On the Properties of Asymptotic Probability for Random Boolean Expression Values in Binary Bases

2005 ◽  
pp. 202-212 ◽  
Author(s):  
Alexey D. Yashunsky
Keyword(s):  
Boolean Expression ◽  
Asymptotic Probability

Corrigendum

1951 ◽  
Vol 47 (3) ◽  
pp. 626-626 ◽  
Keyword(s):  
Probability Distribution ◽  
Asymptotic Probability

On the asymptotic probability distribution for certain Markoff processes 46 (1950), 581.By Walter LedermannMr H. Schneider has drawn my attention to a mistake which occurs on p. 591 of the above paper.

A Streamline Curvature Method for Calculating S1 Stream Surface Flow

1984 ◽  
Vol 106 (2) ◽  
pp. 306-312
Author(s):  
S. K. Mao ◽  
D. T. Li
Keyword(s):  
Surface Flow ◽  
Approximation Technique ◽  
Flow Section ◽  
Boolean Expression ◽  
Simple Method ◽  
Stream Surface ◽  
Streamline Curvature ◽  
Calculation Results ◽  
Good Agreement ◽  
Streamline Curvature Method

A streamline curvature method for calculating S1 surface flow in turbines is presented. The authors propose a simple method in which a domain of calculation can be changed into an orderly rectangle without making coordinate transformations. Calculation results obtained on subsonic and transonic turbine cascades have been compared with those of experiment and another theory. Good agreement has been found. When calculating blade-to-blade flow velocity at subsonic speed, a function approximation technique can be used in lieu of iteration method in order to reduce calculation time. If the calculated flow section is of a mixed (subsonic-supersonic) flow type, a Boolean expression obtained from the truth table of flow states is proposed to judge the integrated character of the mixed flow section. Similarly, another Boolean expression is used to determine whether there exists a “choking” of the relevant section. Periodical conditions are satisfied by iterating the first-order derivative of stagnation streamline, which is formed simultaneously. It can be proved that the stagnation streamline formed in this way is unique.

scholarly journals On the Isolated Vertices and Connectivity in Random Intersection Graphs

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Yilun Shang
Keyword(s):  
Random Graphs ◽  
Intersection Graph ◽  
Intersection Graphs ◽  
Random Intersection Graph ◽  
Probability Of Connectivity ◽  
Asymptotic Probability

We study isolated vertices and connectivity in the random intersection graph . A Poisson convergence for the number of isolated vertices is determined at the threshold for absence of isolated vertices, which is equivalent to the threshold for connectivity. When and , we give the asymptotic probability of connectivity at the threshold for connectivity. Analogous results are well known in Erdős-Rényi random graphs.

scholarly journals Excursion sets of infinitely divisible random fields with convolution equivalent Lévy measure

2017 ◽  
Vol 54 (3) ◽  
pp. 833-851 ◽  
Author(s):  
Anders Rønn-Nielsen ◽  
Eva B. Vedel Jensen
Keyword(s):  
Random Field ◽  
Large Class ◽  
Random Fields ◽  
Lévy Measure ◽  
Infinitely Divisible ◽  
Excursion Sets ◽  
Excursion Set ◽  
Fixed Radius ◽  
Asymptotic Probability ◽  
The Right

Abstract We consider a continuous, infinitely divisible random field in ℝd, d = 1, 2, 3, given as an integral of a kernel function with respect to a Lévy basis with convolution equivalent Lévy measure. For a large class of such random fields, we compute the asymptotic probability that the excursion set at level x contains some rotation of an object with fixed radius as x → ∞. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure.

Satisfiability checking using Boolean Expression Diagrams

2002 ◽  
Vol 5 (1) ◽  
pp. 4-14 ◽  
Author(s):  
Poul F. Williams ◽  
Henrik R. Andersen ◽  
Henrik Hulgaard
Keyword(s):  
Boolean Expression ◽  
Satisfiability Checking

scholarly journals On the Number of Indecomposable Permutations with a Given Number of Cycles

10.37236/2071 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Robert Cori ◽  
Claire Mathieu ◽  
John Michael Robson
Keyword(s):  
Fixed Ratio ◽  
Threshold Phenomenon ◽  
Asymptotic Probability ◽  
Number Of Cycles

A permutation $a_1a_2\ldots a_n$ is indecomposable if there does not exist $p<n$ such that $a_1a_2\ldots a_p$ is a permutation of $\{ 1,2,\ldots,p\}$. We consider the  probability that a permutation of ${\mathbb S}_n$  with $m$ cycles is indecomposable and prove that  this probability is monotone non-increasing in $n$.We compute  also the asymptotic probability when  $n$ goes to infinity with $m/n$ tending to a fixed ratio.  The asymptotic probability is monotone in $m/n$, and there is no threshold phenomenon: it degrades gracefully from 1 to 0. When $n=2m$, a slight majority ($51.117\ldots$ percent) of the permutations are indecomposable.

An Extensive Karnaugh Mapping Tool for Boolean Expression Simplification

2019 ◽  
Author(s):  
Md. Saidur Rahman ◽  
Rifat Hasib ◽  
Babe Sultana ◽  
Md Gulzar Hussain ◽  
Mahmuda Rahman ◽  
...  
Keyword(s):  
Boolean Expression ◽  
Mapping Tool

Retrieving Medical Records Using Bayesian Networks

2011 ◽  
pp. 2274-2280
Author(s):  
Luis M. De Campos
Keyword(s):  
Information Retrieval ◽  
Bayesian Networks ◽  
Graphical Models ◽  
Medical Records ◽  
Network Models ◽  
Boolean Expression ◽  
Wide Range ◽  
Structured Information Retrieval ◽  
Structured Information ◽  
Bayesian Network Models

Bayesian networks (Jensen, 2001) are powerful tools for dealing with uncertainty. They have been successfully applied in a wide range of domains where this property is an important feature, as in the case of information retrieval (IR) (Turtle & Croft, 1991). This field (Baeza-Yates & Ribeiro- Neto, 1999) is concerned with the representation, storage, organization, and accessing of information items (the textual representation of any kind of object). Uncertainty is also present in this field, and, consequently, several approaches based on these probabilistic graphical models have been designed in an attempt to represent documents and their contents (expressed by means of indexed terms), and the relationships between them, so as to retrieve as many relevant documents as possible, given a query submitted by a user. Classic IR has evolved from flat documents (i.e., texts that do not have any kind of structure relating their contents) with all the indexing terms directly assigned to the document itself toward structured information retrieval (SIR) (Chiaramella, 2001), where the structure or the hierarchy of contents of a document is taken into account. For instance, a book can be divided into chapters, each chapter into sections, each section into paragraphs, and so on. Terms could be assigned to any of the parts where they occur. New standards, such as SGML or XML, have been developed to represent this type of document. Bayesian network models also have been extended to deal with this new kind of document. In this article, a structured information retrieval application in the domain of a pathological anatomy service is presented. All the medical records that this service stores are represented in XML, and our contribution involves retrieving records that are relevant for a given query that could be formulated by a Boolean expression on some fields, as well as using a text-free query on other different fields. The search engine that answers this second type of query is based on Bayesian networks.

Deep Belief Networks Are Compact Universal Approximators

2010 ◽  
Vol 22 (8) ◽  
pp. 2192-2207 ◽  
Author(s):  
Nicolas Le Roux ◽  
Yoshua Bengio
Keyword(s):  
Learning Algorithm ◽  
Feedforward Neural Networks ◽  
Generative Models ◽  
Universal Approximation ◽  
Belief Networks ◽  
Proof Technique ◽  
Deep Belief Networks ◽  
Boolean Expression ◽  
Universal Approximators ◽  
Causal Variables

Deep belief networks (DBN) are generative models with many layers of hidden causal variables, recently introduced by Hinton, Osindero, and Teh ( 2006 ), along with a greedy layer-wise unsupervised learning algorithm. Building on Le Roux and Bengio ( 2008 ) and Sutskever and Hinton ( 2008 ), we show that deep but narrow generative networks do not require more parameters than shallow ones to achieve universal approximation. Exploiting the proof technique, we prove that deep but narrow feedforward neural networks with sigmoidal units can represent any Boolean expression.

Sign in / Sign up

Export Citation Format

Share Document