MODp-tests, almost independence and small probability spaces

It is shown that the formation of the so-called rotator phase of alkanes (one of the high temperature crystalline phases) might be connected with a partial increase of the conformational flexibility of chains. The conformations with higher number of kinks per chain, which have been neglected till now, are shown to contribute effectively to the conformational partition function. Small probability of these states given by the Boltzmann exponent is compensated by a large number of ways in which they can be distributed along the chain. The deduced features of the rotator phase seem to be in agreement with the experimentally observed properties.

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Factorization of an adjontable Markov operator

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025719500139 ◽

2019 ◽

Vol 22 (02) ◽

pp. 1950013

Author(s):

Carlo Pandiscia

Keyword(s):

Hilbert Space ◽

Matrix Algebra ◽

Unitary Operator ◽

Markov Operator ◽

Factorization Property ◽

Markov Operators ◽

Dilation Theory ◽

Probability Spaces

In this work, we propose a method to investigate the factorization property of a adjontable Markov operator between two algebraic probability spaces without using the dilation theory. Assuming the existence of an anti-unitary operator on Hilbert space related to Stinespring representations of our Markov operator, which satisfy some particular modular relations, we prove that it admits a factorization. The method is tested on the two typologies of maps which we know admits a factorization, the Markov operators between commutative probability spaces and adjontable homomorphism. Subsequently, we apply these methods to particular adjontable Markov operator between matrix algebra which fixes the diagonal.

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A Radiated-Noise Simulator for Underwater Target Based on Vector Time Series

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.644-650.4023 ◽

2014 ◽

Vol 644-650 ◽

pp. 4023-4026

Author(s):

Yang Ju ◽

Xin Yong Wang

Keyword(s):

Time Series ◽

Confidence Interval ◽

Time Series Model ◽

Experimental Results ◽

Small Probability ◽

Radiated Noise ◽

True Value ◽

Underwater Target ◽

Vector Time Series

The vector time series model for simulating the underwater target radiated-noise is developed in this paper. Experimental results show that the true value lying outside the confidence interval would be a small probability event.

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On the cohomology equivalence classes for non-singular mappings

Ergodic Theory and Dynamical Systems ◽

10.1017/s014338579812093x ◽

1998 ◽

Vol 18 (6) ◽

pp. 1385-1397

Author(s):

ISAAC KORNFELD ◽

ANDREI KRYGIN

Keyword(s):

Ergodic Theorem ◽

Equivalence Classes ◽

Probability Spaces

The structure of the cohomology equivalence classes for non-singular, not necessarily invertible mappings of probability spaces is studied. In particular, some results of Kochergin and Ornstein–Smorodinsky on the structure of these classes for measure-preserving automorphisms are generalized to the case of non-singular endomorphisms. Our approach is based on Hopf's maximal ergodic theorem and its proof by Garsia.

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THE FIVE INDEPENDENCES AS NATURAL PRODUCTS

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025703001365 ◽

2003 ◽

Vol 06 (03) ◽

pp. 337-371 ◽

Cited By ~ 29

Author(s):

NAOFUMI MURAKI

Keyword(s):

Probability Theory ◽

Natural Products ◽

Tensor Product ◽

Natural Product ◽

Free Product ◽

Noncommutative Probability ◽

Stochastic Independence ◽

Boolean Product ◽

Probability Spaces ◽

Noncommutative Probability Theory

Let [Formula: see text] be the class of all algebraic probability spaces. A "natural product" is, by definition, a map [Formula: see text] which is required to satisfy all the canonical axioms of Ben Ghorbal and Schürmann for "universal product" except for the commutativity axiom. We show that there exist only five natural products, namely tensor product, free product, Boolean product, monotone product and anti-monotone product. This means that, in a sense, there exist only five universal notions of stochastic independence in noncommutative probability theory.

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Hiding Data in Plain Sight: Towards Provably Unbreakable Encryption with Short Secret Keys and One-Way Functions

10.5121/csit.2021.110914 ◽

2021 ◽

Author(s):

Mircea-Adrian Digulescu

Keyword(s):

Encryption Scheme ◽

Secret Key ◽

Small Probability ◽

Random Data ◽

Computing Power ◽

Plain Text ◽

Secret Keys ◽

The One ◽

One Way Function ◽

The Cost

It has long been known that cryptographic schemes offering provably unbreakable security exist, namely the One Time Pad (OTP). The OTP, however, comes at the cost of a very long secret key - as long as the plain-text itself. In this paper we propose an encryption scheme which we (boldly) claim offers the same level of security as the OTP, while allowing for much shorter keys, of size polylogarithmic in the computing power available to the adversary. The Scheme requires a large sequence of truly random words, of length polynomial in the both plain-text size and the logarithm of the computing power the adversary has. We claim that it ensures such an attacker cannot discern the cipher output from random data, except with small probability. We also show how it can be adapted to allow for several plain-texts to be encrypted in the same cipher output, with almost independent keys. Also, we describe how it can be used in lieu of a One Way Function.

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