Related papers: Linear rank inequalities on five or more variables
This paper is divided into two parts. In the first part, we develop a general method for expressing ranks of matrix expressions that involve Moore-Penrose inverses, group inverses, Drazin inverses, as well as weighted Moore-Penrose inverses…
Ranked set sampling is a sampling design which has a wide range of applications in industrial statistics, and environmental and ecological studies, etc.. It is well known that ranked set samples provide more Fisher information than simple…
The $X$-rank of a point $p$ in projective space is the minimal number of points of an algebraic variety $X$ whose linear span contains $p$. This notion is naturally submultiplicative under tensor product. We study geometric conditions that…
The statistical analysis of data stemming from dynamical systems, including, but not limited to, time series, routinely relies on the estimation of information theoretical quantities, most notably Shannon entropy. To this purpose, possibly…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
In this paper we survey some recent results on the central limit theorem and its weak invariance principle for stationary sequences. We also describe several maximal inequalities that are the main tool for obtaining the invariance…
We prove the sufficiency of the Linear Superposition Principle for linear trees, which characterizes the spectra achievable by a real symmetric matrix whose underlying graph is a linear tree. The necessity was previously proven in 2014.…
In this paper we prove some exponential inequalities involving the sinc function. We analyze and prove inequalities with constant exponents as well as inequalities with certain polynomial exponents. Also, we establish intervals in which…
For any Bell locality scenario (or Kochen-Specker noncontextuality scenario), the joint Shannon entropies of local (or noncontextual) models define a convex cone for which the non-trivial facets are tight entropic Bell (or contextuality)…
Many issues combine for consideration when speaking of Bell's Inequalities: nonlocality, realism, hidden variables, incompatible measures, wave function collapse, other. Each of these issues then may be viewed from several viewpoints:…
Based on collection of bijections, variable and function are extended into ``isomorphic variable'' and ``dual-variable-isomorphic function'', then mean values such as arithmetic mean and mean of a function are extended to ``isomorphic…
This paper studies inference in linear models with a high-dimensional parameter matrix that can be well-approximated by a ``spiked low-rank matrix.'' A spiked low-rank matrix has rank that grows slowly compared to its dimensions and nonzero…
We study the rank weight hierarchy of linear codes which are stable under a linear endomorphism defined over the base field, in particular when the endomorphism is cyclic. In this last case, we give a necessary and sufficient condition for…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
This is a short overview of some recent tendencies in the theory of linear inequalities that are evoked by Boolean valued analysis.
Information inequalities appear in many database applications such as query output size bounds, query containment, and implication between data dependencies. Recently Khamis et al. proposed to study the algorithmic aspects of information…
A general expression for a relative invariant of a linear ordinary differential equations is given in terms of the fundamental semi-invariant and an absolute invariant. This result is used to established a number of properties of relative…
A new class of general exponential ranking models is introduced which we label angle-based models for ranking data. A consensus score vector is assumed, which assigns scores to a set of items, where the scores reflect a consensus view of…
We study the problem of score and rank monotonicity for spectral ranking methods, such as eigenvector centrality and PageRank, in the case of undirected networks. Score monotonicity means that adding an edge increases the score at both ends…
The comparison of alternative rankings of a set of items is a general and prominent task in applied statistics. Predictor variables are ranked according to magnitude of association with an outcome, prediction models rank subjects according…