Related papers: Filtered moment graph sheaves
In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…
Let $X$ be a smooth scheme with an action of an algebraic group $G$. We establish an equivalence of two categories related to the corresponding moment map $\mu : T^*X \to Lie(G)^*$ - the derived category of G-equivariant coherent sheaves on…
The conditional particle filter (CPF) is a promising algorithm for general hidden Markov model smoothing. Empirical evidence suggests that the variant of CPF with backward sampling (CBPF) performs well even with long time series. Previous…
We introduce torsoids, a canonical structure in matching covered graphs, corresponding to the bricks and braces of the graph. This allows a more fine-grained understanding of the structure of finite and infinite directed graphs with respect…
Let $G$ denote a countable inverse semigroup. We construct a kind of a Baum--Connes map $K(\tilde A \rtimes G) \rightarrow K(A \rtimes G)$ by a categorial approach via localization of triangulated categories, developed by R. Meyer and R.…
Jerrum, Sinclair and Vigoda (2004) showed that the permanent of any square matrix can be estimated in polynomial time. This computation can be viewed as approximating the partition function of edge-weighted matchings in a bipartite graph.…
Existing approaches for classifying dynamic graphs either lift graph kernels to the temporal domain, or use graph neural networks (GNNs). However, current baselines have scalability issues, cannot handle a changing node set, or do not take…
This paper investigates a general framework to discover categories of unlabeled scene images according to their appearances (i.e., textures and structures). We jointly solve the two coupled tasks in an unsupervised manner: (i) classifying…
The bipolar filtration of Cochran, Harvey and Horn presents a framework of the study of deeper structures in the smooth concordance group of topologically slice knots. We show that the graded quotient of the bipolar filtration of…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…
We derive upper and lower bounds on the convergence behavior of certain classes of one-parameter quantum dynamical semigroups. The classes we consider consist of tensor product channels and of channels with commuting Liouvillians. We…
Under certain conditions, a scheme can be reconstructed from its category of quasi-coherent sheaves. The Tannakian reconstruction theorem provides another example where a geometric object can be reconstructed from an associated category, in…
We introduce a new class of structured symmetric matrices by extending the notion of perfect elimination ordering from graphs to weighted graphs or matrices. This offers a common framework capturing common vertex elimination orderings of…
A number of inference problems with sensor networks involve projecting a measured signal onto a given subspace. In existing decentralized approaches, sensors communicate with their local neighbors to obtain a sequence of iterates that…
In this paper we prove first a general theorem on semiorthogonal decompositions in derived categories of coherent sheaves for flat families over a smooth base. Based on the results of math.AG/0510670, we then show that the derived…
We introduce a convolutional neural network that operates directly on graphs. These networks allow end-to-end learning of prediction pipelines whose inputs are graphs of arbitrary size and shape. The architecture we present generalizes…
Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational…
An unrepresentable cohomological functor of finite type of the bounded derived category of coherent sheaves of a compact complex manifold of dimension greater than one with no proper closed subvariety is given explicitly in categorical…
Massive networks have shown that the determination of dense subgraphs, where vertices interact a lot, is necessary in order to visualize groups of common interest, and therefore be able to decompose a big graph into smaller structures. Many…
We construct a quasi-coherent sheaf of associative algebras which controls a category of $AV$-modules over a smooth quasi-projective variety. We establish a local structure theorem, proving that in \'etale charts these associative algebras…