Related papers: Advances in the merit factor problem for binary se…
Schur introduced the problem on the smallest limit point for the arithmetic means of totally positive conjugate algebraic integers. This area was developed further by Siegel, Smyth and others. We consider several generalizations of the…
Combining a modular approach to the $abc$ conjecture developed by the second author with the classical method of linear forms in logarithms, we obtain improved unconditional bounds for two classical problems. First, for Szpiro's conjecture…
Motivated by fast matrix multiplication and recent connections between asymptotic tensor rank and fine-grained complexity, we revisit classical tools from the matrix multiplication literature and develop a framework for obtaining improved…
Once a gravitational wave signal is detected, the measurement of its source parameters is important to achieve various scientific goals. This is done through Bayesian inference, where the analysis cost increases with the model complexity…
In this paper, a new method is presented to compute the 2-adic complexity of pseudo-random sequences. With this method, the 2-adic complexities of all the known sequences with ideal 2-level autocorrelation are uniformly determined. Results…
We investigate the asymptotic behavior of perfect matchings on rail-yard graphs with doubly free boundary conditions and Jack weights. While a special case of this model reduces to the half space Macdonald process with Jack weights…
A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various…
We consider redundant binary joint digital expansions of integer vectors. The redundancy is used to minimize the Hamming weight, i.e., the number of nonzero digit vectors. This leads to efficient linear combination algorithms in abelian…
In a recent paper, J. Lovejoy and the second author conjectured that ranks for four types of unimodal like sequences satisfy certain inequalities. In this paper, we prove these conjectures asymptotically. For this, we extend Wright's Circle…
We obtain new bounds for the optimal matching cost for empirical measures with unbounded support. For a large class of radially symmetric and rapidly decaying probability laws, we prove for the first time the asymptotic rate of convergence…
The asymptotic dimension of metric spaces is an important notion in geometric group theory introduced by Gromov. The metric spaces considered in this paper are the ones whose underlying spaces are the vertex-sets of graphs and whose metrics…
This work presents several new results concerning the analysis of the convergence of binary, univariate, and linear subdivision schemes, all related to the {\it contractivity factor} of a convergent scheme. First, we prove that a convergent…
Sequential change-point detection when the distribution parameters are unknown is a fundamental problem in statistics and machine learning. When the post-change parameters are unknown, we consider a set of detection procedures based on…
With many pretreatment covariates and treatment factors, the classical factorial experiment often fails to balance covariates across multiple factorial effects simultaneously. Therefore, it is intuitive to restrict the randomization of the…
We study a family of nonlinear initial value partial differential equations in the complex domain under the action of two asymmetric time variables. Different Gevrey bounds and multisummability results are obtain depending on each element…
A sequential design problem for rank aggregation is commonly encountered in psychology, politics, marketing, sports, etc. In this problem, a decision maker is responsible for ranking $K$ items by sequentially collecting pairwise noisy…
Gyarmati, Mauduit and S\'ark\"ozy introduced the cross-correlation measure $\Phi_k(G)$ of order $k$ to measure the level of pseudorandom properties of families of finite binary sequences. In an earlier paper we estimated the…
For the differential privacy under the sub-Gamma noise, we derive the asymptotic properties of a class of network models with binary values with a general link function. In this paper, we release the degree sequences of the binary networks…
Many sparse linear discriminant analysis (LDA) methods have been proposed to overcome the major problems of the classic LDA in high-dimensional settings. However, the asymptotic optimality results are limited to the case that there are only…
Assuming that data are collected sequentially from independent streams, we consider the simultaneous testing of multiple binary hypotheses under two general setups; when the number of signals (correct alternatives) is known in advance, and…