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The effect of direct processes on the statistical properties of deterministic scattering processes in a chaotic waveguide is examined. The single channel Poisson kernel describes well the distribution of S-matrix eigenphases when evaluated…
Diffusion-based classifiers such as those relying on the Personalized PageRank and the Heat kernel, enjoy remarkable classification accuracy at modest computational requirements. Their performance however is affected by the extent to which…
We study the problems of estimating the past and future evolutions of two diffusion processes that spread concurrently on a network. Specifically, given a known network $G=(V, \overrightarrow{E})$ and a (possibly noisy) snapshot…
A common assumption in the literature on information diffusion is that populations are homogeneous regarding individuals' information acquisition and propagation process: Individuals update their informed and actively communicating state…
Recent observations in the theory of verse and empirical metrics have suggested that constructing a verse line involves a pattern-matching search through a source text, and that the number of found elements (complete words totaling a…
Amorphous particulate matter constitutes a wide range of natural and synthetic materials. Despite this ubiquity, the way in which these systems' disordered microstructure couples to their often subtle and complex dynamical behavior is not…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
Complex network theory is used to investigate the structure of meaningful concepts in written texts of individual authors. Networks have been constructed after a two phase filtering, where words with less meaning contents are eliminated,…
The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…
The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one…
Neural systems face the challenge of maintaining reliable representations amid variations from plasticity and spontaneous activity. In particular, the spontaneous dynamics in neuronal circuit is known to operate near a highly variable…
Infiltration of diffusing particles from one material to another where the diffusion mechanism is either normal or anomalous is a widely observed phenomena. When the diffusion is anomalous we find interesting behaviors: diffusion may lead…
Spreading processes on networks are ubiquitous in both human-made and natural systems. Understanding their behavior is of broad interest; from the control of epidemics to understanding brain dynamics. While in some cases there exists a…
We identify the algebraic structure of the material histories generated by concurrent processes. Specifically, we extend existing categorical theories of resource convertibility to capture concurrent interaction. Our formalism admits an…
Diffusion models offer appealing properties for language generation, such as parallel decoding and iterative refinement, but the discrete and highly structured nature of text challenges the direct application of diffusion principles. In…
Recent work has shown that despite their impressive capabilities, text-to-image diffusion models such as DALL-E 2 (Ramesh et al., 2022) can display strange behaviours when a prompt contains a word with multiple possible meanings, often…
Spurious correlations threaten the validity of statistical classifiers. While model accuracy may appear high when the test data is from the same distribution as the training data, it can quickly degrade when the test distribution changes.…
Understanding the causal effects of text on downstream outcomes is a central task in many applications. Estimating such effects requires researchers to run controlled experiments that systematically vary textual features. While large…
Spreading processes on graphs arise in a host of application domains, from the study of online social networks to viral marketing to epidemiology. Various discrete-time probabilistic models for spreading processes have been proposed. These…
Many natural or human-made systems encompassing local reactions and diffusion processes exhibit spatially distributed patterns of some relevant dynamical variable. These interactions, through self-organization and critical phenomena, give…