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Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Accordingly, Combinatorial Optimization is a sub field of this domain of…

The problem of ranking can be described as follows. We have a set of combinatorial objects $S$, such as, say, the k-subsets of n things, and we can imagine that they have been arranged in some list, say lexicographically, and we want to…

Virtually anything can be and is ranked; people, institutions, countries, words, genes. Rankings reduce complex systems to ordered lists, reflecting the ability of their elements to perform relevant functions, and are being used from…

Cascade ranking is widely used for large-scale top-k selection problems in online advertising and recommendation systems, and learning-to-rank is an important way to optimize the models in cascade ranking. Previous works on learning-to-rank…

The matrix rank minimization problem has applications in many fields such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization…

Problems with solutions represented by permutations are very prominent in combinatorial optimization. Thus, in recent decades, a number of evolutionary algorithms have been proposed to solve them, and among them, those based on probability…

The problem of frequent pattern mining has been studied quite extensively for various types of data, including sets, sequences, and graphs. Somewhat surprisingly, another important type of data, namely rank data, has received very little…

Matrix rank minimization problems are gaining a plenty of recent attention in both mathematical and engineering fields. This class of problems, arising in various and across-discipline applications, is known to be NP-hard in general. In…

We consider the problem of counting the number of possible sets of rankings (called ranking patterns) generated by unfolding models of codimension one. We express the ranking patterns as slices of the braid arrangement and show that all…

Predicting protein interactions is one of the more interesting challenges of the post-genomic era. Many algorithms address this problem as a binary classification problem: given two proteins represented as two vectors of features, predict…

In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly…

In real life, mostly problems are dynamic. Many algorithms have been proposed to handle the static problems, but these algorithms do not handle or poorly handle the dynamic environment problems. Although, many algorithms have been proposed…

In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant…

A common way of doing algorithm selection is to train a machine learning model and predict the best algorithm from a portfolio to solve a particular problem. While this method has been highly successful, choosing only a single algorithm has…

The matrices of spanning rooted forests are studied as a tool for analysing the structure of networks and measuring their properties. The problems of revealing the basic bicomponents, measuring vertex proximity, and ranking from preference…

Learning from many real-world datasets is limited by a problem called the class imbalance problem. A dataset is imbalanced when one class (the majority class) has significantly more samples than the other class (the minority class). Such…

We consider the link prediction problem in a partially observed network, where the objective is to make predictions in the unobserved portion of the network. Many existing methods reduce link prediction to binary classification problem.…

The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…

We investigate how the pattern of contacts between species in mutualistic ecosystems is affected by the phylogenetic proximity between the species of each guild. We develop several theoretical tools to measure that effect and we use them to…

We study the estimation of a planted signal hidden in a recently introduced nested matrix-tensor model, which is an extension of the classical spiked rank-one tensor model, motivated by multi-view clustering. Prior work has theoretically…