Related papers: Multiple-inheritance hazards in dependently-typed …

Let R be a local ring and A a connected differential graded algebra over R which is free as a graded R-module. Using homological perturbation theory techniques, we construct a minimal free multi model for A having properties similar to that…

A hierarchy of type universes is a rudimentary ingredient in the type theories of many proof assistants to prevent the logical inconsistency resulting from combining dependent functions and the type-in-type rule. In this work, we argue that…

We provide a unified approach, via deformations of incidence algebras, to several important types of representations with finiteness conditions, as well as the combinatorial algebras which produce them. We show that over finite dimensional…

This chapter of the forthcoming Handbook of Graphical Models contains an overview of basic theorems and techniques from algebraic geometry and how they can be applied to the study of conditional independence and graphical models. It also…

Finite-dimensional Reedy algebras form a ring-theoretic analogue of Reedy categories and were recently proved to be quasi-hereditary. We identify Reedy algebras with quasi-hereditary algebras admitting a triangular (or…

Semifields are semirings in which every nonzero element has a multiplicative inverse. A rough classification uses the characteristic of the semifield, that is the isomorphism type of the semifield generated by the two neutral elements. For…

We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…

An extension of the latent class model is presented for clustering categorical data by relaxing the classical "class conditional independence assumption" of variables. This model consists in grouping the variables into inter-independent and…

The main aim of this paper is to classify the distinct multiplicative Lie algebra structures (up to isomorphism) on a given group. We also see that for a given group $G$, every homomorphism from the non-abelian exterior square $G \wedge G$…

We investigate bicomplex analogues of fundamental notions from classical algebraic number theory. In particular, we show that the primitive element theorem admits a natural generalization to bicomplex extensions, giving rise to two distinct…

This paper considers networks where relationships between nodes are represented by directed dissimilarities. The goal is to study methods that, based on the dissimilarity structure, output hierarchical clusters, i.e., a family of nested…

We classify the almost abelian Lie algebras $\mathfrak g_A=\mathbb R e_0 \ltimes_A \mathbb R^{2n-1}$ admitting complex or symplectic structures. The matrix $A\in M(2n-1,\mathbb R )$ encodes the adjoint action of $e_0$ on the abelian ideal…

The foundational character of certain algebraic structures as Boolean algebras and Heyting algebras is rooted in their potential to model classical and constructive logic, respectively. In this paper we discuss the contributions of…

We describe the problem of aggregating the label predictions of diverse classifiers using a class taxonomy. Such a taxonomy may not have been available or referenced when the individual classifiers were designed and trained, yet mapping the…

A new algebraic treatment of dependent type theory is proposed using ideas derived from topos theory and algebraic set theory.

We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their…

The conception of multi-alphabetical genetics is represented. Matrix forms of the representation of the multi-level system of molecular-genetic alphabets have revealed algebraic properties of this system. These properties are connected with…

It has long been noticed that high dimension data exhibits strange patterns. This has been variously interpreted as either a "blessing" or a "curse", causing uncomfortable inconsistencies in the literature. We propose that these patterns…

We show that after mapping each element of a set of second class constraints to the surface of the other ones, half of them form a subset of abelian first class constraints. The explicit form of the map is obtained considering the most…

Many real-world systems can be modeled as interconnected multilayer networks, namely a set of networks interacting with each other. Here we present a perturbative approach to study the properties of a general class of interconnected…