Related papers: Sparse Versions of the Cayley-Bacharach Theorem
We extend the closed graph theorem and the open mapping theorem to a context in which a natural duality interchanges their extensions.
It is shown that certain lower semi-continuous maps from a paracompact space to the family of closed subsets of the bundle space of a Banach bundle admit continuous selections. This generalization of the theorem of Douady, dal…
We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley-Hamilton theorem for hypermatrices.
In this note, we use the concept of a polynomial ring to give an elementary proof to Cayley-Hamilton Theorem. We also give an elementary proof to Birkhoff theorem on Bi-stochastic matrices.
Conley index theory is a very powerful tool in the study of dynamical systems, differential equations and bifurcation theory. In this paper, we make an attempt to generalize the Conley index to discrete random dynamical systems. And we…
Matrix field theory is a combinatorially non-local field theory which has recently been found to be a non-trivial but solvable QFT example. To generalize such non-perturbative structures to other models, a more combinatorial understanding…
In a recent work, Andrews gave analytic proofs of two conjectures concerning some variations of two combinatorial identities between partitions of a positive integer into odd parts and partitions into distinct parts discovered by Beck.…
We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or other more general exponential models. This result…
We extend the the combinatorics of tableaux to the study of diagram algebras and give a uniform construction of their quasi-hereditary covers.
We extend Painlev\'e's determinateness theorem from the theory of ordinary differential equations in the complex domain allowing more general 'multiple-valued' Cauchy's problems. We study $C^0-$continuability (near singularities) of…
Pure combinatorial models for BPL_n and Gauss map of a combinatorial manifold are described.
We introduce a general framework that extends Bayesian inference by allowing the researcher to explicitly encode confidence in each source of uncertainty within the model. This mechanism provides a new handle for model design and…
In this paper, we study the geometric configurations of a finite set of points having the Cayley-Bacharach property in the $n$-dimensional projective space $\bbP^n$. Our main contribution is the proof of the Levinson-Ullery conjecture for…
In this article we consider combinatorial maps approach to graphs on surfaces, and how between them can be establish terminological uniformity in favor of combinatorial maps in way rotations are set as base structural elements and all other…
This tutorial provides a concise introduction to modern causal modeling by integrating potential outcomes and graphical methods. We motivate causal questions such as counterfactual reasoning under interventions and define binary treatments…
In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior…
Structured prediction requires searching over a combinatorial number of structures. To tackle it, we introduce SparseMAP: a new method for sparse structured inference, and its natural loss function. SparseMAP automatically selects only a…
For every strong coarse homology theory we construct a coarse assembly map as a natural transformation between coarse homology theories. We provide various conditions implying that this assembly map is an equivalence. These results…
We introduce complex cones and associated projective gauges, generalizing a real Birkhoff cone and its Hilbert metric to complex vector spaces. We deduce a variety of spectral gap theorems in complex Banach spaces. We prove a dominated…
We describe an algorithm to factor sparse multivariate polynomials using O(d) bivariate factorizations where d is the number of variables. This algorithm is implemented in the Giac/Xcas computer algebra system.