders at regular intervals of 100 years, but not year by year. This leaves out many important turning points in history. Euratlas is considered a digital humanities company, and a scholar research software used in the field of historic cartography. It is broadly known among American and European universities, who mainly use Euratlas as a research tool and as a digital library atlas. == Sequential mapping policy == This concept was first designed by the German scholar Christian Kruse (1753–1827). Kruse, well aware that historical accounts are often biased for geographical, philosophical or political reasons, created a set of sequential maps in order to give a global vision of the successive political situations. Nowadays, the majority of atlases don't use this approach, but are event-based, like the well-known Penguin Atlas of History. The sequential approach intends to make the sequence of maps more neutral and suitable for students, historians and professionals of several fields. Although, this approach has been discussed as it leaves out many important history events that are not reflected on any of the maps because of the century interval. == Geo-referenced historical data == Initially, the European maps by century were developed as vector maps. From 2006 on, they have been converted to a geographic information system (GIS) database, enabling geo-referenced data capabilities. The map information is distributed in several layers: physical (geography information layer); political information layer (supranational entities, sovereign states, administrative divisions, dependent states and autonomous peoples); and special layers for cities and uncertain borders. The software database also contains much non-geographical information about political relationships between the various kinds of territories. == Map projection == Euratlas History Maps uses a Mercator projection, with the center in Europe. The maps include the North-African coast and the Near-East, offering a complete view of the Mediterranean Basin. The European Russia plains are shown, but not Scandinavia, specially Finland, which is cropped off the map view.
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Richard Zemel

Richard Stanley Zemel (born 1963) is a Canadian-American computer scientist and professor at Columbia University, Department of Computer Science, and a leading figure in the field of machine learning and computer vision. Zemel studied the history of science at Harvard University and obtained his B.A. in 1984. He continued his study at the Department of Computer Science of the University of Toronto under the supervision of Geoffrey Hinton. He obtained his M.Sc. and Ph.D. both in computer science in 1989 and 1994, respectively.
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Judea Pearl

Judea Pearl (Hebrew: יהודה פרל; born September 4, 1936) is an Israeli-American electrical engineer, computer scientist and philosopher, best known for championing the probabilistic approach to artificial intelligence and the development of Bayesian networks (see the article on belief propagation). He is also credited for developing a theory of causal and counterfactual inference based on structural models (see article on causality). In 2011, the Association for Computing Machinery (ACM) awarded Pearl with the Turing Award, the highest distinction in computer science, "for fundamental contributions to artificial intelligence through the development of a calculus for probabilistic and causal reasoning". He is the author of several books, including the technical Causality: Models, Reasoning and Inference, and The Book of Why, a book on causality aimed at the general public. Judea Pearl is the father of journalist Daniel Pearl, who was kidnapped and murdered by terrorists in Pakistan connected with Al-Qaeda and the International Islamic Front in 2002. == Biography == Judea Pearl was born in Tel Aviv, British Mandate for Palestine, in 1936 to Eliezer and Tova Pearl, who were Polish Jewish immigrants, grew up in Bnei Brak. His grandfather Chaim Pearl was one of Bnei Brak's founders. He is a descendant of Menachem Mendel of Kotzk on his mother's side. After serving in the Israel Defense Forces and joining a kibbutz, Pearl decided to study engineering in 1956. He received a B.S. in electrical engineering from the Technion 1960. That same year, he emigrated to the United States and pursued graduate studies. He received an M.S. in electrical engineering from the Newark College of Engineering (now New Jersey Institute of Technology) in 1961, and went on to receive an M.S. in physics from Rutgers University and a PhD in electrical engineering from the Polytechnic Institute of Brooklyn (now the New York University Tandon School of Engineering) in 1965. He worked at RCA Research Laboratories (now SRI International) in Princeton, New Jersey on superconductive parametric amplifiers and storage devices and at Electronic Memories, Inc., on advanced memory systems. When semiconductors "wiped out" Pearl's work, as he later expressed it, he joined UCLA's School of Engineering in 1970 and started work on probabilistic artificial intelligence. He is one of the founding editors of the Journal of Causal Inference. Pearl is currently a professor of computer science and statistics and director of the Cognitive Systems Laboratory at UCLA. He and his wife, Ruth, had three children. In addition, as of 2011, he is a member of the International Advisory Board of NGO Monitor. Former Israeli Chief Rabbi, Rabbi Yisrael Meir Lau, partnered with Judea Pearl in the documentary With My Whole Broken Heart. == Murder of Daniel Pearl == In 2002, his son, Daniel Pearl, a journalist working for the Wall Street Journal was kidnapped and murdered in Pakistan, leading Judea and the other members of the family and friends to create the Daniel Pearl Foundation. On the seventh anniversary of Daniel's death, Judea wrote an article in the Wall Street Journal titled Daniel Pearl and the Normalization of Evil: When will our luminaries stop making excuses for terror?. Emeritus Chief Rabbi Jonathan Sacks quoted Judea Pearl's beliefs in a lesson on Judaism: "I asked Judea Pearl, father of the murdered journalist Daniel Pearl, why he was working for reconciliation between Jews and Muslims...he replied with heartbreaking lucidity, 'Hate killed my son. Therefore I am determined to fight hate.'" == Views == On his religious views, Pearl states that he is a "practicing disbeliever." He is very connected to Jewish traditions such as holidays and kiddush on Friday night. Pearl sits on the NGO Monitor international advisory board, a right-wing organization based in Jerusalem that reports on non-governmental organization activity from a pro-Israel perspective. == Research == Pearl is credited for "laying the foundations of modern artificial intelligence, so computer systems can process uncertainty and relate causes to effects." He is one of the pioneers of Bayesian networks and the probabilistic approach to artificial intelligence, and one of the first to mathematize causal modeling in the empirical sciences. His work is also intended as a high-level cognitive model. He is interested in the philosophy of science, knowledge representation, nonstandard logics, and learning. Pearl is described as "one of the giants in the field of artificial intelligence" by UCLA computer science professor Richard E. Korf. His work on causality has "revolutionized the understanding of causality in statistics, psychology, medicine and the social sciences" according to the Association for Computing Machinery. === Notable contributions === A summary of Pearl's scientific contributions is available in a chronological account authored by Stuart J. Russell (2012). An annotated bibliography of Pearl's contributions was compiled by the ACM in 2012. A video describing Pearl's major contributions to AI is available here. Pearl's opinion pieces, touching on Jewish identity, the war on terrorism, and the Middle East conflict can be accessed here. === Books === Heuristics, Addison-Wesley, 1984 Probabilistic Reasoning in Intelligent Systems, Morgan-Kaufmann, 1988 Pearl, Judea (2000). Causality: Models, Reasoning, and Inference. Cambridge University Press. I Am Jewish: Personal Reflections Inspired by the Last Words of Daniel Pearl, Jewish Lights, 2004. (Winner of a 2004 National Jewish Book Award) Causal Inference in Statistics: A Primer, (with Madelyn Glymour and Nicholas Jewell), Wiley, 2016. ISBN 978-1-119-18684-7 A previous survey: Causal inference in statistics: An overview, Statistics Surveys, 3:96–146, 2009. Pearl, Judea; Dana Mackenzie (2018). "The Book of Why: The New Science of Cause and Effect". Science. 361 (6405): 855. Bibcode:2018Sci...361..855.. doi:10.1126/science.aau9731. === Awards ===
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Top 10 AI Clip Makers Compared (2026)

Comparing the best AI clip maker? An AI clip maker 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 AI clip maker slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
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Social software engineering

Social software engineering (SSE) is a branch of software engineering that is concerned with the social aspects of software development and the developed software. SSE focuses on the socialness of both software engineering and developed software. On the one hand, the consideration of social factors in software engineering activities, processes and CASE tools is deemed to be useful to improve the quality of both development process and produced software. Examples include the role of situational awareness and multi-cultural factors in collaborative software development. On the other hand, the dynamicity of the social contexts in which software could operate (e.g., in a cloud environment) calls for engineering social adaptability as a runtime iterative activity. Examples include approaches which enable software to gather users' quality feedback and use it to adapt autonomously or semi-autonomously. SSE studies and builds socially-oriented tools to support collaboration and knowledge sharing in software engineering. SSE also investigates the adaptability of software to the dynamic social contexts in which it could operate and the involvement of clients and end-users in shaping software adaptation decisions at runtime. Social context includes norms, culture, roles and responsibilities, stakeholder's goals and interdependencies, end-users perception of the quality and appropriateness of each software behaviour, etc. The participants of the 1st International Workshop on Social Software Engineering and Applications (SoSEA 2008) proposed the following characterization: Community-centered: Software is produced and consumed by and/or for a community rather than focusing on individuals Collaboration/collectiveness: Exploiting the collaborative and collective capacity of human beings Companionship/relationship: Making explicit the various associations among people Human/social activities: Software is designed consciously to support human activities and to address social problems Social inclusion: Software should enable social inclusion enforcing links and trust in communities Thus, SSE can be defined as "the application of processes, methods, and tools to enable community-driven creation, management, deployment, and use of software in online environments". One of the main observations in the field of SSE is that the concepts, principles, and technologies made for social software applications are applicable to software development itself as software engineering is inherently a social activity. SSE is not limited to specific activities of software development. Accordingly, tools have been proposed supporting different parts of SSE, for instance, social system design or social requirements engineering. Consequently vertical market software, such as software development tools, engineering tools, marketing tools or software that helps users in a decision-making process can profit from social components. Such vertical social software differentiates strongly in its user-base from traditional social software such as Yammer.
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Cobham's theorem

Cobham's theorem is a theorem in combinatorics on words that has important connections with number theory, notably transcendental numbers, and automata theory. Informally, the theorem gives the condition for the members of a set S of natural numbers written in bases b1 and base b2 to be recognised by finite automata. Specifically, consider bases b1 and b2 such that they are not powers of the same integer. Cobham's theorem states that S written in bases b1 and b2 is recognised by finite automata if and only if S differs by a finite set from a finite union of arithmetic progressions. The theorem was proved by Alan Cobham in 1969 and has since given rise to many extensions and generalisations. == Definitions == Let n > 0 {\displaystyle n>0} be an integer. The representation of a natural number n {\textstyle n} in base b {\textstyle b} is the sequence of digits n 0 n 1 ⋯ n h {\displaystyle n_{0}n_{1}\cdots n_{h}} such that n = n 0 + n 1 b + ⋯ + n h b h {\displaystyle n=n_{0}+n_{1}b+\cdots +n_{h}b^{h}} where 0 ≤ n 0 , n 1 , … , n h < b {\displaystyle 0\leq n_{0},n_{1},\ldots ,n_{h} 0 {\displaystyle n_{h}>0} . The word n 0 n 1 ⋯ n h {\displaystyle n_{0}n_{1}\cdots n_{h}} is often denoted ⟨ n ⟩ b {\displaystyle \langle n\rangle _{b}} , or more simply, n b {\displaystyle n_{b}} . A set of natural numbers S is recognisable in base b {\textstyle b} or more simply b {\textstyle b} -recognisable or b {\textstyle b} -automatic if the set { n b ∣ n ∈ S } {\displaystyle \{n_{b}\mid n\in S\}} of the representations of its elements in base b {\displaystyle b} is a language recognisable by a finite automaton on the alphabet { 0 , 1 , … , b − 1 } {\displaystyle \{0,1,\ldots ,b-1\}} . Two positive integers k {\displaystyle k} and ℓ {\displaystyle \ell } are multiplicatively independent if there are no non-negative integers p {\displaystyle p} and q {\displaystyle q} such that k p = ℓ q {\displaystyle k^{p}=\ell ^{q}} . For example, 2 and 3 are multiplicatively independent, but 8 and 16 are not since 8 4 = 16 3 {\displaystyle 8^{4}=16^{3}} . Two integers are multiplicatively dependent if and only if they are powers of a same third integer. == Problem statements == === Original problem statement === More equivalent statements of the theorem have been given. The original version by Cobham is the following: Another way to state the theorem is by using automatic sequences. Cobham himself calls them "uniform tag sequences." The following form is found in Allouche and Shallit's book:We can show that the characteristic sequence of a set of natural numbers S recognisable by finite automata in base k is a k-automatic sequence and that conversely, for all k-automatic sequences u {\displaystyle u} and all integers 0 ≤ i < k {\displaystyle 0\leq i 1 {\displaystyle \alpha >1} is the dominant eigenvalue of the matrix of morphism f {\displaystyle f} , namely, the matrix M ( f ) = ( m x , y ) x ∈ B , y ∈ A {\displaystyle M(f)=(m_{x,y})_{x\in B,y\in A}} , where m x , y {\displaystyle m_{x,y}} is the number of occurrences of the letter x {\displaystyle x} in the word f ( y ) {\displaystyle f(y)} . A set S of natural numbers is α {\displaystyle \alpha } -recognisable if its characteristic sequence s {\displaystyle s} is α {\displaystyle \alpha } -substitutive. A last definition: a Perron number is an algebraic number z > 1 {\displaystyle z>1} such that all its conjugates belong to the disc { z ′ ∈ C , | z ′ | < z } {\displaystyle \{z'\in \mathbb {C} ,|z'| Read more →
Best AI Content Generators in 2026

Trying to pick the best AI content generator? An AI content generator is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI content generator slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
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