Unlike the classical deterministic digital circuit analysis, we consider the analysis of digital circuits with uncertain inputs. Thus, given a binary function of n uncertain input binary variables, we introduce a new way of using K-maps to express the probability of this binary function in terms of the probabilities of the corresponding input binary variables. This in turn, allows us to estimat...

In contrast to mono-constrained flows with N degrees of freedom, binary constrained flows of soliton equations, admitting 2 × 2 Lax matrices, have 2N degrees of freedom. By means of the existing method, Lax matrices only yield the first N pairs of canonical separated variables. An approach for constructing the second N pairs of canonical separated variables with additional N separated equations...

A binary string of length 2 induces the Boolean function of k variables whose Shannon expansion is the given binary string. This Boolean function then is representable via a unique reduced ordered binary decision diagram (ROBDD). The given binary string is fully recoverable from this ROBDD. We exhibit a lossless data compression algorithm in which a binary string of length a power of two is com...

Many pattern classification algorithms such as Support Vector Machines (SVMs), MultiLayer Perceptrons (MLPs), and K-Nearest Neighbors (KNNs) require data to consist of purely numerical variables. However many real world data consist of both categorical and numerical variables. In this paper we suggest an effective method of converting the mixed data of categorical and numerical variables into d...

We consider mixed-integer linear programs with arbitrary bounded integer variables. We first describe a cutting plane approach based on the reformulation of integer variables into binary variables and describe a practical algorithm to compute these cuts for the original problem. We use the term “Binarize and Project” to highlight the similarity to the lift-andproject idea of lifting the problem...

An automated binary change detection model using a threshold-based calibration approach was introduced in the study. The burdensome processes required in binary change detection, including calibration, calculation of accuracy, extraction of optimum threshold(s), generation of a binary change mask, and removal of “salt-and-pepper” noise were integrated and automated in the model. For practical p...

Logistic multiple regression using the method of maximum likelihood is now the method of choice for many regression-type problems involving binary, ordinal. or nominal dependent variables. Logistic regression does not require grouping of observations to obtain valid estimates of effects and of outcome probabilities, and it has been shown in the binary case to provide more accurate probability e...

Tests for dependence of continuous, discrete and mixed continuous-discrete variables are ubiquitous in science. The goal of this paper is to derive Bayesian alternatives to frequentist null hypothesis significance tests for dependence. In particular, we will present three Bayesian tests for dependence of binary, continuous and mixed variables. These tests are nonparametric and based on the Diri...

Quantization of continuous variables is important in data analysis, especially for some model classes such as Bayesian networks and decision trees, which use discrete variables. Often, the discretization is based on the distribution of the input variables only whereas additional information, for example in form of class membership is frequently present and could be used to improve the quality o...

We ropose in this paper a new exact algorithm and gr aduay improvement methods of minimizing binary decision diagrams (BDD’s). In the exact minimization algorithm the o timum order is searched by the exchanges o! variabyes of BDD’s based on the framework of Friedman’s algorithm. The use of BDD representation of a given function and intermediate functions makes it possible to introduce pruning i...