32,753 research outputs found
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
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 () 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 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
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
A new look at the problem of gauge invariance in quantum field theory
Quantum field theory is assumed to be gauge invariant. However it is well
known that when certain quantities are calculated using perturbation theory the
results are not gauge invariant. The non-gauge invariant terms have to be
removed in order to obtain a physically correct result. In this paper we will
examine this problem and determine why a theory that is supposed to be gauge
invariant produces non-gauge invariant results.Comment: Accepted by Physica Scripta. 27 page
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Models for discriminating image blur from loss of contrast
Observers can discriminate between blurry and low-contrast images (Morgan, 2017). Wang and Simoncelli (2004) demonstrated that a code for blur is inherent to the phase relationships between localized pattern detectors of different scale. To test whether human observers actually use local phase coherence when discriminating between image blur and loss of contrast, we compared phase-scrambled chessboards with unscrambled chessboards. Although both stimuli had identical amplitude spectra, local phase coherence was disrupted by phase-scrambling. Human observers were required to concurrently detect and identify (as contrast or blur) image manipulations in the 2x2 forced-choice paradigm (Nachmias & Weber, 1975; Watson & Robson, 1981) traditionally considered to be a litmus test for "labelled lines" (i.e. detection mechanisms that can be distinguished on the basis of their preferred stimuli). Phase scrambling reduced some observers’ ability to discriminate between blur and a reduction in contrast. However, none of our observers produced data consistent with Watson & Robson’s most stringent test for labelled lines, regardless whether phases were scrambled or not. Models of performance fit significantly better when either a) the blur detector also responded to contrast modulations, b) the contrast detector also responded to blur modulations, or c) noise in the two detectors was anticorrelate
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