In probability theory, an interacting particle system (IPS) is a stochastic process ( X ( t ) ) t ∈ R + {\displaystyle (X(t))_{t\in \mathbb {R} ^{+}}} on some configuration space Ω = S G {\displaystyle \Omega =S^{G}} given by a site space, a countably-infinite-order graph G {\displaystyle G} and a local state space, a compact metric space S {\displaystyle S} . More precisely IPS are continuous-time Markov jump processes describing the collective behavior of stochastically interacting components. IPS are the continuous-time analogue of stochastic cellular automata. Among the main examples are the voter model, the contact process, the asymmetric simple exclusion process (ASEP), the Glauber dynamics and in particular the stochastic Ising model. IPS are usually defined via their Markov generator giving rise to a unique Markov process using Markov semigroups and the Hille-Yosida theorem. The generator again is given via so-called transition rates c Λ ( η , ξ ) > 0 {\displaystyle c_{\Lambda }(\eta ,\xi )>0} where Λ ⊂ G {\displaystyle \Lambda \subset G} is a finite set of sites and η , ξ ∈ Ω {\displaystyle \eta ,\xi \in \Omega } with η i = ξ i {\displaystyle \eta _{i}=\xi _{i}} for all i ∉ Λ {\displaystyle i\notin \Lambda } . The rates describe exponential waiting times of the process to jump from configuration η {\displaystyle \eta } into configuration ξ {\displaystyle \xi } . More generally the transition rates are given in form of a finite measure c Λ ( η , d ξ ) {\displaystyle c_{\Lambda }(\eta ,d\xi )} on S Λ {\displaystyle S^{\Lambda }} . The generator L {\displaystyle L} of an IPS has the following form. First, the domain of L {\displaystyle L} is a subset of the space of "observables", that is, the set of real valued continuous functions on the configuration space Ω {\displaystyle \Omega } . Then for any observable f {\displaystyle f} in the domain of L {\displaystyle L} , one has L f ( η ) = ∑ Λ ∫ ξ : ξ Λ c = η Λ c c Λ ( η , d ξ ) [ f ( ξ ) − f ( η ) ] {\displaystyle Lf(\eta )=\sum _{\Lambda }\int _{\xi :\xi _{\Lambda ^{c}}=\eta _{\Lambda ^{c}}}c_{\Lambda }(\eta ,d\xi )[f(\xi )-f(\eta )]} . For example, for the stochastic Ising model we have G = Z d {\displaystyle G=\mathbb {Z} ^{d}} , S = { − 1 , + 1 } {\displaystyle S=\{-1,+1\}} , c Λ = 0 {\displaystyle c_{\Lambda }=0} if Λ ≠ { i } {\displaystyle \Lambda \neq \{i\}} for some i ∈ G {\displaystyle i\in G} and c i ( η , η i ) = exp [ − β ∑ j : | j − i | = 1 η i η j ] {\displaystyle c_{i}(\eta ,\eta ^{i})=\exp[-\beta \sum _{j:|j-i|=1}\eta _{i}\eta _{j}]} where η i {\displaystyle \eta ^{i}} is the configuration equal to η {\displaystyle \eta } except it is flipped at site i {\displaystyle i} . β {\displaystyle \beta } is a new parameter modeling the inverse temperature. == The Voter model == The voter model (usually in continuous time, but there are discrete versions as well) is a process similar to the contact process. In this process η ( x ) {\displaystyle \eta (x)} is taken to represent a voter's attitude on a particular topic. Voters reconsider their opinions at times distributed according to independent exponential random variables (this gives a Poisson process locally – note that there are in general infinitely many voters so no global Poisson process can be used). At times of reconsideration, a voter chooses one neighbor uniformly from amongst all neighbors and takes that neighbor's opinion. One can generalize the process by allowing the picking of neighbors to be something other than uniform. === Discrete time process === In the discrete time voter model in one dimension, ξ t ( x ) : Z → { 0 , 1 } {\displaystyle \xi _{t}(x):\mathbb {Z} \to \{0,1\}} represents the state of particle x {\displaystyle x} at time t {\displaystyle t} . Informally each individual is arranged on a line and can "see" other individuals that are within a radius, r {\displaystyle r} . If more than a certain proportion, θ {\displaystyle \theta } of these people disagree then the individual changes her attitude, otherwise she keeps it the same. Durrett and Steif (1993) and Steif (1994) show that for large radii there is a critical value θ c {\displaystyle \theta _{c}} such that if θ > θ c {\displaystyle \theta >\theta _{c}} most individuals never change, and for θ ∈ ( 1 / 2 , θ c ) {\displaystyle \theta \in (1/2,\theta _{c})} in the limit most sites agree. (Both of these results assume the probability of ξ 0 ( x ) = 1 {\displaystyle \xi _{0}(x)=1} is one half.) This process has a natural generalization to more dimensions, some results for this are discussed in Durrett and Steif (1993). === Continuous time process === The continuous time process is similar in that it imagines each individual has a belief at a time and changes it based on the attitudes of its neighbors. The process is described informally by Liggett (1985, 226), "Periodically (i.e., at independent exponential times), an individual reassesses his view in a rather simple way: he chooses a 'friend' at random with certain probabilities and adopts his position." A model was constructed with this interpretation by Holley and Liggett (1975). This process is equivalent to a process first suggested by Clifford and Sudbury (1973) where animals are in conflict over territory and are equally matched. A site is selected to be invaded by a neighbor at a given time.
Non-local means
Non-local means is an algorithm in image processing for image denoising. Unlike "local mean" filters, which take the mean value of a group of pixels surrounding a target pixel to smooth the image, non-local means filtering takes a mean of all pixels in the image, weighted by how similar these pixels are to the target pixel. This results in much greater post-filtering clarity, and less loss of detail in the image compared with local mean algorithms. If compared with other well-known denoising techniques, non-local means adds "method noise" (i.e. error in the denoising process) which looks more like white noise, which is desirable because it is typically less disturbing in the denoised product. Recently non-local means has been extended to other image processing applications such as deinterlacing, view interpolation, and depth maps regularization. == Definition == Suppose Ω {\displaystyle \Omega } is the area of an image, and p {\displaystyle p} and q {\displaystyle q} are two points within the image. Then, the algorithm is: u ( p ) = 1 C ( p ) ∫ Ω v ( q ) f ( p , q ) d q . {\displaystyle u(p)={1 \over C(p)}\int _{\Omega }v(q)f(p,q)\,\mathrm {d} q.} where u ( p ) {\displaystyle u(p)} is the filtered value of the image at point p {\displaystyle p} , v ( q ) {\displaystyle v(q)} is the unfiltered value of the image at point q {\displaystyle q} , f ( p , q ) {\displaystyle f(p,q)} is the weighting function, and the integral is evaluated ∀ q ∈ Ω {\displaystyle \forall q\in \Omega } . C ( p ) {\displaystyle C(p)} is a normalizing factor, given by C ( p ) = ∫ Ω f ( p , q ) d q . {\displaystyle C(p)=\int _{\Omega }f(p,q)\,\mathrm {d} q.} == Common weighting functions == The purpose of the weighting function, f ( p , q ) {\displaystyle f(p,q)} , is to determine how closely related the image at the point p {\displaystyle p} is to the image at the point q {\displaystyle q} . It can take many forms. === Gaussian === The Gaussian weighting function sets up a normal distribution with a mean, μ = B ( p ) {\displaystyle \mu =B(p)} and a variable standard deviation: f ( p , q ) = e − | B ( q ) − B ( p ) | 2 h 2 {\displaystyle f(p,q)=e^{-{{\left\vert B(q)-B(p)\right\vert ^{2}} \over h^{2}}}} where h {\displaystyle h} is the filtering parameter (i.e., standard deviation) and B ( p ) {\displaystyle B(p)} is the local mean value of the image point values surrounding p {\displaystyle p} . == Discrete algorithm == For an image, Ω {\displaystyle \Omega } , with discrete pixels, a discrete algorithm is required. u ( p ) = 1 C ( p ) ∑ q ∈ Ω v ( q ) f ( p , q ) {\displaystyle u(p)={1 \over C(p)}\sum _{q\in \Omega }v(q)f(p,q)} where, once again, v ( q ) {\displaystyle v(q)} is the unfiltered value of the image at point q {\displaystyle q} . C ( p ) {\displaystyle C(p)} is given by: C ( p ) = ∑ q ∈ Ω f ( p , q ) {\displaystyle C(p)=\sum _{q\in \Omega }f(p,q)} Then, for a Gaussian weighting function, f ( p , q ) = e − | B ( q ) 2 − B ( p ) 2 | h 2 {\displaystyle f(p,q)=e^{-{{\left\vert B(q)^{2}-B(p)^{2}\right\vert } \over h^{2}}}} where B ( p ) {\displaystyle B(p)} is given by: B ( p ) = 1 | R ( p ) | ∑ i ∈ R ( p ) v ( i ) {\displaystyle B(p)={1 \over |R(p)|}\sum _{i\in R(p)}v(i)} where R ( p ) ⊆ Ω {\displaystyle R(p)\subseteq \Omega } and is a square region of pixels surrounding p {\displaystyle p} and | R ( p ) | {\displaystyle |R(p)|} is the number of pixels in the region R {\displaystyle R} . == Efficient implementation == The computational complexity of the non-local means algorithm is quadratic in the number of pixels in the image, making it particularly expensive to apply directly. Several techniques were proposed to speed up execution. One simple variant consists of restricting the computation of the mean for each pixel to a search window centred on the pixel itself, instead of the whole image. Another approximation uses summed-area tables and fast Fourier transform to calculate the similarity window between two pixels, speeding up the algorithm by a factor of 50 while preserving comparable quality of the result.
Model Context Protocol
The Model Context Protocol (MCP) is an open standard and open-source framework introduced by Anthropic in November 2024 to standardize the way artificial intelligence (AI) systems like large language models (LLMs) integrate and share data with external tools, systems, and data sources. MCP provides a standardized interface for reading files, executing functions, and handling contextual prompts. Following its announcement, the protocol was adopted by major AI providers, including OpenAI and Google DeepMind. == Background == MCP was announced by Anthropic in November 2024 as an open standard for connecting AI assistants to data systems such as content repositories, business management tools, and development environments. The protocol was created at Anthropic by engineers David Soria Parra and Justin Spahr-Summers. It aims to address the challenge of information silos and legacy systems. Before MCP, developers often had to build custom connectors for each data source or tool, resulting in what Anthropic described as an "N×M" data integration problem. Earlier stop-gap approaches—such as OpenAI's 2023 "function-calling" API and the ChatGPT plug-in framework—solved similar problems but required vendor-specific connectors. MCP re-uses the message-flow ideas of the Language Server Protocol (LSP) and is transported over JSON-RPC 2.0. In December 2025, Anthropic donated the MCP to the Agentic AI Foundation (AAIF), a directed fund under the Linux Foundation, co-founded by Anthropic, Block and OpenAI, with support from other companies. == Features == The protocol was released with software development kits (SDKs) in programming languages including Python, TypeScript, C# and Java. Anthropic maintains an open-source repository of reference MCP server implementations and SDKs. MCP defines a standardized framework for integrating AI systems with external data sources and tools. It includes specifications for data ingestion and transformation, contextual metadata tagging, and AI interoperability across different platforms. The protocol also supports bidirectional connections between data sources and AI tools. MCP enables applications such as querying structured databases with plain language in the field of natural language data access. The protocol is used in AI-assisted software development tools. Integrated development environments (IDEs), coding platforms such as Replit, and code intelligence tools like Sourcegraph have adopted MCP to grant AI coding assistants real-time access to project context. MCP Apps is an official extension to the Model Context Protocol built on mcp-ui. While the base MCP specification is restricted to text and structured data, MCP Apps standardizes the delivery of interactive user interfaces—such as dashboards, forms, and data visualizations—from MCP servers to host applications like Claude and ChatGPT. == Adoption == In March 2025, OpenAI officially adopted the MCP, after having integrated the standard across its products, including the ChatGPT desktop app. In September 2025, OpenAI added support for MCP to ChatGPT apps. This allows for third-party access inside ChatGPT. MCP can be integrated with Microsoft Semantic Kernel, and Azure OpenAI. MCP servers can be deployed to Cloudflare. In April 2026, the AAIF held the MCP Dev Summit North America in New York City, drawing approximately 1,200 attendees. == Reception == The Verge reported that MCP addresses a growing demand for AI agents that are contextually aware and capable of pulling from diverse sources. In April 2025, security researchers released an analysis that concluded there are multiple outstanding security issues with MCP, including prompt injection, tool permissions that allow for combining tools to exfiltrate data, and lookalike tools that can silently replace trusted ones. MCP has been likened to OpenAPI, a similar specification that aims to describe APIs.
Fuzzy architectural spatial analysis
Fuzzy architectural spatial analysis (FASA) (also fuzzy inference system (FIS) based architectural space analysis or fuzzy spatial analysis) is a spatial analysis method of analysing the spatial formation and architectural space intensity within any architectural organization. Fuzzy architectural spatial analysis is used in architecture, interior design, urban planning and similar spatial design fields. == Overview == Fuzzy architectural spatial analysis was developed by Burcin Cem Arabacioglu (2010) from the architectural theories of space syntax and visibility graph analysis, and is applied with the help of a fuzzy system with a Mamdani inference system based on fuzzy logic within any architectural space. Fuzzy architectural spatial analysis model analyses the space by considering the perceivable architectural element by their boundary and stress characteristics and intensity properties. The method is capable of taking all sensorial factors into account during analyses in conformably with the perception process of architectural space which is a multi-sensorial act.
TuVox
TuVox is a company that produces VXML-based telephone speech-recognition applications to replace DTMF touch-tone systems for their clients. == History == TuVox was founded in 2001 by Steven S. Pollock and Ashok Khosla, formerly of Apple Computer Corporation and Claris Corporation. Since then, TuVox has grown to over 150 employees and has US offices in Cupertino, California and Boca Raton, Florida as well as international offices in London, Vancouver and Sydney. In 2005, TuVox acquired the customers and hosting facilities of Net-By-Tel. In 2007, the company raised $20m for its speech recognition, and phone menu software. On July 22, 2010, West Interactive — a subsidiary of West Corporation — announced its acquisition of TuVox. == Customers == TuVox clients include: 1-800-Flowers.com, AMC Entertainment, American Airlines, British Airways, M&T Bank, Canon Inc., Gateway, Inc., Motorola, Progress Energy Inc., Telecom New Zealand, Time, Inc., BECU, Virgin America and USAA.
System appreciation
System appreciation is an activity often included in the maintenance phase of software engineering projects. Key deliverables from this phase include documentation that describes what the system does in terms of its functional features, and how it achieves those features in terms of its architecture and design. Software architecture recovery is often the first step within System appreciation.
Computer-assisted legal research
Computer-assisted legal research (CALR) or computer-based legal research is a mode of legal research that uses databases of court opinions, statutes, court documents, and secondary material. Electronic databases make large bodies of case law easily available. Databases also have additional benefits, such as Boolean searches, evaluating case authority, organizing cases by topic, and providing links to cited material. Databases are available through paid subscription or for free. Subscription-based services include Westlaw, LexisNexis, JustCite, HeinOnline, Bloomberg Law, Lex Intell, VLex and LexEur. As of 2015, the commercial market grossed $8 billion. Free services include OpenJurist, Google Scholar, AltLaw, Ravel Law, WIPO Lex, Law Delta and the databases of the Free Access to Law Movement. == Purposes == Computer-assisted legal research is undertaken by a variety of actors. It is taught as a topic in many law degrees and is used extensively by undergraduate and postgraduate law students in meeting the work requirements of their degree courses. Professors of Law rely on the digitization of primary and secondary sources of law when conducting their research and writing the material that they submit for publication. Professional lawyers rely on computer-assisted legal research in order to properly understand the status of the law and so to act effectively in the best interest of their client. They may also consult the text of case judgements and statutes specifically, as well as wider academic comment, in order to form the basis of (or response to) an appeal. The availability of legal information online differs by type, jurisdiction and subject matter. The types of information available include: Texts of statutes, statutory instruments, civil codes, etc. Explanatory notes and government publications relating to statutes and their operation Texts of governing documents such as constitutions and treaties Case judgements Journals on legal matters or legal theory Dictionaries and legal encyclopedia Legal texts and materials in the form of e-books Current affairs and market information Educational information on the law and its operation == Before the Internet == Prior to the advent and popularization of the World Wide Web, access to digital legal information was largely through the use of CD-ROMs, designed and sold by commercial organizations. Dial-up services were also available from the 1970s. As the use of the Internet spread in the early 1990s, companies such as LexisNexis and Westlaw incorporated Internet connectivity into their software packages. Browser-based legal information started to be published by Legal Information Institutes from 1992. == Publicly available information == The first effort to provide free computer access to legal information was made by two academics, Peter Martin and Tom Bruce, in 1992. Today, the Legal Information Institute freely publishes such resources as the text of the United States Constitution, judgements of the United States Supreme Court, and the text of the United States Code. The Australasian Legal Information Institute (AusLII) was established soon after in 1995. Other legal information institutes, such as those of Great Britain and Ireland (BAILII), Canada (CII) and South Africa (SAfLI) soon followed. LIIs were partially formalized in 2002 following the signing of the Declaration of Free Access to the Law, which has been signed by 54 countries. At the time of writing, the World Legal Information Institute contains in excess of 1800 databases from 123 jurisdictions. Many governments also publish legal information online. For example, UK legislation and statutory instruments have been publicly available online since 2010. Depending on the jurisdiction in question, the decisions of higher appellate courts may also be published online, either by the Legal Information Institute or by the court service directly. Sources of European Union Law are published for free by EUR-Lex in 23 languages, including judgments of the European Courts. Similarly, judgements of the European Court of Human Rights are published on its website.