In mathematics a radial basis function (RBF) is a real-valued function φ {\textstyle \varphi } whose value depends only on the distance between the input and some fixed point, either the origin, so that φ ( x ) = φ ^ ( ‖ x ‖ ) {\textstyle \varphi (\mathbf {x} )={\hat {\varphi }}(\left\|\mathbf {x} \right\|)} , or some other fixed point c {\textstyle \mathbf {c} } , called a center, so that φ ( x ) = φ ^ ( ‖ x − c ‖ ) {\textstyle \varphi (\mathbf {x} )={\hat {\varphi }}(\left\|\mathbf {x} -\mathbf {c} \right\|)} . Any function φ {\textstyle \varphi } that satisfies the property φ ( x ) = φ ^ ( ‖ x ‖ ) {\textstyle \varphi (\mathbf {x} )={\hat {\varphi }}(\left\|\mathbf {x} \right\|)} is a radial function. The distance is usually Euclidean distance, although other metrics are sometimes used. They are often used as a collection { φ k } k {\displaystyle \{\varphi _{k}\}_{k}} which forms a basis for some function space of interest, hence the name. Sums of radial basis functions are typically used to approximate given functions. This approximation process can also be interpreted as a simple kind of neural network; this was the context in which they were originally applied to machine learning, in work by David Broomhead and David Lowe in 1988, which stemmed from Michael J. D. Powell's seminal research from 1977. RBFs are also used as a kernel in support vector classification. The technique has proven effective and flexible enough that radial basis functions are now applied in a variety of engineering applications. == Definition == A radial function is a function φ : [ 0 , ∞ ) → R {\textstyle \varphi :[0,\infty )\to \mathbb {R} } . When paired with a norm ‖ ⋅ ‖ : V → [ 0 , ∞ ) {\textstyle \|\cdot \|:V\to [0,\infty )} on a vector space, a function of the form φ c = φ ( ‖ x − c ‖ ) {\textstyle \varphi _{\mathbf {c} }=\varphi (\|\mathbf {x} -\mathbf {c} \|)} is said to be a radial kernel centered at c ∈ V {\textstyle \mathbf {c} \in V} . A radial function and the associated radial kernels are said to be radial basis functions if, for any finite set of nodes { x k } k = 1 n ⊆ V {\displaystyle \{\mathbf {x} _{k}\}_{k=1}^{n}\subseteq V} , all of the following conditions are true: === Examples === Commonly used types of radial basis functions include (writing r = ‖ x − x i ‖ {\textstyle r=\left\|\mathbf {x} -\mathbf {x} _{i}\right\|} and using ε {\textstyle \varepsilon } to indicate a shape parameter that can be used to scale the input of the radial kernel): == Approximation == Radial basis functions are typically used to build up function approximations of the form where the approximating function y ( x ) {\textstyle y(\mathbf {x} )} is represented as a sum of N {\displaystyle N} radial basis functions, each associated with a different center x i {\textstyle \mathbf {x} _{i}} , and weighted by an appropriate coefficient w i . {\textstyle w_{i}.} The weights w i {\textstyle w_{i}} can be estimated using the matrix methods of linear least squares, because the approximating function is linear in the weights w i {\textstyle w_{i}} . Approximation schemes of this kind have been particularly used in time series prediction and control of nonlinear systems exhibiting sufficiently simple chaotic behaviour and 3D reconstruction in computer graphics (for example, hierarchical RBF and Pose Space Deformation). == RBF Network == The sum can also be interpreted as a rather simple single-layer type of artificial neural network called a radial basis function network, with the radial basis functions taking on the role of the activation functions of the network. It can be shown that any continuous function on a compact interval can in principle be interpolated with arbitrary accuracy by a sum of this form, if a sufficiently large number N {\textstyle N} of radial basis functions is used. The approximant y ( x ) {\textstyle y(\mathbf {x} )} is differentiable with respect to the weights w i {\textstyle w_{i}} . The weights could thus be learned using any of the standard iterative methods for neural networks. Using radial basis functions in this manner yields a reasonable interpolation approach provided that the fitting set has been chosen such that it covers the entire range systematically (equidistant data points are ideal). However, without a polynomial term that is orthogonal to the radial basis functions, estimates outside the fitting set tend to perform poorly. == RBFs for PDEs == Radial basis functions are used to approximate functions and so can be used to discretize and numerically solve Partial Differential Equations (PDEs). This was first done in 1990 by E. J. Kansa who developed the first RBF based numerical method. It is called the Kansa method and was used to solve the elliptic Poisson equation and the linear advection-diffusion equation. The function values at points x {\displaystyle \mathbf {x} } in the domain are approximated by the linear combination of RBFs: The derivatives are approximated as such: where N {\displaystyle N} are the number of points in the discretized domain, d {\displaystyle d} the dimension of the domain and λ {\displaystyle \lambda } the scalar coefficients that are unchanged by the differential operator. Different numerical methods based on Radial Basis Functions were developed thereafter. Some methods are the RBF-FD method, the RBF-QR method and the RBF-PUM method.
Hybrid intelligent system
Hybrid intelligent system denotes a software system which employs, in parallel, a combination of methods and techniques from artificial intelligence subfields, such as: Neuro-symbolic systems Neuro-fuzzy systems Hybrid connectionist-symbolic models Fuzzy expert systems Connectionist expert systems Evolutionary neural networks Genetic fuzzy systems Rough fuzzy hybridization Reinforcement learning with fuzzy, neural, or evolutionary methods as well as symbolic reasoning methods. From the cognitive science perspective, every natural intelligent system is hybrid because it performs mental operations on both the symbolic and subsymbolic levels. For the past few years, there has been an increasing discussion of the importance of A.I. Systems Integration. Based on notions that there have already been created simple and specific AI systems (such as systems for computer vision, speech synthesis, etc., or software that employs some of the models mentioned above) and now is the time for integration to create broad AI systems. Proponents of this approach are researchers such as Marvin Minsky, Ron Sun, Aaron Sloman, Angelo Dalli and Michael A. Arbib. An example hybrid is a hierarchical control system in which the lowest, reactive layers are sub-symbolic. The higher layers, having relaxed time constraints, are capable of reasoning from an abstract world model and performing planning (even by hybrid wisdom). Intelligent systems usually rely on hybrid reasoning processes, which include induction, deduction, abduction and reasoning by analogy.
How to Choose an AI Voice Assistant
Curious about the best AI voice assistant? An AI voice assistant is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI voice assistant slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
Ancient text corpora
Ancient text corpora are the entire collection of texts from the period of ancient history, defined in this article as the period from the beginning of writing up to 300 AD. These corpora are important for the study of literature, history, linguistics, and other fields, and are a fundamental component of the world's cultural heritage. Chinese, Latin, and Greek are examples of ancient languages with significant text corpora, although much of these corpora are known to us via transmission (frequently via medieval manuscript copies) rather than in their original form. These texts – both transmitted and original – provide valuable insights into the history and culture of different regions of the world, and have been studied for centuries by scholars and researchers. Other ancient texts – particularly stone inscriptions and papyrus scrolls – have been published following archaeological research, notably the cuneiform corpus of c.10 million words and the c.5 million words in ancient Egyptian. Through advances in technology and digitization, ancient text corpora are more accessible than ever before. Tools such as the Perseus Digital Library and the Digital Corpus of Sanskrit have made it easier for researchers to access and analyze these texts. == Quantifying the corpora == Two types of ancient texts are known to modern scholars – those that have only survived in younger manuscripts, but whose great age is undisputed (this applies to the bulk of the Chinese, Brahmi, Greek, Latin, Hebrew and Avestan tradition), and those known from original inscriptions, papyri and other manuscripts. Counting of the words in each corpus presents significant methodological challenges – in principle, every single occurrence of a word in the text is counted separately, but in the case of parallel transmission of literary texts, only a single transmission is taken into account. Just as the Book of the Dead and the coffin texts are only included once in the number given for the Egyptian, the Greek and Latin literary works should only be counted according to one manuscript. If, on the other hand, tombs, royal inscriptions or economic documents of certain ancient languages often show a more or less identical form, this is not evaluated as a purely "parallel tradition". Attached prepositions are counted as separate words, except in the case of the definite article in Hebrew, Aramaic and Greek since it has no equivalent in most languages, so its frequency would significantly affect the comparability of numbers. === Languages with known size estimates === === South Asian === Sanskrit (Vedic Sanskrit and Classical Sanskrit) Indus script (3,800 items, c.20,000 characters) Brahmi script Old Tamil Early Indian epigraphy and Indian epic poetry Kharosthi Pali literature List of historic Indian texts === Mesoamerican === Olmec hieroglyphs Maya script === East Asian === Old Chinese Chinese classics The pre-Qin corpus: a collection of ancient Chinese texts written before the Qin dynasty (221 BCE). The corpus includes texts from Confucianism, Taoism, Legalism, and other schools of thought. The pre-Han corpus: a collection of ancient Chinese texts written before the Han dynasty (202 BCE). The corpus includes texts from Confucianism, Taoism, Legalism, and other schools of thought. See the Chinese Text Project Chinese bronze inscriptions, Oracle bone script, Seal script, Clerical script === Central Iranian languages === Prior to 300 AD, the Central Iranian languages are mainly in the form of Sassanid stone inscriptions in the two closely related idioms Middle Persian (Pahlavi scripts and Inscriptional Parthian), there are 5000 for the corpus of Middle Persian (mostly 3rd, but also 4th/5th centuries) and for the corpus of Parthian (3rd century) 3000 words. To what extent some of the Manichaean Middle Persian literary texts may date back to the 3rd century is difficult to estimate; Mani is said to have personally written the Shabuhragan totaling about 5000 words. In any case, if we combine Middle Persian and Parthian, we come to over 10,000 words. === Proto-Sinaitic === Proto-Sinaitic script has no more than about 400 letters (number of words is unknown since the script has not been fully interpreted). To a similar extent, there are probably approximately contemporaneous Proto-Canaanite inscriptions (ibid.). === Anatolian === Luwian cuneiform, approx. 3000 words the Palaic language few hundred words. Hieroglyphic Luwian the Lycian alphabet (the best attested Anatolian successor language written in alphabetic script) with about 5000 words The Lydian alphabet 109 inscriptions comprising about 1500 words The Phrygian alphabet the in-tomb inscriptions from the 2nd and 3rd centuries AD (approx. 1000 words) and in the so-called "old Phrygian" inscriptions less than 300 words The Carian alphabets whose texts, mainly from Egypt, contain around 600 words. === Old Italic === the Umbrian language attested essentially by the sacrificial instructions of the Iguvinian Tables with 5000 words the Oscan language (ibid.) with 2000 words the Messapic language with probably a good 1000 words (the estimate is difficult because most texts in this hardly understandable language do not use word separators) the Venetic language a few hundred words the Faliscan language a few hundred words Cisalpine Celtic inscriptions amount to approximately 2000 words, to which are added a number of glosses by classical authors === Iberia === Iberian scripts, more rarely written in Greek or Latin script, approx. 2500 words Celtiberian script, which refers to Celtic language testimonies in Iberian, but also in Latin script from Spain (approx. 1000 words) Southwest Paleohispanic script, 78 inscriptions, a few hundred words Lusitanian language, three monuments in Latin script, approx. 60 words === Germanic Northern Europe === Runic inscriptions dated before the 4th century amount to about 30 pieces, which contain no more than 50 words in total === Africa === Geʽez script: comparatively few inscriptions with a total of around 1,000 words before 300 AD. Following Christianization in the 4th century, more extensive texts are known. Libyco-Berber alphabet: over 1,000 inscriptions from the Maghreb, which are dated to Roman times. Most texts do not use a word separator; Peust estimates that the total number of words could be around 5,000 Meroitic script (Ancient Nubian): about 900 texts are known, which Peust estimates may contain approximately 10,000 words, albeit with uncertainty from the fact that the word separator is not used consistently in the Meroitic script. === Aegean === The Cretan Linear A inscriptions that have not yet been deciphered are available in about 2500 texts, which contain a total of around 20,000 characters. The total number of words can hardly be determined; Peust tentatively put it in the same order of magnitude as in Meroitic. In addition to the Linear A texts, there are also inscriptions Cretan hieroglyphs of a few hundred characters and texts written in the Greek alphabet, but not in Greek, with a few dozen words Cypriot syllabary in the first millennium BC, in which mostly Greek texts were recorded. The relevant texts comprise around 100 to 200 words. === Micro corpora === There are a significant number of ancient micro-corpus languages. Estimating the total number of attested ancient languages may be as difficult as estimating their corpus size. For example, Greek and Latin sources hand down an enormous amount of foreign-language glosses, the seriousness of which is not always certain. == Preservation and curation == Historic preservation and maintaining ancient text corpora presents several challenges, including issues with preservation, translation, and digitization. Many ancient texts have been lost over time, and those that survive may be damaged or fragmented. Translating ancient languages and scripts requires specialized expertise, and digitizing texts can be time-consuming and resource-intensive. == Corpus linguistics == The field of corpus linguistics studies language as expressed in text corpora. This includes the analysis of word frequency, collocations, grammar, and semantics. Ancient text corpora provide a valuable resource for corpus linguistics research, enabling scholars to explore the evolution of language and culture over time.
Apache cTAKES
Apache cTAKES: clinical Text Analysis and Knowledge Extraction System is an open-source Natural Language Processing (NLP) system that extracts clinical information from electronic health record unstructured text. It processes clinical notes, identifying types of clinical named entities — drugs, diseases/disorders, signs/symptoms, anatomical sites and procedures. Each named entity has attributes for the text span, the ontology mapping code, context (family history of, current, unrelated to patient), and negated/not negated. cTAKES was built using the UIMA Unstructured Information Management Architecture framework and OpenNLP natural language processing toolkit. == Components == Components of cTAKES are specifically trained for the clinical domain, and create rich linguistic and semantic annotations that can be utilized by clinical decision support systems and clinical research. These components include: Named Section identifier Sentence boundary detector Rule-based tokenizer Formatted list identifier Normalizer Context dependent tokenizer Part-of-speech tagger Phrasal chunker Dictionary lookup annotator Context annotator Negation detector Uncertainty detector Subject detector Dependency parser patient smoking status identifier Drug mention annotator == History == Development of cTAKES began at the Mayo Clinic in 2006. The development team, led by Dr. Guergana Savova and Dr. Christopher Chute, included physicians, computer scientists and software engineers. After its deployment, cTAKES became an integral part of Mayo's clinical data management infrastructure, processing more than 80 million clinical notes. When Dr. Savova's moved to Boston Children's Hospital in early 2010, the core development team grew to include members there. Further external collaborations include: University of Colorado Brandeis University University of Pittsburgh University of California at San Diego Such collaborations have extended cTAKES' capabilities into other areas such as Temporal Reasoning, Clinical Question Answering, and coreference resolution for the clinical domain. In 2010, cTAKES was adopted by the i2b2 program and is a central component of the SHARP Area 4. In 2013, cTAKES released their first release as an Apache Software Foundation incubator project: cTAKES 3.0. In March 2013, cTAKES became an Apache Software Foundation Top Level Project (TLP).
FIRST Global Challenge
The FIRST Global Challenge is a yearly robotics competition organized by the International First Committee Association. It promotes STEM education and careers for youth and was created by Dean Kamen in 2016 as an expansion of FIRST, an organization with similar objectives. == History == FIRST Global is a trade name for the International First Committee Association, a nonprofit corporation based in Manchester, New Hampshire, with a 501(c)(3) designation from the IRS. The nonprofit was founded by the co-founder of FIRST, Dean Kamen, with the objective of promoting STEM education and careers in the developing world through Olympics-style robotics competitions. Former US Congressman, Joe Sestak was the organization's president in 2017, but left after the 2017 Challenge. Each year, the FIRST Global Challenge is held in a different city. For example, Mexico City was selected to host the 2018 Challenge after the United States hosted the 2017 edition in Washington, DC. This is a change from FIRST's system of championships, where one city hosts for several years at a time. In May 2020, it was announced that FIRST Global would not host a traditional challenge in 2020 due to the COVID-19 pandemic and shifted to a remote model. One of the three champions were Team Bangladesh. In 2022, FIRST Global returned to in-person events with the 2022 Challenge in Geneva, Switzerland. == Editions == === Washington, D.C. 2017 === The 2017 FIRST Global Challenge was held in Washington, D.C., from July 16–18, and the challenge was the use of robots to separate different colored balls, representing clean water and impurities in water, symbolizing the Engineering Grand Challenge (based on the Millennium Development Goal) of improving access to clean water in the developing world. Around 160 teams composed of 15- to 18-year-olds from 157 countries participated, and around 60% of teams were created or led by young women. Six continental teams also participated. === Mexico City 2018 === The 2018 FIRST Global Challenge was held in Mexico City from August 15–18. The 2018 Challenge was called Energy Impact and explored the impact of various types of energy on the world and how they can be made more sustainable. In the challenge, robots worked together in teams of three to give cubes to human players, turn a crank, and score cubes in goals in order to generate electrical power. The challenge was based on three Engineering Grand Challenges; making solar energy affordable, making fusion energy a reality, and creating carbon sequestration methods. === Dubai 2019 === The 2019 challenge, called Ocean Opportunities, was held in Dubai from October 24–27 and was the first challenge hosted outside of North America. The challenge was themed around clearing the ocean of pollutants, and had two alliances of three teams each attempting to score large and small balls representing pollutants into processing areas and a processing barge. The processing barge had multiple levels, with higher levels worth more points. At the end of the match, robots "docked" with the barge by driving onto or climbing up it, with climbing worth more points. The event was opened by Sheikh Hamdan bin Mohammed Al Maktoum, Crown Prince of Dubai. === Geneva 2022 === The 2022 challenge called Carbon Capture, was held in Geneva from October 13–16. The challenge was themed around removing carbon dioxide (CO2) emissions from the atmosphere. In the Carbon Capture game, six different countries worked together to capture and store black balls representing carbon particles. The storage tower had multiple cantilevered bars that the robots mounted to, with the higher bars worth a greater multiplier. At the end of a match, robots "docked" on the storage tower's base or climbed the bars with their alliance indicator ball. Each match started with a "global alliance" of six countries, then divided into two "regional alliances" each consisting of three countries. The event was opened by Dr. Martina Hirayama, Switzerland State Secretary for Education, Research and Innovation (SERI). === Singapore 2023 === The 2023 challenge, called Hydrogen Horizons, was held in Singapore from October 7–10. The challenge is themed around renewable energy with a focus on hydrogen technologies. === Athens 2024 === The 2024 challenge was hosted in the Peace and Friendship Stadium in Attica, Greece. === Panama 2025 === The 2025 challenge, Eco Equilibrium, was hosted in the Panama Convention Centre in Panama City, Panama. == Subordinate programs == === Global STEM Corps === The Global STEM Corps is a FIRST Global initiative that connects qualified volunteer mentors with students in developing countries to prepare them for competitions. === New Technology Experience === The New Technology Experience (NTE) is an annual component of the FIRST Global Challenge that was added to the organization's offerings in 2021. It was established as a means for the student community to stay current with cutting-edge technology and is integrated with each year's theme. The 2021 NTE was the CubeSat Prototype Challenge. The 2022 NTE, Carbon Countermeasures, was presented in partnership with XPRIZE.
Quotient automaton
In computer science, in particular in formal language theory, a quotient automaton can be obtained from a given nondeterministic finite automaton by joining some of its states. The quotient recognizes a superset of the given automaton; in some cases, handled by the Myhill–Nerode theorem, both languages are equal. == Formal definition == A (nondeterministic) finite automaton is a quintuple A = ⟨Σ, S, s0, δ, Sf⟩, where: Σ is the input alphabet (a finite, non-empty set of symbols), S is a finite, non-empty set of states, s0 is the initial state, an element of S, δ is the state-transition relation: δ ⊆ S × Σ × S, and Sf is the set of final states, a (possibly empty) subset of S. A string a1...an ∈ Σ is recognized by A if there exist states s1, ..., sn ∈ S such that ⟨si-1,ai,si⟩ ∈ δ for i=1,...,n, and sn ∈ Sf. The set of all strings recognized by A is called the language recognized by A; it is denoted as L(A). For an equivalence relation ≈ on the set S of A’s states, the quotient automaton A/≈ = ⟨Σ, S/≈, [s0], δ/≈, Sf/≈⟩ is defined by the input alphabet Σ being the same as that of A, the state set S/≈ being the set of all equivalence classes of states from S, the start state [s0] being the equivalence class of A’s start state, the state-transition relation δ/≈ being defined by δ/≈([s],a,[t]) if δ(s,a,t) for some s ∈ [s] and t ∈ [t], and the set of final states Sf/≈ being the set of all equivalence classes of final states from Sf. The process of computing A/≈ is also called factoring A by ≈. == Example == For example, the automaton A shown in the first row of the table is formally defined by ΣA = {0,1}, SA = {a,b,c,d}, sA0 = a, δA = { ⟨a,1,b⟩, ⟨b,0,c⟩, ⟨c,0,d⟩ }, and SAf = { b,c,d }. It recognizes the finite set of strings { 1, 10, 100 }; this set can also be denoted by the regular expression "1+10+100". The relation (≈) = { ⟨a,a⟩, ⟨a,b⟩, ⟨b,a⟩, ⟨b,b⟩, ⟨c,c⟩, ⟨c,d⟩, ⟨d,c⟩, ⟨d,d⟩ }, more briefly denoted as a≈b,c≈d, is an equivalence relation on the set {a,b,c,d} of automaton A’s states. Building the quotient of A by that relation results in automaton C in the third table row; it is formally defined by ΣC = {0,1}, SC = {a,c}, sC0 = a, δC = { ⟨a,1,a⟩, ⟨a,0,c⟩, ⟨c,0,c⟩ }, and SCf = { a,c }. It recognizes the finite set of all strings composed of arbitrarily many 1s, followed by arbitrarily many 0s, i.e. { ε, 1, 10, 100, 1000, ..., 11, 110, 1100, 11000, ..., 111, ... }; this set can also be denoted by the regular expression "10". Informally, C can be thought of resulting from A by glueing state a onto state b, and glueing state c onto state d. The table shows some more quotient relations, such as B = A/a≈b, and D = C/a≈c. == Properties == For every automaton A and every equivalence relation ≈ on its states set, L(A/≈) is a superset of (or equal to) L(A). Given a finite automaton A over some alphabet Σ, an equivalence relation ≈ can be defined on Σ by x ≈ y if ∀ z ∈ Σ: xz ∈ L(A) ↔ yz ∈ L(A). By the Myhill–Nerode theorem, A/≈ is a deterministic automaton that recognizes the same language as A. As a consequence, the quotient of A by every refinement of ≈ also recognizes the same language as A.