• Corpus ID: 247939964

Minor Invertible Products Assignment and Sparse Hyperdeterminants

  title={Minor Invertible Products Assignment and Sparse Hyperdeterminants},
  author={Mario Angelelli},
We consider an extension of Minor Assignment Problems derived from the determinantal expansion of matrix products, under the condition that the terms of the expansion are units of C ( t ). This restriction places constraints on the sparsity and the factorization properties of a family of hyperdeterminants derived from Grassmann-Plücker relations. We find minimal conditions guaranteeing that allowed assignments returning a determinantal expansion are the trivial ones, i.e. those induced by the… 

Cyber-risk Perception and Prioritization for Decision-Making and Threat Intelligence

This work introduces a general framework supporting the prioritization of cyber-vulnerabilities, using flexible regression models that enhance the interpretability of the analysis for decision-making, and takes advantage of Mid-Quantile regression as a robust method to deal with ordinal severity assessment.




This article is a survey of the recent use of some techniques from computational algebraic geometry to address mathematical challenges in systems biology. (Bio)chemical reaction networks de ne

Complexity reduction for sign configurations through the KP II equation and its information-theoretic aspects

We provide a combinatorial setting to explore the information content associated with the fulfillment of the Kadomtsev-Petviashvili (KP) II equation. We start from a special family of solutions of KP

Generalized Instrumental Variables

This paper provides a generalization of the well-known method of Instrumental Variables, which allows its application to models with few conditional independeces, and provides a description of domain knowledge encoded in the form of a directed acyclic graph.

Invertible minor assignment and complexity of set-valued functions

We introduce an algebraic model based on the expansion of the determinant of two matrices to provide a criterion for the additivity of Z d -valued set functions. Each individual term of the expansion

Combinatorial Reduction of Set Functions and Matroid Permutations through Minor Product Assignment

We introduce an algebraic model, based on the determinantal expansion of the product of two matrices, to test combinatorial reductions of set functions. Each term of the determinantal expansion is

An Algebraic-Geometric Approach for Linear Regression Without Correspondences

The machinery of algebraic geometry is used, which uses symmetric polynomials to extract permutation-invariant constraints that the parameters of the linear regression model must satisfy, to prove that as long as the independent samples are generic, this polynomial system is always consistent with at most n complex roots, regardless of any type of corruption inflicted on the observations.

Comments on bases in dependence structures

  • R. Brualdi
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 1969
Dependence structures (in the finite case, matroids) arise when one tries to abstract the properties of linear dependence of vectors in a vector space. With the help of a theorem due to P. Hall and

Discriminants, Resultants, and Multidimensional Determinants

Preface.- Introduction.- General Discriminants and Resultants.- Projective Dual Varieties and General Discriminants.- The Cayley Method of Studying Discriminants.- Associated Varieties and General