Kinetic distance and kinetic maps from molecular dynamics simulation

Characterizing macromolecular kinetics from molecular dynamics (MD) simulations requires a distance metric that can distinguish slowly-interconverting states. Here we build upon diffusion map theory and define a kinetic distance for irreducible Markov processes that quantifies how slowly molecular conformations interconvert. The kinetic distance can be computed given a model that approximates the eigenvalues and eigenvectors (reaction coordinates) of the MD Markov operator. Here we employ the time-lagged independent component analysis (TICA). The TICA components can be scaled to provide a kinetic map in which the Euclidean distance corresponds to the kinetic distance. As a result, the question of how many TICA dimensions should be kept in a dimensionality reduction approach becomes obsolete, and one parameter less needs to be specified in the kinetic model construction. We demonstrate the approach using TICA and Markov state model (MSM) analyses for illustrative models, protein conformation dynamics in bovine pancreatic trypsin inhibitor and protein-inhibitor association in trypsin and benzamidine

Inequality amongst the wealthiest and its link with economic growth

In this paper we correlate the key features of the distribution of wealth of the 500 wealthiest individuals in the Netherlands with economic growth and stock market returns for 1998 to 2009. We show that each year the distribution obeys a power law and that the key parameter measures the degree of inequality. Our main finding is that more inequality amongst the wealthiest is associated with higher economic growth.economic growth;power law;wealth distribution

Inequality amongst the wealthiest and its link with economic growth

In this paper we correlate the key features of the distribution of wealth of the 500 wealthiest individuals in the Netherlands with economic growth and stock market returns for 1998 to 2009. We show that each year the distribution obeys a power law and that the key parameter measures the degree of inequality. Our main finding is that more inequality amongst the wealthiest is associated with higher economic growth

Scale free chaos in the confined Vicsek flocking model

The Vicsek model encompasses the paradigm of active dry matter. Motivated by collective behavior of insects in swarms, we have studied finite size effects and criticality in the three dimensional, harmonically confined Vicsek model. We have discovered a phase transition that exists for appropriate noise and small confinement strength. On the critical line of confinement versus noise, swarms are in a state of scale-free chaos characterized by minimal correlation time, correlation length proportional to swarm size and topological data analysis. The critical line separates dispersed single clusters from confined multicluster swarms. Scale-free chaotic swarms occupy a compact region of space and comprise a recognizable `condensed' nucleus and particles leaving and entering it. Susceptibility, correlation length, dynamic correlation function and largest Lyapunov exponent obey power laws. The critical line and a narrow criticality region close to it move simultaneously to zero confinement strength for infinitely many particles. At the end of the first chaotic window of confinement, there is another phase transition to infinitely dense clusters of finite size that may be termed flocking black holes.Comment: 24 pages, 26 figures, revte