We study weak convergence of empirical processes of dependent data, indexed by classes of functions. We obtain results that are especially suitable for data arising from dynamical systems and Markov chains, where the Central Limit Theorem for partial sums is commonly derived via the spectral gap technique. Our results apply, e.g. to the empirical process of ergodic torus automorphisms.

"A simplified model of natural convection, similar to the Lorenz (1963) system, is compared to computational fluid dynamics simulations in order to test data assimilation methods and better understand the dynamics of convection. The thermosyphon is represented by a long time flow simulation, which serves as a reference "truth". Forecasts are then made using the Lorenz-like model and synchronized to noisy and limited observations of the truth using data assimilation. The resulting analysis is observed to infer dynamics absent from the model when using short assimilation windows.

Furthermore, chaotic flow reversal occurrence and residency times in each rotational state are forecast using analysis data. Flow reversals have been successfully forecast in the related Lorenz system, as part of a perfect model experiment, but never in the presence of significant model error or unobserved variables. Finally, we provide new details concerning the fluid dynamical processes present in the thermosyphon during these flow reversals."

"This work is devoted to communication approaches, which spread information in robot swarms. These mechanisms are useful for large-scale systems and also for such cases when a limited communication equipment does not allow routing of information packages. We focus on two approaches such as virtual fields and epidemic algorithms, discuss several aspects of hardware implementation and demonstrate experiments performed with microrobots "Jasmine"."

"As in the car industry for quite some time, dynamic simulation of complete vehicles is being practiced more and more in the development of off-road machinery. However, specific questions arise due not only to company structure and size, but especially to the type of product. Tightly coupled, non-linear subsystems of different domains make prediction and optimisation of the complete system's dynamic behaviour a challenge. Furthermore, the demand for versatile machines leads to sometimes contradictory target requirements and can turn the design process into a hunt for the least painful compromise. This can be avoided by profound system knowledge, assisted by simulation-driven product development. This paper gives an overview of joint research into this issue by Volvo Wheel Loaders and Linkoping University on that matter, lists the results of a related literature review and introduces the term "operateability". Rather than giving detailed answers, the problem space for ongoing and future research is examined and possible solutions are sketched."

the journal version

"Over the last 50 years a steady stream of accounts have been written on the separation principle of stochastic control. Even in the context of the linear-quadratic regulator in continuous time with Gaussian white noise, subtle difficulties arise, unexpected by many, that are often overlooked. In this paper we provide a conceptual framework that clarifies pitfalls and possibilities. We also provide a generalizations of the separation theorem to a wide class of feedback laws, models and stochastic noise, including semimartingales with possible jumps."

""We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of the theory of dynamics, as invariant measures and invariant sets, showing that even if they can be computed with arbitrary precision in many interesting cases, there exists some cases in which they can not. We also explain how it is possible to compute the speed of convergence of ergodic averages (when the system is known exactly) and how this entails the computation of arbitrarily good approximations of points of the space having typical statistical behaviour (a sort of constructive version of the pointwise ergodic theorem).""

"This article presents several results establishing connections be- tween Markov chains and dynamical systems, from the point of view of open systems in physics. We show how all Markov chains can be understood as the information on one component that we get from a dynamical system on a product system, when losing information on the other component. We show that passing from the deterministic dynamics to the random one is character- ized by the loss of algebra morphism property; it is also characterized by the loss of reversibility. In the continuous time framework, we show that the solu- tions of stochastic dierential equations are actually deterministic dynamical systems on a particular product space. When losing the information on one component, we recover the usual associated Markov semigroup." Is there anything new there? I've seen numerous constructions of the sort, e.g., in R.F. Streater's "Statistical Dynamics" ...

"Many biological and physical systems exhibit population-density dependent transitions to synchronized oscillations in a process often termed "dynamical quorum sensing". Synchronization frequently arises through chemical communication via signaling molecules distributed through an external media. We study a simple theoretical model for dynamical quorum sensing: a heterogenous population of limit-cycle oscillators diffusively coupled through a common media. We show that this model exhibits a rich phase diagram with four qualitatively distinct mechanisms fueling population-dependent transitions to global oscillations, including a new type of transition we term "dynamic death". We derive a single pair of analytic equations that allows us to calculate all phase boundaries as a function of population density and show that the model reproduces many of the qualitative features of recent experiments of BZ catalytic particles as well as synthetically engineered bacteria."

"Observer Mechanics is an inquiry into the subject of perception. It suggests an approach to the study of perception that attempts to be both rigorous and general. A central thesis of Observer Mechanics is that every perceptual capacity (e.g., stereovision, auditory localization, sentence parsing, haptic recognition, and so on) can be described as an instance of a single formal structure: viz., an "observer.""

"We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space where balanced truncation may be carried out implicitly. This leads to a nonlinear reduction map which can be combined with a representation of the system belonging to a reproducing kernel Hilbert space to give a closed, reduced order dynamical system which captures the essential input-output characteristics of the original model. Empirical simulations illustrating the approach are also provided."

Terry Tao discusses the work of the four 2010 Fields medal winners.

"We study equilibrium configurations of swarming biological organisms subject to exogenous and pairwise endogenous forces. Beginning with a discrete dynamical model, we derive a variational description of the corresponding continuum population density. Equilibrium solutions are extrema of an energy functional, and satisfy a Fredholm integral equation. We find conditions for the extrema to be local minimizers, global minimizers, and minimizers with respect to infinitesimal Lagrangian displacements of mass. In one spatial dimension, for a variety of exogenous forces, endogenous forces, and domain configurations, we find exact analytical expressions for the equilibria.…"

"Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates chaotic patterns of activity can remain sensitive to extrinsic input. We find that inputs not only drive network responses, they also actively suppress ongoing activity, ultimately leading to a phase transition in which chaos is completely eliminated. The critical input intensity at the phase transition is a non-monotonic function of stimulus frequency, revealing a "resonant" frequency at which the input is most effective at suppressing chaos even though the power spectrum of the spontaneous activity peaks at zero and falls exponentially. A prediction of our analysis is that the variance of neural responses should be most strongly suppressed at frequencies matching the range over which many sensory systems operate."

Looks very interesting: "In 1961 Herbert Simon and Albert Ando published the theory behind the long-term behavior of a dynamical system that can be described by a nearly completely decomposable matrix. Over the past fifty years this theory has been used in a variety of contexts, including queueing theory, computer performance, and ecology. In all these applications, the structure of the system is known and the point of interest is the various states the system passes through on its way to some long-term equilibrium.
This paper looks at this problem from the other direction. That is, we develop a technique for using the evolution of the system to tell us about its initial structure, and we use this technique to develop a new algorithm for data clustering."