Abstract. Time-varying network optimization problems have tradition-ally been solved by specialized algorithms. These algorithms have NP-complement time complexity. This paper considers the time-varying short-est path problem, in which can be optimally solved in O(T(m + n)) time,where T is a given integer. For this problem with arbitrary waiting times,we propose an approximation algorithm, whic...

We give an O( √ n)-approximation algorithm for the Sparsest Cut Problem on directed graphs. A näıve reduction from Sparsest Cut to Minimum Multicut would only give an approximation ratio of O( √ n log D), where D is the sum of the demands. We obtain the improvement using a novel LP-rounding method for fractional Sparsest Cut, the dual of Maximum Concurrent Flow.

The problem of finding the correct asymptotic rate of approximation by polynomial loops in dependence of the smoothness of the elements of a loop group seems not well-understood in general. For matrix Lie groups such as SU(N), it can be viewed as a problem of nonlinearly constrained trigonometric approximation. Motivated by applications to optical FIR filter design and control, we present some ...

The leading term in the normal approximation to the distribution of Student’s t statistic is derived in a general setting, with the sole assumption being that the sampled distribution is in the domain of attraction of a normal law. The form of the leading term is shown to have its origin in the way in which extreme data influence properties of the Studentized sum. The leading-term approximation...

In this paper, an approximation for n! (given by Stirling’s formula) is calculated. The accuracy of this formula is also presented. Some improvisations on the accuracy are explored.

We show analytically that the QCD potential can be expressed, up to an O(Λ 3 QCD r 2) uncertainty, as the sum of a " Coulomb " potential (with log corrections at short distances) and a linear potential, within an approximation based on perturbative expansion in α S and the renormalon dominance picture. The expansion of V QCD (r) is truncated at O(α N S) [N = 6π/(β 0 α S)], where the term become...

Considering a given function f ∈ C([0, 1] × [0, 1]), the bivariate interval [0, 1] × [0, 1] is divided in mn equally spaced bivariate subintervals k−1 m , k m × j−1 n , j n , k = 1, m, j = 1, n. On each such type of subinter-vals the Bernstein bivariate approximation formula is applied and a corresponding Bernstein type cubature formula is obtained. Making the sum of mentioned cubature formulas...

The isospin-dependent component of the effective nucleon-nucleon interaction that causes the ∆T = 1 (p, p’) and (p, n) reactions off nuclei is studied. It is shown that the corrections to the impulse approximation comes from the g-matrix type correction and the rearrangement term. They are numerically estimated with the isospin-asymmetric nuclear-matter reaction matrix approach. The analysis of...

We show analytically that the QCD potential can be expressed, up to an O(Λ 3 QCD r 2) uncertainty, as the sum of a " Coulomb " potential (with log corrections at short distances) and a linear potential, within an approximation based on perturbative expansion in α S and the renormalon dominance picture. The expansion of V QCD (r) is truncated at O(α N S) [N = 6π/(β 0 α S)], where the term become...

Стохастическая оптимизация является актуальным направлением исследования в связи со значительными успехами области машинного обучения и их применениями для решения повседневных задач. В данной работе рассматриваются два принципиально различных метода задачи стохастической оптимизации — онлайн- офлайн-алгоритмы. Соответствующие алгоритмы имеют свои качественные преимущества перед друг другом. Та...