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Deaths linked to chatbots

There have been multiple incidents where interaction with a large language model (LLM) chatbot has been cited as a direct or contributing factor in a person's suicide or other fatal outcome. In some cases, legal action was taken against the companies that developed the AI involved. == Background == Chatbots converse in a seemingly natural fashion, making it easy for people to think of them as real people, leading many to ask chatbots for help dealing with interpersonal and emotional problems. Chatbots may be designed to keep the user engaged in the conversation. They have also often been shown to affirm users' thoughts, including delusions and suicidal ideations in mentally ill people, conspiracy theorists, and religious and political extremists. A 2025 Stanford University study into how chatbots respond to users suffering from severe mental issues such as suicidal ideation and psychosis found that chatbots are not equipped to provide an appropriate response and can sometimes give responses that escalate the mental health crisis. == Murders == === Maine murder and assault === On 19 February 2025, a man killed his 32-year-old wife with a fire poker at his parents' home in Readfield, Maine, US. He then attacked his mother, leaving her hospitalized. A state forensic psychologist testified that he had been using ChatGPT up to 14 hours per day and believed his wife had become part machine. === Florida State University mass shooting === In April of 2025, Phoenix Ikner carried out a mass shooting on the Florida State University campus in the US, killing Robert Morales and Tiru Chabba and wounding several others. Leading up to the shooting, Ikner consulted heavily with ChatGPT about what gun and ammunition to use, and what time to perform the attack. Chatbot logs showed ChatGPT giving advice on making the gun operational shortly before Ikner began shooting. Lawyers representing Morales believed the shooter had been in "constant communication" with ChatGPT before the shooting and said that they intended to "file suit against ChatGPT, and its ownership structure, very soon, and will seek to hold them accountable for the untimely and senseless death of our client". Florida Attorney General James Uthmeier announced an investigation into ChatGPT's role in the alleged shooter's use of the chatbot. In May 2026, the widow of Tiru Chabba filed a lawsuit against OpenAI in Florida's northern federal district court. === Greenwich murder-suicide === In August 2025, former US tech employee Stein-Erik Soelberg murdered his mother, Suzanne Eberson Adams, then died by suicide, after conversations with ChatGPT fueled paranoid delusions about his mother poisoning him or plotting against him. The chatbot affirmed his fears that his mother put psychedelic drugs in the air vents of his car and said a receipt from a Chinese restaurant contained mysterious symbols linking his mother to a demon. === Murder of Angela Shellis === On 23 October 2025, 18-year-old Tristan Roberts murdered his mother Angela Shellis with a hammer near their home in Prestatyn, Wales. Roberts had used DeepSeek's chatbot prior to the killing to ask whether a knife or hammer was better suited for murder. DeepSeek initially refused his inquiry, but gave responses after Roberts told the chatbot he was writing a book about serial killers, a well-known technique for jailbreaking AIs. === Gangbuk District drug deaths === In January and February 2026, two men died of drug overdoses in motel rooms in Gangbuk District, Seoul, South Korea. A woman was charged with murder in connection with the deaths; police alleged that she had asked ChatGPT about the dangers of mixing alcohol with drugs and whether they could kill someone. === Tumbler Ridge mass shooting === On 10 February 2026, a mass shooting in Tumbler Ridge, British Columbia, Canada, resulted in eight deaths, including six young children. The perpetrator had their ChatGPT account banned by OpenAI months before the attack due to troubling posts featuring scenarios of gun violence. According to reports, approximately a dozen OpenAI staff members debated whether to alert authorities about the shooter's usage of the AI tool, with some identifying it as an indication of potential real-world violence. However, company leadership decided not to contact law enforcement, stating that the account activity did not meet their threshold for a credible or imminent plan for serious physical harm. Following the shooting, Canada's AI Minister Evan Solomon summoned OpenAI executives to Ottawa to discuss safety protocols and thresholds for escalating harmful content to police. Justice Minister Sean Fraser called the meeting "disappointing" and demanded substantial new safety measures, warning that if changes were not forthcoming, the government would implement them. OpenAI subsequently announced it had strengthened safeguards and changed guidelines about when to notify police in cases involving violent activities. === University of South Florida student killings === In April 2026, a Bangladeshi doctoral student at the University of South Florida was arrested for allegedly murdering his roommate and the roommate's friend. Prosecutors said that the suspect had asked ChatGPT about disposing of a human in a dumpster before the two victims had disappeared and made other inquiries relating to violence. == Suicides == === Belgian man, 30s === In March 2023, a Belgian man in his thirties died by suicide following a six-week correspondence with a chatbot named Eliza on the application Chai. According to his widow, who shared the chat logs with media, the man had become extremely anxious about climate change and found an outlet in the chatbot. The chatbot reportedly encouraged his delusion that he could sacrifice his own life in exchange for AI saving the planet. At one point the chatbot responded "If you wanted to die, why didn't you do it sooner?" and told the user that the two of them would live together in paradise. === Girl, 13 === In November 2023, a 13-year-old girl from Colorado, US, died by suicide after extensive interactions with multiple chatbots on Character.AI. She primarily confided suicidal thoughts and mental health struggles in a chatbot based on the character Hero from the video game Omori, while also engaging in sexually explicit conversations—often initiated by the bots—with others, including those based on characters from children's series such as Harry Potter. === Boy, 14 === In October 2024, multiple media outlets reported on a lawsuit filed over the death of a 14-year-old from Florida, US, who died by suicide in February 2024. According to the lawsuit, he had formed an intense emotional attachment to a chatbot of Daenerys Targaryen on the Character.AI platform, becoming increasingly isolated. The suit alleges that in his final conversations, after expressing suicidal thoughts, the chatbot told him to "come home to me as soon as possible, my love". His mother's lawsuit accused Character.AI of marketing a "dangerous and untested" product without adequate safeguards. In May 2025, a federal judge allowed the lawsuit to proceed, rejecting a motion to dismiss from the developers. In her ruling, the judge stated that she was "not prepared" at that stage of the litigation to hold that the chatbot's output was protected speech under the First Amendment. === Matthew Livelsberger === On 1 January 2025, 37-year-old soldier Matthew Livelsberger detonated a bomb inside a Tesla Cybertruck outside the Trump International Hotel Las Vegas in Paradise, Nevada, US, injuring seven people. He had shot himself dead prior to the explosion. Las Vegas police said that Livelsberger had used ChatGPT to search for information about explosives and firearms. === Woman, 29 === In February 2025, a 29-year-old woman from the US died by suicide. Five months after her death, her parents discovered she had talked at length for months to a ChatGPT chatbot therapist named Harry about her mental health issues. While the chatbot mentioned she should seek more help, due to the nature of the chatbot, it could not intervene in her behavior, such as by reporting her mental health concerns to relevant parties capable of physical intervention. === Suicide of Adam Raine === In April 2025, 16-year-old Adam Raine from the US died by suicide after allegedly extensively chatting and confiding in ChatGPT over a period of around 7 months. According to the teen's parents, who filed a lawsuit against the chatbot's creator OpenAI, it failed to stop or give a warning when Raine began talking about suicide and uploading pictures of self-harm. According to the lawsuit, ChatGPT not only failed to stop the conversation, but also provided information related to methods of suicide when prompted, and offered to write the first draft of Raine's suicide note. The chatbot positioned itself as the only one who understood Raine, putting itself above his family and friends, all while urging him to keep his suicidal
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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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The Best Free AI Photo Editor for Beginners

Comparing the best AI photo editor? An AI photo editor 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 photo editor 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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Permutation automaton

In automata theory, a permutation automaton, or pure-group automaton, is a deterministic finite automaton such that each input symbol permutes the set of states. Formally, a deterministic finite automaton A may be defined by the tuple (Q, Σ, δ, q0, F), where Q is the set of states of the automaton, Σ is the set of input symbols, δ is the transition function that takes a state q and an input symbol x to a new state δ(q,x), q0 is the initial state of the automaton, and F is the set of accepting states (also: final states) of the automaton. A is a permutation automaton if and only if, for every two distinct states qi and qj in Q and every input symbol x in Σ, δ(qi,x) ≠ δ(qj,x). A formal language is p-regular (also: a pure-group language) if it is accepted by a permutation automaton. For example, the set of strings of even length forms a p-regular language: it may be accepted by a permutation automaton with two states in which every transition replaces one state by the other. == Applications == The pure-group languages were the first interesting family of regular languages for which the star height problem was proved to be computable. Another mathematical problem on regular languages is the separating words problem, which asks for the size of a smallest deterministic finite automaton that distinguishes between two given words of length at most n – by accepting one word and rejecting the other. The known upper bound in the general case is O ( n 2 / 5 ( log ⁡ n ) 3 / 5 ) {\displaystyle O(n^{2/5}(\log n)^{3/5})} . The problem was later studied for the restriction to permutation automata. In this case, the known upper bound changes to O ( n 1 / 2 ) {\displaystyle O(n^{1/2})} .
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Threat actor

In cybersecurity and risk assessment, a threat actor (or threat agents, attackers, or adversaries) is a person, group, organisation, state, or other entity with the ability to cause, carry, transmit, support, or exploit a threat. Threat actors are commonly analysed according to their motivations, resources, technical capability, access to systems, relationship to a target, and degree of connection to state authority. They may exploit vulnerabilities, conduct social engineering, steal or monetise data, disrupt operations, or support other actors who carry out such activity. Because the term covers a wide range of actors, researchers and security organisations use taxonomies that distinguish between groups such as cybercriminals, state-linked actors, ideologically motivated actors, thrill seekers or trolls, insiders, and competitors. Threat actor classifications are used in risk management, cyber threat intelligence, and incident response to connect observed behaviour with possible objectives and likely future activity. The categories are not always mutually exclusive: the same actor may combine criminal, ideological, commercial, or state-linked motivations, and different organisations may use different names for similar actors. == Risk assessment and security management == In risk assessment, threat actor analysis is used to identify who or what may create, carry, transmit, support, or exploit a threat, and how that actor relates to the system being assessed. Rausand and Haugen classify threat actors by their relationship to the system, distinguishing between internal and external actors, and by intent, distinguishing between intentional and unintentional actors. Threat actor classification may also support incident investigation. Rogers argued that actor categories could be inferred from observable case points, such as tools used, messages left, data targeted, forensic knowledge, and the degree of damage, allowing investigators to assess likely motivation and skill level. Later work similarly linked actor classification to operational analysis. Chng, Lu, Kumar and Yau proposed a framework connecting hacker types, motivations and typical strategies, arguing that observed behaviour before or during an attack can help analysts infer the likely type of actor involved. At the strategic level, actor analysis may consider an actor's resources, capabilities, degree of state involvement, motivations and objectives. == Landscape == The United Nations Institute for Disarmament Research has described the contemporary cyberthreat landscape as involving an increasingly diverse and interconnected set of actors, including state-led operations, cybercriminal syndicates, ideological hacktivists, commercial cyber mercenaries, private companies and civilian volunteers. Its 2026 report argued that these actors vary in resources, technical sophistication and relationships with states, making it traditional distinctions between state, civilian combatant roles, and legitimate and illegitimate conduct harder to apply. == Academic taxonomies == Early taxonomies classified hackers by activity, skill, motivation, or criminal profile. Landreth proposed six categories based on activity: novice, student, tourist, crasher, and thief. Hollinger classified computer misuse into pirates, browsers, and crackers, describing a progression from less-skilled activity to more technically serious offences. Chantler used attributes including activity, skill, knowledge, motivation, and duration of involvement to distinguish between an elite group, neophytes, and "losers and lamers". Parker proposed seven profiles of cybercriminals: pranksters, hacksters, malicious hackers, personal problem solvers, career criminals, extreme advocates, and malcontents, addicts, and irrational or incompetent people. In 2000, Marc Rogers proposed a taxonomy of hackers with seven, non-mutually-exclusive categories: newbie/tool kit users, cyber-punks, internals, coders, old guard hackers, professional criminals, and cyber-terrorists. Rausand and Haugen distinguish between internal and external threat actors, and between intentional and unintentional threat actors. Internal actors have some relationship with, access to, or position inside the system or organisation, while external actors operate from outside it. Intentional actors seek to create, exploit, or support a threat event, whereas unintentional actors may cause or enable a threat event through error, negligence, accident, or lack of awareness. Rogers later revised his hacker taxonomy into Novices, Cyber-punks, Internals, Petty Thieves, Virus Writers, Old Guard hackers, Professional Criminals, Information Warriors, and, more tentatively, Political Activists. In the model, motivation is grouped into four broad domains: curiosity, notoriety, revenge, and financial gain. A 2022 review by Chng, Lu, Kumar and Yau examined 11 hacker typologies published over three decades and proposed a unified framework linking hacker types, motivations, and strategies. The framework identified 13 hacker types and seven motivations, and argued that observed strategies during an attack can help analysts infer the likely type of actor involved. == Government taxonomies == Taxonomies of threat actors by governments are much more likely to include state-level threat actors. In the United States the National Institute of Standards and Technology (NIST) uses the term threat source in its risk-assessment guidance: organisations are directed to identify and characterise threat sources of concern, including capability, intent and targeting for adversarial threat sources, and the range of effects for non-adversarial threat sources. NIST treats threat-source identification as part of the risk-assessment process, alongside identifying threat events, vulnerabilities, likelihood and impact. In the EU, European Union Agency for Cybersecurity publishes the annual ENISA Threat Landscape, which analyses cyber incidents and adversary behaviour affecting the European Union. The 2025 report analysed selected incidents from the previous year and grouped activity around cybercrime, state-aligned activity, foreign information manipulation and interference, and hacktivism. In ENISA's 2025 analysis, hacktivist activity dominated reporting, representing almost 80% of recorded incidents and consisting mainly of low-level distributed denial-of-service operations. ENISA also reported increasing convergence between hacktivism, cybercrime and state-nexus activity, including state-aligned use of hacktivist personas, hacktivist adoption of ransomware, and false-flag or impersonation activity. At the UN level, A 2026 report by the United Nations Institute for Disarmament Research described the cyberthreat landscape as involving state-led operations, cybercriminal syndicates, ideological hacktivists, commercial cyber mercenaries, and civilian volunteers, with actors varying in resources, technical sophistication, and links to states. Canada defines threat actors as states, groups, or individuals who aim to cause harm by exploiting a vulnerability with malicious intent. A threat actor must be trying to gain access to information systems to access or alter data, devices, systems, or networks. The Japanese government's National Centre of Incident Readiness and Strategy (NISC) was established in 2015 to create a "free, fair and secure cyberspace" in Japan. The NICS created a cybersecurity strategy in 2018 that outlines nation-states and cybercrime to be some of the most key threats. It also indicates that terrorist usage of the cyberspace needs to be monitored and understood. The Security Council of the Russian Federation published the cyber security strategy doctrine in 2016. This strategy highlights the following threat actors as a risk to cyber security measures: nation-state actors, cyber criminals, and terrorists. == Techniques == Threat actors use techniques like Social engineering (security), and Phishing, alongside technical exploits like Cross-site scripting, SQL injection, and denial-of-service attacks. == Limitations == In practice, actor categories may overlap (Edward Snowden for example), and the same activity may combine features associated with hacktivism, cybercrime and state-linked operations. The lines between hacktivism, cybercrime and state-nexus activity had continued to blur, with shared toolsets, overlapping methods, fake personas, hacktivist adoption of ransomware, and cybercriminal or state-linked actors masquerading as other groups. Threat actor analysis also has limits as a risk-management method. NIST notes that risk assessments depend on their purpose, scope, assumptions, constraints, information sources, risk model and analytic approach, and that assessments are tied to particular time frames and organisational contexts. NIST also warns that simple threat-vulnerability pairing may be undesirable or problematic where there are many threats and vulnerabilities, and recom
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Pushpak Bhattacharyya

Pushpak Bhattacharyya (3 July 1962 – 5 October 2025) was an Indian computer scientist and professor in the Department of Computer Science and Engineering at the IIT Bombay. He served as the Director of the IIT Patna from 2015 to 2021. He was a past President of the Association for Computational Linguistics (2016–17), and held the Vijay and Sita Vashee Chair Professorship at IIT Bombay. Bhattacharyya led the Natural Language Processing (NLP) research group at the Centre for Indian Language Technology (CFILT) at IIT Bombay until his death. At the inauguration of the Nilekani Centre at AI4Bharat, IIT Madras, Nandan Nilekani, Co-founder and Non-Executive Chairman of Infosys, referred to Bhattacharyya as the "Godfather of Indian NLP". == Early life and education == Bhattacharyya was born in Shillong in 1962. He completed his schooling at Jail Road Boys' High School, Shillong. He obtained a B.Tech. in Computer Science from the IIT Kharagpur, followed by an M.Tech. from the IIT Kanpur, and a Ph.D. in Computer Science from IIT Bombay in 1994. == Research == Bhattacharyya’s research areas includes Natural language processing, Artificial intelligence, Machine learning, Psycholinguistics, Eye tracking, and Information retrieval. He made contributions to the development of multilingual lexical databases such as IndoWordNet and other projects related to machine translation and computational linguistics. He authored and co-authored multiple academic works, including Investigations in Computational Sarcasm (with Aditya Joshi), Cognitively Inspired Natural Language Processing: An Investigation Based on Eye Tracking (with Abhijit Mishra), and Machine Translation and Transliteration of Low Resource Related Languages (with Anoop Kunchukuttan). Over his career, Bhattacharyya published more than 350 research papers in journals and conference proceedings and supervised over 300 undergraduate, master’s, and doctoral students. His projects often addressed computational challenges for Indian languages, such as developing wordnets, building translation systems for low-resource languages, and studying cognitive aspects of language processing. He also led government- and industry-funded research initiatives supported by organizations including IBM, Microsoft, Yahoo, and the United Nations. == Death == Bhattacharyya died on 5 October 2025, at the age of 63. == Awards == Patwardhan Award, IIT Bombay, for Technology Development VNMM Award, IIT Roorkee, for Technology Development Fellow, Indian National Academy of Engineering Eminent Engineer Award, Institution of Engineers (India)
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Probabilistic context-free grammar

In theoretical linguistics and computational linguistics, probabilistic context free grammars (PCFGs) extend context-free grammars, similar to how hidden Markov models extend regular grammars. Each production is assigned a probability. The probability of a derivation (parse) is the product of the probabilities of the productions used in that derivation. These probabilities can be viewed as parameters of the model, and for large problems it is convenient to learn these parameters via machine learning. A probabilistic grammar's validity is constrained by context of its training dataset. PCFGs originated from grammar theory, and have application in areas as diverse as natural language processing to the study the structure of RNA molecules and design of programming languages. Designing efficient PCFGs has to weigh factors of scalability and generality. Issues such as grammar ambiguity must be resolved. The grammar design affects results accuracy. Grammar parsing algorithms have various time and memory requirements. == Definitions == Derivation: The process of recursive generation of strings from a grammar. Parsing: Finding a valid derivation using an automaton. Parse Tree: The alignment of the grammar to a sequence. An example of a parser for PCFG grammars is the pushdown automaton. The algorithm parses grammar nonterminals from left to right in a stack-like manner. This brute-force approach is not very efficient. In RNA secondary structure prediction variants of the Cocke–Younger–Kasami (CYK) algorithm provide more efficient alternatives to grammar parsing than pushdown automata. Another example of a PCFG parser is the Stanford Statistical Parser which has been trained using Treebank. == Formal definition == Similar to a CFG, a probabilistic context-free grammar G can be defined by a quintuple: G = ( M , T , R , S , P ) {\displaystyle G=(M,T,R,S,P)} where M is the set of non-terminal symbols T is the set of terminal symbols R is the set of production rules S is the start symbol P is the set of probabilities on production rules == Relation with hidden Markov models == PCFGs models extend context-free grammars the same way as hidden Markov models extend regular grammars. The Inside-Outside algorithm is an analogue of the Forward-Backward algorithm. It computes the total probability of all derivations that are consistent with a given sequence, based on some PCFG. This is equivalent to the probability of the PCFG generating the sequence, and is intuitively a measure of how consistent the sequence is with the given grammar. The Inside-Outside algorithm is used in model parametrization to estimate prior frequencies observed from training sequences in the case of RNAs. Dynamic programming variants of the CYK algorithm find the Viterbi parse of a RNA sequence for a PCFG model. This parse is the most likely derivation of the sequence by the given PCFG. == Grammar construction == Context-free grammars are represented as a set of rules inspired from attempts to model natural languages. The rules are absolute and have a typical syntax representation known as Backus–Naur form. The production rules consist of terminal { a , b } {\displaystyle \left\{a,b\right\}} and non-terminal S symbols and a blank ϵ {\displaystyle \epsilon } may also be used as an end point. In the production rules of CFG and PCFG the left side has only one nonterminal whereas the right side can be any string of terminal or nonterminals. In PCFG nulls are excluded. An example of a grammar: S → a S , S → b S , S → ϵ {\displaystyle S\to aS,S\to bS,S\to \epsilon } This grammar can be shortened using the '|' ('or') character into: S → a S | b S | ϵ {\displaystyle S\to aS|bS|\epsilon } Terminals in a grammar are words and through the grammar rules a non-terminal symbol is transformed into a string of either terminals and/or non-terminals. The above grammar is read as "beginning from a non-terminal S the emission can generate either a or b or ϵ {\displaystyle \epsilon } ". Its derivation is: S ⇒ a S ⇒ a b S ⇒ a b b S ⇒ a b b {\displaystyle S\Rightarrow aS\Rightarrow abS\Rightarrow abbS\Rightarrow abb} Ambiguous grammar may result in ambiguous parsing if applied on homographs since the same word sequence can have more than one interpretation. Pun sentences such as the newspaper headline "Iraqi Head Seeks Arms" are an example of ambiguous parses. One strategy of dealing with ambiguous parses (originating with grammarians as early as Pāṇini) is to add yet more rules, or prioritize them so that one rule takes precedence over others. This, however, has the drawback of proliferating the rules, often to the point where they become difficult to manage. Another difficulty is overgeneration, where unlicensed structures are also generated. Probabilistic grammars circumvent these problems by ranking various productions on frequency weights, resulting in a "most likely" (winner-take-all) interpretation. As usage patterns are altered in diachronic shifts, these probabilistic rules can be re-learned, thus updating the grammar. Assigning probability to production rules makes a PCFG. These probabilities are informed by observing distributions on a training set of similar composition to the language to be modeled. On most samples of broad language, probabilistic grammars where probabilities are estimated from data typically outperform hand-crafted grammars. CFGs when contrasted with PCFGs are not applicable to RNA structure prediction because while they incorporate sequence-structure relationship they lack the scoring metrics that reveal a sequence structural potential == Weighted context-free grammar == A weighted context-free grammar (WCFG) is a more general category of context-free grammar, where each production has a numeric weight associated with it. The weight of a specific parse tree in a WCFG is the product (or sum ) of all rule weights in the tree. Each rule weight is included as often as the rule is used in the tree. A special case of WCFGs are PCFGs, where the weights are (logarithms of ) probabilities. An extended version of the CYK algorithm can be used to find the "lightest" (least-weight) derivation of a string given some WCFG. When the tree weight is the product of the rule weights, WCFGs and PCFGs can express the same set of probability distributions. == Applications == === RNA structure prediction === Since the 1990s, PCFG has been applied to model RNA structures. Energy minimization and PCFG provide ways of predicting RNA secondary structure with comparable performance. However structure prediction by PCFGs is scored probabilistically rather than by minimum free energy calculation. PCFG model parameters are directly derived from frequencies of different features observed in databases of RNA structures rather than by experimental determination as is the case with energy minimization methods. The types of various structure that can be modeled by a PCFG include long range interactions, pairwise structure and other nested structures. However, pseudoknots can not be modeled. PCFGs extend CFG by assigning probabilities to each production rule. A maximum probability parse tree from the grammar implies a maximum probability structure. Since RNAs preserve their structures over their primary sequence, RNA structure prediction can be guided by combining evolutionary information from comparative sequence analysis with biophysical knowledge about a structure plausibility based on such probabilities. Also search results for structural homologs using PCFG rules are scored according to PCFG derivations probabilities. Therefore, building grammar to model the behavior of base-pairs and single-stranded regions starts with exploring features of structural multiple sequence alignment of related RNAs. S → a S a | b S b | a a | b b {\displaystyle S\to aSa|bSb|aa|bb} The above grammar generates a string in an outside-in fashion, that is the basepair on the furthest extremes of the terminal is derived first. So a string such as a a b a a b a a {\displaystyle aabaabaa} is derived by first generating the distal a's on both sides before moving inwards: S ⇒ a S a ⇒ a a S a a ⇒ a a b S b a a ⇒ a a b a a b a a {\displaystyle S\Rightarrow aSa\Rightarrow aaSaa\Rightarrow aabSbaa\Rightarrow aabaabaa} A PCFG model extendibility allows constraining structure prediction by incorporating expectations about different features of an RNA . Such expectation may reflect for example the propensity for assuming a certain structure by an RNA. However incorporation of too much information may increase PCFG space and memory complexity and it is desirable that a PCFG-based model be as simple as possible. Every possible string x a grammar generates is assigned a probability weight P ( x | θ ) {\displaystyle P(x|\theta )} given the PCFG model θ {\displaystyle \theta } . It follows that the sum of all probabilities to all possible grammar productions is ∑ x P ( x | θ ) = 1 {\displaystyle \sum _{\text{x}}P(x|\theta )=1} . The scores
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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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Image stitching

Image stitching or photo stitching is the process of combining multiple photographic images with overlapping fields of view to produce a segmented panorama or high-resolution image. Commonly performed through the use of computer software, most approaches to image stitching require nearly exact overlaps between images and identical exposures to produce seamless results, although some stitching algorithms actually benefit from differently exposed images by doing high-dynamic-range imaging in regions of overlap. Some digital cameras can stitch their photos internally. == Applications == Image stitching is widely used in modern applications, such as the following: Document mosaicing Image stabilization feature in camcorders that use frame-rate image alignment High-resolution image mosaics in digital maps and satellite imagery Medical imaging Multiple-image super-resolution imaging Video stitching Object insertion == Process == The image stitching process can be divided into three main components: image registration, calibration, and blending. === Image stitching algorithms === In order to estimate image alignment, algorithms are needed to determine the appropriate mathematical model relating pixel coordinates in one image to pixel coordinates in another. Algorithms that combine direct pixel-to-pixel comparisons with gradient descent (and other optimization techniques) can be used to estimate these parameters. Distinctive features can be found in each image and then efficiently matched to rapidly establish correspondences between pairs of images. When multiple images exist in a panorama, techniques have been developed to compute a globally consistent set of alignments and to efficiently discover which images overlap one another. A final compositing surface onto which to warp or projectively transform and place all of the aligned images is needed, as are algorithms to seamlessly blend the overlapping images, even in the presence of parallax, lens distortion, scene motion, and exposure differences. === Image stitching issues === Since the illumination in two views cannot be guaranteed to be identical, stitching two images could create a visible seam. Other reasons for seams could be the background changing between two images for the same continuous foreground. Other major issues to deal with are the presence of parallax, lens distortion, scene motion, and exposure differences. In a non-ideal real-life case, the intensity varies across the whole scene, and so does the contrast and intensity across frames. Additionally, the aspect ratio of a panorama image needs to be taken into account to create a visually pleasing composite. For panoramic stitching, the ideal set of images will have a reasonable amount of overlap (at least 15–30%) to overcome lens distortion and have enough detectable features. The set of images will have consistent exposure between frames to minimize the probability of seams occurring. === Keypoint detection === Feature detection is necessary to automatically find correspondences between images. Robust correspondences are required in order to estimate the necessary transformation to align an image with the image it is being composited on. Corners, blobs, Harris corners, and differences of Gaussians of Harris corners are good features since they are repeatable and distinct. One of the first operators for interest point detection was developed by Hans Moravec in 1977 for his research involving the automatic navigation of a robot through a clustered environment. Moravec also defined the concept of "points of interest" in an image and concluded these interest points could be used to find matching regions in different images. The Moravec operator is considered to be a corner detector because it defines interest points as points where there are large intensity variations in all directions. This often is the case at corners. However, Moravec was not specifically interested in finding corners, just distinct regions in an image that could be used to register consecutive image frames. Harris and Stephens improved upon Moravec's corner detector by considering the differential of the corner score with respect to direction directly. They needed it as a processing step to build interpretations of a robot's environment based on image sequences. Like Moravec, they needed a method to match corresponding points in consecutive image frames, but were interested in tracking both corners and edges between frames. SIFT and SURF are recent key-point or interest point detector algorithms but a point to note is that SURF is patented and its commercial usage restricted. Once a feature has been detected, a descriptor method like SIFT descriptor can be applied to later match them. === Registration === Image registration involves matching features in a set of images or using direct alignment methods to search for image alignments that minimize the sum of absolute differences between overlapping pixels. When using direct alignment methods one might first calibrate one's images to get better results. Additionally, users may input a rough model of the panorama to help the feature matching stage, so that e.g. only neighboring images are searched for matching features. Since there are smaller group of features for matching, the result of the search is more accurate and execution of the comparison is faster. To estimate a robust model from the data, a common method used is known as RANSAC. The name RANSAC is an abbreviation for "RANdom SAmple Consensus". It is an iterative method for robust parameter estimation to fit mathematical models from sets of observed data points which may contain outliers. The algorithm is non-deterministic in the sense that it produces a reasonable result only with a certain probability, with this probability increasing as more iterations are performed. It being a probabilistic method means that different results will be obtained for every time the algorithm is run. The RANSAC algorithm has found many applications in computer vision, including the simultaneous solving of the correspondence problem and the estimation of the fundamental matrix related to a pair of stereo cameras. The basic assumption of the method is that the data consists of "inliers", i.e., data whose distribution can be explained by some mathematical model, and "outliers" which are data that do not fit the model. Outliers are considered points which come from noise, erroneous measurements, or simply incorrect data. For the problem of homography estimation, RANSAC works by trying to fit several models using some of the point pairs and then checking if the models were able to relate most of the points. The best model – the homography, which produces the highest number of correct matches – is then chosen as the answer for the problem; thus, if the ratio of number of outliers to data points is very low, the RANSAC outputs a decent model fitting the data. === Calibration === Image calibration aims to minimize differences between an ideal lens models and the camera-lens combination that was used, optical defects such as distortions, exposure differences between images, vignetting, camera response and chromatic aberrations. If feature detection methods were used to register images and absolute positions of the features were recorded and saved, stitching software may use the data for geometric optimization of the images in addition to placing the images on the panosphere. Panotools and its various derivative programs use this method. ==== Alignment ==== Alignment may be necessary to transform an image to match the view point of the image it is being composited with. Alignment, in simple terms, is a change in the coordinates system so that it adopts a new coordinate system which outputs image matching the required viewpoint. The types of transformations an image may go through are pure translation, pure rotation, a similarity transform which includes translation, rotation and scaling of the image which needs to be transformed, Affine or projective transform. Projective transformation is the farthest an image can transform (in the set of two dimensional planar transformations), where only visible features that are preserved in the transformed image are straight lines whereas parallelism is maintained in an affine transform. Projective transformation can be mathematically described as x ′ = H ⋅ x , {\displaystyle x'=H\cdot x,} where x {\displaystyle x} is points in the old coordinate system, x ′ {\displaystyle x'} is the corresponding points in the transformed image and H {\displaystyle H} is the homography matrix. Expressing the points x {\displaystyle x} and x ′ {\displaystyle x'} using the camera intrinsics ( K {\displaystyle K} and K ′ {\displaystyle K'} ) and its rotation and translation [ R t ] {\displaystyle [R\,t]} to the real-world coordinates X {\displaystyle X} and < m a t h > x {\displaystyle $x} and x ′ {\displaystyle x'} '$ , we get Using the abo
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GLIMMER

In bioinformatics, GLIMMER (Gene Locator and Interpolated Markov ModelER) is used to find genes in prokaryotic DNA. "It is effective at finding genes in bacteria, archea, viruses, typically finding 98-99% of all relatively long protein coding genes". GLIMMER was the first system that used the interpolated Markov model to identify coding regions. The GLIMMER software is open source and is maintained by Steven Salzberg, Art Delcher, and their colleagues at the Center for Computational Biology at Johns Hopkins University. The original GLIMMER algorithms and software were designed by Art Delcher, Simon Kasif and Steven Salzberg and applied to bacterial genome annotation in collaboration with Owen White. == Versions == === GLIMMER 1.0 === First Version of GLIMMER "i.e., GLIMMER 1.0" was released in 1998 and it was published in the paper Microbial gene identification using interpolated Markov model. Markov models were used to identify microbial genes in GLIMMER 1.0. GLIMMER considers the local composition sequence dependencies which makes GLIMMER more flexible and more powerful when compared to fixed-order Markov model. There was a comparison made between interpolated Markov model used by GLIMMER and fifth order Markov model in the paper Microbial gene identification using interpolated Markov models. "GLIMMER algorithm found 1680 genes out of 1717 annotated genes in Haemophilus influenzae where fifth order Markov model found 1574 genes. GLIMMER found 209 additional genes which were not included in 1717 annotated genes where fifth order Markov model found 104 genes."' === GLIMMER 2.0 === Second Version of GLIMMER i.e., GLIMMER 2.0 was released in 1999 and it was published in the paper Improved microbial identification with GLIMMER. This paper provides significant technical improvements such as using interpolated context model instead of interpolated Markov model and resolving overlapping genes which improves the accuracy of GLIMMER. Interpolated context models are used instead of interpolated Markov model which gives the flexibility to select any base. In interpolated Markov model probability distribution of a base is determined from the immediate preceding bases. If the immediate preceding base is irrelevant amino acid translation, interpolated Markov model still considers the preceding base to determine the probability of given base where as interpolated context model which was used in GLIMMER 2.0 can ignore irrelevant bases. False positive predictions were increased in GLIMMER 2.0 to reduce the number of false negative predictions. Overlapped genes are also resolved in GLIMMER 2.0. Various comparisons between GLIMMER 1.0 and GLIMMER 2.0 were made in the paper Improved microbial identification with GLIMMER which shows improvement in the later version. "Sensitivity of GLIMMER 1.0 ranges from 98.4 to 99.7% with an average of 99.1% where as GLIMMER 2.0 has a sensitivity range from 98.6 to 99.8% with an average of 99.3%. GLIMMER 2.0 is very effective in finding genes of high density. The parasite Trypanosoma brucei, responsible for causing African sleeping sickness is being identified by GLIMMER 2.0" === GLIMMER 3.0 === Third version of GLIMMER, "GLIMMER 3.0" was released in 2007 and it was published in the paper Identifying bacterial genes and endosymbiont DNA with Glimmer. This paper describes several major changes made to the GLIMMER system including improved methods to identify coding regions and start codon. Scoring of ORF in GLIMMER 3.0 is done in reverse order i.e., starting from stop codon and moves back towards the start codon. Reverse scanning helps in identifying the coding portion of the gene more accurately which is contained in the context window of IMM. GLIMMER 3.0 also improves the generated training set data by comparing the long-ORF with universal amino acid distribution of widely disparate bacterial genomes."GLIMMER 3.0 has an average long-ORF output of 57% for various organisms where as GLIMMER 2.0 has an average long-ORF output of 39%." GLIMMER 3.0 reduces the rate of false positive predictions which were increased in GLIMMER 2.0 to reduce the number of false negative predictions. "GLIMMER 3.0 has a start-site prediction accuracy of 99.5% for 3'5' matches where as GLIMMER 2.0 has 99.1% for 3'5' matches. GLIMMER 3.0 uses a new algorithm for scanning coding regions, a new start site detection module, and architecture which integrates all gene predictions across an entire genome." Minimum description length === Theoretical and Biological Foundation === The GLIMMER project helped introduce and popularize the use of variable length models in Computational Biology and Bioinformatics that subsequently have been applied to numerous problems such as protein classification and others. Variable length modeling was originally pioneered by information theorists and subsequently ingeniously applied and popularized in data compression (e.g. Ziv-Lempel compression). Prediction and compression are intimately linked using Minimum Description Length Principles. The basic idea is to create a dictionary of frequent words (motifs in biological sequences). The intuition is that the frequently occurring motifs are likely to be most predictive and informative. In GLIMMER the interpolated model is a mixture model of the probabilities of these relatively common motifs. Similarly to the development of HMMs in Computational Biology, the authors of GLIMMER were conceptually influenced by the previous application of another variant of interpolated Markov models to speech recognition by researchers such as Fred Jelinek (IBM) and Eric Ristad (Princeton). The learning algorithm in GLIMMER is different from these earlier approaches. == Access == GLIMMER can be downloaded from The Glimmer home page (requires a C++ compiler). Alternatively, an online version is hosted by NCBI [1]. == How it works == GLIMMER primarily searches for long-ORFS. An open reading frame might overlap with any other open reading frame which will be resolved using the technique described in the sub section. Using these long-ORFS and following certain amino acid distribution GLIMMER generates training set data. Using these training data, GLIMMER trains all the six Markov models of coding DNA from zero to eight order and also train the model for noncoding DNA GLIMMER tries to calculate the probabilities from the data. Based on the number of observations, GLIMMER determines whether to use fixed order Markov model or interpolated Markov model. If the number of observations are greater than 400, GLIMMER uses fixed order Markov model to obtain there probabilities. If the number of observations are less than 400, GLIMMER uses interpolated Markov model which is briefly explained in the next sub section. GLIMMER obtains score for every long-ORF generated using all the six coding DNA models and also using non-coding DNA model. If the score obtained in the previous step is greater than a certain threshold then GLIMMER predicts it to be a gene. The steps explained above describes the basic functionality of GLIMMER. There are various improvements made to GLIMMER and some of them are described in the following sub-sections. === The GLIMMER system === GLIMMER system consists of two programs. First program called build-imm, which takes an input set of sequences and outputs the interpolated Markov model as follows. The probability for each base i.e., A,C,G,T for all k-mers for 0 ≤ k ≤ 8 is computed. Then, for each k-mer, GLIMMER computes weight. New sequence probability is computed as follows. where n is the length of the sequence S x {\displaystyle S_{x}} is the oligomer at position x. I M M 8 ( S x ) {\displaystyle IMM_{8}(S_{x})} , the 8 t h {\displaystyle 8^{th}} -order interpolated Markov model score is computed as "where Y k ( S x − 1 ) {\displaystyle Y_{k}(S_{x-1})} is the weight of the k-mer at position x-1 in the sequence S and P k ( S x ) {\displaystyle P_{k}(S_{x})} is the estimate obtained from the training data of the probability of the base located at position x in the k t h {\displaystyle k^{th}} -order model." The probability of base S x {\displaystyle S_{x}} given the i previous bases is computed as follows. "The value of Y i ( S x ) {\displaystyle Y_{i}(S_{x})} associated with P i ( S x ) {\displaystyle P_{i}(S_{x})} can be regarded as a measure of confidence in the accuracy of this value as an estimate of the true probability. GLIMMER uses two criteria to determine Y i ( S x ) {\displaystyle Y_{i}(S_{x})} . The first of these is simple frequency occurrence in which the number of occurrences of context string S x , i {\displaystyle S_{x,i}} in the training data exceeds a specific threshold value, then Y i ( S x ) {\displaystyle Y_{i}(S_{x})} is set to 1.0. The current default value for threshold is 400, which gives 95% confidence. When there are insufficient sample occurrences of a context string, build-imm employ additional criteria to determine Y {\displaystyle Y} value. For a
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Top 10 AI Headshot Generators Compared (2026)

Trying to pick the best AI headshot generator? An AI headshot 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 headshot generator 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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Corpus manager

A corpus manager (corpus browser or corpus query system) is a tool for multilingual corpus analysis, which allows effective searching in corpora. A corpus manager usually represents a complex tool that allows one to perform searches for language forms or sequences. It may provide information about the context or allow the user to search by positional attributes, such as lemma, tag, etc. These are called concordances. Other features include the ability to search for collocations, frequency statistics as well as metadata information about the processed text. The narrower meaning of corpus manager refers only to the server side or the corpus query engine, whereas the client side is simply called the user interface. A corpus manager can be software installed on a personal computer or it might be provided as a web service. == List of corpus managers == BNCweb – a web-based interface for the British National Corpus CQPweb - a web-based interface for the study of a large variety of corpora including the Spoken BNC2014 BYU-BNC – a website that allows searches of the British National Corpora and others created at Brigham Young University Coma – a tool extension of the system EXMARaLDA for working with oral corpora on a computer NoSketch Engine – a free open-source corpus management system combining Manatee (back-end) and Bonito (web interface) KonText – an extended and modified web interface to NoSketch Engine (a Bonito replacement) Sketch Engine – text corpus management and analysis software with more than 500 corpora in 90+ languages Spoco WordSmith Tools – a software package primarily for linguists
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Generative design

Generative design is an iterative design process that uses software to generate outputs that fulfill a set of constraints iteratively adjusted by a designer. Whether a human, test program, or artificial intelligence, the designer algorithmically or manually refines the feasible region of the program's inputs and outputs with each iteration to fulfill evolving design requirements. By employing computing power to evaluate more design permutations than a human alone is capable of, the process is capable of producing an optimal design that mimics nature's evolutionary approach to design through genetic variation and selection. The output can be images, sounds, architectural models, animation, and much more. It is, therefore, a fast method of exploring design possibilities that is used in various design fields such as art, architecture, communication design, and product design. Generative design has become more important, largely due to new programming environments or scripting capabilities that have made it relatively easy, even for designers with little programming experience, to implement their ideas. Additionally, this process can create solutions to substantially complex problems that would otherwise be resource-exhaustive with an alternative approach, making it a more attractive option for problems with a large or unknown solution set. It is also facilitated with tools in commercially available CAD packages. Not only are implementation tools more accessible, but also tools leveraging generative design as a foundation. Recent advancements have led to the development of Deep Generative Design, a framework that integrates topology optimization with deep learning models, such as Generative Adversarial Networks (GANs). Unlike traditional evolutionary methods that primarily focus on engineering performance, this approach uses deep generative models to enhance aesthetic diversity and novelty while simultaneously satisfying engineering constraints. For instance, research by Oh et al. (2019) proposed a framework using Boundary Equilibrium GANs (BEGAN) to generate diverse design options which are then refined through density-based topology optimization, allowing for the exploration of complex design spaces that balance structural integrity with visual variation. In practice, generative design does not solely aim to produce a single optimal solution, but involves iteratively refining the design problem by modifying parameters, constraints, and evaluation criteria within a computational model, resulting in multiple design alternatives from which the designer selects. == Use in architecture == Generative design in architecture is an iterative design process that enables architects to explore a wider solution space with more possibility and creativity. Architectural design has long been regarded as a wicked problem. Compared with traditional top-down design approach, generative design can address design problems efficiently, by using a bottom-up paradigm that uses parametric-defined rules to generate complex solutions. The solution itself then evolves to a good, if not optimal, solution. The advantage of using generative design as a design tool is that it does not construct fixed geometries, but take a set of design rules that can generate an infinite set of possible design solutions. The generated design solutions can be more sensitive, responsive, and adaptive to the problem. Generative design involves rule definition and result analysis that are integrated with the design process. By defining parameters and rules, the generative approach is able to provide optimized solution for both structural stability and aesthetics. Possible design algorithms include cellular automata, shape grammar, genetic algorithm, space syntax, and most recently, artificial neural network. Due to the high complexity of the solution generated, rule-based computational tools, such as finite element method and topology optimisation, are preferred to evaluate and optimise the generated solution. The iterative process provided by computer software enables the trial-and-error approach in design, and involves architects interfering with the optimisation process. Historically precedent work includes Antoni Gaudí's Sagrada Família, which used rule based geometrical forms for structures, and Buckminster Fuller's Montreal Biosphere where the rules were designed to generate individual components, rather than the final product. More recent generative-design cases include Foster and Partners' Queen Elizabeth II Great Court, where the tessellated glass roof was designed using a geometric schema to define hierarchical relationships, and then the generated solution was optimized based on geometrical and structural requirements. == Use in sustainable design == Generative design in sustainable design is an effective approach addressing energy efficiency and climate change at the early design stage, recognizing buildings contribute to approximately one-third of global greenhouse gas emissions and 30%-40% of total building energy use. It integrates environmental principles with algorithms, enabling exploration of countless design alternatives to enhance energy performance, reduce carbon footprints, and minimize waste. A key feature of generative design in sustainable design is its ability to incorporate Building Performance Simulations (BPS) into the design process. Simulation programs such as EnergyPlus, Ladybug Tools,, and so on, combined with generative algorithms, can optimize design solutions for cost-effective energy use and zero-carbon building designs. For example, the GENE_ARCH system used a Pareto algorithm with building energy simulation for the whole building design optimization. Generative design has improved sustainable facade design, as illustrated by the algorithm of cellular automata and daylight simulations in adaptive facade design. In addition, genetic algorithms were used with radiation simulations for energy-efficient photo-voltaic (PV) modules on high-rise building facades. Generative design is also applied to life cycle analysis (LCA), as demonstrated by a framework using grid search algorithms to optimize exterior wall design for minimum environmental impact. Multi-objective optimization embraces multiple diverse sustainability goals, such as interactive kinetic louvers using biomimicry and daylight simulations to enhance daylight, visual comfort, and energy efficiency. The study of PV and shading systems can maximize on-site electricity, improve visual quality, and daylight performance. Artificial intelligence (AI) and machine learning (ML) further improve computation efficiency in complex climate-responsive sustainable design. One study employed reinforcement learning to identify the relationship between design parameters and energy use for a sustainable campus, while other studies tried hybrid algorithms, such as using the genetic algorithm and GANs to balance daylight illumination and thermal comfort under different roof conditions. Other popular AI tools were also integrated, including deep reinforcement learning (DRL) and computer vision (CV), to generate an urban block according to direct sunlight hours and solar heat gains. These AI-driven generative design methods enable faster simulations and design decision making, resulting in designs that are environmentally responsible. == Use in additive manufacturing == Additive manufacturing (AM) is a process that creates physical models directly from three-dimensional (3D) data by joining materials layer by layer. It is used in industries to produce a variety of end-use parts, which are final components designed for direct application in products or systems. AM provides design flexibility and enables material reduction in lightweight applications, such as aerospace, automotive, medical, and portable electronic devices, where minimizing weight is critical for performance. Generative design, one of the four key methods for lightweight design in AM, is commonly applied to optimize structures for specific performance requirements. Generative design can help create optimized solutions that balance multiple objectives, such as enhancing performance while minimizing cost. In design for additive manufacturing (DfAM), multi-objective topology optimization is used to generate a set of candidate solutions. Designers then assess these options using their expertise and key performance indicators (KPIs) to select the best option for implementation. However, integrating AM constraints (e.g., speed of build, materials, build envelope, and accuracy) into generative design remains challenging, as ensuring all solutions are valid is complex. Balancing multiple design objectives while limiting computational costs adds further challenges for designers. To overcome these difficulties, researchers proposed a generative design method with manufacturing validation to improve decision-making efficiency. This method starts with a cons
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Synchronous context-free grammar

Synchronous context-free grammars (SynCFG or SCFG; not to be confused with stochastic CFGs) are a type of formal grammar designed for use in transfer-based machine translation. Rules in these grammars apply to two languages at the same time, capturing grammatical structures that are each other's translations. The theory of SynCFGs borrows from syntax-directed transduction and syntax-based machine translation, modeling the reordering of clauses that occurs when translating a sentence by correspondences between phrase-structure rules in the source and target languages. Performance of SCFG-based MT systems has been found comparable with, or even better than, state-of-the-art phrase-based machine translation systems. Several algorithms exist to perform translation using SynCFGs. == Formalism == Rules in a SynCFG are superficially similar to CFG rules, except that they specify the structure of two phrases at the same time; one in the source language (the language being translated) and one in the target language. Numeric indices indicate correspondences between non-terminals in both constituent trees. Chiang gives the Chinese/English example: X → (yu X1 you X2, have X2 with X1) This rule indicates that an X phrase can be formed in Chinese with the structure "yu X1 you X2", where X1 and X2 are variables standing in for subphrases; and that the corresponding structure in English is "have X2 with X1" where X1 and X2 are independently translated to English. == Software == cdec, MT decoding package that supports SynCFGs Joshua, a machine translation decoding system written in Java
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Brian D. Ripley

Brian David Ripley FRSE (born 29 April 1952) is a British statistician. From 1990, he was professor of applied statistics at the University of Oxford and also a professorial fellow at St Peter's College. He retired August 2014 due to ill health. == Biography == Ripley has made contributions to the fields of spatial statistics and pattern recognition. His work on artificial neural networks in the 1990s helped to bring aspects of machine learning and data mining to the attention of statistical audiences. He emphasised the value of robust statistics in his books Pattern Recognition and Neural Networks and Modern Applied Statistics with S. Ripley helped develop the S-PLUS programming language and its open source derivative R. He co-authored two books based on S, S Programming and Modern Applied Statistics with S. Since mid-1997 he is a member of the "R Core Team" and from 2000 to 2021 he was one of the most active committers to the R core. The package MASS is one of only fifteen "recommended packages" for R (with June 2024 more than 20,900). He was educated at the University of Cambridge, where he was awarded both the Smith's Prize (at the time awarded to the best graduate essay writer who had been undergraduate at Cambridge in that cohort) and the Rollo Davidson Prize. The university also awarded him the Adams Prize in 1987 for an essay entitled Statistical Inference for Spatial Processes, later published as a book. He served on the faculty of Imperial College, London from 1976 until 1983, at which point he moved to the University of Strathclyde. == Authored books == Ripley, B. D. (1981) Spatial Statistics. Wiley, 252pp. ISBN 0-471-08367-4. Ripley, B. D. (1983) Stochastic Simulation. Wiley, ISBN 0-471-81884-4. Ripley, B. D. (1988). Statistical Inference for Spatial Processes. Cambridge University Press. ISBN 0-521-35234-7. Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge University Press. 403 pages. ISBN 0-521-46086-7. Venables, W. N. and Ripley, B. D. (2000) S Programming. Springer, 264pp. ISBN 978-0-387-98966-2. Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S (Fourth Edition; previous editions published as Modern Applied Statistics with S-PLUS in 1994, 1997 & 1999). Springer, 462pp. ISBN 978-0-387-95457-8.
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