Search results for "probability"

Analysis of random walks on a hexagonal lattice

2019

We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a 2-dimensional Brownian motion is also discussed. Furthermore, we obtain some results on its asymptotic behavior making use of large deviation theory. Finally, we investigate the first-passage-time problem of the random walk through a vertical straight-line. Under suitable symmetry assumptions we are able to determine the first-passage-time probabilities in a closed form, which deserve interest in applied fields.

Contextuality Analysis of the Double Slit Experiment (With a Glimpse Into Three Slits)

2018

The Contextuality-by-Default theory is illustrated on contextuality analysis of the idealized double-slit experiment. The experiment is described by a system of contextually labeled binary random variables each of which answers the question: has the particle hit the detector, having passed through a given slit (left or right) in a given state (open or closed)? This system of random variables is a cyclic system of rank 4, formally the same as the system describing the EPR/Bell paradigm with signaling. Unlike the latter, however, the system describing the double-slit experiment is always noncontextual, i.e., the context-dependence in it is entirely explainable in terms of direct influences of…

Bayesian Modelling of Confusability of Phoneme-Grapheme Connections

2007

Deficiencies in the ability to map letters to sounds are currently considered to be the most likely early signs of dyslexia. This has motivated the use of Literate, a computer game for training this skill, in several Finnish schools and households as a tool in the early prevention of reading disability. In this paper, we present a Bayesian model that uses a student's performance in a game like Literate to infer which phoneme-grapheme connections student currently confuses with each other. This information can be used to adapt the game to a particular student's skills as well as to provide information about the student's learning progress to their parents and teachers. We apply our model to …

Inequalities for Information Potentials and Entropies

2020

We consider a probability distribution p0(x),p1(x),&hellip

Tetrolet-based reduced reference image quality assessment approach

2014

In this paper, we propose a new reduced reference image quality assessment (RRIQA) scheme. For this purpose, we use a statistical-based method in a new adaptive Haar wavelet transform domain, called Tetrolet. Firstly, we decompose the reference and distorted images and we obtain the Tetrolet coefficients for each image. Secondly, we use a marginal Generalized Gaussian Density (GGD) to model each subband coefficients. Finally, the distortion measure is computed using the Kullback Leibler Divergence (KLD) between GGD Probability density function (PDFs). Experimental results show the efficiency of the proposed method when comparing to those reported in the literature.

Survival probability approach to the relaxation of a macroscopic system in the defect-diffusion framework

2004

A Qualified Kolmogorovian Account of Probabilistic Contextuality

2014

We describe a mathematical language for determining all possible patterns of contextuality in the dependence of stochastic outputs of a system on its deterministic inputs. The central principle contextuality-by-default is that the outputs indexed by mutually incompatible values of inputs are stochastically unrelated; but they can be coupled imposed a joint distribution on in a variety of ways. A system is characterized by a pattern of which outputs can be "directly influenced" by which inputs a primitive relation, hypothetical or normative, and by certain constraints imposed on the outputs such as Bell-type inequalities or their quantum analogues. The set of couplings compatible with these …

Tool-life modelling as a stochastic process

1998

Abstract In a previous paper [G. Galante, A. Lombardo, A. Passannanti, Proceedings of XXXVII Scientific Meeting of the Italian Statistical Society, 1994, p. 553] the Authors proposed to model cutting tool wear behaviour as a stochastic process with independent Gaussian increments plus drift. Such a model implies that the tool-life, i.e. the time to reach a fixed value of flank wear, has an inverse Gaussian probability distribution. The model has several practical and theoretical advantages. In fact, it is based on an easily and cheaply experimentally verifiable wear behaviour hypothesis, it is more flexible because it is not limited to a particular wear level and, finally, the data are bett…

Generalized Entropies, Variance and Applications

2020

The generalized cumulative residual entropy is a recently defined dispersion measure. In this paper, we obtain some further results for such a measure, in relation to the generalized cumulative residual entropy and the variance of random lifetimes. We show that it has an intimate connection with the non-homogeneous Poisson process. We also get new expressions, bounds and stochastic comparisons involving such measures. Moreover, the dynamic version of the mentioned notions is studied through the residual lifetimes and suitable aging notions. In this framework we achieve some findings of interest in reliability theory, such as a characterization for the exponential distribution, various resul…

System Times and Channel Availability for Secondary Transmissions in CRNs: A Dependability Theory based Analysis

2017

[EN] Reliability is of fundamental importance for the performance of secondary networks in cognitive radio networks (CRNs). To date, most studies have focused on predicting reliability parameters based on prior statistics of traffic patterns from user behavior. In this paper, we define a few reliability metrics for channel access in multichannel CRNs that are analogous to the concepts of reliability and availability in classical dependability theory. Continuous-time Markov chains are employed to model channel available and unavailable time intervals based on channel occupancy status. The impact on user access opportunities based on channel availability is investigated by analyzing the stead…