相关论文: Abstract homotopical methods for theoretical compu…
This is the second in a series of papers. Here we develop here an intersection theory for manifolds equipped with an action of a finite group. As in our previous paper, our approach will be homotopy theoretic, enabling us to circumvent the…
A set of analytical and computational tools based on transition path theory (TPT) is proposed to analyze flows in complex networks. Specifically, TPT is used to study the statistical properties of the reactive trajectories by which…
The aim of this paper is to obtain an asymptotic expansion for ergodic integrals of translation flows on flat surfaces of higher genus (Theorem 1) and to give a limit theorem for these flows (Theorem 2).
Flow cytometry is a powerful quantitative assay supporting high-throughput collection of single-cell data with a high dynamic range. For flow cytometry to yield reproducible data with a quantitative relationship to the underlying biology,…
These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.
The main results of this paper are limit theorems for horocycle flows on compact surfaces of constant negative curvature. One of the main objects of the paper is a special family of horocycle-invariant finitely-additive Hoelder measures on…
In this chapter tools and techniques from the mathematical theory of formal concept analysis are applied to hypertext systems in general, and the World Wide Web in particular. Various processes for the conceptual structuring of hypertext…
Topological techniques are used to study the motions of systems of point vortices in the infinite plane, in singly-periodic arrays, and in doubly-periodic lattices. The reduction of each system using its symmetries is described in detail.…
We define two model structures on the category of bicomplexes concentrated in the right half plane. The first model structure has weak equivalences detected by the totalisation functor. The second model structure's weak equivalences are…
This is a survey about finite group actions on CW-complexes and related topics, primarily based on our joint work. The main applications are to finite $G$-CW-complexes which are homotopy equivalent to spheres. We have tried to give a fairly…
Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these…
We construct a Quillen model structure on the category of spectral categories, where the weak equivalences are the symmetric spectra analogue of the notion of equivalence of categories.
In this chapter we describe a selection of mathematical techniques and results that suggest interesting links between the theory of gratings and the theory of homogenization, including a brief introduction to the latter. By no means do we…
Homotopy Quantum Field Theories (HQFTs) were introduced by the second author to extend the ideas and methods of Topological Quantum Field Theories to closed $d$-manifolds endowed with extra structure in the form of homotopy classes of maps…
The flow is very useful in studying dynamical systems. However, many modern systems--notably differential inclusions--do not have unique solutions, and therefore cannot be described by flows. Richard McGehee has proposed an object, the…
A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of…
We use topological methods to study complexity of deep computations and limit computations. We use topology of function spaces, specifically, the classification Rosenthal compacta, to identify new complexity classes. We use the language of…
We refine the understanding of continuous dependence on coefficients of solution operators under the nonlocal $H$-topology viz Schur topology in the setting of evolutionary equations in the sense of Picard. We show that certain components…
The main goal of this paper is to prove $L^1$-comparison and contraction principles for weak solutions (in the sense of distributions) of Hele-Shaw flow with a linear Drift. The flow is considered with a general reaction term including the…
Homotopy type theory is a modern foundation for mathematics that introduces the univalence axiom and is particularly suitable for the study of homotopical mathematics and its formalization via proof assistants. In order to better comprehend…