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24,800 | If spheres are packed into square pyramids whose number of layers is 1, 2, 3, etc., then the square pyramidal numbers giving the numbers of spheres in each pyramid are: These numbers can be calculated algebraically, as follows. If a pyramid of spheres is decomposed into its square layers with a square number of spheres... | Square pyramidal number | 0.807973 |
24,801 | In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the number of stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part of a broader topic of figurate numbers representing the numbers of points forming r... | Square pyramidal number | 0.807972 |
24,802 | In analytical chemistry, crossed molecular beam experiments involve two beams of atoms or molecules which are collided together to study the dynamics of the chemical reaction, and can detect individual reactive collisions. | Crossed molecular beam | 0.807972 |
24,803 | The crossed molecular beam technique was developed by Dudley Herschbach and Yuan T. Lee, for which they were awarded the 1986 Nobel Prize in Chemistry. While the technique was demonstrated in 1953 by Taylor and Datz of Oak Ridge National Laboratory, Herschbach and Lee refined the apparatus and began probing gas-phase r... | Crossed molecular beam | 0.807972 |
24,804 | Sporogenesis is the production of spores in biology. The term is also used to refer to the process of reproduction via spores. Reproductive spores were found to be formed in eukaryotic organisms, such as plants, algae and fungi, during their normal reproductive life cycle. Dormant spores are formed, for example by cert... | Spore formation | 0.807971 |
24,805 | Local elevation is a technique used in computational chemistry or physics, mainly in the field of molecular simulation (including molecular dynamics (MD) and Monte Carlo (MC) simulations). It was developed in 1994 by Huber, Torda and van Gunsteren to enhance the searching of conformational space in molecular dynamics s... | Local elevation | 0.807971 |
24,806 | Stem-cell lines are used in research and regenerative medicine. They can be used to study stem-cell biology and early human development. In the field of regenerative medicine, it has been proposed that stem cells be used in cell-based therapies to replace injured or diseased cells and tissues. Examples of conditions th... | Stem-cell lines | 0.807964 |
24,807 | The DSV is fitted with a single Kraft Telerobotics "Raptor" hydraulically powered 7-function manipulator with force feedback, at the starboard side of the pressure hull. | DSV Limiting Factor | 0.80796 |
24,808 | Pediatric genetics Birth defects Developmental disability, autism, epilepsy short stature and skeletal dysplasia 3. Adult genetics cardiomyopathy and cardiac dysrhythmias inherited kidney disease dementia and neurodegeneration connective tissue disease 4. Cancer genetics breast/ovarian cancer bowel cancer endocrine tum... | Clinical geneticist | 0.80796 |
24,809 | Clinical genetics a medical specialty with particular attention to hereditary disorders. Branches of clinical genetics include: 1. Prenatal genetics Couples at risk of having a child with a genetic disorder preconception or while pregnant High risk prenatal screening results Abnormal fetal ultrasound 2. | Clinical geneticist | 0.80796 |
24,810 | Metabolic (or biochemical) genetics involves the diagnosis and management of inborn errors of metabolism in which patients have enzymatic deficiencies that perturb biochemical pathways involved in metabolism of carbohydrates, amino acids, and lipids. Examples of metabolic disorders include galactosemia, glycogen storag... | Clinical geneticist | 0.80796 |
24,811 | The broad range of research in medical genetics reflects the overall scope of this field, including basic research on genetic inheritance and the human genome, mechanisms of genetic and metabolic disorders, translational research on new treatment modalities, and the impact of genetic testing | Clinical geneticist | 0.80796 |
24,812 | One area in which population categories can be important considerations in genetics research is in controlling for confounding between population substructure, environmental exposures, and health outcomes. Association studies can produce spurious results if cases and controls have differing allele frequencies for genes... | Clinical geneticist | 0.80796 |
24,813 | Medical genetics encompasses many different areas, including clinical practice of physicians, genetic counselors, and nutritionists, clinical diagnostic laboratory activities, and research into the causes and inheritance of genetic disorders. Examples of conditions that fall within the scope of medical genetics include... | Clinical geneticist | 0.80796 |
24,814 | The European Journal of Combinatorics is a closed-access peer-reviewed scientific journal for combinatorics. It is an international, bimonthly journal of discrete mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures withi... | European Journal of Combinatorics | 0.807957 |
24,815 | The application of time-dependent perturbation theory in quantum mechanics shows that the relaxation rates (and times) depend on spectral density functions that are the Fourier transforms of the autocorrelation function of the fluctuating magnetic dipole interactions. The form of the spectral density functions depend o... | Magnetic relaxation | 0.807953 |
24,816 | The nuclear quadrupole has an interaction with the electric field gradient at the nucleus which is again orientation dependent as with the other mechanisms described above, leading to the so-called quadrupolar relaxation mechanism. Molecular reorientation or tumbling can then modulate these orientation-dependent spin i... | Magnetic relaxation | 0.807953 |
24,817 | The space V ∞ ( X ) {\displaystyle {\mathcal {V}}^{\infty }(X)} admits a natural product. This product is continuous, commutative, associative, compatible with the filtration: and has the Euler characteristic as the identity element. It also commutes with the restriction to embedded submanifolds, and the diffeomorphism... | Valuation (geometry) | 0.807951 |
24,818 | The product of two smooth valuations ϕ , ψ ∈ Val ∞ ( V ) {\displaystyle \phi ,\psi \in \operatorname {Val} ^{\infty }(V)} is defined by where Δ: V → V × V {\displaystyle \Delta :V\to V\times V} is the diagonal embedding. The product is a continuous map Equipped with this product, Val ∞ ( V ) {\displaystyle \operato... | Valuation (geometry) | 0.807951 |
24,819 | The following are examples of smooth valuations on a smooth manifold X {\displaystyle X}: Smooth measures on X . {\displaystyle X.} The Euler characteristic; this follows from the work of Chern on the Gauss-Bonnet theorem, where such μ {\displaystyle \mu } and ω {\displaystyle \omega } were constructed to represent the... | Valuation (geometry) | 0.807951 |
24,820 | Other examples of valuations on finite unions of convex bodies of R n {\displaystyle \mathbb {R} ^{n}} are surface area, mean width, and Euler characteristic. In geometry, continuity (or smoothness) conditions are often imposed on valuations, but there are also purely discrete facets of the theory. In fact, the concept... | Valuation (geometry) | 0.807951 |
24,821 | In geometry, a valuation is a finitely additive function from a collection of subsets of a set X {\displaystyle X} to an abelian semigroup. For example, Lebesgue measure is a valuation on finite unions of convex bodies of R n . {\displaystyle \mathbb {R} ^{n}.} | Valuation (geometry) | 0.807951 |
24,822 | For simplicity, fix Lebesgue measures on U {\displaystyle U} and V . {\displaystyle V.} The pushforward can be uniquely characterized by describing its action on valuations of the form vol ( ∙ + A ) , {\displaystyle \operatorname {vol} (\bullet +A),} for all A ∈ K ( U ) , {\displaystyle A\in {\mathcal {K}}(U),} and t... | Valuation (geometry) | 0.807951 |
24,823 | Every smooth immersion f: X → Y {\displaystyle f:X\to Y} of smooth manifolds induces a pullback map f ∗: V ∞ ( Y ) → V ∞ ( X ) . {\displaystyle f^{*}:{\mathcal {V}}^{\infty }(Y)\to {\mathcal {V}}^{\infty }(X).} If f {\displaystyle f} is an embedding, then The pullback is a morphism of filtered algebras. | Valuation (geometry) | 0.807951 |
24,824 | By a theorem of Alesker, the restriction of the product is a non-degenerate pairing. This motivates the definition of the k {\displaystyle k} -homogeneous generalized valuation, denoted Val k − ∞ ( V ) , {\displaystyle \operatorname {Val} _{k}^{-\infty }(V),} as Val n − k ∞ ( V ) ∗ ⊗ Dens ( V ) , {\displaystyle \... | Valuation (geometry) | 0.807951 |
24,825 | For any (complex-valued) smooth differential form ω ∈ Ω n − 1 ( R n × S n − 1 ) {\displaystyle \omega \in \Omega ^{n-1}(\mathbb {R} ^{n}\times S^{n-1})} that is invariant under all the translations ( x , u ) ↦ ( x + t , u ) {\displaystyle (x,u)\mapsto (x+t,u)} and every number c ∈ C , {\displaystyle c\in \mathbb {C} ,}... | Valuation (geometry) | 0.807951 |
24,826 | The classical theorems of Hadwiger, Schneider and McMullen give fairly explicit descriptions of valuations that are homogeneous of degree 1 , {\displaystyle 1,} n − 1 , {\displaystyle n-1,} and n = dim V . {\displaystyle n=\operatorname {dim} V.} But for degrees 1 < i < n − 1 {\displaystyle 1 | Valuation (geometry) | 0.807951 |
24,827 | Hence defines a continuous section of the line bundle D e n s {\displaystyle Dens} over Gr i ( V ) {\displaystyle \operatorname {Gr} _{i}(V)} with fiber over E {\displaystyle E} equal to the 1 {\displaystyle 1} -dimensional space Dens ( E ) {\displaystyle \operatorname {Dens} (E)} of densities (Lebesgue measures) o... | Valuation (geometry) | 0.807951 |
24,828 | The Klain embedding is a linear injection of Val i + ( V ) , {\displaystyle \operatorname {Val} _{i}^{+}(V),} the space of even i {\displaystyle i} -homogeneous valuations, into the space of continuous sections of a canonical complex line bundle over the Grassmannian Gr i ( V ) {\displaystyle \operatorname {Gr} _{i... | Valuation (geometry) | 0.807951 |
24,829 | For a precise statement, let be the kinematic operator, that is, the map determined by the kinematic formulas (2). Let denote the Alesker-Poincaré duality, which is a linear isomorphism. Finally let m G ∗ {\displaystyle m_{G}^{*}} be the adjoint of the product map The Fundamental theorem of algebraic integral geometry ... | Valuation (geometry) | 0.807951 |
24,830 | In fact already in the step from real to complex space forms, considerable difficulties arise and these have only recently been resolved by Bernig, Fu, and Solanes. The key insight responsible for this progress is that the kinematic formulas contain the same information as the algebra of invariant valuations V ∞ ( M ) ... | Valuation (geometry) | 0.807951 |
24,831 | The topology on Val ( V ) {\displaystyle \operatorname {Val} (V)} is the topology of uniform convergence on compact subsets of K ( V ) . {\displaystyle {\mathcal {K}}(V).} Equipped with the norm where B ⊂ V {\displaystyle B\subset V} is a bounded subset with nonempty interior, Val ( V ) {\displaystyle \operatorname... | Valuation (geometry) | 0.807951 |
24,832 | {\displaystyle i.} It follows from the Irreducibility Theorem, in combination with the Casselman-Wallach theorem, that any smooth even valuation can be represented in this way. Such a representation is sometimes called a Crofton formula. | Valuation (geometry) | 0.807951 |
24,833 | A valuation ϕ ∈ Val ( V ) {\displaystyle \phi \in \operatorname {Val} (V)} is called smooth if the map g ↦ g ⋅ ϕ {\displaystyle g\mapsto g\cdot \phi } from G L ( V ) {\displaystyle GL(V)} to Val ( V ) {\displaystyle \operatorname {Val} (V)} is smooth. In other words, ϕ {\displaystyle \phi } is smooth if and only if... | Valuation (geometry) | 0.807951 |
24,834 | McMullen's decomposition theorem states that In particular, the degree of a homogeneous valuation is always an integer between 0 {\displaystyle 0} and n = dim V . {\displaystyle n=\operatorname {dim} V.} | Valuation (geometry) | 0.807951 |
24,835 | Here a polynomial f ( t ) = t 3 + 1 , {\displaystyle f(t)=t^{3}+1,} for example, is evaluated on a matrix A {\displaystyle A} simply as f ( A ) = A 3 + I . {\displaystyle f(A)=A^{3}+I.} The theorem applies to matrices and polynomials over any field or commutative ring. However, the assumption that p A ( t ) {\displayst... | Secular equation | 0.80795 |
24,836 | If λ {\displaystyle \lambda } is an eigenvalue of a square matrix A {\displaystyle A} with eigenvector v , {\displaystyle \mathbf {v} ,} then λ k {\displaystyle \lambda ^{k}} is an eigenvalue of A k {\displaystyle A^{k}} because The multiplicities can be shown to agree as well, and this generalizes to any polynomial in... | Secular equation | 0.80795 |
24,837 | If A {\displaystyle A} and B {\displaystyle B} are two square n × n {\displaystyle n\times n} matrices then characteristic polynomials of A B {\displaystyle AB} and B A {\displaystyle BA} coincide: When A {\displaystyle A} is non-singular this result follows from the fact that A B {\displaystyle AB} and B A {\displayst... | Secular equation | 0.80795 |
24,838 | When the characteristic of the field of the coefficients is 0 , {\displaystyle 0,} each such trace may alternatively be computed as a single determinant, that of the k × k {\displaystyle k\times k} matrix, The Cayley–Hamilton theorem states that replacing t {\displaystyle t} by A {\displaystyle A} in the characteristic... | Secular equation | 0.80795 |
24,839 | For a 2 × 2 {\displaystyle 2\times 2} matrix A , {\displaystyle A,} the characteristic polynomial is thus given by Using the language of exterior algebra, the characteristic polynomial of an n × n {\displaystyle n\times n} matrix A {\displaystyle A} may be expressed as where tr ( ⋀ k A ) {\textstyle \operatorname {tr... | Secular equation | 0.80795 |
24,840 | An example of a simply connected group is the special unitary group SU(2), which as a manifold is the 3-sphere. The rotation group SO(3), on the other hand, is not simply connected. (See Topology of SO(3).) The failure of SO(3) to be simply connected is intimately connected to the distinction between integer spin and h... | Lie Groups | 0.80795 |
24,841 | A Lie group G {\displaystyle G} is said to be simply connected if every loop in G {\displaystyle G} can be shrunk continuously to a point in G {\displaystyle G} . This notion is important because of the following result that has simple connectedness as a hypothesis: Theorem: Suppose G {\displaystyle G} and H {\displays... | Lie Groups | 0.80795 |
24,842 | One important aspect of the study of Lie groups is their representations, that is, the way they can act (linearly) on vector spaces. In physics, Lie groups often encode the symmetries of a physical system. The way one makes use of this symmetry to help analyze the system is often through representation theory. Consider... | Lie Groups | 0.80795 |
24,843 | The classification is in terms of the "highest weight" of the representation. The classification is closely related to the classification of representations of a semisimple Lie algebra. One can also study (in general infinite-dimensional) unitary representations of an arbitrary Lie group (not necessarily compact). For ... | Lie Groups | 0.80795 |
24,844 | As an aside, it may be noted that not all authors in the field of geometric algebra use the term pseudovector, and some authors follow the terminology that does not distinguish between the pseudovector and the cross product. However, because the cross product does not generalize to other than three dimensions, the noti... | Axial vector | 0.807949 |
24,845 | The entire body of physics that deals with (right-handed) pseudovectors and the right hand rule could be replaced by using (left-handed) pseudovectors and the left hand rule without issue. The (left) pseudovectors so defined would be opposite in direction to those defined by the right-hand rule. While vector relationsh... | Axial vector | 0.807949 |
24,846 | Continuing this way, it is straightforward to classify any of the common vectors in physics as either a pseudovector or polar vector. (There are the parity-violating vectors in the theory of weak-interactions, which are neither polar vectors nor pseudovectors. However, these occur very rarely in physics.) | Axial vector | 0.807949 |
24,847 | But reflecting the magnetic field as a vector through that plane would be expected to reverse it; this expectation is corrected by realizing that the magnetic field is a pseudovector, with the extra sign flip leaving it unchanged. In physics, pseudovectors are generally the result of taking the cross product of two pol... | Axial vector | 0.807949 |
24,848 | Since dimers cause a disruptive kink in DNA structure, polymerases often have trouble reading the region, slowing down DNA replication. Base Analogs- Chemical compounds that are sufficiently similar in structure and chemistry to the nitrogenous bases of DNA, such that they are able to be incorporated in the sequence. T... | Postzygotic mutation | 0.807947 |
24,849 | In 1978, a Nobel prize-winning physicist, electronics inventor, and electrical engineering professor, William Shockley, was concerned about relatively high reproductive rates among people of African descent, because he believed that genetics doomed black people to be intellectually inferior to white people. He stated t... | Scientific freedom | 0.807947 |
24,850 | The university he founded later became a model and inspiration for modern colleges in Germany and universities in the West.The concept of academic freedom was also clearly formulated in response to the encroachments of the totalitarian state on science and academia in general for the furtherance of its own goals. For i... | Scientific freedom | 0.807947 |
24,851 | But, In 2021, an academic committee of the prestigious Israel Prize decided to award the Israel Prize in the field of mathematics and computer science to Professor Oded Goldreich from the Weizmann Institute of Science. The Minister of Education did not accept the committee's recommendation on the grounds that Goldreich... | Scientific freedom | 0.807947 |
24,852 | For example, in North Africa, a professor of public health discovered that his country's infant mortality rate was higher than government figures indicated. He lost his job and was imprisoned.The fate of biology in the Soviet Union is also cited as a reason why society has an interest in protecting academic freedom. A ... | Scientific freedom | 0.807947 |
24,853 | The algebraic form of many observables—i.e., Hermitian operators representing observable quantities—is obtained by the following quantization rules: Write the classical form of the observable in Hamilton form (as a function of momenta p and positions q). Both vectors are expressed with respect to an arbitrary inertial ... | Molecular Hamiltonian | 0.807946 |
24,854 | The Fast Library for Number Theory (FLINT) is a C library for number theory applications. The two major areas of functionality currently implemented in FLINT are polynomial arithmetic over the integers and a quadratic sieve. The library is designed to be compiled with the GNU Multi-Precision Library (GMP) and is releas... | Fast Library for Number Theory | 0.807944 |
24,855 | In singularity theory, there is a different meaning, of a decomposition of a topological space X into disjoint subsets each of which is a topological manifold (so that in particular a stratification defines a partition of the topological space). This is not a useful notion when unrestricted; but when the various strata... | Stratification (mathematics) | 0.807944 |
24,856 | As is the case with spherical coordinates and spherical harmonics, Laplace's equation may be solved by the method of separation of variables to yield solutions in the form of oblate spheroidal harmonics, which are convenient to use when boundary conditions are defined on a surface with a constant oblate spheroidal coor... | Oblate spheroidal coordinates | 0.80794 |
24,857 | Oblate spheroidal coordinates can also be considered as a limiting case of ellipsoidal coordinates in which the two largest semi-axes are equal in length. Oblate spheroidal coordinates are often useful in solving partial differential equations when the boundary conditions are defined on an oblate spheroid or a hyperbol... | Oblate spheroidal coordinates | 0.80794 |
24,858 | Landau LD, Lifshitz EM, Pitaevskii LP (1984). Electrodynamics of Continuous Media (Volume 8 of the Course of Theoretical Physics) (2nd ed.). New York: Pergamon Press. pp. | Oblate spheroidal coordinates | 0.80794 |
24,859 | Like Korn and Korn (1961), but uses colatitude θ = 90° - ν instead of latitude ν. Moon PH, Spencer DE (1988). "Oblate spheroidal coordinates (η, θ, ψ)". Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions (corrected 2nd ed., 3rd print ed.). | Oblate spheroidal coordinates | 0.80794 |
24,860 | Margenau H, Murphy GM (1956). The Mathematics of Physics and Chemistry. New York: D. van Nostrand. | Oblate spheroidal coordinates | 0.80794 |
24,861 | Morse PM, Feshbach H (1953). Methods of Theoretical Physics, Part I. New York: McGraw-Hill. p. 662. | Oblate spheroidal coordinates | 0.80794 |
24,862 | In probability theory, an elementary event, also called an atomic event or sample point, is an event which contains only a single outcome in the sample space. Using set theory terminology, an elementary event is a singleton. Elementary events and their corresponding outcomes are often written interchangeably for simpli... | Sample point | 0.807937 |
24,863 | Victor Ufnarovski and Bo Åhlander expanded it to the irrationals that can be written as the product of primes raised to arbitrary rational powers, allowing expressions like D ( 3 ) {\displaystyle D({\sqrt {3}}\,)} to be computed. The arithmetic derivative can also be extended to any unique factorization domain (UFD), s... | Arithmetic derivative | 0.807935 |
24,864 | In number theory, the Lagarias arithmetic derivative or number derivative is a function defined for integers, based on prime factorization, by analogy with the product rule for the derivative of a function that is used in mathematical analysis. There are many versions of "arithmetic derivatives", including the one disc... | Arithmetic derivative | 0.807935 |
24,865 | An eval function is possible with static typing, but requires advanced uses of algebraic data types. Further, dynamic typing better accommodates transitional code and prototyping, such as allowing a placeholder data structure (mock object) to be transparently used in place of a full data structure (usually for the purp... | Dynamic typing | 0.807935 |
24,866 | Some dynamically typed languages such as Common Lisp allow optional type declarations for optimization for this reason. By contrast, dynamic typing may allow compilers to run faster and interpreters to dynamically load new code, because changes to source code in dynamically typed languages may result in less checking t... | Dynamic typing | 0.807935 |
24,867 | Multiple-birth infants are usually admitted to neonatal intensive care or a special care nursery in the hospital immediately after being born. The records for all the triplet pregnancies managed and delivered from 1992 to 1996 were looked over to see what the neonatal statistics were. Kaufman found from reviewing these... | Multiple gestation | 0.807933 |
24,868 | Coordination complexes have been known since the beginning of modern chemistry. Early well-known coordination complexes include dyes such as Prussian blue. Their properties were first well understood in the late 1800s, following the 1869 work of Christian Wilhelm Blomstrand. | Coordination complexes | 0.807931 |
24,869 | Metal complexes that have unpaired electrons are magnetic. Considering only monometallic complexes, unpaired electrons arise because the complex has an odd number of electrons or because electron pairing is destabilized. Thus, monomeric Ti(III) species have one "d-electron" and must be (para)magnetic, regardless of the... | Coordination complexes | 0.807931 |
24,870 | Patch dynamics is a term used in physics to bridge, using algorithms, the models describing macroscale behavior and to predict large-scale patterns in fluid flow. It uses locally averaged properties of short space-time scales to advance and predict long space-time scale dynamics. In patch dynamics and finite difference... | Patch dynamics (physics) | 0.807927 |
24,871 | Informally, a flow may be viewed as a continuous motion of points over time. More formally, a flow is a group action of the real numbers on a set. The idea of a vector flow, that is, the flow determined by a vector field, occurs in the areas of differential topology, Riemannian geometry and Lie groups. | Flow (mathematics) | 0.807927 |
24,872 | The flows of time-independent and time-dependent vector fields are defined on smooth manifolds exactly as they are defined on the Euclidean space R n {\displaystyle \mathbb {R} ^{n}} and their local behavior is the same. However, the global topological structure of a smooth manifold is strongly manifest in what kind of... | Flow (mathematics) | 0.807927 |
24,873 | This follows from the above definition, and the real parameter t may be taken as a generalized functional power, as in function iteration. Flows are usually required to be compatible with structures furnished on the set X. In particular, if X is equipped with a topology, then φ is usually required to be continuous. If ... | Flow (mathematics) | 0.807927 |
24,874 | In mathematics, a flow formalizes the idea of the motion of particles in a fluid. Flows are ubiquitous in science, including engineering and physics. The notion of flow is basic to the study of ordinary differential equations. | Flow (mathematics) | 0.807927 |
24,875 | Yarrow's main design principles are: resistance to attacks, easy use by programmers with no cryptography background, and reusability of existing building blocks. The former widely used designs such as ANSI X9.17 and RSAREF 2.0 PRNG have loopholes that provide attack opportunities under some circumstances. Some of them ... | Yarrow algorithm | 0.807925 |
24,876 | Yarrow reuses existing building blocks. Compared to previous PRNGs, Yarrow is reasonably efficient. Yarrow can be used by programmers with no cryptography background in a reasonably secure way. Yarrow is portable and precisely defined. | Yarrow algorithm | 0.807925 |
24,877 | The Yarrow algorithm is a family of cryptographic pseudorandom number generators (CPRNG) devised by John Kelsey, Bruce Schneier, and Niels Ferguson and published in 1999. The Yarrow algorithm is explicitly unpatented, royalty-free, and open source; no license is required to use it. An improved design from Ferguson and ... | Yarrow algorithm | 0.807925 |
24,878 | Dynamicism, also termed the dynamic hypothesis or the dynamic hypothesis in cognitive science or dynamic cognition, is a new approach in cognitive science exemplified by the work of philosopher Tim van Gelder. It argues that differential equations are more suited to modelling cognition than more traditional computer mo... | Mathematical system theory | 0.807922 |
24,879 | These links form the structure of a new state of order in the mind through a process called scalloping (the repeated building up and collapsing of complex performance.) This new, novel state is progressive, discrete, idiosyncratic and unpredictable.Dynamic systems theory has recently been used to explain a long-unanswe... | Mathematical system theory | 0.807922 |
24,880 | In other words, dynamicists argue that psychology should be (or is) the description (via differential equations) of the cognitions and behaviors of an agent under certain environmental and internal pressures. The language of chaos theory is also frequently adopted. In it, the learner's mind reaches a state of disequili... | Mathematical system theory | 0.807922 |
24,881 | Dynamical system theory has been applied in the field of neuroscience and cognitive development, especially in the neo-Piagetian theories of cognitive development. It is the belief that cognitive development is best represented by physical theories rather than theories based on syntax and AI. It also believed that diff... | Mathematical system theory | 0.807922 |
24,882 | Projected dynamical systems is a mathematical theory investigating the behaviour of dynamical systems where solutions are restricted to a constraint set. The discipline shares connections to and applications with both the static world of optimization and equilibrium problems and the dynamical world of ordinary differen... | Mathematical system theory | 0.807922 |
24,883 | Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics. | Mathematical system theory | 0.807922 |
24,884 | Arithmetic dynamics is a field that emerged in the 1990s that amalgamates two areas of mathematics, dynamical systems and number theory. Classically, discrete dynamics refers to the study of the iteration of self-maps of the complex plane or real line. Arithmetic dynamics is the study of the number-theoretic properties... | Mathematical system theory | 0.807922 |
24,885 | IPAB links computational action, perception, representation, transformation and generation processes to real or virtual worlds: statistical machine learning, computer vision, mobile and humanoid robotics, motor control, graphics and visualization. | Bayes Centre | 0.807918 |
24,886 | ILCC performs research on all aspects of natural language processing, drawing on machine learning, statistical modeling, and computational, psychological, and linguistic theories of communication among humans and between humans and machines using text, speech and other modalities. | Bayes Centre | 0.807918 |
24,887 | Donald Michie , founder of Artificial Intelligence in the UK Sidney Michaelson , foundation chair of the former computer science department. Jon Oberlander | Bayes Centre | 0.807918 |
24,888 | ANC investigates theoretical and empirical study of brain processes and artificial learning systems, drawing on neuroscience, cognitive science, computer science, computational science, mathematics and statistics. | Bayes Centre | 0.807918 |
24,889 | The School of Informatics was awarded a 5*A in the UK HEFCE's 2001 RAE, the only computer science department in the country to achieve this highest possible rating. In the 2008 RAE, the School's "Quality Profile" was 35/50/15/0/0, which means that of the over 100 Full-time equivalent (FTE) staff research outputs evalua... | Bayes Centre | 0.807918 |
24,890 | The School of Informatics is an academic unit of the University of Edinburgh, in Scotland, responsible for research, teaching, outreach and commercialisation in informatics. It was created in 1998 from the former department of artificial intelligence, the Centre for Cognitive Science and the department of computer scie... | Bayes Centre | 0.807918 |
24,891 | The 2002 Cowgate fire destroyed a number of buildings, including 80 South Bridge, which housed around a quarter of the school and its renowned AI library. By January 2003, space was made available in the University's Appleton Tower as a replacement.Until June 2008, the School was dispersed over five sites: three in the... | Bayes Centre | 0.807918 |
24,892 | Previously known as CISA (Centre for Intelligent Systems and their Applications), the Artificial Intelligence and its Applications Institute (AIAI) works on the foundations of artificial intelligence and autonomous systems, and their application to real-world problems. | Bayes Centre | 0.807918 |
24,893 | Although Lindström had only partially developed the hierarchy of quantifiers which now bear his name, it was enough for him to observe that some nice properties of first-order logic are lost when it is extended with certain generalized quantifiers. For example, adding a "there exist finitely many" quantifier results in... | Lindström quantifier | 0.807915 |
24,894 | In mathematical logic, a Lindström quantifier is a generalized polyadic quantifier. Lindström quantifiers generalize first-order quantifiers, such as the existential quantifier, the universal quantifier, and the counting quantifiers. They were introduced by Per Lindström in 1966. They were later studied for their appli... | Lindström quantifier | 0.807915 |
24,895 | Production Engineering — a term used in the UK and Europe similar to Industrial Engineering in North America. It includes the engineering of machines, people, processes and management. Explores the applications of the theoretical field of Mechanics. Textile Engineering — based on the conversion of three types of fiber ... | Bachelor of Engineering | 0.807913 |
24,896 | May also include radiation protection, particle detectors and medical physics. Petroleum Engineering — a field of engineering concerned with the activities related to exploration and production of hydrocarbons from the Earth's subsurface. Plastics Engineering — A vast field which includes plastic processing, mold desig... | Bachelor of Engineering | 0.807913 |
24,897 | Mechanical Engineering — includes engineering of total systems where mechanical science principles apply to objects in motion including transportation, energy, buildings, aerospace and machine design. Explores the applications of the theoretical fields of Mechanics, kinematics, thermodynamics, materials science, struct... | Bachelor of Engineering | 0.807913 |
24,898 | Manufacturing Engineering: Includes methods engineering, manufacturing process planning, tool design, metrology, Robotics, Computer integrated manufacturing, operations management and manufacturing management Materials Engineering — includes metallurgy, polymer and ceramic engineering Marine Engineering — includes the ... | Bachelor of Engineering | 0.807913 |
24,899 | Information Engineering — same as Information Technology. Industrial Engineering — studies facilities planning, plant layout, work measurement, job design, methods engineering, human factors, manufacturing processes, operations management, statistical quality control, systems, psychology and basic operations management... | Bachelor of Engineering | 0.807913 |
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