Related papers: A short proof for the parameter continuation theor…
Dependence on the parameter is continuous when perturbations of the parameter preserves strict preference for one alternative over another. We characterise this property via a utility function over alternatives that depends continuously on…
Vietoris-Rips and degree Rips complexes are represented as homotopy types by their underlying posets of simplices, and basic homotopy stability theorems are recast in these terms. These homotopy types are viewed as systems (or functors),…
This paper gives a necessary and sufficient condition for robust D-stability of Polytopic Polynomial Matrices. Edge theorem is extended to multi-input-multi-output case.
By introducing the notion of distributive constant for a family of closed subschemes, we establish a general form of the second main theorem for algebraic nondegenerate meromorphic mappings from a generalized $p$-Parabolic manifold into a…
We present a geometric proof for the duality theorem of linear programming. Besides being self-contained and simple, the present approach also provides a transparent way for understanding this fundamental result.
In this paper we build on the work of \cite{kaber} where it was shown that the one-parameter family of Gegenbauer Polynomials (GP) exhibit a Gibbs Phenomenon at a jump discontinuity. We show that the one-parameter family of Generalized…
We generalize signature Gr\"obner bases, previously studied in the free algebra over a field or polynomial rings over a ring, to ideals in the mixed algebra $R[x_1,...,x_k]\langle y_1,\dots,y_n \rangle$ where $R$ is a principal ideal…
Strongly continuous one-parameter representations on C*-algebras and their extension to the multiplier algebra are investigated. We give also a proof of the Stone theorem on Hilbert C*-modules and look into some related problems.
We prove a generalization of van der Corput's difference theorem for sequences of vectors in a Hilbert space. This generalization is obtained by establishing a connection between sequences of vectors in the first Hilbert space with a vector…
A generalized criterion for signature-based algorithms to compute Gr\"obner bases is proposed in this paper. This criterion is named by "generalized criterion", because it can be specialized to almost all existing criteria for…
In this paper, we examine the structure of systems that are weighted homogeneous for several systems of weights, and how it impacts the computation of Gr\"obner bases. We present several linear algebra algorithms for computing Gr\"obner…
In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals…
We previously extended the Marsden-Ratiu reduction theorem in Poisson geometry by means of graded geometry (see Part I of Arxiv:1009.0948) . In this note we provide the background material about graded geometry necessary for the proof.…
We give a general method of deriving statistical limit theorems, such as the central limit theorem and its functional version, in the setting of ergodic measure preserving transformations. This method is applicable in situations where the…
A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a module over a principal ideal domain to a one-parameter…
A smooth curve in the real projective plane is hyperbolic if its ovals are maximally nested. By the Helton-Vinnikov Theorem, any such curve admits a definite symmetric determinantal representation. We use polynomial homotopy continuation to…
We prove an analog of Perron-Frobenius theorem for multilinear forms with nonnegative coefficients, and more generally, for polynomial maps with nonnegative coefficients. We determine the geometric convergence rate of the power algorithm to…
Parameterizing mathematical models of biological systems often requires fitting to stable periodic data. In cardiac electrophysiology this typically requires converging to a stable action potential through long simulations. We explore this…
In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into compact sets. We also provide a partial answer to the…
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent…