Found 451 bookmarks
Newest
Topological sorting - Wikipedia
Topological sorting - Wikipedia
In computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering. For instance, the vertices of the graph may represent tasks to be performed, and the edges may represent constraints that one task must be performed before another; in this application, a topological ordering is just a valid sequence for the tasks. Precisely, a topological sort is a graph traversal in which each node v is visited only after all its dependencies are visited. A topological ordering is possible if and only if the graph has no directed cycles, that is, if it is a directed acyclic graph (DAG). Any DAG has at least one topological ordering, and algorithms are known for constructing a topological ordering of any DAG in linear time. Topological sorting has many applications especially in ranking problems such as feedback arc set. Topological sorting is possible even when the DAG has disconnected components.
·en.wikipedia.org·
Topological sorting - Wikipedia
(PDF) Hand-Grip Dynamometry Predicts Future Outcomes in Aging Adults
(PDF) Hand-Grip Dynamometry Predicts Future Outcomes in Aging Adults
PDF | One use of clinical measures is the prediction of future outcomes. The purpose of this systematic review was to summarize the literature... | Find, read and cite all the research you need on ResearchGate
The evidence gathered from diverse samples of individuals, employing several dynamometers, and using different strength measures sup-ports the value of grip strength as a predictor of mortality, disability, complications, and increased length of stay.
·researchgate.net·
(PDF) Hand-Grip Dynamometry Predicts Future Outcomes in Aging Adults
Linear subspace - Wikipedia
Linear subspace - Wikipedia
In mathematics, and more specifically in linear algebra, a linear subspace, also known as a vector subspace[1][note 1] is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces.
·en.wikipedia.org·
Linear subspace - Wikipedia
Linear span - Wikipedia
Linear span - Wikipedia
In mathematics, the linear span (also called the linear hull[1] or just span) of a set S of vectors (from a vector space), denoted span(S),[2] is the smallest linear subspace that contains the set.[3] It can be characterized either as the intersection of all linear subspaces that contain S, or as the set of linear combinations of elements of S. The linear span of a set of vectors is therefore a vector space. Spans can be generalized to matroids and modules.
·en.wikipedia.org·
Linear span - Wikipedia
Topology - Wikipedia
Topology - Wikipedia
In mathematics, topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself
·en.wikipedia.org·
Topology - Wikipedia
Ohm's law - Wikipedia
Ohm's law - Wikipedia
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points
·en.wikipedia.org·
Ohm's law - Wikipedia
Kirchhoff's circuit laws - Wikipedia
Kirchhoff's circuit laws - Wikipedia
Kirchhoff's first law, or Kirchhoff's junction rule, states that, for any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node; or equivalently: The algebraic sum of currents in a network of conductors meeting at a point is zero
·en.wikipedia.org·
Kirchhoff's circuit laws - Wikipedia
Open-Ended Learning Leads to Generally Capable Agents
Open-Ended Learning Leads to Generally Capable Agents
Artificial agents have achieved great success in individual challenging simulated environments, mastering the particular tasks they were trained for, with their behaviour even generalising to maps and opponents that were never encountered in training. In this work we create agents that can perform well beyond a single, individual task, that exhibit much wider generalisation of behaviour to a massive, rich space of challenges. We define a universe of tasks within an environment domain and demonstrate the ability to train agents that are generally capable across this vast space and beyond. The environment is natively multi-agent, spanning the continuum of competitive, cooperative, and independent games, which are situated within procedurally generated physical 3D worlds. The resulting space is exceptionally diverse in terms of the challenges posed to agents, and as such, even measuring the learning progress of an agent is an open research problem. We propose an iterative notion of improvement between successive generations of agents, rather than seeking to maximise a singular objective, allowing us to quantify progress despite tasks being incomparable in terms of achievable rewards. Training an agent that is performant across such a vast space of tasks is a central challenge, one we find that pure reinforcement learning on a fixed distribution of training tasks does not succeed in. We show that through constructing an open-ended learning process, which dyna
We show that through constructing an open-ended learning process, which dynamically changes the training task distributions and training objectives such that the agent never stops learning, we achieve consistent learning of new behaviours. The resulting agent is able to score reward in every one of our humanly solvable evaluation levels, with behaviour generalising to many held-out points in the universe of tasks
·deepmind.com·
Open-Ended Learning Leads to Generally Capable Agents
Monoid - Wikipedia
Monoid - Wikipedia
In abstract algebra, a branch of mathematics, a monoid is a set equipped with an associative binary operation and an identity element. For example, the nonnegative integers with addition form a monoid, the identity element being 0. Monoids are semigroups with identity. Such algebraic structures occur in several branches of mathematics. The functions from a set into itself form a monoid with respect to function composition. More generally, in category theory, the morphisms of an object to itself form a monoid, and, conversely, a monoid may be viewed as a category with a single object. In computer science and computer programming, the set of strings built from a given set of characters is a free monoid. Transition monoids and syntactic monoids are used in describing finite-state machines. Trace monoids and history monoids provide a foundation for process calculi and concurrent computing. In theoretical computer science, the study of monoids is fundamental for automata theory (Krohn–Rhodes theory), and formal language theory (star height problem).
In computer science, many abstract data types can be endowed with a monoid structure. In a common pattern, a sequence of elements of a monoid is "folded" or "accumulated" to produce a final value. For instance, many iterative algorithms need to update some kind of "running total" at each iteration; this pattern may be elegantly expressed by a monoid operation. Alternatively, the associativity of monoid operations ensures that the operation can be parallelized by employing a prefix sum or similar algorithm, in order to utilize multiple cores or processors efficiently.
An application of monoids in computer science is the so-called MapReduce programming model (see Encoding Map-Reduce As A Monoid With Left Folding). MapReduce, in computing, consists of two or three operations. Given a dataset, "Map" consists of mapping arbitrary data to elements of a specific monoid. "Reduce" consists of folding those elements, so that in the end we produce just one element
·en.wikipedia.org·
Monoid - Wikipedia
Bigram - Wikipedia
Bigram - Wikipedia
A bigram or digram is a sequence of two adjacent elements from a string of tokens, which are typically letters, syllables, or words. A bigram is an n-gram for n=2. The frequency distribution of every bigram in a string is commonly used for simple statistical analysis of text in many applications, including in computational linguistics, cryptography, speech recognition, and so on. Gappy bigrams or skipping bigrams are word pairs which allow gaps (perhaps avoiding connecting words, or allowing some simulation of dependencies, as in a dependency grammar). Head word bigrams are gappy bigrams with an explicit dependency relationship.
·en.wikipedia.org·
Bigram - Wikipedia
Combinatory logic - Wikipedia
Combinatory logic - Wikipedia
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel[1] and Haskell Curry,[2] and has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming languages. It is based on combinators, which were introduced by Schönfinkel in 1920 with the idea of providing an analogous way to build up functions—and to remove any mention of variables—particularly in predicate logic. A combinator is a higher-order function that uses only function application and earlier defined combinators to define a result from its arguments.
·en.wikipedia.org·
Combinatory logic - Wikipedia
Visualizing the 3D Schrödinger Equation: Quantum Eigenstates of a Particle Confined in 3D Wells
Visualizing the 3D Schrödinger Equation: Quantum Eigenstates of a Particle Confined in 3D Wells
What do the quantum eigenstates of 3D wells look like? In this video, we visualize the solutions of the 3D Schrödinger Equation computed for more than a total of 500 eigenstates of 2, 4, 8, and 12 wells, illustrating what the molecular orbitals for a molecule with that number of atoms look like. These simulations are made with qmsolve, an open-source python package that we are developing for solving and visualizing quantum physics. You can find the source code here: https://github.com/quantum-visualizations/qmsolve The way this simulator works is by discretizing the Hamiltonian of an arbitrary potential and diagonalizing it for getting the energies and the eigenstates of the system. The eigenstates of this video are computed with high accuracy (less than 1% of relative error) by diagonalizing a Hamiltonian matrix with a shape of 1,000,000 x 1,000,000. For a molecule that contains only a single electron, an orbital is exactly the same that its eigenstate. Therefore in these examples, the eigenstates are equivalent to the orbitals. In the video, it can be noticed that the first molecular orbitals can be visualized as a first-order approximation as a simple linear combination of the orbitals of a single well. However, as the energy of the eigenstates raises, their wave function starts to take much more complex shapes. Between each eigenstate is plotted a transition between two eigenstates. This is made by preparing a quantum superposition of the two eigenstates involved. #QuantumPhysics #MolecularOrbitals #QuantumChemistry
·youtube.com·
Visualizing the 3D Schrödinger Equation: Quantum Eigenstates of a Particle Confined in 3D Wells
Determinant - Wikipedia
Determinant - Wikipedia
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It allows characterizing some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the linear map represented by the matrix is an isomorphism. The determinant of a product of matrices is the product of their determinants (the preceding property is a corollary of this one). The determinant of a matrix A is denoted det(A), det A, or |A|.
·en.wikipedia.org·
Determinant - Wikipedia
Jacobian matrix and determinant - Wikipedia
Jacobian matrix and determinant - Wikipedia
In vector calculus, the Jacobian matrix (/dʒəˈkoʊbiən/,[1][2][3] /dʒɪ-, jɪ-/) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. When this matrix is square, that is, when the function takes the same number of variables as input as the number of vector components of its output, its determinant is referred to as the Jacobian determinant. Both the matrix and (if applicable) the determinant are often referred to simply as the Jacobian in literature
·en.wikipedia.org·
Jacobian matrix and determinant - Wikipedia
Chain rule - Wikipedia
Chain rule - Wikipedia
if a car travels twice as fast as a bicycle and the bicycle is four times as fast as a walking man, then the car travels 2 × 4 = 8 times as fast as the man
·en.wikipedia.org·
Chain rule - Wikipedia
Derivative - Wikipedia
Derivative - Wikipedia
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances
·en.wikipedia.org·
Derivative - Wikipedia
Effects of light on human circadian rhythms, sleep and mood
Effects of light on human circadian rhythms, sleep and mood
Humans live in a 24-hour environment, in which light and darkness follow a diurnal pattern. Our circadian pacemaker, the suprachiasmatic nuclei (SCN) in the hypothalamus, is entrained to the 24-hour solar day via a pathway from ...
Rather recently, the availability of artificial light has substantially changed the light environment, especially during evening and night hours. This may increase the risk of developing circadian rhythm sleep–wake disorders (CRSWD), which are often caused by a misalignment of endogenous circadian rhythms and external light–dark cycles
On the other hand, light can also be used as an effective and noninvasive therapeutic option with little to no side effects, to improve sleep, mood and general well-being
The antidepressant effect of light is most pronounced when it is administered in the early morning hours
Previous cataract surgery or lens removal
Light at the wrong time may disrupt circadian rhythms and sleep, but in the form of light therapy, light exposure can be used as an intervention for psychiatric and other medical conditions.
·ncbi.nlm.nih.gov·
Effects of light on human circadian rhythms, sleep and mood
Natural-language understanding - Wikipedia
Natural-language understanding - Wikipedia
Natural-language understanding (NLU) or natural-language interpretation (NLI)[1] is a subtopic of natural-language processing in artificial intelligence that deals with machine reading comprehension. Natural-language understanding is considered an AI-hard problem.[2] There is considerable commercial interest in the field because of its application to automated reasoning,[3] machine translation,[4] question answering,[5] news-gathering, text categorization, voice-activation, archiving, and large-scale content analysis.
·en.wikipedia.org·
Natural-language understanding - Wikipedia
Natural Language Inference: An Overview
Natural Language Inference: An Overview
Benchmark and models
Natural Language Inference (NLI) is the task of determining whether the given “hypothesis” logically follows from the “premise”. In layman’s terms, you need to understand whether the hypothesis is true, while the premise is your only knowledge about the subject.
·towardsdatascience.com·
Natural Language Inference: An Overview
Recursive definition - Wikipedia
Recursive definition - Wikipedia
In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set (Aczel 1977:740ff). Some examples of recursively-definable objects include factorials, natural numbers, Fibonacci numbers, and the Cantor ternary set.
·en.wikipedia.org·
Recursive definition - Wikipedia