Related papers: A Module-theoretic Introduction to Abstract Elemen…
The Drinfeld module is a tool of the explicit class field theory for the function fields. We first observe a similarity of such modules with the noncommutative tori, and then use it to develop an explicit class field theory for the number…
In the present paper, modules over integral domains and principal ideal domains that are proper essential extensions of some submodules are classified. We introduce a new class of modules that we call $\mathrm{SM}$ modules and show that the…
The literature on machine teaching, machine education, and curriculum design for machines is in its infancy with sparse papers on the topic primarily focusing on data and model engineering factors to improve machine learning. In this paper,…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation…
We look at equivalence relations on the set of models of a theory -- MERs, for short -- such that the class of equivalent pairs is itself an elementary class, in a language appropriate for pairs of models. We provide many examples of…
We present modular implicits, an extension to the OCaml language for ad-hoc polymorphism inspired by Scala implicits and modular type classes. Modular implicits are based on type-directed implicit module parameters, and elaborate…
The cohomology of the degree-$n$ general linear group over a finite field of characteristic $p$, with coefficients also in characteristic $p$, remains poorly understood. For example, the lowest degree previously known to contain nontrivial…
Transfer learning has recently become the dominant paradigm of machine learning. Pre-trained models fine-tuned for downstream tasks achieve better performance with fewer labelled examples. Nonetheless, it remains unclear how to develop…
Modularity is a general principle present in many fields. It offers attractive advantages, including, among others, ease of conceptualization, interpretability, scalability, module combinability, and module reusability. The deep learning…
In this paper we develop the theory of operads, algebras and modules in cofibrantly generated symmetric monoidal model categories. We give J-semi model strucures, which are a slightly weaker version of model structures, for operads and…
In the setting of modern mathematical logic and model theory, classification theory has been one of the landmark achievements of the field. Likewise, the classification of UHF-algebras and AF-algebras were substantial contributions to the…
Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…
The main purpose of this survey is to introduce an inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic…
The present survey aims at being a list of Conjectures and Problems in an area of model-theoretic algebra wide open for research, not a list of known results. To keep the text compact, it focuses on structures of finite Morley rank,…
In this paper, we develop 2-dimensional algebraic theory which closely follows the classical theory of modules. The main results are giving definitions of 2-module and the representation of 2-ring. Moreover, for a 2-ring $\cR$, we prove…
The modeling theory of instruction is widely applied and highly successful in high-school instruction, and seldom in university physics. One reason is lack of familiarity with models in the physics classroom. Ongoing curriculum development…
This article is based on lecture notes for the Marie Curie Training school "Initial Training on Numerical Methods for Active Matter". It provides an introductory overview of modeling approaches for active matter and is primarily targeted at…
Neural Module Networks, originally proposed for the task of visual question answering, are a class of neural network architectures that involve human-specified neural modules, each designed for a specific form of reasoning. In current…
In this paper, we mainly focus on formal deformation theory of module homomorphisms. We first introduce the cohomology of module homomorphisms and study formal one-parameter deformation. We obtain some properties about obstructions. Then we…