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Network embedding which encodes all vertices in a network as a set of numerical vectors in accordance with it's local and global structures, has drawn widespread attention. Network embedding not only learns significant features of a…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Inspired by birds flying through cluttered environments such as dense forests, this paper studies the theoretical foundations of a novel motion planning problem: high-speed navigation through a randomly-generated obstacle field when only…
Finding a set of nested partitions of a dataset is useful to uncover relevant structure at different scales, and is often dealt with a data-dependent methodology. In this paper, we introduce a general two-step methodology for model-based…
Recent studies have revealed that neural networks learn interpretable algorithms for many simple problems. However, little is known about how these algorithms emerge during training. In this article, I study the training dynamics of a small…
The evolution of a planar perturbation in a Einstein-de Sitter Universe is studied using a previously introduced Lagrangian scheme. An approximate discrete dynamical system is derived, which describes the mass agglomeration process…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
Behavior sequences, composed of executable steps, serve as the operational foundation for multi-constraint planning problems such as travel planning. In such tasks, each planning step is not only constrained locally but also influenced by…
A hybrid percolation transition (HPT) exhibits both discontinuity of the order parameter and critical behavior at the transition point. Such dynamic transitions can occur in two ways: by cluster pruning with suppression of loop formation of…
Systems comprising a turbulent channel flow overlaying a permeable bed can be found in a variety of industrial and natural applications (e.g. urban planning, fracking, submerged vegetation). One important realization of this system is at…
Population structure induced by both spatial embedding and more general networks of interaction, such as model social networks, have been shown to have a fundamental effect on the dynamics and outcome of evolutionary games. These effects…
The escalating process of urbanization has raised concerns about incidents arising from overcrowding, necessitating a deep understanding of large human crowd behavior and the development of effective crowd management strategies. This study…
In order to study convergences of looptrees, we construct continuum trees and looptrees from real-valued c\`adl\`ag functions without negative jumps called excursions. We then provide a toolbox to manipulate the two resulting codings of…
Consider a stochastic process that behaves as a $d$-dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to jump to a given site with probability proportional to the…
Consider two urns, $A$ and $B$, where initially $A$ contains a large number $n$ of balls and $B$ is empty. At each step, with equal probability, either we pick a ball at random in $A$ and place it in $B$, or vice-versa (provided of course…
We present a new method for analyzing the running time of parallel evolutionary algorithms with spatially structured populations. Based on the fitness-level method, it yields upper bounds on the expected parallel running time. This allows…
Finding the most powerful node in a dynamic random network, the largest set in a partition-valued stochastic process, or the largest family in an evolving population at a given time, can be a very difficult problem. This is particularly the…
Stochastic particle--based models are useful tools for describing the collective movement of large crowds of pedestrians in crowded confined environments. Using descriptions based on the simple exclusion process, two populations of…
The Brownian web is a random object that occurs as the scaling limit of an infinite system of coalescing random walks. Perturbing this system of random walks by, independently at each point in space-time, resampling the random walk…
Understanding characteristics of temporal correlations in time series is crucial for developing accurate models in natural and social sciences. The burst-tree decomposition method was recently introduced to reveal higher-order temporal…