scholarly journals No Shannon effect on probability distributions on Boolean functions induced by random expressions

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Antoine Genitrini ◽  
Bernhard Gittenberger
Keyword(s):  
Probability Distribution ◽  
Boolean Functions ◽  
Probability Distributions ◽  
Uniform Probability ◽  
Uniform Probability Distribution ◽  
International Audience ◽  
Almost All

International audience The Shannon effect states that "almost all'' Boolean functions have a complexity close to the maximal possible for the uniform probability distribution. In this paper we use some probability distributions on functions, induced by random expressions, and prove that this model does not exhibit the Shannon effect.

scholarly journals Some New Constructions of Authentication Codes with Arbitration and Multi-Receiver from Singular Symplectic Geometry

2011 ◽  
Vol 2011 ◽  
pp. 1-18
Author(s):  
You Gao ◽  
Huafeng Yu
Keyword(s):  
Probability Distribution ◽  
Finite Fields ◽  
Symplectic Geometry ◽  
Authentication Codes ◽  
Uniform Probability ◽  
Different Types ◽  
Uniform Probability Distribution ◽  
New Construction

A new construction of authentication codes with arbitration and multireceiver from singular symplectic geometry over finite fields is given. The parameters are computed. Assuming that the encoding rules are chosen according to a uniform probability distribution, the probabilities of success for different types of deception are also computed.

scholarly journals Finite Dimensional Approximations to Some Flows on the Projective Limit Space of Spheres

1966 ◽  
Vol 28 ◽  
pp. 167-177
Author(s):  
Hisao Nomoto
Keyword(s):  
Probability Distribution ◽  
Probability Space ◽  
Essential Role ◽  
Projective Limit ◽  
Dimensional Sphere ◽  
Basic Space ◽  
Limit Space ◽  
Finite Dimensional ◽  
Uniform Probability ◽  
Uniform Probability Distribution

Let Ω be the projective limit space of a sequence of probability space Ωn which is a certain subset of (n − 1)-dimensional sphere with the usual uniform probability distribution on it. T. Hida [2], starting from a sequence of finite dimensional flows which are derived from some one-parameter subgroups of rotations of spheres, constructed a flow {Tt} on Ω as the limit of them. Observing his method, the concept of consistency of flows which approximate {Tt} seems to play an essential role in his work [2]. As will be made clear in the following sections, the concept of consistency is closely related to the projective limiting structure of our basic space Ω. The purpose of this paper is to determine all the flows on Ω which can be approximated in the sense of [2] by finite dimensional flows.

scholarly journals Uncertainty, equality, fraternity

Synthese ◽  
2021 ◽  
Author(s):  
Rush T. Stewart
Keyword(s):  
Probability Distribution ◽  
General Framework ◽  
Utility Functions ◽  
Social Planner ◽  
Imprecise Probabilities ◽  
Veil Of Ignorance ◽  
Epistemic States ◽  
Uniform Probability ◽  
Uniform Probability Distribution

AbstractEpistemic states of uncertainty play important roles in ethical and political theorizing. Theories that appeal to a “veil of ignorance,” for example, analyze fairness or impartiality in terms of certain states of ignorance. It is important, then, to scrutinize proposed conceptions of ignorance and explore promising alternatives in such contexts. Here, I study Lerner’s probabilistic egalitarian theorem in the setting of imprecise probabilities. Lerner’s theorem assumes that a social planner tasked with distributing income to individuals in a population is “completely ignorant” about which utility functions belong to which individuals. Lerner models this ignorance with a certain uniform probability distribution, and shows that, under certain further assumptions, income should be equally distributed. Much of the criticism of the relevance of Lerner’s result centers on the representation of ignorance involved. Imprecise probabilities provide a general framework for reasoning about various forms of uncertainty including, in particular, ignorance. To what extent can Lerner’s conclusion be maintained in this setting?

scholarly journals Exponential Negation of a Probability Distribution

2021 ◽  
Author(s):  
Qinyuan Wu ◽  
Yong Deng ◽  
Neal Xiong
Keyword(s):  
Information Processing ◽  
Probability Distribution ◽  
Uniform Distribution ◽  
Probability Distributions ◽  
Numerical Examples ◽  
Entropy Increase ◽  
Intelligent Information Processing ◽  
Uniform Probability Distribution ◽  
Intelligent Information ◽  
Number Of Iterations

Abstract Negation operation is important in intelligent information processing. Different with existing arithmetic negation, an exponential negation is presented in this paper. The new negation can be seen as a kind of geometry negation. Some basic properties of the proposed negation are investigated, we find that the fix point is the uniform probability distribution. The proposed exponential negation is an entropy increase operation and all the probability distributions will converge to the uniform distribution after multiple negation iterations. The convergence speed of the proposed negation is also faster than the existed negation. The number of iterations of convergence is inversely proportional to the number of elements in the distribution. Some numerical examples are used to illustrate the efficiency of the proposed negation.

Use in Probabilistic Design of the Maximum Entrophy Distribution Based on Ranked Data

1980 ◽  
Vol 102 (3) ◽  
pp. 460-468
Author(s):  
J. N. Siddall ◽  
Ali Badawy
Keyword(s):  
Probability Distribution ◽  
Maximum Entropy ◽  
Probability Distributions ◽  
Maximum Entropy Principle ◽  
Random Variable ◽  
Probabilistic Design ◽  
Entropy Principle ◽  
Almost All ◽  
New Distribution

A new algorithm using the maximum entropy principle is introduced to estimate the probability distribution of a random variable, using directly a ranked sample. It is demonstrated that almost all of the analytical probability distributions can be approximated by the new algorithm. A comparison is made between existing methods and the new algorithm; and examples are given of fitting the new distribution to an actual ranked sample.

New methods of construction of cartesian authentication codes from geometries over finite commutative rings

2018 ◽  
Vol 12 (3) ◽  
pp. 119-136 ◽  
Author(s):  
Wachirapong Jirakitpuwapat ◽  
Parin Chaipunya ◽  
Poom Kumam ◽  
Sompong Dhompongsa ◽  
Phatiphat Thounthong
Keyword(s):  
Probability Distribution ◽  
Commutative Rings ◽  
Impersonation Attack ◽  
Authentication Codes ◽  
New Methods ◽  
Uniform Probability ◽  
Cartesian Authentication Codes ◽  
Uniform Probability Distribution ◽  
Finite Commutative Rings

Abstract In this paper, we construct some cartesian authentication codes from geometries over finite commutative rings. We only assume the uniform probability distribution over the set of encoding rules in order to be able to compute the probabilities of successful impersonation attack and substitution attack. Our methods are comfortable and secure for users, i.e., our encoding rules reduce the probabilities of successful impersonation attack and substitution attack.

A CONSTRUCTION OF CARTESIAN AUTHENTICATION CODE FROM SINGULAR SYMPLECTIC SPACES OVER A FINITE FIELD

2014 ◽  
Vol 06 (02) ◽  
pp. 1450027
Author(s):  
SHUFANG ZHAO ◽  
ZENGTI LI
Keyword(s):  
Probability Distribution ◽  
Finite Field ◽  
Symplectic Space ◽  
Impersonation Attack ◽  
Authentication Code ◽  
Uniform Probability ◽  
Uniform Probability Distribution ◽  
Symplectic Spaces

In this paper, we construct a Cartesian authentication code from subspaces of singular symplectic space [Formula: see text] and compute its parameters. Assuming that the encoding rules of the transmitter and the receiver are chosen according to a uniform probability distribution, the probabilities of successful impersonation attack and substitution attack are also computed.

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