Related papers: An unexpected application of minimization theory t…

The framework of templicial objects was put forth in arXiv:2302.02484v1 in order to develop higher categorical concepts in the presence of enrichment. In particular, quasi-categories in modules constitute a subclass of templicial modules…

Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…

Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…

We use cell decomposition techniques to study additive reducts of p- adic fields. We consider a very general class of fields, including fields with infinite residue fields, which we study using a multi-sorted language. The results are used…

Primary decomposition is a very important tool of commutative algebra and geometry. In this paper we generalized some of the existing algorithms of primary decomposition developed by Eisenbud et al. (cf. [EHV]) for free modules and also…

Let $K$ be a complete non-archimedean valuation field of characteristic $0$, with non-trivial valuation, equipped with (possibly multiple) commuting bounded derivations. We prove a decomposition theorem for finite differential modules over…

Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…

Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…

We give a method for constructing (possible large) self--small modules via some special homomorphisms of rings, called here weak epimorphisms.

We introduce decomposition complexes of posets, which generalize order complexes. The main advantage of our construction is that decomposition complexes are closed under taking products. Other special instances of this theory include nested…

The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple…

The main purpose of this paper is to present a decomposition theorem for nonnegative sesquilinear forms. The key notion is the short of a form to a linear subspace. This is a generalization of the well-known operator short defined by M. G.…

We propose a modular method for proving termination of general logic programs (i.e., logic programs with negation). It is based on the notion of acceptable programs, but it allows us to prove termination in a truly modular way. We consider…

We develop the theory of versal deformations of dialgebras and describe a method for constructing a miniversal deformation of a dialgebra.

This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…

We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…

Modular exponentiation is crucial to number theory and cryptography, yet remains largely unexplored from a mechanistic interpretability standpoint. We train a 4-layer encoder-decoder Transformer model to perform this operation and…

The subfactor approach to modular invariants gives insight into the fusion rule structure of the modular invariants.

This paper consider the problem of determining the reliability of a software system which can be decomposed in a number of modules. We have derived the expression of the reliability of a system using the Markovian model for the transfer of…

Many prediction problems, such as those that arise in the context of robotics, have a simplifying underlying structure that, if known, could accelerate learning. In this paper, we present a strategy for learning a set of neural network…