Related papers: Correlated Boolean Operators for Uncertainty Logic
Canalizing functions have important applications in physics and biology. For example, they represent a mechanism capable of stabilizing chaotic behavior in Boolean network models of discrete dynamical systems. When comparing the class of…
Several collective risk models have recently been proposed by relaxing the widely used but controversial assumption of independence between claim frequency and severity. Approaches include the bivariate copula model, random effect model,…
In this paper, we analyze the relative errors in various reliability measures due to the tacit assumption that the components associated with a $n$-component series system or a parallel system are independently working where the components…
We show an analytic method to construct a bivariate distribution function (DF) with given marginal distributions and correlation coefficient. We introduce a convenient mathematical tool, called a copula, to connect two DFs with any…
We analyze a method to produce pairs of non independent Poisson processes $M(t),N(t)$ from positively correlated, self-decomposable, exponential renewals. In particular the present paper provides the family of copulas pairing the renewals,…
It has previously been shown that probabilistic quantum logic operations can be performed using linear optical elements, additional photons (ancilla), and post-selection based on the output of single-photon detectors. Here we describe the…
Uncertain information on input parameters of reliability models is usually modeled by considering these parameters as random, and described by marginal distributions and a dependence structure of these variables. In numerous real-world…
The basic goal of computer engineering is the analysis of data. Such data are often large data sets distributed according to various distribution models. In this manuscript we focus on the analysis of non-Gaussian distributed data. In the…
We expose the information flow capabilities of pure bipartite entanglement as a theorem -- which embodies the exact statement on the `seemingly acausal flow of information' in protocols such as teleportation. We use this theorem to…
Many underlying structural and functional factors that determine the fault behavior of a combinational network, are not yet fully understood. In this paper, we show that there exists a large class of Boolean functions, called root…
Multivariate datasets are common in various real-world applications. Recently, copulas have received significant attention for modeling dependencies among random variables. A copula-based information measure is required to quantify the…
Partial information decomposition (PID) partitions the information that a set of sources has about a target variable into synergistic, unique, and redundant contributions. This information-theoretic tool has recently attracted attention due…
Transient algebra is a multi-valued algebra for hazard detection in gate circuits. Sequences of alternating 0's and 1's, called transients, represent signal values, and gates are modeled by extensions of boolean functions to transients.…
We introduce a series of numbers which serve as a generalization of Bernoulli, Euler numbers and binomial coefficients. Their properties are applied to solve a probability problem and suggest a statistical test for independence and…
While useful probability bounds for $n$ pairwise independent Bernoulli random variables adding up to at least an integer $k$ have been proposed in the literature, none of these bounds are tight in general. In this paper, we provide several…
For almost a century, since Bernal\'s attempts at a molecular theory of liquid structure(Bernal [1]), correlation functions have been the bridge to compare theoretical calculations with experimental measurements in the study of disordered…
Probabilistic sentential decision diagrams are logic circuits where the inputs of disjunctive gates are annotated by probability values. They allow for a compact representation of joint probability mass functions defined over sets of…
This paper establishes quantitative correlation inequalities between monotone events and structured threshold objects in both the discrete cube and Gaussian space. We prove that for any increasing balanced family, there exists a linear…
In this work we consider random Boolean networks that provide a general model for genetic regulatory networks. We extend the analysis of James Lynch who was able to proof Kauffman's conjecture that in the ordered phase of random networks,…
A very common task in data visualization is to plot many data points with some measured y-value as a function of fixed x-values. Uncertainties on the y-values are typically presented as vertical error bars that represent either a…