相关论文: A New Decidable Class of Tuple Generating Dependen…
A family of deformed models of the sine-Gordon-type can be generated by twisting the sine-Gordon model. As a particular case, the 3-sine-Gordon model is here addressed, whose differential configurational entropy and the differential…
Consider a finite group $G$ acting on a triangulated category $\mathcal T$. In this paper we investigate triangulated structure on the category $\mathcal T^G$ of $G$-equivariant objects in $\mathcal T$. We prove (under some technical…
Let X(1,3,a) be a crepant resolution of the quotient singularity C^3/G, where G is a diagonal cyclic subgroup of SL(3,\C) acting on C^3 with weights (1,3,a). For each such X(1,3,a), we construct a (Q,W)-configuration of spherical objects in…
In the projective space $\mathrm{PG}(3,q)$, we consider the orbits of lines under the stabilizer group of the twisted cubic. It is well known that the lines can be partitioned into classes every of which is a union of line orbits. All types…
In this article we describe indecomposable objects of the derived categories of a branch class of associative algebras. To this class belong such known classes of algebras as gentle algebras, skew-gentle algebras and certain degenerations…
A discrete subset $S$ of a topologically gyrogroup $G$ is called a {\it suitable set} for $G$ if $S\cup \{1\}$ is closed and the subgyrogroup generated by $S$ is dense in $G$, where $1$ is the identity element of $G$. In this paper, we…
We provide an axiomatic approach for studying support varieties of objects in a triangulated category via the action of a tensor triangulated category, where the tensor product is not necessarily symmetric. This is illustrated by examples,…
Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract…
Constructive type theory combines logic and programming in one language. This is useful both for reasoning about programs written in type theory, as well as for reasoning about other programming languages inside type theory. It is…
We consider the abelian group $PT$ generated by quasi-equivalence classes of pretriangulated DG categories with relations coming from semi-orthogonal decompositions of corresponding triangulated categories. We introduce an operation of…
We tackle the generalized category discovery (GCD) problem, which aims to discover novel classes in unlabeled datasets by leveraging the knowledge of known classes. Previous works utilize the known class knowledge through shared…
In this short note, we study dg categories with homotopy kernels, whose homotopy categories are known to admit a natural left triangulated structure. Prototypical examples of such dg categories arise as dg quotients of exact dg categories.…
Answering Boolean conjunctive queries over the guarded fragment is decidable, however, as yet no practical decision procedure exists. Meanwhile, ordered resolution, as a practically oriented algorithm, is widely used in state-of-art modern…
This paper surveys the recent advances concerning the relations between triangulated (or derived) categories and their dg enhancements. We explain when some interesting triangulated categories arising in algebraic geometry have a unique dg…
There exist two approaches for exact probabilistic inference of UCQs on tuple-independent databases. In the extensional approach, query evaluation is performed within a DBMS by exploiting the structure of the query. In the intensional…
In this paper we introduce the notion of twisted symplectic reflection algebras and describe the category of representations of such an algebra associated to a non-faithful G-action in terms of those for faithful actions of G.
Structure-based drug design involves finding ligand molecules that exhibit structural and chemical complementarity to protein pockets. Deep generative methods have shown promise in proposing novel molecules from scratch (de-novo design),…
We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied.
Casting neural networks in generative frameworks is a highly sought-after endeavor these days. Contemporary methods, such as Generative Adversarial Networks, capture some of the generative capabilities, but not all. In particular, they lack…
Given a conjunctive query $Q$ and a database $D$, a direct access to the answers of $Q$ over $D$ is the operation of returning, given an index $k$, the $k$-th answer for some order on its answers. While this problem is $\#\mathcal{P}$-hard…