Related papers: How useful are formal hierarchies? A case study on…
In this paper, we study the statistical evolution of the large-scale structure (LSS), focusing on the joint probability distribution function (PDF) of the coarse-grained cosmic field and its role in constructing effective dynamics. As the…
We study hierarchical clusterings of metric spaces that change over time. This is a natural geometric primitive for the analysis of dynamic data sets. Specifically, we introduce and study the problem of finding a temporally coherent…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
Organizational charts, also known as org charts, are critical representations of an organization's structure and the hierarchical relationships between its components and positions. However, manually extracting information from org charts…
We consider an unpinned chain of harmonic oscillators with periodic boundary conditions, whose dynamics is perturbed by a random flip of the sign of the velocities. The dynamics conserves the total volume (or elongation) and the total…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…
We demonstrate the usefulness of anholonomic frames in the contexts of nonholonomic and vakonomic systems. We take a consistently differential-geometric approach. As an application, we investigate the conditions under which the dynamics of…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
We give a bird's-eye view of the plastic deformation of crystals aimed at the statistical physics community, and a broad introduction into the statistical theories of forced rigid systems aimed at the plasticity community. Memory effects in…
Formal modelling provides a toolkit for understanding cultural dynamics, from individual decisions to recurring patterns of change. This chapter explains what models are and why they matter. Using a precise, shared language, they aid…
Recent developments in multiscale computation allow the solution of ``coarse equations'' for the expected macroscopic behavior of microscopically/stochastically evolving particle distributions without ever obtaining these coarse equations…
We present an approximate and heuristic scheme for the derivation of continuum kinetic equations from microscopic dynamics for stochastic, interacting systems. The method consists of a mean-field type, decoupled approximation of the master…
Evolutionary forms are skew-symmetric differential forms the basis of which, as opposed to exterior forms, are deforming manifolds (with unclosed metric forms). Such differential forms arise when describing physical processes. A specific…
We present a framework for learning to plan hierarchically in domains with unknown dynamics. We enhance planning performance by exploiting problem structure in several ways: (i) We simplify the search over plans by leveraging knowledge of…
In this paper a geometric field theory of dislocation dynamics and finite plasticity in single crystals is formulated. Starting from the multiplicative decomposition of the deformation gradient into elastic and plastic parts, we use…
Even the simplest of animals exhibit behavioral sequences with complex temporal dynamics. Prominent amongst the proposed organizing principles for these dynamics has been the idea of a hierarchy, wherein the movements an animal makes can be…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
The critical dynamics of dislocation avalanches in plastic flow is examined using a phase field crystal (PFC) model. In the model, dislocations are naturally created, without any \textit{ad hoc} creation rules, by applying a shearing force…
When a dynamical system is subject to a periodic perturbation, the averaging method can be applied to obtain an autonomous leading order "guiding system", placing the time dependence at higher orders. Recent research focused on…