Concept
Simplicial set
Related publications (41)
A unified framework for Simplicial Kuramoto models
Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models, categorized into three ...
2023Connecting Hodge and Sakaguchi-Kuramoto through a mathematical framework for coupled oscillators on simplicial complexes
Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model ...
NATURE PORTFOLIO2022Reduced representations of complexes, signals, and multifiltrations
The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...
EPFL2022A Shadow Perspective on Equivariant Hochschild Homologies
Kathryn Hess Bellwald, Inbar Klang
Shadows for bicategories, defined by Ponto, provide a useful framework that generalizes classical and topological Hochschild homology. In this paper, we define Hochschild-type invariants for monoids in a symmetric monoidal, simplicial model category V, as ...
OXFORD UNIV PRESS2022Collapse-invariant properties of spaces equipped with signals or directions
Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...
EPFL2022A Wasserstein-based measure of conditional dependence
Negar Kiyavash, Seyed Jalal Etesami, Kun Zhang
Measuring conditional dependencies among the variables of a network is of great interest to many disciplines. This paper studies some shortcomings of the existing dependency measures in detecting direct causal influences or their lack of ability for group ...
2022Quasi-categories vs. Segal spaces: Cartesian edition
We prove that four different ways of defining Cartesian fibrations and the Cartesian model structure are all Quillen equivalent: 1.On marked simplicial sets (due to Lurie [31]), 2.On bisimplicial spaces (due to deBrito [12]), 3.On bisimplicial sets, 4.On m ...
2021The physics of higher-order interactions in complex systems
Enrico Amico, Benedetta Franceschiello
Network representations of complex systems are limited to pairwise interactions, but real-world systems often involve higher-order interactions. This Perspective looks at the new physics emerging from attempts to characterize these interactions. Complex ne ...
NATURE PORTFOLIO2021MOCCA: Modeling and Optimizing Cone-joints for Complex Assemblies
We present a computational framework for modeling and optimizing complex assemblies using cone joints. Cone joints are integral joints that generalize traditional single-direction joints such as mortise and tenon joints to support a general cone of directi ...
ASSOC COMPUTING MACHINERY2021The algebra of Boolean matrices, correspondence functors, and simplicity
We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a simple correspondence ...
2020