相关论文: Global stucture of webs in codimension one

We show that moduli spaces of transversely cut-out (perturbed) pseudo-holomorphic curves in an almost complex manifold carry canonical relative smooth structures ("relative to the moduli space of domain curves"). The main point is that…

We investigate the coset structures which appear in the dimensional reduction of supergravity theories. Especially we investigate how to recognize the global symmetry groups if the coset is non-split. As an example we apply our analysis to…

Solutions of an implicit ODE form a web. Already for cubic ODEs the 3-web of solutions has a nontrivial local invariant, namely the curvature form. Thus any local classification of implicit ODEs necessarily has functional moduli if no…

We define the characteristic numbers of a holomorphic k-distribution of any dimension on $mathbb P^n$ and obtain relations between these numbers and the characteristic numbers of an invariant subvariety. As an application we bound the…

Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…

It is now well accepted that the galaxies are distributed in filaments, sheets and clusters all of which form an interconnected network known as the Cosmic Web. It is a big challenge to quantify the shapes of the interconnected structural…

Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global…

The topological structures of the Internet and the Web have received considerable attention. However, there has been little research on the topological properties of individual web sites. In this paper, we consider whether web sites (as…

The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…

A meromorphic connection on the complex projective line induces formal connections at each singular point, and these formal connections constitute the local behavior at the singularities. In this primarily expository paper, we discuss the…

The paper puts into discussion the concept of universality, in particular for structures not of the power of Turing computability. The question arises if for such structures a universal structure of the same kind exists or not. For that the…

Using the Kodaira dimension and the fundamental group of X, we succeed in classifying algebraic surfaces which are dominable by C^2 except for certain cases in which X is an algebraic surface of Kodaira dimension zero and the case when X is…

Hyperuniformity refers to the suppression of density fluctuations at large scales. Typical for ordered systems, this property also emerges in several disordered physical and biological systems, where it is particularly relevant to…

This work introduces a general theory of universal pseudomorphisms and develops their connection to diagrammatic coherence. The main results give hypotheses under which pseudomorphism coherence is equivalent to the coherence theory of…

Structural controllability has been proposed as an analytical framework for making predictions regarding the control of complex networks across myriad disciplines in the physical and life sciences (Liu et al., Nature:473(7346):167-173,…

In this paper, we present a novel way to summarize the structure of large graphs, based on non-parametric estimation of edge density in directed multigraphs. Following coclustering approach, we use a clustering of the vertices, with a…

Many real-world complex systems such as social, biological, information as well as technological systems results of a decentralized and unplanned evolution which leads to a common structuration. Irrespective of their origin, these so-called…

In this note we propose the generalization of the notion of a holomorphic contact structure on a manifold (smooth variety) to varieties with rational singularities and prove basic properties of such objects. Natural examples of singular…

General relativity does not allow one to specify the topology of space, leaving the possibility that space is multi-- rather than simply--connected. We review the main mathematical properties of multi--connected spaces, and the different…

We study the problem of constructing strong approximate unitary $k$-designs on $D$-dimensional grids (and more generally on Cartesian products of graphs), building on the work of Schuster et al. arXiv:2509.26310 which establishes strong…