相关论文: A structure theorem for stochastic processes index…

Learning causal structure among event types from discrete-time event sequences is a particularly important but challenging task. Existing methods, such as the multivariate Hawkes processes based methods, mostly boil down to learning the…

Jamming is a phenomenon shared by a wide variety of systems, such as granular materials, foams, and glasses in their high density regime. This has motivated the development of a theoretical framework capable of explaining many of their…

The main result of this article is: THEOREM. Every homogeneous locally conical connected separable metric space that is not a $1$-manifold is strongly $n$-homogeneous for each $n \geq 2$ and countable dense homogeneous. Furthermore,…

Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…

Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form…

Unobserved discrete data are ubiquitous in many scientific disciplines, and how to learn the causal structure of these latent variables is crucial for uncovering data patterns. Most studies focus on the linear latent variable model or…

The Hales numbered $n$-dimensional hypercube and the corresponding adjacency matrix exhibit interesting recursive structures in $n$. These structures lead to a very simple proof of the well-known bandwidth formula for hypercube, whose proof…

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…

We develop a hierarchical structure (HS) analysis for quantitative description of statistical states of spatially extended systems. Examples discussed here include an experimental reaction-diffusion system with Belousov-Zhabotinsky…

This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…

We demonstrate the effectiveness of the categorical distribution as a neural network output for next event prediction. This is done for both discrete-time and continuous-time event sequences. To model continuous-time processes, the…

Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting,…

A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…

Multidimensional record patterns are random sets of lattice points defined by means of a recursive stochastic construction. The patterns thus generated owe their richness to the fact that the construction is not based on a total order,…

We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…

The number of distinguishable inherent structures of a liquid is the key component to understanding the thermodynamics of glass formers. In the case of hard potential systems such as hard discs, spheres and ellipsoids, an inherent structure…

A finite dimensional quantum system for which the quantum chaos conjecture applies has eigenstates, which show the same statistical properties than the column vectors of random orthogonal or unitary matrices. Here, we consider the different…

In this paper, we consider event structures and their probabilistic and quantum extensions as originally defined by Winskel. If these structures have already been part of sophisticated computational models, they have rarely been directly…

Human language has a distinct systematic structure, where utterances break into individually meaningful words which are combined to form phrases. We show that natural-language-like systematicity arises in codes that are constrained by a…

Starting from a classical mechanics of a ``colloid particle'' and $N$ ``water molecules'', we study effective stochastic dynamics of the particle which jumps between deep potential wells. We prove that the effective transition probability…