Search results for "Random variable"
showing 10 items of 151 documents
A Novel Non-Stationary Channel Model Utilizing Brownian Random Paths
2014
This paper proposes a non-stationary channel model in which real-time dynamics of the mobile station (MS) are taken into account. We utilize Brownian motion (BM) processes to model targeted and non-targeted dynamics of the MS. The proposed trajectory model consists of both drift and random components to capture both targeted and non-targeted motions of the MS. The Brownian trajectory model is then employed to provide a non-stationary channel model, in which the scattering effects of the propagation area are modelled by a non-centred one-ring geometric scattering model. The starting point of the motion is a fixed point in the propagation environment, whereas its terminating point is a random…
Probabilistic foundations of contextuality
2017
Contextuality is usually defined as absence of a joint distribution for a set of measurements (random variables) with known joint distributions of some of its subsets. However, if these subsets of measurements are not disjoint, contextuality is mathematically impossible even if one generally allows (as one must) for random variables not to be jointly distributed. To avoid contradictions one has to adopt the Contextuality-by-Default approach: measurements made in different contexts are always distinct and stochastically unrelated to each other. Contextuality is reformulated then in terms of the (im)possibility of imposing on all the measurements in a system a joint distribution of a particul…
Quantum Entanglement and the Issue of Selective Influences in Psychology: An Overview
2012
Similar formalisms have been independently developed in psychology, to deal with the issue of selective influences (deciding which of several experimental manipulations selectively influences each of several, generally non-independent, response variables), and in quantum mechanics (QM), to deal with the EPR entanglement phenomena (deciding whether an EPR experiment allows for a "classical" account). The parallels between these problems are established by observing that any two noncommuting measurements in QM are mutually exclusive and can therefore be treated as analogs of different values of one and the same input. Both problems reduce to that of the existence of a jointly distributed syst…
Contextuality in canonical systems of random variables
2017
Random variables representing measurements, broadly understood to include any responses to any inputs, form a system in which each of them is uniquely identified by its content (that which it measures) and its context (the conditions under which it is recorded). Two random variables are jointly distributed if and only if they share a context. In a canonical representation of a system, all random variables are binary, and every content-sharing pair of random variables has a unique maximal coupling (the joint distribution imposed on them so that they coincide with maximal possible probability). The system is contextual if these maximal couplings are incompatible with the joint distributions o…
Contextuality is About Identity of Random Variables
2014
Contextual situations are those in which seemingly "the same" random variable changes its identity depending on the conditions under which it is recorded. Such a change of identity is observed whenever the assumption that the variable is one and the same under different conditions leads to contradictions when one considers its joint distribution with other random variables (this is the essence of all Bell-type theorems). In our Contextuality-by-Default approach, instead of asking why or how the conditions force "one and the same" random variable to change "its" identity, any two random variables recorded under different conditions are considered different "automatically". They are never the…
Information Functionals and the Notion of (Un)Certainty: Random Matrix Theory - Inspired Case
2007
Information functionals allow one to quantify the degree of randomness of a given probability distribution, either absolutely (through min/max entropy principles) or relative to a prescribed reference one. Our primary aim is to analyze the “minimum information” assumption, which is a classic concept (R. Balian, 1968) in the random matrix theory. We put special emphasis on generic level (eigenvalue) spacing distributions and the degree of their randomness, or alternatively — information/organization deficit.
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…
A geometric street scattering channel model for car-to-car communication systems
2011
This paper presents a geometric street scattering channel model for car-to-car (C2C) communication systems under line-of-sight (LOS) and non-LOS (NLOS) propagation conditions. Starting from the geometric model, we develop a stochastic reference channel model, where the scatterers are uniformly distributed in rectangles in the form of stripes parallel to both sides of the street. We derive analytical expressions for the probability density functions (PDFs) of the angle-of-departure (AOD) and the angle-of-arrival (AOA). We also investigate the Doppler power spectral density (PSD) and the autocorrelation function (ACF) of the proposed model, assuming that the mobile transmitter (MT) and the mo…
Management of uncertain pairwise comparisons in AHP through probabilistic concepts
2019
Abstract Fast and judicious decision-making is paramount for the success of many activities and processes. However, various degrees of difficulty may affect the achievement of effective and optimal solutions. Decisions should ideally meet the best trade-off among as many of the involved factors as possible, especially in the case of complex problems. Substantial cognitive and technical skills are indispensable, while not always sufficient, to carry out optimal evaluations. One of the most common causes of wrong decisions derives from uncertainty and vagueness in making forecasts or attributing judgments. The literature shows numerous efforts towards the optimization and modeling of uncertai…
Quantum Hopfield Model
2020
We find the free-energy in the thermodynamic limit of a one-dimensional XY model associated to a system of N qubits. The coupling among the &sigma