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We consider the classical problem of estimating the mixing distribution of binomial mixtures, but under trial heterogeneity and smoothness. This problem has been studied extensively when the trial parameter is homogeneous, but not under the…
We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form $xy-zw=r$, where $r$ is a non-zero integer, with an explicit main term and a strong bound on the error term in terms of the…
The extended definition of the polynomial B-splines may give a chance to improve the results obtained by the classical cubic polynomial B-splines. Determination of the optimum value of the extension parameter can be achieved by scanning…
We deal with the problem to find the number $P(b)$ of integer non-negative solutions of an equation $\sum_{i=1}^{n} a_i x_i=b$, where $a_1,a_2,...,a_n$ are natural numbers and $b$ is a non-negative integer. As different from the traditional…
Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…
Proposals for Bell inequality tests on systems restricted by superselection rules often require operations that are difficult to implement in practice. In this paper, we derive a new Bell inequality, where pairs of states are used to…
In this paper we study a new metric for comparing Betti numbers functions in bidimensional persistent homology, based on coherent matchings, i.e. families of matchings that vary in a continuous way. We prove some new results about this…
This paper investigates linear programming based branch-and-bound using general disjunctions, also known as stabbing planes, for solving integer programs. We derive the first sub-exponential lower bound (in the encoding length $L$ of the…
Smoothing is essential to many oceanographic, meteorological and hydrological applications. The interval smoothing problem updates all desired states within a time interval using all available observations. The fixed-lag smoothing problem…
We introduce a new -as far as we know- problem, according to which we are asked to match sequences of two digits in matrices having entries among those two digits (but others too) and prove that this problem is NP-complete
An instance of a strongly stable matching problem (SSMP) is an undirected bipartite graph $G=(A \cup B, E)$, with an adjacency list of each vertex being a linearly ordered list of ties, which are subsets of vertices equally good for a given…
Building on previous results of Xing, we give new lower bounds on the rate of intersecting codes over large alphabets. The proof is constructive, and uses algebraic geometry, although nothing beyond the basic theory of linear systems on…
A rectangle blanket is a set of non-overlapping axis-aligned rectangles, used to approximately represent the two dimensional image of a shape approximately. The use of a rectangle blanket is a widely considered strategy for speeding-up the…
This paper introduces a new method to find the next prime number after a given prime ${P}$. The proposed method is used to derive a system of inequalities, that serve as constraints which should be satisfied by all primes whose successor is…
Despite the success of branch-and-cut methods for solving mixed integer bilevel linear optimization problems (MIBLPs) in practice, there are still gaps in both the theory and practice surrounding these methods. In the first part of this…
Bipartite graphs serve as a natural model for representing relationships between two different types of entities. When analyzing bipartite graphs, butterfly counting is a fundamental research problem that aims to count the number of…
We consider the problem of finding $A_2(n,\{d_1,d_2\})$ defined as the maximal size of a binary (non-linear) code of length $n$ with two distances $d_1$ and $d_2$. Binary codes with distances $d$ and $d+2$ of size…
Let $p\equiv 1\bmod 4$ be a prime number. We use a number field variant of Vinogradov's method to prove density results about the following four arithmetic invariants: (i) $16$-rank of the class group $\mathrm{Cl}(-4p)$ of the imaginary…
Maintaining the pair similarity relationship among originally high-dimensional data into a low-dimensional binary space is a popular strategy to learn binary codes. One simiple and intutive method is to utilize two identical code matrices…
B\"uchi's problem asks whether there exists a positive integer $M$ such that any sequence $(x_n)$ of at least $M$ integers, whose second difference of squares is the constant sequence $(2)$, satisifies $x_n^2=(x+n)^2$ for some $x\in\Z$. A…