Related papers: Majorization: Here, There and Everywhere

This paper surveys the machine learning literature and presents in an optimization framework several commonly used machine learning approaches. Particularly, mathematical optimization models are presented for regression, classification,…

The concept of torsion in geometry, although known for a long time, has not gained considerable attention by the physics community until relatively recently, due to its diverse and potentially important applications to a plethora of…

The goal of this survey paper is to present, in chronological order, certain research works on continued fractions in power series fields over a finite field, all of them being derivated from some examples introduced thirty years ago by…

For more than half a century, dualities have been at the heart of modern physics. From quantum mechanics to statistical mechanics, condensed matter physics, quantum field theory and quantum gravity, dualities have proven useful in solving…

The subject of graph pebbling has seen dramatic growth recently, both in the number of publications and in the breadth of variations and applications. Here we update the reader on the many developments that have occurred since the original…

Left and right "generalized Schur algebras", previously introduced by the author, are defined and analyzed. Filtrations of these algebras lead, in most cases, to parameterizations of the their irreducible representations over fields of…

The authors are doing the readers of Statistical Science a true service with a well-written and up-to-date overview of boosting that originated with the seminal algorithms of Freund and Schapire. Equally, we are grateful for high-level…

Citation distributions for 1992, 1994, 1996, 1997, 1999, and 2001, which were published in the 2004 report of the National Science Foundation, USA, are analyzed. It is shown that the ratio of the total number of citations of any two broad…

There is strong expectation that cities, across time, culture and level of development, share much in common in terms of their form and function. Recently, attempts to formalize mathematically these expectations have led to the hypothesis…

Gaussian processes can be considered as subsets of a standard Hilbert space, but the geometric understanding that would relate the size of a set with the size of its convex hull is still lacking. In this work, we adopt a geometric approach…

This book is an exposition of the current state of research of affine Schubert calculus and $k$-Schur functions. This text is based on a series of lectures given at a workshop titled "Affine Schubert Calculus" that took place in July 2010…

Olkin and Shepp (2005, J. Statist. Plann. Inference, vol. 130, pp. 351--358) presented a matrix form of Chernoff's inequality for Normal and Gamma (univariate) distributions. We extend and generalize this result, proving Poincare-type and…

In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…

Using the referencing patterns in articles in Cognitive Science over three decades, we analyze the knowledge base of this literature in terms of its changing disciplinary composition. Three periods are distinguished: (1) construction of the…

Measures of voting power have been the subject of extensive research since the mid 1940s. More recently, similar measures of relative importance have been studied in other domains that include inconsistent knowledge bases, intensity of…

In this paper we study some weak majorization properties with applications for the trees. A strongly notion of majorization is introduced and Hardy-Littlewood-Polya's inequality is generalized.

In an Euclidean Jordan algebra V of rank n, an element x is said to be majorized by an element y, if the corresponding eigenvalue vector of x is majorized by the eigenvalue vector of y in R^n. In this article, we describe pointwise…

In this presentation, we will develop a short overview of main trends of optimization in systems and control, and from there outline some new perspectives emerging today. More specifically, we will focus on the current situation, where it…

We investigate different aspects of area convexity [Sherman '17], a mysterious tool introduced to tackle optimization problems under the challenging $\ell_\infty$ geometry. We develop a deeper understanding of its relationship with more…

H\"{o}lder's inequality, since its appearance in 1888, has played a fundamental role in Mathematical Analysis and it is, without any doubt, one of the milestones in Mathematics. It may seem strange that, nowadays, it keeps resurfacing and…