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We present a new structural (or syntatic) approach for estimating the satisfiability threshold of random 3-SAT formulae. We show its efficiency in obtaining a jump from the previous upper bounds, lowering them to 4.506. The method combines…

We propose a polynomially bounded, in time and space, method to decide whether a given 3-SAT formula is satisfiable or not. The tools we use here are, in fact, very simple. We first decide satisfiability for a particular 3-SAT formula,…

A variational approach to finite connectivity spin-glass-like models is developed and applied to describe the structure of optimal solutions in random satisfiability problems. Our variational scheme accurately reproduces the known replica…

The problem of identifying the satisfiability threshold of random $3$-SAT formulas has received a lot of attention during the last decades and has inspired the study of other threshold phenomena in random combinatorial structures. The…

The basic random $k$-SAT problem is: Given a set of $n$ Boolean variables, and $m$ clauses of size $k$ picked uniformly at random from the set of all such clauses on our variables, is the conjunction of these clauses satisfiable? Here we…

We obtain the best possible upper bounds for the moments of a single order statistic from independent, non-negative random variables, in terms of the population mean. The main result covers the independent identically distributed case.…

Statisticians have recently developed propensity score methods to improve generalizations from randomized experiments that do not employ random sampling. However, these methods typically rely on assumptions whose plausibility may be…

Data from spectrophotometers form vectors of a large number of exploitable variables. Building quantitative models using these variables most often requires using a smaller set of variables than the initial one. Indeed, a too large number…

A solution to a 3-satisfiability (3-SAT) formula can be expanded into a cluster, all other solutions of which are reachable from this one through a sequence of single-spin flips. Some variables in the solution cluster are frozen to the same…

We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…

Mutual information has been successfully adopted in filter feature-selection methods to assess both the relevancy of a subset of features in predicting the target variable and the redundancy with respect to other variables. However,…

We study a class of random 3-SAT instances having exactly one solution. The properties of this ensemble considerably differ from those of a random 3-SAT ensemble. It is numerically shown that the running time of several complete and…

The estimation of phase transitions in random boolean Constraint Satisfaction Problems (CSP) is based on two fundamental tools: the first and second moment methods. While the first moment method on the number of solutions permits to compute…

Partial orderings and measures of information for continuous univariate random variables with special roles of Gaussian and uniform distributions are discussed. The information measures and measures of non-Gaussianity including third and…

This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…

Boolean satisfiability ({\SAT}) has played a key role in diverse areas spanning testing, formal verification, planning, optimization, inferencing and the like. Apart from the classical problem of checking boolean satisfiability, the…

In many data classification problems, there is no linear relationship between an explanatory and the dependent variables. Instead, there may be ranges of the input variable for which the observed outcome is signficantly more or less likely.…

Random $k$-SAT is the single most intensely studied example of a random constraint satisfaction problem. But despite substantial progress over the past decade, the threshold for the existence of satisfying assignments is not known precisely…

The nonlinear model of the best-worst method frequently produces multiple optimal weight sets, which are conventionally determined through optimization software. While an analytical approach exists that provides both a closed-form…

We study the structure of satisfying assignments of a random 3-SAT formula. In particular, we show that a random formula of density 4.453 or higher almost surely has no non-trivial "core" assignments. Core assignments are certain partial…