Frenesy: time-symmetric dynamical activity in nonequilibria

We review the concept of dynamical ensembles in nonequilibrium statistical mechanics as specified from an action functional or Lagrangian on spacetime. There, under local detailed balance, the breaking of time-reversal invariance is quantified via the entropy flux, and we revisit some of the consequences for fluctuation and response theory. Frenesy is the time-symmetric part of the path-space action with respect to a reference process. It collects the variable quiescence and dynamical activity as function of the system's trajectory, and as has been introduced under different forms in studies of nonequilibria. We discuss its various realizations for physically inspired Markov jump and diffusion processes and why it matters a good deal for nonequilibrium physics. This review then serves also as an introduction to the exploration of frenetic contributions in nonequilibrium phenomena

Optimization of Trading Physics Models of Markets

We describe an end-to-end real-time S&P futures trading system. Inner-shell stochastic nonlinear dynamic models are developed, and Canonical Momenta Indicators (CMI) are derived from a fitted Lagrangian used by outer-shell trading models dependent on these indicators. Recursive and adaptive optimization using Adaptive Simulated Annealing (ASA) is used for fitting parameters shared across these shells of dynamic and trading models

Jarzynski's equality, fluctuation theorems, and variance reduction: Mathematical analysis and numerical algorithms

In this paper, we study Jarzynski's equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, we review and generalize these nonequilibrium theorems using mathematical arguments, therefore enabling further investigations in the mathematical community. On the numerical side, variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on Jarzynski's equality.Comment: journal versio

Hunter-gatherers in a howling wilderness: Neoliberal capitalism as a language that speaks itself

The 'self-referential' character of evolutionary process noted by Goldenfeld and Woese (2010) can be restated in the context of a generalized Darwinian theory applied to economic process through a 'language' model: The underlying inherited and learned culture of the firm, the short-time cognitive response of the firm to patterns of threat and opportunity that is sculpted by that culture, and the embedding socioeconomic environment, are represented as interacting information sources constrained by the asymptotic limit theorems of information theory. If unregulated, the larger, compound, source that characterizes high probability evolutionary paths of this composite then becomes, literally, a self-dynamic language that speaks itself. Such a structure is, for those enmeshed in it, more akin to a primitive hunter-gatherer society at the mercy of internal ecological dynamics than to, say, a neolithic agricultural community in which a highly ordered, deliberately adapted, ecosystem is consciously farmed so as to match its productivity to human needs

Randomness and Complexity in Networks

I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key idea is that in many cases the process involves copying of properties of near neighbours in the network and this is a type of short random walk which in turn produce a natural preferential attachment mechanism. Applying this to networks of fixed size I show that copying and innovation are processes with special mathematical properties which include the ability to solve a simple model exactly for any parameter values and at any time. I finish by looking at variations of this basic model.Comment: Survey paper based on talk given at the workshop on ``Stochastic Networks and Internet Technology'', Centro di Ricerca Matematica Ennio De Giorgi, Matematica nelle Scienze Naturali e Sociali, Pisa, 17th - 21st September 2007. To appear in proceeding

Pathwise Sensitivity Analysis in Transient Regimes

The instantaneous relative entropy (IRE) and the corresponding instanta- neous Fisher information matrix (IFIM) for transient stochastic processes are pre- sented in this paper. These novel tools for sensitivity analysis of stochastic models serve as an extension of the well known relative entropy rate (RER) and the corre- sponding Fisher information matrix (FIM) that apply to stationary processes. Three cases are studied here, discrete-time Markov chains, continuous-time Markov chains and stochastic differential equations. A biological reaction network is presented as a demonstration numerical example