Related papers: Contracting The Well-Rounded Retract
The purpose of this article is towards systematically characterizing (holomorphic) retracts of domains of holomorphy; to begin with, bounded balanced pseudoconvex domains $B \subset \mathbb{C}^N$. Specifically, we show that every retract of…
We prove a general representation stability result for polynomial coefficient systems which lets us prove representation stability and secondary homological stability for many families of groups with polynomial coefficients. This gives two…
Given a homotopy equivalence f between two topological spaces we assemble well known pieces and unfold them into an explicit formula for a strong deformation retraction of the mapping cylinder of f onto its top.
We study cut algebras which are toric rings associated to graphs. The key idea is to consider suitable retracts to understand algebraic properties and invariants of such algebras like being a complete intersection, having a linear…
The paper proposes a novel regularization procedure for machine learning. The proposed high-order regularization (HR) provides new insight into regularization, which is widely used to train a neural network that can be utilized to…
We study linear programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT), referred to as RLT relaxations. We investigate the relations between the polyhedral properties of the feasible…
This work concerns in part the construction of conformal Jordan cells of infinite rank and their reductions to conformal Jordan cells of finite rank. It is also discussed how a procedure similar to Lie algebra contractions may reduce a…
A Redheffer type description of the set of all contractive solutions to the relaxed commutant lifting problem is given. The description involves a set of Schur class functions which is obtained by combining the method of isometric coupling…
We discuss a discretisation of the de Rham-Hodge theory in the two-dimensional case based on a discrete exterior calculus framework. We present discrete analogues of the Hodge-Dirac and Laplace operators in which key geometric aspects of…
We investigate the rank gradient and growth of torsion in homology in residually finite groups. As a tool, we introduce a new complexity notion for generating sets, using measured groupoids and combinatorial cost. As an application we prove…
Although information extraction and coreference resolution appear together in many applications, most current systems perform them as ndependent steps. This paper describes an approach to integrated inference for extraction and coreference…
In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a…
We introduce the notion of a random relaxed asymptotic contraction in the setting of random normed modules. The contraction condition employs two quasi-metrics that are built directly from the random operator: a lower quasi-metric which…
We introduce a space of stable meromorphic differentials with poles of prescribed orders and define its tautological cohomology ring. This space, just as the space of holomorphic differentials, is stratified according to the set of…
In this article we develop the cotangent complex and (co)homology theories for spectral categories. Along the way, we reproduce standard model structures on spectral categories. As applications, we show that the invariants to descend to…
Tracking on the rotation group is a key component of many modern systems for estimation of the motion of rigid bodies. To address this problem, here we describe a Bayesian algorithm that relies on directional measurements for tracking on…
This is essentially an illustration for the general technology of homotopical enhancements developed recently in arxiv:2409.17489. We take the derived category of an abelian category, and we look at the full subcategory spanned by complexes…
We present a method to obtain congruences modulo powers of 2 for sequences given by recurrences of finite depth with polynomial coefficients. We apply this method to Catalan numbers, Fu\ss-Catalan numbers, and to subgroup counting functions…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex…