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Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the…
Massive sizes of real-world graphs, such as social networks and web graph, impose serious challenges to process and perform analytics on them. These issues can be resolved by working on a small summary of the graph instead . A summary is a…
A unary constraint (on the Boolean domain) is a function from {0,1} to the set of real numbers. A free use of auxiliary unary constraints given besides input instances has proven to be useful in establishing a complete classification of the…
This paper introduces a new method for redefining the Roman factorial using universally applicable functions that are not expressed in closed form. We present a set of foundational functions, similar to Boolean operations, to simplify the…
Using multiple ion beam analysis measurements, or techniques, combined with self-consistent data processing, generally allows extracting more (or more accurate) information from the measurements than processing separately data from single…
Summation arithmetic functions with asymptotically independent terms are studied in the paper, the limit of which is the law of normal distribution. Assertions about the asymptotic behavior of the indicated functions are proved.
A number of complexity measures for Boolean functions have previously been introduced. These include (1) sensitivity, (2) block sensitivity, (3) witness complexity, (4) subcube partition complexity and (5) algorithmic complexity. Each of…
In this paper we obtain new sufficient conditions for representation of a function as an absolutely convergent Fourier integral. Unlike those known earlier, these conditions are given in terms of belonging to weighted spaces. Adding weights…
For a general family of non-negative functions matching upper and lower bounds are established for their average over the values of any equidistributed sequence.
We prove an asymptotic formula for the smoothed shifted convolution of the generalised divisor function $d_k(n)$ and the divisor function $d(n)$, with a power-saving error term independent of $k$. In particular, when $k$ is large, this is…
We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from…
An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large enough. Applications to the syndrome computation…
The natural generalization of the Boolean satisfiability problem to optimization problems is the task of determining the maximum number of clauses that can simultaneously be satisfied in a propositional formula in conjunctive normal form.…
In our setting enumeration amounts to generate all solutions of a problem instance without duplicates. We address the problem of enumerating the models of B-formulae. A B-formula is a propositional formula whose connectives are taken from a…
Let $X, X_1, X_2,...$ be a sequence of non-degenerate i.i.d. random variables with mean zero. The best possible weighted approximations are investigated in $D[0, 1]$ for the partial sum processes $\{S_{[nt]}, 0\le t\le 1\}$, where…
In observational causal inference, in order to emulate a randomized experiment, weights are used to render treatments independent of observed covariates. This property is known as balance; in its absence, estimated causal effects may be…
The aim of this paper is to generalize a main theorem concerning weighted mean summability to absolute matrix summability which plays a vital role in summability theory and applications to the other sciences by using quasi-$f$-power…
Standardness is a popular assumption in the literature on set estimation. It also appears in statistical approaches to topological data analysis, where it is common to assume that the data were sampled from a probability measure that…
We use M\"obius inversion and the Bernoulli polynomials to prove inequalities between the logarithmic summatory function of the M\"obius function and weighted averages of its ordinary summatory function.
In this paper, we generalize the combinatorial Laplace operator of Horak and Jost by introducing the $\phi$-weighted coboundary operator induced by a weight function $\phi$. Our weight function $\phi$ is a generalization of Dawson's…