Related papers: A scheme-theoretic interpretation of generalized s…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
The theory of spin models intersects with condensed matter physics, complex systems, graph theory, combinatorial optimization, computational complexity and neural networks. Many ensuing applications rely on the fact that complicated spin…
In this paper we consider the relation between the spectrum and the number of short cycles in large graphs. Suppose $G_1, G_2, G_3, \ldots$ is a sequence of finite and connected graphs that share a common universal cover $T$ and such that…
We discuss a partial normalisation of a finite graph of finite groups $(\Gamma(-), X)$ which leaves invariant the fundamental group. In conjunction with an easy graph-theoretic result, this provides a flexible and rather useful tool in the…
Generalized global symmetries are a common feature of many quantum field theories decoupled from gravity. By contrast, in quantum gravity / the Swampland program, it is widely expected that all global symmetries are either gauged or broken,…
We introduce a general theory of parametrized objects in the setting of infinity categories. Although spaces and spectra parametrized over spaces are the most familiar examples, we establish our theory in the generality of objects of a…
This research focuses on analyzing the depth of generalized binomial edge ideals. We extend the notion of $d$-compatible map for the pairs of a complete graph and an arbitrary graph, and using it, we give a combinatorial lower bound for the…
The notion of a spherical space over an arbitrary base scheme is introduced as a generalization of a spherical variety over an algebraically closed field. It is studied how the sphericity condition behaves in families. In particular it is…
We study what we call quasi-spline sheaves over locally Noetherian schemes. This is done with the intention of considering splines from the point of view of moduli theory. In other words, we study the way in which certain objects that arise…
A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate…
In this paper, we extend original Neural Collapse Phenomenon by proving Generalized Neural Collapse hypothesis. We obtain Grassmannian Frame structure from the optimization and generalization of classification. This structure maximally…
We expose in detail the principle that the relative geometric invariant theory of equivariant morphisms is related to the GIT for linearizations near the boundary of the $G$-effective ample cone. We then apply this principle to construct…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
We prove a sheaf-theoretic derived-category generalization of Greenlees-May duality (a far-reaching generalization of Grothendieck's local duality theorem): for a quasi-compact separated scheme X and a "proregular" subscheme Z---for…
A generalized top-spin analysis proposed some time ago in the context of Standard Model and subsequently studied in varying contexts is now applied primarily to the case of $e^+e^-\rightarrow t\bar{t}$ with transversely polarized beams.…
The main purpose of this paper is to give a generalization of Dijkgraaf-Witten theory. Consider a morphism from a smash product of spectra E,F to another spectrum G. We construct a TQFT for E-oriented manifolds using a representative of an…
We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and…
A spin system is a framework in which the vertices of a graph are assigned spins from a finite set. The interactions between neighbouring spins give rise to weights, so a spin assignment can also be viewed as a weighted graph homomorphism.…
We analyze the universality and generalization of graph neural networks (GNNs) on attributed graphs, i.e., with node attributes. To this end, we propose pseudometrics over the space of all attributed graphs that describe the fine-grained…
Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and…