Sparse identification of nonlinear dynamics (SINDy) is a data-driven algorithm for obtaining dynamical systems from data. Given a series of snapshots of a dynamical system and its corresponding time derivatives, SINDy performs a sparsity-promoting regression (such as LASSO and sparse Bayesian inference) on a library of nonlinear candidate functions of the snapshots against the derivatives to find the governing equations. This procedure relies on the assumption that most physical systems only have a few dominant terms which dictate the dynamics, given an appropriately selected coordinate system and quality training data. It has been applied to identify the dynamics of fluids, based on proper orthogonal decomposition, as well as other complex dynamical systems, such as biological networks. == Mathematical Overview == First, consider a dynamical system of the form x ˙ = d d t x ( t ) = f ( x ( t ) ) , {\displaystyle {\dot {\textbf {x}}}={\frac {d}{dt}}{\textbf {x}}(t)={\textbf {f}}({\textbf {x}}(t)),} where x ( t ) ∈ R n {\displaystyle {\textbf {x}}(t)\in \mathbb {R} ^{n}} is a state vector (snapshot) of the system at time t {\displaystyle t} and the function f ( x ( t ) ) {\displaystyle {\textbf {f}}({\textbf {x}}(t))} defines the equations of motion and constraints of the system. The time derivative may be either prescribed or numerically approximated from the snapshots. With x {\displaystyle {\textbf {x}}} and x ˙ {\displaystyle {\dot {\textbf {x}}}} sampled at m {\displaystyle m} equidistant points in time ( t 1 , t 2 , ⋯ , t m {\displaystyle t_{1},t_{2},\cdots ,t_{m}} ), these can be arranged into matrices of the form X = [ x T ( t 1 ) x T ( t 2 ) ⋮ x T ( t m ) ] = [ x 1 ( t 1 ) x 2 ( t 1 ) ⋯ x n ( t 1 ) x 1 ( t 2 ) x 2 ( t 2 ) ⋯ x n ( t 2 ) ⋮ ⋮ ⋱ ⋮ x 1 ( t m ) x 2 ( t m ) ⋯ x n ( t m ) ] , {\displaystyle {\bf {{X}={\begin{bmatrix}\mathbf {x} ^{\mathsf {T}}(t_{1})\\\mathbf {x} ^{\mathsf {T}}(t_{2})\\\vdots \\\mathbf {x} ^{\mathsf {T}}(t_{m})\end{bmatrix}}={\begin{bmatrix}x_{1}(t_{1})&x_{2}(t_{1})&\cdots &x_{n}(t_{1})\\x_{1}(t_{2})&x_{2}(t_{2})&\cdots &x_{n}(t_{2})\\\vdots &\vdots &\ddots &\vdots \\x_{1}(t_{m})&x_{2}(t_{m})&\cdots &x_{n}(t_{m})\end{bmatrix}},}}} and similarly for X ˙ {\displaystyle {\dot {\mathbf {X} }}} . Next, a library Θ ( X ) {\displaystyle \mathbf {\Theta } (\mathbf {X} )} of nonlinear candidate functions of the columns of X {\displaystyle {\textbf {X}}} is constructed, which may be constant, polynomial, or more exotic functions (like trigonometric and rational terms, and so on): Θ ( X ) = [ | | | | | | 1 X X 2 X 3 ⋯ sin ( X ) cos ( X ) ⋯ | | | | | | ] {\displaystyle \ \ \ {\bf {{\Theta }({\bf {{X})={\begin{bmatrix}\vline &\vline &\vline &\vline &&\vline &\vline &\\1&{\bf {X}}&{\bf {{X}^{2}}}&{\bf {{X}^{3}}}&\cdots &\sin({\bf {{X})}}&\cos({\bf {{X})}}&\cdots \\\vline &\vline &\vline &\vline &&\vline &\vline &\end{bmatrix}}}}}}} The number of possible model structures from this library is combinatorially high. f ( x ( t ) ) {\displaystyle {\textbf {f}}({\textbf {x}}(t))} is then substituted by Θ ( X ) {\displaystyle {\bf {{\Theta }({\textbf {X}})}}} and a vector of coefficients Ξ = [ ξ 1 ξ 2 ⋯ ξ n ] {\displaystyle {\bf {{\Xi }=\left[{\bf {{\xi }_{1}{\bf {{\xi }_{2}\cdots {\bf {{\xi }_{n}}}}}}}\right]}}} determining the active terms in f ( x ( t ) ) {\displaystyle {\textbf {f}}({\textbf {x}}(t))} : X ˙ = Θ ( X ) Ξ {\displaystyle {\dot {\bf {X}}}={\bf {{\Theta }({\bf {{X}){\bf {\Xi }}}}}}} Because only a few terms are expected to be active at each point in time, an assumption is made that f ( x ( t ) ) {\displaystyle {\textbf {f}}({\textbf {x}}(t))} admits a sparse representation in Θ ( X ) {\displaystyle {\bf {{\Theta }({\textbf {X}})}}} . This then becomes an optimization problem in finding a sparse Ξ {\displaystyle {\bf {\Xi }}} which optimally embeds X ˙ {\displaystyle {\dot {\textbf {X}}}} . In other words, a parsimonious model is obtained by performing least squares regression on the system (4) with sparsity-promoting ( L 1 {\displaystyle L_{1}} ) regularization ξ k = arg min ξ k ′ | | X ˙ k − Θ ( X ) ξ k ′ | | 2 + λ | | ξ k ′ | | 1 , {\displaystyle {\bf {{\xi }_{k}={\underset {\bf {{\xi }'_{k}}}{\arg \min }}\left|\left|{\dot {\bf {X}}}_{k}-{\bf {{\Theta }({\bf {{X}){\bf {{\xi }'_{k}}}}}}}\right|\right|_{2}+\lambda \left|\left|{\bf {{\xi }'_{k}}}\right|\right|_{1},}}} where λ {\displaystyle \lambda } is a regularization parameter. Finally, the sparse set of ξ k {\displaystyle {\bf {{\xi }_{k}}}} can be used to reconstruct the dynamical system: x ˙ k = Θ ( x ) ξ k {\displaystyle {\dot {x}}_{k}={\bf {{\Theta }({\bf {{x}){\bf {{\xi }_{k}}}}}}}}
Apps to analyse COVID-19 sounds
Apps to analyse COVID-19 sounds are mobile software applications designed to collect respiratory sounds and aid diagnosis in response to the COVID-19 pandemic. Numerous applications are in development, with different institutions and companies taking various approaches to privacy and data collection. Current efforts are aimed at gathering data. In a later stage, it is possible that sound apps will have the capacity (and ethical approvals) to provide information back to users. In order to develop and train signal analysis approaches, large datasets are required. == History == The COVID-19 outbreak was announced as a global pandemic by the World Health Organization in March 2020 and has affected a growing number of people globally. In this context, advanced artificial intelligence techniques are being considered as tools in aiding our response to global health crisis. Other COVID-19 apps which offer solutions for user tracking have been developed. At the same time a number of approaches which tries to use respiratory sounds and artificial intelligence to understand if the disease can be diagnosed have been proposed. A few studies are available as preprints (i.e. not yet peer-reviewed) documents. == Methodologies == The potential for using speech and sound analysis by artificial intelligence to help in this scenario, by surveying which types of related or contextually significant phenomena can be automatically assessed from speech or sound has been recently overviewed. These include the automatic recognition and monitoring of breathing, dry and wet coughing or sneezing sounds, speech under cold, eating behaviour, sleepiness, or pain. Additionally, the potential use-cases of intelligent speech analysis for COVID-19 diagnosed patients has also been presented. In particular, by analysing speech recordings from these patients, an audio-only-based model to automatically categorise the health state of patients from four aspects, including the severity of illness, sleep quality, fatigue, and anxiety, is constructed. This work shows promise in estimating the severity of illness. Machine learning methods have been explored to recognize and diagnose coughs from different diseases. These included a low complexity, automated recognition and diagnostic tool for screening respiratory infections that utilizes convolutional neural networks (CNNs) to detect cough within environment audio and diagnose three potential illnesses (i.e. bronchitis, bronchiolitis and pertussis) based on their unique cough audio features. A large-scale crowdsourced dataset of respiratory sounds has been collected to aid diagnosis of COVID-19: coughs and breathing sounds are sufficient to distinguish users affected by COVID-19 versus those affected by asthma or healthy controls. Behind these studies is the ambition that automated systems to screen for respiratory diseases based on voice, raw cough or other sound data would have positive medical applications in both clinical and public health arenas. == List of apps to analyse COVID-19 sounds ==
Instantaneously trained neural networks
Instantaneously trained neural networks are feedforward artificial neural networks that create a new hidden neuron node for each novel training sample. The weights to this hidden neuron separate out not only this training sample but others that are near it, thus providing generalization. This separation is done using the nearest hyperplane that can be written down instantaneously. In the two most important implementations the neighborhood of generalization either varies with the training sample (CC1 network) or remains constant (CC4 network). These networks use unary coding for an effective representation of the data sets. This type of network was first proposed in a 1993 paper of Subhash Kak. Since then, instantaneously trained neural networks have been proposed as models of short term learning and used in web search, and financial time series prediction applications. They have also been used in instant classification of documents and for deep learning and data mining. As in other neural networks, their normal use is as software, but they have also been implemented in hardware using FPGAs and by optical implementation. == CC4 network == In the CC4 network, which is a three-stage network, the number of input nodes is one more than the size of the training vector, with the extra node serving as the biasing node whose input is always 1. For binary input vectors, the weights from the input nodes to the hidden neuron (say of index j) corresponding to the trained vector is given by the following formula: w i j = { − 1 , for x i = 0 + 1 , for x i = 1 r − s + 1 , for i = n + 1 {\displaystyle w_{ij}={\begin{cases}-1,&{\mbox{for }}x_{i}=0\\+1,&{\mbox{for }}x_{i}=1\\r-s+1,&{\mbox{for }}i=n+1\end{cases}}} where r {\displaystyle r} is the radius of generalization and s {\displaystyle s} is the Hamming weight (the number of 1s) of the binary sequence. From the hidden layer to the output layer the weights are 1 or -1 depending on whether the vector belongs to a given output class or not. The neurons in the hidden and output layers output 1 if the weighted sum to the input is 0 or positive and 0, if the weighted sum to the input is negative: y = { 1 if ∑ x i ≥ 0 0 if ∑ x i < 0 {\displaystyle y=\left\{{\begin{matrix}1&{\mbox{if }}\sum x_{i}\geq 0\\0&{\mbox{if }}\sum x_{i}<0\end{matrix}}\right.} == Other networks == The CC4 network has also been modified to include non-binary input with varying radii of generalization so that it effectively provides a CC1 implementation. In feedback networks the Willshaw network as well as the Hopfield network are able to learn instantaneously.
Artificial intelligence safety institute
An artificial intelligence safety institute is a type of state-backed organization aiming to evaluate and ensure the safety of advanced artificial intelligence (AI) models, also called frontier AI models. AI safety gained prominence in 2023, notably with public declarations about potential existential risks from AI. During the AI Safety Summit in November 2023, the United Kingdom and the United States both created their own AISI. During the AI Seoul Summit in May 2024, international leaders agreed to form a network of AI Safety Institutes, comprising institutes from the UK, the US, Japan, France, Germany, Italy, Singapore, South Korea, Australia, Canada and the European Union. In 2025, the UK's AI Safety Institute was renamed the "AI Security Institute", and its US counterpart became the Center for AI Standards and Innovation (CAISI). == Timeline == In 2023, Rishi Sunak, the Prime Minister of the United Kingdom, expressed his intention to "make the UK not just the intellectual home but the geographical home of global AI safety regulation" and unveiled plans for an AI Safety Summit. He emphasized the need for independent safety evaluations, stating that AI companies cannot "mark their own homework". During the summit in November 2023, the UK AISI was officially established as an evolution of the Frontier AI Taskforce, and the US AISI as part of the National Institute of Standards and Technology. Japan followed by launching an AI safety institute in February 2024. Politico reported in April 2024 that many AI companies had not shared pre-deployment access to their most advanced AI models for evaluation. Meta's president of global affairs Nick Clegg said that many AI companies were waiting for the UK and the US AI Safety Institutes to work out common evaluation rules and procedures. An agreement was indeed concluded between the UK and the US in April 2024 to collaborate on at least one joint safety test. Initially established in London, the UK AI Safety Institute announced in May 2024 that it would open an office in San Francisco, where many AI companies are located. This is part of a plan to "set new, international standards on AI safety", according to UK's technology minister Michele Donelan. == International network == At the AI Seoul Summit in May 2024, the European Union and other countries agreed to create their own AI safety institutes, forming an international network. In July 2025, the international network held an exercise to explore issues with evaluating AI agents, especially when it came to leaking sensitive information or cybersecurity. Network members also met at NeurIPS 2025 in the city of San Diego. == Specific institutes == === Australia === The Albanese government announced the creation of the Australian AI Safety Institute on 25 November 2025. === Canada === Canada announced in April 2024 that it would create an AI safety institute, and such an institute was officially founded in November 2024. The institute is housed under Innovation, Science and Economic Development Canada, though it also partners with the Canadian Institute for Advanced Research (CIFAR). It is supported by a budget of CA$50,000,000 for a five-year timespan. === European Union === The EU AI office, founded in May 2024, is a member of the international network of AI safety institutes. === France === On 31 January 2025, the government of France created the Institut national pour l'évaluation et la sécurité de l'intelligence artificielle (INESIA), or the National Institute for AI Evaluation and Security. === India === The Ministry of Electronics and Information Technology held consultations with Meta Platforms, Google, Microsoft, IBM, OpenAI, NASSCOM, Broadband India Forum, Software Alliance, Indian Institutes of Technology (IITs), The Quantum Hub, Digital Empowerment Foundation, and Access Now on October 7, 2024, in relation to the establishment of the AI Safety Institute. The decision was made to shift focus from regulation to standards-setting, risk identification, and damage detection—all of which require interoperable technologies. The AISI may spend the ₹20 crore allotted to the Safe and Trusted Pillar of the IndiaAI Mission for the initial budget. Future funding may come from other components of the IndiaAI Mission. UNESCO and MeitY began consulting on AI Readiness Assessment Methodology under Safety and Ethics in Artificial Intelligence from 2024. It is to encourage the ethical and responsible use of AI in industries. The study will find areas where government can become involved, especially in attempts to strengthen institutional and regulatory capabilities. Minister for Electronics & Information Technology Ashwini Vaishnaw announced the creation of an IndiaAI Safety Institute on January 30, 2025, to ensure the ethical and safe application of AI models. The institute will promote domestic R&D that is grounded in India's social, economic, cultural, and linguistic diversity and is based on Indian datasets. With the help of academic and research institutions, as well as private sector partners, the institute will follow the hub-and-spoke approach to carry out projects within Safe and Trusted Pillar of the IndiaAI Mission. It operates under a "hub-and-spoke" model with collaboration from academic institutions (e.g., IITs), tech firms, and international organizations like UNESCO. === Japan === The Japan AISI (or J-AISI) was founded in February 2024. Part of the Information Technology Promotion Agency, it employs about 23 people. The institute consists of the Council of AISI, the AISI Steering Committee, and a secretariat with six teams. Akiko Murakami (previously of IBM Japan and Sompo Japan) serves as the institute's executive director, and Kenji Hiramoto and Suguru Nishimura serve as the institute's two deputy executive directors. === Kenya === Kenya agreed to join the international network of AI safety institutes, but the country has not announced any details yet. It is the only African state in the network. === Singapore === The Digital Trust Centre was initially founded in June 2022. In May 2024, it was renamed to the Singapore AISI. Part of Nanyang Technological University, the institute partners with Infocomm Media Development Authority and is supported by an investment of S$10,000,000 per year. === South Korea === South Korea announced in May 2024 that it would create an AI safety institute under the umbrella of the Electronics and Telecommunications Research Institute. It will be supported by a tentative investment of somewhere between 10 and 20 million South Korean won per year, and employ at least 30 people. The institute was founded in November 2024 and is based in Bundang District within the city of Seongnam. === United Kingdom === The United Kingdom founded in April 2023 a safety organisation called Frontier AI Taskforce, with an initial budget of £100 million. In November 2023, it evolved into the AI Safety Institute, and continued to be led by Ian Hogarth. The AISI is part of the United Kingdom's Department for Science, Innovation and Technology. The United Kingdom's AI strategy aims to balance safety and innovation. Unlike the European Union which adopted the AI Act, the UK is reluctant to legislate early, considering that it may lower the sector's growth, and that laws might be rendered obsolete by technological progress. In May 2024, the institute open-sourced an AI safety tool called "Inspect", which evaluates AI model capabilities such as reasoning and their degree of autonomy. In February 2025, the UK body was renamed the AI Security Institute. Observers saw the name change as a signal that the institute will not focus on ethical issues such as algorithmic bias or freedom of speech in AI applications. === United States === The US AISI was founded in November 2023 as part of the National Institute of Standards and Technology (NIST). This happened the day after the signature of the Executive Order 14110. In February 2024, Joe Biden's former economic policy adviser Elizabeth Kelly was appointed to lead it. In February 2024, the US government created the US AI Safety Institute Consortium (AISIC), regrouping more than 200 organizations such as Google, Anthropic or Microsoft. In March 2024, a budget of $10 million was allocated. Observers noted that this investment is relatively small, especially considering the presence of many big AI companies in the US. The NIST itself, which hosts the AISI, is also known for its chronic lack of funding. Biden administration's request for additional funding was met with further budget cuts from congressional appropriators. Under President Trump, plans for members of the agency to attend the February 2025 AI Action Summit in Paris were scrapped. The US and the UK refused to sign the summit's final communique. US Vice President JD Vance said "pro-growth AI policies" should be prioritised over safety. The name of the agency was changed in June 2025 to the Center for AI Standards and Innovation
General Data Protection Regulation
The General Data Protection Regulation (Regulation (EU) 2016/679), abbreviated GDPR, is a European Union regulation on information privacy in the European Union (EU) and the European Economic Area (EEA). The GDPR is an important component of EU privacy law and human rights law, in particular Article 8(1) of the Charter of Fundamental Rights of the European Union. It also governs the transfer of personal data outside the EU and EEA. The GDPR's goals are to enhance individuals' control and rights over their personal information and to simplify the regulations for international business. It supersedes the Data Protection Directive 95/46/EC and, among other things, simplifies the terminology. The European Parliament and Council of the European Union adopted the GDPR on 14 April 2016, to become effective on 25 May 2018. As an EU regulation (instead of a directive), the GDPR has direct legal effect and does not require transposition into national law. However, it also provides flexibility for individual member states to modify (derogate from) some of its provisions. As an example of the Brussels effect, the regulation became a model for many other laws around the world, including in Brazil, Japan, Singapore, South Africa, South Korea, Sri Lanka, and Thailand. After leaving the European Union, the United Kingdom enacted its "UK GDPR", identical to the GDPR. The California Consumer Privacy Act (CCPA), adopted on 28 June 2018, has many similarities with the GDPR. == Contents == The GDPR 2016 has eleven chapters, concerning general provisions, principles, rights of the data subject, duties of data controllers or processors, transfers of personal data to third-party countries, supervisory authorities, cooperation among member states, remedies, liability or penalties for breach of rights, provisions related to specific processing situations, and miscellaneous final provisions. The GDPR also contains 173 recitals purposed to clarify scope and rationale for the regulatory provisions, as well as its legislative intents – Recital 4, for instance, begins by saying that the processing of personal data should be "designed to serve mankind". === General provisions === The regulation applies if the data controller, or processor, or the data subject (person) is based in the EU. The regulation also applies to organisations based outside the EU if they collect or process personal data of individuals located inside the EU. The regulation does not apply to the processing of data by private persons provided that the purpose has no connection to a professional or commercial activity." (Recital 18). According to the European Commission, "Personal data is information that relates to an identified or identifiable individual. If you cannot directly identify an individual from that information, then you need to consider whether the individual is still identifiable. You should take into account the information you are processing together with all the means reasonably likely to be used by either you or any other person to identify that individual." The precise definitions of terms such as "personal data", "processing", "data subject", "controller", and "processor" are stated in Article 4. The regulation does not purport to apply to the processing of personal data for national security activities or law enforcement of the EU; however, industry groups concerned about facing a potential conflict of laws have questioned whether Article 48 could be invoked to seek to prevent a data controller subject to a third country's laws from complying with a legal order from that country's law enforcement, judicial, or national security authorities to disclose to such authorities the personal data of an EU person, regardless of whether the data resides in or out of the EU. Article 48 states that any judgement of a court or tribunal and any decision of an administrative authority of a third country requiring a controller or processor to transfer or disclose personal data may not be recognised or enforceable in any manner unless based on an international agreement, like a mutual legal assistance treaty in force between the requesting third (non-EU) country and the EU or a member state. The data protection reform package also includes a separate Data Protection Directive for the police and criminal justice sector that provides rules on personal data exchanges at State level, Union level, and international levels. A single set of rules applies to all EU member states. Each member state establishes an independent supervisory authority (SA) to hear and investigate complaints, sanction administrative offences, etc. SAs in each member state co-operate with other SAs, providing mutual assistance and organising joint operations. If a business has multiple establishments in the EU, it must have a single SA as its "lead authority", based on the location of its "main establishment" where the main processing activities take place. The lead authority thus acts as a "one-stop shop" to supervise all the processing activities of that business throughout the EU. A European Data Protection Board (EDPB) co-ordinates the SAs. EDPB thus replaces the Article 29 Data Protection Working Party. There are exceptions for data processed in an employment context or in national security that still might be subject to individual country regulations. === Principles and lawful purposes === Article 5 sets out six principles relating to the lawfulness of processing personal data. The first of these specifies that data must be processed lawfully, fairly and in a transparent manner. Article 6 develops this principle by specifying that personal data may not be processed unless there is at least one legal basis for doing so. The other principles refer to "purpose limitation", "data minimisation", "accuracy", "storage limitation", and "integrity and confidentiality". Article 6 states that the lawful purposes are: (a) If the data subject has given consent to the processing of his or her personal data; (b) To fulfill contractual obligations with a data subject, or for tasks at the request of a data subject who is in the process of entering into a contract; (c) To comply with a data controller's legal obligations; (d) To protect the vital interests of a data subject or another individual; (e) To perform a task in the public interest or in official authority; (f) For the legitimate interests of a data controller or a third party, unless these interests are overridden by interests of the data subject or her or his rights according to the Charter of Fundamental Rights (especially in the case of children). If informed consent is used as the lawful basis for processing, consent must have been explicit for data collected and each purpose data is used for. Consent must be a specific, freely given, plainly worded, and unambiguous affirmation given by the data subject; an online form which has consent options structured as an opt-out selected by default is a violation of the GDPR, as the consent is not unambiguously affirmed by the user. In addition, multiple types of processing may not be "bundled" together into a single affirmation prompt, as this is not specific to each use of data, and the individual permissions are not freely given. (Recital 32). Data subjects must be allowed to withdraw this consent at any time, and the process of doing so must not be harder than it was to opt in. A data controller may not refuse service to users who decline consent to processing that is not strictly necessary in order to use the service. Consent for children, defined in the regulation as being less than 16 years old (although with the option for member states to individually make it as low as 13 years old), must be given by the child's parent or custodian, and verifiable. If consent to processing was already provided under the Data Protection Directive, a data controller does not have to re-obtain consent if the processing is documented and obtained in compliance with the GDPR's requirements (Recital 171). === Rights of the data subject === ==== Transparency and modalities ==== Article 12 requires the data controller to provide information to the "data subject in a concise, transparent, intelligible and easily accessible form, using clear and plain language, in particular for any information addressed specifically to a child." ==== Information and access ==== The right of access (Article 15) is a data subject right. It gives people the right to access their personal data and information about how this personal data is being processed. A data controller must provide, upon request, an overview of the categories of data that are being processed as well as a copy of the actual data; furthermore, the data controller has to inform the data subject on details about the processing, such as the purposes of the processing, with whom the data is shared, and how it acquired the data. A data subject must be able to transfer personal data from one electro
Vulnerability Discovery Model
A Vulnerability Discovery Model (VDM) uses discovery event data with software reliability models for predicting the same. A thorough presentation of VDM techniques is available in. Numerous model implementations are available in the MCMCBayes open source repository. Several VDM examples include: Alhazmi-Malaiya: Time based model (Alhazmi-Malaiya Logistic (AML) model) Alhazmi-Malaiya: Effort based model Rescorla: Quadratic Model and Exponential Model Anderson: Thermodynamic Model Kim: Weibull Model Linear Model Hump-Shaped Model Independent and Dependent Model Vulnerability Discovery Modeling using Bayesian model averaging Multivariate Vulnerability Discovery Models
Linguistic value
In artificial intelligence, fuzzy logic operations research, and related fields, a linguistic value is a natural language term which is derived using quantitative or qualitative reasoning such as with probability and statistics or fuzzy sets and systems. Variables that take linguistic values are called linguistic variables. == Examples of linguistic variables and values == For example, "age" may be a linguistic variable if its values are not numerical, e.g. very young, quite young, not young, old, not very old etc. These values could be derived from the numeric values for age. As another example, if a shuttle heat shield is deemed of having a linguistic value of a "very low" percentage of damage in re-entry, based upon knowledge from experts in the field, that probability would be given a value of say, 5%. From there on out, if it were to be used in an equation, the variable of percentage of damage will be at 5% if it deemed very low percentage.