In computational linguistics, second-order co-occurrence pointwise mutual information (SOC-PMI) is a method used to measure semantic similarity, or how close in meaning two words are. The method does not require the two words to appear together in a text. Instead, it works by analyzing the "neighbor" words that typically appear alongside each of the two target words in a large body of text (corpus). If the two target words frequently share the same neighbors, they are considered semantically similar. For example, the words "cemetery" and "graveyard" may not appear in the same sentence often, but they both frequently appear near words like "buried," "dead," and "funeral." SOC-PMI uses this shared context to determine that they have a similar meaning. The method is called "second-order" because it doesn't look at the direct co-occurrence of the target words (which would be first-order), but at the co-occurrence of their neighbors (a second level of association). The strength of these associations is quantified using pointwise mutual information (PMI). == History == The method builds on earlier work like the PMI-IR algorithm, which used the AltaVista search engine to calculate word association probabilities. The key advantage of a second-order approach like SOC-PMI is its ability to measure similarity between words that do not co-occur often, or at all. The British National Corpus (BNC) has been used as a source for word frequencies and contexts for this method. == Methodology == The SOC-PMI algorithm measures the similarity between two words, w 1 {\displaystyle w_{1}} and w 2 {\displaystyle w_{2}} , in several steps. === Step 1: Score neighboring words with PMI === First, for each target word ( w 1 {\displaystyle w_{1}} and w 2 {\displaystyle w_{2}} ), the algorithm identifies its "neighbor" words within a certain text window (e.g., within 5 words to the left or right) across a large corpus. The strength of the association between a target word t i {\displaystyle t_{i}} and its neighbor w {\displaystyle w} is calculated using pointwise mutual information (PMI). A higher PMI value means the two words appear together more often than would be expected by chance. The PMI between a target word t i {\displaystyle t_{i}} and a neighbor word w {\displaystyle w} is calculated as: f pmi ( t i , w ) = log 2 f b ( t i , w ) × m f t ( t i ) f t ( w ) {\displaystyle f^{\text{pmi}}(t_{i},w)=\log _{2}{\frac {f^{b}(t_{i},w)\times m}{f^{t}(t_{i})f^{t}(w)}}} where: f b ( t i , w ) {\displaystyle f^{b}(t_{i},w)} is the number of times t i {\displaystyle t_{i}} and w {\displaystyle w} appear together in the context window. f t ( t i ) {\displaystyle f^{t}(t_{i})} is the total number of times t i {\displaystyle t_{i}} appears in the corpus. f t ( w ) {\displaystyle f^{t}(w)} is the total number of times w {\displaystyle w} appears in the corpus. m {\displaystyle m} is the total number of tokens (words) in the corpus. === Step 2: Create a semantic 'signature' for each word === For each target word ( w 1 {\displaystyle w_{1}} and w 2 {\displaystyle w_{2}} ), the algorithm creates a list of its most significant neighbors. This is done by taking the top β {\displaystyle \beta } neighbor words, sorted in descending order by their PMI score with the target word. This list of top neighbors, X w {\displaystyle X^{w}} , acts as a semantic "signature" for the word w {\displaystyle w} . X w = { X i w } {\displaystyle X^{w}=\{X_{i}^{w}\}} , for i = 1 , 2 , … , β {\displaystyle i=1,2,\ldots ,\beta } The size of this list, β {\displaystyle \beta } , is a parameter of the method. === Step 3: Compare the signatures === The algorithm then compares the signatures of w 1 {\displaystyle w_{1}} and w 2 {\displaystyle w_{2}} . It looks for words that are present in both signatures. The similarity of w 1 {\displaystyle w_{1}} to w 2 {\displaystyle w_{2}} is calculated by summing the PMI scores of w 2 {\displaystyle w_{2}} with every word in w 1 {\displaystyle w_{1}} 's signature list. The β {\displaystyle \beta } -PMI summation function defines this score. The score for w 1 {\displaystyle w_{1}} with respect to w 2 {\displaystyle w_{2}} is: f ( w 1 , w 2 , β ) = ∑ i = 1 β ( f pmi ( X i w 1 , w 2 ) ) γ {\displaystyle f(w_{1},w_{2},\beta )=\sum _{i=1}^{\beta }(f^{\text{pmi}}(X_{i}^{w_{1}},w_{2}))^{\gamma }} This sum only includes terms where the PMI value is positive. The exponent γ {\displaystyle \gamma } (with a value > 1) is used to give more weight to neighbors that are more strongly associated with w 2 {\displaystyle w_{2}} . This calculation is done in both directions: The similarity of w 1 {\displaystyle w_{1}} with respect to w 2 {\displaystyle w_{2}} : f ( w 1 , w 2 , β 1 ) = ∑ i = 1 β 1 ( f pmi ( X i w 1 , w 2 ) ) γ {\displaystyle f(w_{1},w_{2},\beta _{1})=\sum _{i=1}^{\beta _{1}}(f^{\text{pmi}}(X_{i}^{w_{1}},w_{2}))^{\gamma }} The similarity of w 2 {\displaystyle w_{2}} with respect to w 1 {\displaystyle w_{1}} : f ( w 2 , w 1 , β 2 ) = ∑ i = 1 β 2 ( f pmi ( X i w 2 , w 1 ) ) γ {\displaystyle f(w_{2},w_{1},\beta _{2})=\sum _{i=1}^{\beta _{2}}(f^{\text{pmi}}(X_{i}^{w_{2}},w_{1}))^{\gamma }} === Step 4: Calculate final similarity score === Finally, the total semantic similarity is the average of the two scores from the previous step. S i m ( w 1 , w 2 ) = f ( w 1 , w 2 , β 1 ) β 1 + f ( w 2 , w 1 , β 2 ) β 2 {\displaystyle \mathrm {Sim} (w_{1},w_{2})={\frac {f(w_{1},w_{2},\beta _{1})}{\beta _{1}}}+{\frac {f(w_{2},w_{1},\beta _{2})}{\beta _{2}}}} This score can be normalized to fall between 0 and 1. For example, using this method, the words cemetery and graveyard achieve a high similarity score of 0.986 (with specific parameter settings).
Integrated writing environment
An integrated writing environment (IWE) is software that provides comprehensive writing and knowledge management functionality for writers and information workers. IWEs enable writers and information workers to perform a variety of tasks related to the document in the IWE in a single environment. This provides a distraction-free workspace and streamlined writing experience. IWEs provide similar efficiency and functionality benefits to writers and information professionals that integrated development environments (IDEs) provide to software developers. == Overview == IWEs are designed to maximize productivity and help improve the quality of written work by integrating together tools that allow users to work effectively in a single application. The IWE features may include integrated content search, reversion management, outlining, note management, and reference management, as may be suitable for the target field of use. == List of IWEs == Celtx This IWE is intended for screenplay writers and has screenplay writing and management tools. Celtex provides tools for the pre-production work phase, story development, storyboarding, script breakdowns, production scheduling, and reports. Scrivener This IWE targets novel, research paper, and script writing. Scrivener provides tools to organize notes and research documents for easy access and referencing. After completing the writing, Scrivener allows the user to export the document to formats supported by common word processors, such as Microsoft Word. TeXstudio This IWE targets LaTeX documents and provides interactive spelling checker, code folding, and syntax highlighting.
How to Choose an AI Marketing Tool
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Co-Büchi automaton
In automata theory, a co-Büchi automaton is a variant of Büchi automaton. The only difference is the accepting condition: a Co-Büchi automaton accepts an infinite word w {\displaystyle w} if there exists a run, such that all the states occurring infinitely often in the run are in the final state set F {\displaystyle F} . In contrast, a Büchi automaton accepts a word w {\displaystyle w} if there exists a run, such that at least one state occurring infinitely often in the final state set F {\displaystyle F} . (Deterministic) Co-Büchi automata are strictly weaker than (nondeterministic) Büchi automata. == Formal definition == Formally, a deterministic co-Büchi automaton is a tuple A = ( Q , Σ , δ , q 0 , F ) {\displaystyle {\mathcal {A}}=(Q,\Sigma ,\delta ,q_{0},F)} that consists of the following components: Q {\displaystyle Q} is a finite set. The elements of Q {\displaystyle Q} are called the states of A {\displaystyle {\mathcal {A}}} . Σ {\displaystyle \Sigma } is a finite set called the alphabet of A {\displaystyle {\mathcal {A}}} . δ : Q × Σ → Q {\displaystyle \delta :Q\times \Sigma \rightarrow Q} is the transition function of A {\displaystyle {\mathcal {A}}} . q 0 {\displaystyle q_{0}} is an element of Q {\displaystyle Q} , called the initial state. F ⊆ Q {\displaystyle F\subseteq Q} is the final state set. A {\displaystyle {\mathcal {A}}} accepts exactly those words w {\displaystyle w} with the run ρ ( w ) {\displaystyle \rho (w)} , in which all of the infinitely often occurring states in ρ ( w ) {\displaystyle \rho (w)} are in F {\displaystyle F} . In a non-deterministic co-Büchi automaton, the transition function δ {\displaystyle \delta } is replaced with a transition relation Δ {\displaystyle \Delta } . The initial state q 0 {\displaystyle q_{0}} is replaced with an initial state set Q 0 {\displaystyle Q_{0}} . Generally, the term co-Büchi automaton refers to the non-deterministic co-Büchi automaton. For more comprehensive formalism see also ω-automaton. == Acceptance Condition == The acceptance condition of a co-Büchi automaton is formally ∃ i ∀ j : j ≥ i ρ ( w j ) ∈ F . {\displaystyle \exists i\forall j:\;j\geq i\quad \rho (w_{j})\in F.} The Büchi acceptance condition is the complement of the co-Büchi acceptance condition: ∀ i ∃ j : j ≥ i ρ ( w j ) ∈ F . {\displaystyle \forall i\exists j:\;j\geq i\quad \rho (w_{j})\in F.} == Properties == Co-Büchi automata are closed under union, intersection, projection and determinization.
AI Paragraph Rewriters: Free vs Paid (2026)
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Dhammin
Dhammin (Arabic: ضمّن) is a political platform that manages candidates' electoral campaigns for the National Assembly, Municipal Council or Cooperative Society councils of Kuwait. The platform was founded by Abdullah Al-Salloum and it is, according to news reports and interviews, the first within the field to apply distributed-systems' methodologies.
Vera Demberg
Vera Demberg (born 1981) is a German computational linguist and professor of computer science and computational linguistics at Saarland University. Her research interests include cognitive models of human language comprehension, natural language generation, experimental psycholinguistics, multimodal language processing in a dual-task setting, and experimental and computational discourse research and pragmatics. == Career and research == Vera Demberg studied computational linguistics at the Institute for Machine Language Processing at the University of Stuttgart from 2001 to 2006. She then completed a Master's degree in Artificial Intelligence at the University of Edinburgh from 2004 to 2005. She received her Ph.D. from the Department of Computer Science there from 2006 to 2010. Her dissertation paper, titled “Broad-Coverage Model of Prediction in Human Sentence Processing”, was awarded the Cognitive Science Society's “Glushko Dissertation Prize in Cognitive Science” in 2011. In her work, she designed a model of human sentence processing that can be used to predict difficulties in processing at the syntactic level. From 2010 to 2016, Vera Demberg led an independent research group on cognitive models of human language processing and their application to speech dialog systems in the Cluster of Excellence “Multimodal Computing and Interaction” at the University of Saarland. In 2016, she was appointed there to a professorship in computer science and computational linguistics. Demberg's professorship is in the Department of Computer Science (Faculty of Mathematics and Computer Science). She is also a co-opted professor in the Department of Linguistics and Language Technology (Faculty of Philosophy). Since 2020, she has led the ERC Starting Grant “Individualized Interaction in Discourse”. The project conducts research on how to make linguistic interaction with computer systems more natural. She has authored and co-authored numerous papers on the study of computational linguistics and natural language processing. According to Google Scholar, Vera Demberg has an H-index of 30. == Publications == Vera Demberg has authored more than 200 papers; please refer to her scholar page at https://scholar.google.com/citations?user=l2CFSAMAAAAJ == Awards == 2011: Cognitive Science Society Glushko Dissertation Prize in Cognitive Science 2020: ERC Starting Grant “Individualized Interaction in Discourse” 2024: Member of the Academy of Sciences and Literature