Formalizing “meaning as context” mathematically leads to a new, algebraic theory of meaning, in which composition is bilinear and associative. These properties are shared by other methods that have been proposed in the literature, including the tensor product, vector addition, pointwise multiplication, and matrix multiplication. Entailment can be represented by a vector lattice ordering, inspir...

This paper relates both to the metaphysics of probability and to the physics of time asymmetry. Using the formalism of decoherent histories, it investigates whether intuitions about intrinsic time directedness that are often associated with probability can be justified in the context of no-collapse approaches to quantum mechanics. The standard (two-vector) approach to time symmetry in the decoh...

This study provides a principal component analysis-fuzzy-support vector regression model for stock price prediction. Stocks with similar historical trends are selected using principal component analysis. Fuzzy information granulation is performed to construct a probability density for stock prices. Support vector regression is implemented to generate a regression function for future price predi...

Our goal is to produce the best reconstructions of an image given a noisy input image I0. We write any possible reconstruction of the image as a random vector I of pixel values. The best reconstruction is the one that maximizes the posterior probability p(I|I0) = p(I0|I) p(I) (1) This posterior probability is constructed as a Markov Random Field (MRF). More specifically, the random variable I =...

Consider a C vector field together with an ergodic invariant probability that has l nonzero Lyapunov exponents. Using orthonormal moving frames along certain transitive orbits we construct a linear system of l differential equations which is a reduced form of Liao’s “standard system”. We show that the Lyapunov exponents of this linear system coincide with all the nonzero exponents of the given ...

Human learning inspires a large amount of algorithms and techniques to solve problems in image understanding. Supervised learning algorithms based on support vector machines are currently one of the most effective methods in machine learning. A support vector approach is used in this paper to solve a typical problem in image registration, this is, the joint probability density function estimati...

This paper relates both to the metaphysics of probability and to the physics of time asymmetry. Using the formalism of decoherent histories , it investigates whether intuitions about intrinsic time directedness that are often associated with probability can be justified in the context of no-collapse approaches to quantum mechanics. The standard (two-vector) approach to time symmetry in the deco...

We consider disparity based test statistics to test the equality of a multinomial probability vector to a given probability vector against an isotonic=antitonic order restriction. The problem of testing the isotonic restriction as a null hypothesis against unrestricted alternatives is also considered. In both cases the asymptotic distributions of these test statistics are found to be of the chi...

We are going to consider a variation of the PageRank vector called the personal PageRank vector. Where PageRank measures the importance of nodes overall, the personal PageRank vector measures the importance of nodes with respect to a give node u. It does this by modifying the walk so that with probability α it jumps back to u, rather than to a random node. We denote the vector that satisfies th...