Spontaneous Scaling Emergence in Generic Stochastic Systems

We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for certain parameter ranges, the new systems fulfill nonlinear time evolution equations similar to the ones encountered in Spontaneous Symmetry Breaking (SSB) dynamics and evolve spontaneously towards "fixed trajectories" indexed by the average value of their degrees of freedom (which corresponds to the SSB order parameter). The "fixed trajectories" dynamics evolves on the edge between explosion and collapse/extinction. The systems present power laws with exponents which in a wide range ($\alpha < -2.$) are universally determined by the ratio between the minimal and the average values of the degrees of freedom. The time fluctuations are governed by Levy distributions of corresponding power. For exponents $\alpha > -2$ there is no "thermodynamic limit" and the fluctuations are dominated by a few, largest degrees of freedom which leads to macroscopic fluctuations, chaos and bursts/intermitency.Comment: latex, 11 page

Power Laws are Logarithmic Boltzmann Laws

Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized elementary variables. In terms of the original variables this gives a power-law distribution. This mechanism implies certain relations between the constraints of the system, the power of the distribution and the dispersion law of the fluctuations. These predictions are validated by Monte Carlo simulations and experimental data. We speculate that stochastic multiplicative dynamics might be the natural origin for the emergence of criticality and scale hierarchies without fine-tuning.Comment: latex, 9 pages with 3 figure

Unresolved issues in monetary policy

Solomon held the office of president during a period of notably successful anti-inflationary monetary policy as well as rapid financial innovation and deregulation. In this speech, he discusses monetary strategy — in particular the targeting of monetary aggregates, interest rates, and nominal GNP — in light of trends in inflation and the uncertainties introduced by changing financial markets.Monetary policy ; Money supply ; Federal Reserve System - History ; Gross national product

Efficient collinear third-harmonic generation in a single two-dimensional nonlinear photonic crystal

We propose novel multi-phase-matched process that starts with generation of a pair of symmetric second-harmonic waves. Each of them interacts again with the fundamental wave to produce two constructively interfering third harmonic waves collinear to the fundamental input wave.Comment: Summary of presentation at the IQEC/LAT-2002 conferenc

Gain control of saccadic eye movements is probabilistic

Saccades are rapid eye movements that orient the visual axis toward objects of interest to allow their processing by the central, highacuity retina. Our ability to collect visual information efficiently relies on saccadic accuracy, which is limited by a combination of uncertainty in the location of the target and motor noise. It has been observed that saccades have a systematic tendency to fall short of their intended targets, and it has been suggested that this bias originates from a cost function that overly penalizes hypermetric errors. Here we tested this hypothesis by systematically manipulating the positional uncertainty of saccadic targets. We found that increasing uncertainty produced not only a larger spread of the saccadic endpoints but also more hypometric errors and a systematic bias toward the average of target locations in a given block, revealing that prior knowledge was integrated into saccadic planning. Moreover, by examining how variability and bias co-varied across conditions, we estimated the asymmetry of the cost function and found that it was related to individual differences in the additional time needed to program secondary saccades for correcting hypermetric errors, relative to hypometric ones. Taken together, these findings reveal that the saccadic system uses a probabilistic-Bayesian control strategy to compensate for uncertainty in a statistically principled way and to minimize the expected cost of saccadic errors