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We obtain several sharp spectral bounds, approximations, and exact values for the isoperimetric number and related edge-expansion parameters of graphs. Our results focus on graph powers and on families of graphs with rich algebraic or…
Lower and upper bounds are explored for the uniform (Kolmogorov) and $L^2$-distances between the distributions of weighted sums of dependent summands and the normal law. The results are illustrated for several classes of random variables…
We prove a new lower bound for the exponent of growth of the best two-dimensional Diophantine approximations with respect to Euclidean norm.
Salazar, Dunn and Graham in [Salazar et. al., 2006] presented an improved Feng-Rao bound for the minimum distance of dual codes. In this work we take the improvement a step further. Both the original bound by Salazar et. al., as well as our…
We improve the Bend-and-Break result of Miyaoka and Mori by establishing the optimal degree bound. Our result also yields optimal bounds on lengths of extremal rays of log canonical pairs.
This work provides a framework to compute an upper bound on the robust peak-to-peak gain of discrete-time uncertain linear systems using integral quadratic constraints (IQCs). Such bounds are of particular interest in the computation of…
We address the problem of producing a lower bound for the mean of a discrete probability distribution, with known support over a finite set of real numbers, from an iid sample of that distribution. Up to a constant, this is equivalent to…
We discuss a class of binary parametric families with conditional probabilities taking the form of generalized linear models and show that this approach allows to model high-dimensional random binary vectors with arbitrary mean and…
In this paper, we prove two normality criteria for families of some functions concerning shared values, the results generalize those given by Hu and Meng. Some examples are given to show the sharpness of our results.
This study proposes improved chain-ratio type estimator for estimating population mean using some known values of population parameter(s) of the second auxiliary character. The proposed estimators have been compared with two-phase ratio…
This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise…
In statistics on manifolds, the notion of the mean of a probability distribution becomes more involved than in a linear space. Several location statistics have been proposed, which reduce to the ordinary mean in Euclidean space. A…
The families of $f$-divergences (e.g. the Kullback-Leibler divergence) and Integral Probability Metrics (e.g. total variation distance or maximum mean discrepancies) are widely used to quantify the similarity between probability…
We study generalized means whose domain may contain unbounded sets as well. We investigate usual properties of this type of means and also new attributes that regard for such means only. We examine how a mean defined on bounded sets can be…
For an affine two factor model, we study the asymptotic properties of the maximum likelihood and least squares estimators of some appearing parameters in the so-called subcritical (ergodic) case based on continuous time observations. We…
In this paper, for a family of second-order parabolic system or equation with rapidly oscillating and time-dependent periodic coefficients over rough boundaries, we obtain the large-scale boundary estimates, by a quantitative approach. The…
New positivity bounds are derived for generalized (off-forward) parton distributions using the impact parameter representation. These inequalities are stable under the evolution to higher normalization points. The full set of inequalities…
We give elementary proofs of two theorems concerning bounds on the maximum argument of the eigenvalues of a product of two unitary matrices --- one by Childs \emph{et al.} [J. Mod. Phys., \textbf{47}, 155 (2000)] and the other one by Chau…
A description of solutions of some integral equations has been obtained. A two-radii theorem is obtained as well.
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…