Related papers: The Parameterized Complexity Analysis of Partition…
The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…
The computation and inversion of the binomial and negative binomial cumulative distribution functions play a key role in many applications. In this paper, we explain how methods used for the central beta distribution function (described in…
A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a "multi-scoop" generalization of the beta-Bernoulli process. The BNB process is augmented into a beta-gamma-gamma-Poisson…
This paper studies the problem of decomposing a low-rank positive-semidefinite matrix into symmetric factors with binary entries, either $\{\pm 1\}$ or $\{0,1\}$. This research answers fundamental questions about the existence and…
To enhance solution accuracy and training efficiency in neural network approximation to partial differential equations, partitioned neural networks can be used as a solution surrogate instead of a single large and deep neural network…
Power systems are very large and complex, it can be influenced by many unexpected events this makes power system optimization problems difficult to solve, hence methods for solving these problems ought to be an active research topic. This…
An algorithm for number-partitioning is called value-monotone if whenever one of the input numbers increases, the objective function (the largest sum or the smallest sum of a subset in the output) weakly increases. This note proves that the…
Non-Negative Matrix Factorization, NMF, attempts to find a number of archetypal response profiles, or parts, such that any sample profile in the dataset can be approximated by a close profile among these archetypes or a linear combination…
In many submodular optimization applications, datasets are naturally partitioned into disjoint subsets. These scenarios give rise to submodular optimization problems with partition-based constraints, where the desired solution set should be…
In this paper we present an alternative approach to symbolic segmentation; instead of implementing a new method we approach symbolic segmentation as an algorithm selection problem. That is, let there be $n$ available algorithms for symbolic…
Model-based sequential approaches to discrete "black-box" optimization, including Bayesian optimization techniques, often access the same points multiple times for a given objective function in interest, resulting in many steps to find the…
We propose two-stage and sequential procedures to estimate the unknown parameter N of a binomial distribution with unknown parameter p, when we reinforce data with an independent sample of a negative-binomial experiment having the same p.
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
In sorting literature, comparative statics for multidimensional assignment models with general output functions and input distributions is an important open question. We provide a complete theory of comparative statics for technological…
The number partitioning problem consists of partitioning a sequence of positive numbers ${a_1,a_2,..., a_N}$ into two disjoint sets, ${\cal A}$ and ${\cal B}$, such that the absolute value of the difference of the sums of $a_j$ over the two…
We consider procedures of sampling parts from a random integer partition. We determine asymptotically the probabilty distribution of the randomly-selected part whenever the positive integer that is partitioned becomes large.
We compare different partitioning schemes for the box-counting algorithm in the multifractal analysis by computing the singularity spectrum and the distribution of the box probabilities. As model system we use the Anderson model of…
In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…
In this paper, we introduce a space fractional negative binomial (SFNB) process by subordinating the space fractional Poisson process to a gamma subordinator. Its one-dimensional distributions are derived in terms of generalized Wright…
Simon's problem is one of the most important problems demonstrating the power of quantum computing. Recently, an interesting distributed quantum algorithm for Simon's problem was proposed, where a key sorting operator requiring a large…