• stochastic
• These sources are frequently described in terms of probability distributions to account for the stochastic nature of complex engineering systems. (wikipedia.org)
• Travel distance and residence time probability distributions are the key components of stochastic models for coarse sediment transport. (wiley.com)
• As in many fields with stochastic approaches to particle transport, the conceptual model used to represent sediment transport through time in gravel bed rivers equates the distribution of overall travel distance at time t of a single particle as the sum of a random number of randomly sized step lengths. (wiley.com)
• The first relation between supersymmetry and stochastic dynamics was established by Giorgio Parisi and Nicolas Sourlas who demonstrated that the application of the BRST gauge fixing procedure to Langevin SDEs, i.e., to SDEs with linear phase spaces, gradient flow vector fields, and additive noises, results in N=2 supersymmetric models. (wikipedia.org)
• finite
• It represents the limiting distribution for a sum of independent, identically distributed random variables with finite variance and covariance where the number of elements to be summed is itself an independent random variable distributed according to a geometric distribution. (wikipedia.org)
• The distribution may also be applicable in broader situations to model multivariate data with heavier tails than a normal distribution but finite moments. (wikipedia.org)
• Learning algorithms based on this framework exhibit good generalization ability and finite sample convergence, while often being simpler and more effective than information theoretic methods Thus, learning via the kernel embedding of distributions offers a principled drop-in replacement for information theoretic approaches and is a framework which not only subsumes many popular methods in machine learning and statistics as special cases, but also can lead to entirely new learning algorithms. (wikipedia.org)
• This definition makes sense if x is an integrable function (in L1), a compactly supported distribution, or is a finite Borel measure. (wikipedia.org)
• Some statistical methods that were originally motivated by the study of the normal distribution have good performance for general elliptical distributions (with finite variance), particularly for spherical distributions (which are defined below). (wikipedia.org)
• seismology
• It has applications in statistical mechanics, quantum chemistry, quantum optics, classical optics and signal analysis in diverse fields such as electrical engineering, seismology, time-frequency analysis for music signals, spectrograms in biology and speech processing, and engine design. (wikipedia.org)
• The Quake Markup Language (QuakeML) is a flexible, extensible and modular XML representation of seismological data (e.g. epicenter, hypocenter, magnitude) which is intended to cover a broad range of fields of application in modern seismology. (wikipedia.org)
• empirical
• The distribution patterns and volumes of coarse-grained channel-fill deposits developed mainly during falling- and lowstand stages can be estimated from outcrop and seismic data on the basis of several empirical relationships among width, depth, and sinuosity of deep-water channels. (go.jp)
• However, bed elevation time series collected using sonar transducers and lidar can be translated into empirical residence time distributions at each elevation in the bed and for the entire bed thickness. (wiley.com)
• random
• We introduce an automated segmentation method, extended Markov Random Field ( eMRF ) to classify 21 neuroanatomical structures of mouse brain based on three dimensional (3D) magnetic resonance imaging (MRI). (pubmedcentralcanada.ca)
• Hill and Monticino (1998) introduced a constructive method for generating random probability measures with a prescribed mean or distribution on the mean. (unt.edu)
• uniquely
• In 1949, José Enrique Moyal elucidated how the Wigner function provides the integration measure (analogous to a probability density function) in phase space, to yield expectation values from phase-space c-number functions g(x,p) uniquely associated to suitably ordered operators Ĝ through Weyl's transform (cf. (wikipedia.org)
• The method involves sequentially generating an array of barycenters that uniquely defines a probability measure. (unt.edu)
• Statistics
• Brittle materials like ceramics are commonly characterized using Weibull distribution function [ 6 , 10 ] because the statistics of the mechanical and failure properties adequately fit into the Weibull distribution [ 11 ]. (hindawi.com)
• Handbook of Exploration Geochemistry, Volume 2: Statistics and Data Analysis in Geochemical Prospecting aims to survey the techniques available for the quality control of laboratory data, storage and retrieval of field and laboratory information, statistical analysis of single- and multi-element data, and presentation of geochemical data as maps. (elsevier.com)
• The analysis of distributions is fundamental in machine learning and statistics, and many algorithms in these fields rely on information theoretic approaches such as entropy, mutual information, or Kullback-Leibler divergence. (wikipedia.org)
• The American Statistical Association has described him as "a living legend whose work has influenced not just statistics, but has had far reaching implications for fields as varied as economics, genetics, anthropology, geology, national planning, demography, biometry, and medicine. (wikipedia.org)
• laboratory
• Residence time for individual grains is difficult to measure, and residence time distributions appropriate to field and laboratory settings are typically inferred theoretically or from overall transport characteristics. (wiley.com)
• normal distribution
• The use of the normal distribution is appealing because of its simplicity. (hindawi.com)
• Furthermore, the chance of obtaining the crack size greater than critical crack increases with volume of test specimens and this volume dependency is responsible for a decrease in the mean strength as the volume of specimen increases bringing about invariant problem with respect to parameters of normal distribution [ 6 , 7 ]. (hindawi.com)
• The log-normal distribution mass median diameter. (wikipedia.org)
• frequency
• The Wigner distribution P(x,p) of a pure state is defined as: where ψ is the wavefunction and x and p are position and momentum but could be any conjugate variable pair (i.e. real and imaginary parts of the electric field or frequency and time of a signal). (wikipedia.org)
• Field potential signals were recorded from an epidural electrode array and decomposed into their frequency components. (jneurosci.org)
• These moments can then be used to determine an appropriate frequency distribution, which can then be used as a probability model. (wikipedia.org)
• The frequency of extremal events, such as severe droughts and storms, often requires the use of distributions that focus on the tail of the distribution, rather than the data nearest the mean. (wikipedia.org)
• work
• This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (hindawi.com)
• material
• The broadness of strength distribution of quasi-brittle to brittle materials depends strongly on the existence of flaws such as voids, microcracks, and impurities in the material. (hindawi.com)
• In flexure, Weibull modulus increased with POFA replacement, indicating reduced broadness of strength distribution from an increased homogeneity of the material. (hindawi.com)
• Curiosity and taste for learning new material from new fields is essential. (universite-paris-saclay.fr)
• With the net redistribution of electrons into the dark regions of the material, leaving holes in the bright areas, the resulting charge distribution causes an electric field, known as a space charge field to be set up in the crystal. (wikipedia.org)
• mathematics
• As Head and later Director of the Research and Training School at the Indian Statistical Institute for a period of over 40 years, Rao developed research and training programs and produced several leaders in the field of Mathematics. (wikipedia.org)
• stimuli
• Neural decoding is a neuroscience-related field concerned with the reconstruction of sensory and other stimuli from information that has already been encoded and represented in the brain by networks of neurons. (wikipedia.org)
• Class
• In machine learning, the kernel embedding of distributions (also called the kernel mean or mean map) comprises a class of nonparametric methods in which a probability distribution is represented as an element of a reproducing kernel Hilbert space (RKHS). (wikipedia.org)
• include
• They include the length of coastlines, fully developed turbulence, real world scenes, the Sun's magnetic field time series, heartbeat dynamics, human gait, and natural luminosity time series. (wikipedia.org)
• yield
• Smoothing the Wigner distribution through a filter of size larger than ħ (e.g., convolving with a phase-space Gaussian, a Weierstrass transform, to yield the Husimi representation, below), results in a positive-semidefinite function, i.e., it may be thought to have been coarsened to a semi-classical one. (wikipedia.org)
• known
• Mertens and Zamir implemented John Harsanyi's proposal to model games with incomplete information by supposing that each player is characterized by a privately known type that describes his feasible strategies and payoffs as well as a probability distribution over other players' types. (wikipedia.org)
• results
• Mortar prisms and cubes were used to test the materials in flexure and compression, respectively, at 28 days and the results were analyzed using Weibull distribution. (hindawi.com)
• From the results of the 2D and 3D seismic survey acquired in the Nankai Trough area by METI in 2001 and 2002, widely-distributed BSR was recognized in the area, which was expected the wide distribution of methane hydrate. (go.jp)