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Activated Random Walk is a system of interacting particles which presents a phase transition and a conjectured phenomenon of self-organized criticality. In this note, we prove that, in dimension 1, in the supercritical case, when a segment…
Occurrence reporting is a commonly used method in safety management systems to obtain insight in the prevalence of hazards and accident scenarios. In support of safety data analysis, reports are often categorized according to a taxonomy.…
We study a deliberately simple, fully non-linguistic model of text: a sequence of independent draws from a finite alphabet of letters plus a single space symbol. A word is defined as a maximal block of non-space symbols. Within this…
In the presence of extended defects, familiar incoming particles can scatter into exotic outgoing states created by twist operators. We show that one possible mechanism driving these "categorical scattering" processes is the presence of…
Charge transport processes in disordered complex media are accompanied by anomalously slow relaxation for which usually a broad distribution of relaxation times is adopted. To account for those properties of the environment, a standard…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…
Given a set of graphs from some unknown family, we want to generate new graphs from that family. Recent methods use diffusion on either graph embeddings or the discrete space of nodes and edges. However, simple changes to embeddings (say,…
We tackle some fundamental problems in probability theory on corrupted random processes on the integer line. We analyze when a biased random walk is expected to reach its bottommost point and when intervals of integer points can be detected…
A linear dispersive mechanism for error focusing in polychromatic solutions is identified. This local error pile-up corresponds to the existence of spurious caustics, which are allowed by the dispersive nature of the numerical error. From…
In this article, we study branching random walks on graphs modeling division-mutation processes inspired by adaptive immunity. We apply the theory of expander graphs on mutation rules in evolutionary processes and obtain estimates for the…
This papers develops a logical language for representing probabilistic causal laws. Our interest in such a language is twofold. First, it can be motivated as a fundamental study of the representation of causal knowledge. Causality has an…
Concurrent systems identify systems, either software, hardware or even biological systems, that are characterized by sets of independent actions that can be executed in any order or simultaneously. Computer scientists resort to a causal…
Using exact expressions for the persistence probability and for the leading eigenvalue of the Focker-Planck operator of a random walk in a random environment we establish a fundamental relation between the statistical properties of…
In numerous domains in cognitive science it is often useful to have a source for randomly generated corpora. These corpora may serve as a foundation for artificial stimuli in a learning experiment (e.g., Ellefson & Christiansen, 2000), or…
Text-conditioned diffusion models can generate impressive images, but fall short when it comes to fine-grained control. Unlike direct-editing tools like Photoshop, text conditioned models require the artist to perform "prompt engineering,"…
A parametric point process model is developed, with modeling based on the assumption that sequential observations often share latent phenomena, while also possessing idiosyncratic effects. An alternating optimization method is proposed to…
The well-scaled transition to the diffusion limit in the framework of the theory of continuous-time random walk (CTRW)is presented starting from its representation as an infinite series that points out the subordinated character of the CTRW…
We propose a means to relate properties of an interconnected system to its separate component systems in the presence of cascade-like phenomena. Building on a theory of interconnection reminiscent of the behavioral approach to systems…
In all existing quantum walk models, the assumption about a pre-existing fixed background causal structure is always made and has been taken for granted. Nevertheless, in this work we will get rid of this tacit assumption especially by…
We present a probabilistic language model for time-stamped text data which tracks the semantic evolution of individual words over time. The model represents words and contexts by latent trajectories in an embedding space. At each moment in…