Comment on “Quantum and classical probability distributions for position and momentum,’’ by R. W. Robinett [Am. J. Phys. 63 (9), 823–832 (1995)]

1997 ◽  
Vol 65 (2) ◽  
pp. 157-158 ◽  
Author(s):  
C. C. Real ◽  
J. G. Muga ◽  
S. Brouard
Keyword(s):  
Probability Distributions ◽  
Classical Probability

Neutrosophic Perspective of Neutrosophic Probability Distributions and its Application

2021 ◽  
pp. 96-109
Author(s):  
M. Lathamaheswari ◽  
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◽  
◽  
◽  
...  
Keyword(s):  
Stochastic Process ◽  
Uniform Distribution ◽  
Binomial Distribution ◽  
Probability Distributions ◽  
Statistical Distributions ◽  
Classical Probability ◽  
Numerical Examples ◽  
Limiting Case ◽  
First Time

Neutrosophical probability is concerned with inequitable and defective topics and processes. This is a subset of Neutrosophic measures that includes a prediction of an event (as opposed to indeterminacy) as well as a prediction of some unpredictability. When there is no such thing as a non-stochastic occurrence, the Neutrosophic probability is the probability of determining a stochastic process. It is a generalisation of classical probability, which states that the probability of correctly predicting an occurrence is zero. Until now, neutrosophic probability distributions have been derived directly from conventional statistical distributions, with fewer contributions to the determination of the for statistical distribution. We introduced the Poission distribution as a limiting case of the Binomial distribution for the first time in this study, and we also proposed Neutrosophic Exponential Distribution and Uniform Distribution for the first time. With numerical examples, the validity and soundness of the proposed notions were also tested.

Taylor's law, via ratios, for some distributions with infinite mean

2017 ◽  
Vol 54 (3) ◽  
pp. 657-669 ◽  
Author(s):  
Mark Brown ◽  
Joel E. Cohen ◽  
Victor H. de la Peña
Keyword(s):  
Population Density ◽  
Probability Distributions ◽  
Branching Processes ◽  
Population Variance ◽  
Classical Probability ◽  
Birth And Death Processes ◽  
Taylor’S Law ◽  
The Mean ◽  
Fluctuation Scaling ◽  
First Time

Abstract Taylor's law (TL) originated as an empirical pattern in ecology. In many sets of samples of population density, the variance of each sample was approximately proportional to a power of the mean of that sample. In a family of nonnegative random variables, TL asserts that the population variance is proportional to a power of the population mean. TL, sometimes called fluctuation scaling, holds widely in physics, ecology, finance, demography, epidemiology, and other sciences, and characterizes many classical probability distributions and stochastic processes such as branching processes and birth-and-death processes. We demonstrate analytically for the first time that a version of TL holds for a class of distributions with infinite mean. These distributions, a subset of stable laws, and the associated TL differ qualitatively from those of light-tailed distributions. Our results employ and contribute to the methodology of Albrecher and Teugels (2006) and Albrecher et al. (2010). This work opens a new domain of investigation for generalizations of TL.

scholarly journals Malevich’s Suprematist Composition Picture for Spin States

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 870
Author(s):  
Vladimir I. Man’ko ◽  
Liubov A. Markovich
Keyword(s):  
Probability Distributions ◽  
Classical System ◽  
Quantum States ◽  
Elementary Geometry ◽  
Spin States ◽  
Classical Probability ◽  
Quantum Properties ◽  
Metropolis Monte Carlo ◽  
Single Qudit ◽  
Noncomposite Systems

This paper proposes an alternative geometric representation of single qudit states based on probability simplexes to describe the quantum properties of noncomposite systems. In contrast to the known high dimension pictures, we present the planar picture of quantum states, using the elementary geometry. The approach is based on, so called, Malevich square representation of the single qubit state. It is shown that the quantum statistics of the single qudit with some spin j and observables are formally equivalent to statistics of the classical system with N 2 - 1 random vector variables and N 2 - 1 classical probability distributions, obeying special constrains, found in this study. We present a universal inequality, that describes the single qudits state quantumness. The inequality provides a possibility to experimentally check up entanglement of the system in terms of the classical probabilities. The simulation study for the single qutrit and ququad systems, using the Metropolis Monte-Carlo method, is obtained. The geometrical representation of the single qudit states, presented in the paper, is useful in providing a visualization of quantum states and illustrating their difference from the classical ones.

scholarly journals Manifolds of classical probability distributions and quantum density operators in infinite dimensions

2019 ◽  
Vol 2 (2) ◽  
pp. 231-271 ◽  
Author(s):  
F. M. Ciaglia ◽  
A. Ibort ◽  
J. Jost ◽  
G. Marmo
Keyword(s):  
Disjoint Union ◽  
Separable Hilbert Space ◽  
Probability Distributions ◽  
Classical Case ◽  
Infinite Dimensions ◽  
Classical Probability ◽  
Infinite Dimensional ◽  
Density Operators ◽  
Banach Manifolds ◽  
Invertible Elements

Abstract The manifold structure of subsets of classical probability distributions and quantum density operators in infinite dimensions is investigated in the context of $$C^{*}$$C∗-algebras and actions of Banach-Lie groups. Specificaly, classical probability distributions and quantum density operators may be both described as states (in the functional analytic sense) on a given $$C^{*}$$C∗-algebra $$\mathscr {A}$$A which is Abelian for Classical states, and non-Abelian for Quantum states. In this contribution, the space of states $$\mathscr {S}$$S of a possibly infinite-dimensional, unital $$C^{*}$$C∗-algebra $$\mathscr {A}$$A is partitioned into the disjoint union of the orbits of an action of the group $$\mathscr {G}$$G of invertible elements of $$\mathscr {A}$$A. Then, we prove that the orbits through density operators on an infinite-dimensional, separable Hilbert space $$\mathcal {H}$$H are smooth, homogeneous Banach manifolds of $$\mathscr {G}=\mathcal {GL}(\mathcal {H})$$G=GL(H), and, when $$\mathscr {A}$$A admits a faithful tracial state $$\tau $$τ like it happens in the Classical case when we consider probability distributions with full support, we prove that the orbit through $$\tau $$τ is a smooth, homogeneous Banach manifold for $$\mathscr {G}$$G.

On a Quantum Model of Brain Activities — Distribution of the Outcomes of EEG-Measurements and Random Point Fields

2012 ◽  
Vol 19 (04) ◽  
pp. 1250025 ◽  
Author(s):  
Karl-Heinz Fichtner ◽  
Kei Inoue ◽  
Masanori Ohya
Keyword(s):  
Stochastic Process ◽  
Probability Theory ◽  
Probability Distributions ◽  
Quantum States ◽  
Random Point ◽  
Quantum Model ◽  
Classical Probability ◽  
Point Configurations ◽  
Point Field ◽  
The Brain

Considering models based on classical probability theory, states of signals in the brain should be identified with probability distributions of certain random point fields representing the configuration of excited neurons. Then the outcomes of EEG-measurements can be considered as random variables being certain functions of that random point field. In practice, specialists use certain statistical methods evaluating the outcomes of the sequence of these measurements. To make these statistical investigations precise, one should know the distribution of the stochastic process on the space of point configurations representing the time evolution of the configuration of excited neurons in the brain. Up to now that distribution is totally unknown. In this paper we consider time evolutions of random point fields as well as the distribution of the outcomes of EEG-measurements related to unitary evolutions of certain quantum states used in [4, 5, 10 – 14] in order to describe activities of the brain.

Asteroid and Comet Impact Speeds upon Mars: Significance for Panspermia and the Supply of Organics

1997 ◽  
Vol 161 ◽  
pp. 197-201 ◽  
Author(s):  
Duncan Steel
Keyword(s):  
Probability Distributions ◽  
Regions Of Interest ◽  
Significant Fraction ◽  
Organic Chemicals ◽  
Impact Speed ◽  
The Mean ◽  
The Impact

AbstractWhilst lithopanspermia depends upon massive impacts occurring at a speed above some limit, the intact delivery of organic chemicals or other volatiles to a planet requires the impact speed to be below some other limit such that a significant fraction of that material escapes destruction. Thus the two opposite ends of the impact speed distributions are the regions of interest in the bioastronomical context, whereas much modelling work on impacts delivers, or makes use of, only the mean speed. Here the probability distributions of impact speeds upon Mars are calculated for (i) the orbital distribution of known asteroids; and (ii) the expected distribution of near-parabolic cometary orbits. It is found that cometary impacts are far more likely to eject rocks from Mars (over 99 percent of the cometary impacts are at speeds above 20 km/sec, but at most 5 percent of the asteroidal impacts); paradoxically, the objects impacting at speeds low enough to make organic/volatile survival possible (the asteroids) are those which are depleted in such species.

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