Related papers: Hypercurrents
We extend a recent model of temporal random hyperbolic graphs by allowing connections and disconnections to persist across network snapshots with different probabilities, $\omega_1$ and $\omega_2$. This extension, while conceptually simple,…
For the purposes of abstract theory of signal propagation, a signal is a submanifold of a Riemannian manifold. We obtain energy inequalities, or upper bounds, lower bounds on energy in a number of specific cases, including parameter spaces…
Quantum contextuality is a source of quantum computational power and a theoretical delimiter between classical and quantum structures. It has been substantiated by numerous experiments and prompted generation of state independent contextual…
Following a stimulus, the neural response typically strongly varies in time and across neurons before settling to a steady-state. While classical population coding theory disregards the temporal dimension, recent works have argued that…
Identifying central entities and interactions is a fundamental problem in network science. While well-studied for graphs (pairwise relations), many biological and social systems exhibit higher-order interactions best modeled by hypergraphs.…
Topological states of matter exhibit many novel properties due to the presence of robust topological invariants such as the Chern index. These global characteristics pertain to the system as a whole and are not locally defined. However,…
Centers of categories capture the natural operations on their objects. Homotopy coherent centers are introduced here as an extension of this notion to categories with an associated homotopy theory. These centers can also be interpreted as…
Topological superconductors are gapped superconductors with gapless and topologically robust quasiparticles propagating on the boundary. In this paper, we present a topological field theory description of three-dimensional time-reversal…
We introduce topological methods for quantifying spatially heterogeneous dynamics, and use these tools to analyze particle-tracking data for a quasi-two-dimensional granular system of air-fluidized beads on approach to jamming. In…
We recently introduced a formalism for the modeling of temporal networks, that we call stream graphs. It emphasizes the streaming nature of data and allows rigorous definitions of many important concepts generalizing classical graphs. This…
We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this…
A topological argument is presented for nodal structures of superconducting states with time-reversal invariance. A generic Hamiltonian which describes a quasiparticle in superconducting states with time-reversal invariance is derived, and…
We consider diffusion on discrete measure spaces as encoded by Markovian semigroups arising from weighted graphs. We study whether the graph is uniquely determined if the diffusion is given up to order isomorphism. If the graph is recurrent…
We introduce a framework to describe probabilistic models in Bell experiments, and more generally in contextuality scenarios. Such a scenario is a hypergraph whose vertices represent elementary events and hyperedges correspond to…
Topolectrical circuits have emerged as a pivotal platform for realizing static topological states that are challenging to construct in other systems, facilitating the design of robust circuit devices. In addition to spatial dimensionality,…
Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…
We propose a method to search for signs of causal structure in spatiotemporal data making minimal a priori assumptions about the underlying dynamics. To this end, we generalize the elementary concept of recurrence for a point process in…
Connectionist temporal classification (CTC) has matured as an alignment free to sequence transduction and shows competitive for end-to-end speech recognition. In the CTC topology, the blank symbol occupies more than half of the state…
A class of linear hyperbolic partial differential equations, sometimes called networks of waves, is considered. For this class of systems, necessary and sufficient conditions are formulated on the system matrices for the operator dynamics…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…