Related papers: On positive local combinatorial dividing-lines in …
We construct normal hypersurfaces whose local cohomology modules have infinitely many associated primes. These include unique factorization domains of characteristic zero with rational singularities, as well as F-regular unique…
We introduce a new nonlinear model for classification, in which we model the joint distribution of response variable, y, and covariates, x, non-parametrically using Dirichlet process mixtures. We keep the relationship between y and x linear…
In this paper we study injective modules over universal enveloping algebras of finite-dimensional Lie algebras over fields of arbitrary characteristic. Most of our results are dealing with fields of prime characteristic but we also…
In this article new cases of the Inverse Galois Problem are established. The main result is that for a fixed integer n, there is a positive density set of primes p such that PSL_2(F_{p^n}) occurs as the Galois group of some finite extension…
In this paper, for an odd prime $p$, several classes of two-weight linear codes over the finite field $\mathbb{F}_p$ are constructed from the defining sets, and then their complete weight distributions are determined by employing character…
We initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain…
We study the training dynamics of neural classifiers through the lens of binary hypothesis testing. We re-formalize classification as a collection of binary tests between class-conditional distributions induced by learned representations…
We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some…
Let p be an odd prime. We show that the classification of p-divisible groups by Breuil windows and the classification of finite flat group schemes of p-power order by Breuil modules hold over any complete regular local ring with perfect…
In this paper, we provide constructions to enumerate large numbers of CI-liaison classes. To this end, we introduce a liaison invariant and prove several results concerning it, notably that it commutes with hypersurface sections. This…
We study set systems formed by neighborhoods in graphs of bounded twin-width. We start by proving that such graphs have linear neighborhood complexity, in analogy to previous results concerning graphs from classes with bounded expansion and…
Let $F$ be a local non-archimedian field of positive characteristic, $D$ be a skew-field with center $F$ and $ G=D^{\star}$ be the multiplicative group of $D$. The goal of this paper is to provide a canonical decomposition of any complex…
Invariants of generalized tensor fields on a line are classified using special polynomials P_mk^(-1/lambda) introduced here for this purpose. For the case of positive characteristic, a new invariant of formal power series, a width, is…
The study of geometric group theory has suggested several theorems related to subdivision tilings that have a natural hyperbolic structure. However, few examples exist. We construct subdivision tilings for the complement of every…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
Parametric models in vector spaces are shown to possess an associated linear map. This linear operator leads directly to reproducing kernel Hilbert spaces and affine- / linear- representations in terms of tensor products. From the…
We study the Fraisse limit of the class of all finite simplicial complexes. Whilst the natural model-theoretic setting for this class uses an infinite language, a range of results associated with Fraisse limits of structures for finite…
We consider a type of long-range percolation problem on the positive integers, motivated by earlier work of others on the appearance of (in)finite words within a site percolation model. The main issue is whether a given infinite binary word…
A famous result due to L. S. Levy provides a classification of all finitely generated indecomposable modules over Dedekind-like rings. This motivates us to outline an approach to the classification of indecomposable pseudo-absorbing primary…
Existing works on "black-box" model interpretation use local-linear approximations to explain the predictions made for each data instance in terms of the importance assigned to the different features for arriving at the prediction. These…