Related papers: Families of cellular resolutions, their syzygies, …

We give an algorithm for computing the V-saturation of any finitely-generated submodule of a power of V[X], where V is a valuation domain. Our algorithm is based on a notion of "echelon form" which ensures its correctness. This allows us to…

We relate finite generation of cones, monoids, and ideals in increasing chains (the local situation) to equivariant finite generation of the corresponding limit objects (the global situation). For cones and monoids there is no analog of…

For every quiver (valued) of finite representation type we define a finitely presented group called a picture group. This group is very closely related to the cluster theory of the quiver. For example, positive expressions for the Coxeter…

We study the problem of constructing positive representations of complex measures. In this paper we consider complex densities on a direct product of $U(1)$ groups and look for representations by probability distributions on the…

A number of machine learning models have been proposed with the goal of achieving systematic generalization: the ability to reason about new situations by combining aspects of previous experiences. These models leverage compositional…

Species or population that proliferate faster than others become dominant in numbers. Catalysis allows catalytic sets within a molecular reaction network to dominate the non catalytic parts of the network by processing most of the available…

It is well known that results on zero-sum sequences over a finitely generated abelian group can be translated to statements on generators of rings of invariants of the dual group. Here the direction of the transfer of information between…

We study the category whose objects are trees (with or without roots) and whose morphisms are contractions. We show that the corresponding contravariant module categories are Noetherian, and we study two natural families of modules over…

We provide constructive versions of Hilbert's syzygy theorem for Z and Z/nZ following Schreyer's method. Moreover, we extend these results to arbitrary coherent strict B\'ezout rings with a divisibility test for the case of finitely…

We investigate Tate cohomology of modules over a commutative noetherian ring with respect to semidualizing modules. We identify classes of modules admitting Tate resolutions and analyze the interaction between the corresponding relative and…

We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of difference equations are introduced as invariants…

Torsion pairs in the category of finitely presented modules over a noetherian ring can be parametrised by the class of cosilting modules. In this paper, we characterise such modules in terms of their indecomposable summands, providing a new…

There is a one-to-one correspondence between geometric lattices and the intersection lattices of arrangements of homotopy spheres. When the arrangements are essential and fully partitioned, Zaslavsky's enumeration of the cells of the…

This paper introduces a new method to solve the problem of the approximation of the diagonal for face-coherent families of polytopes. We recover the classical cases of the simplices and the cubes and we solve it for the associahedra, also…

This review was written for the Encyclopedia of Complexity and System Science (Springer-Verlag, Berlin, 2008), and is intended as a guide to the growing literature which approaches the phenomena of cell biology from a more theoretical point…

We discuss some recent developments in the theory of abelian model categories. The emphasis is on the hereditary condition and applications to homotopy categories of chain complexes and stable module categories.

A cell algebra structure is found for a family of generalized Schur algebras previously studied by the author. This cell algebra structure is then used to construct the irreducible representations of these algebras and to determine when the…

Although widely used in practice, the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts. Here, we present a broad characterization of its…

Network equilibrium models represent a versatile tool for the analysis of interconnected objects and their relationships. They have been widely employed in both science and engineering to study the behavior of complex systems under various…

We develop the rudiments of a finite-dimensional representation theory of groups over idempotent semifields by considering linear actions on tropical linear spaces. This can be considered a tropical representation theory, a characteristic…