Power laws of complex systems from Extreme physical information

Many complex systems obey allometric, or power, laws y=Yx^{a}. Here y is the measured value of some system attribute a, Y is a constant, and x is a stochastic variable. Remarkably, for many living systems the exponent a is limited to values +or- n/4, n=0,1,2... Here x is the mass of a randomly selected creature in the population. These quarter-power laws hold for many attributes, such as pulse rate (n=-1). Allometry has, in the past, been theoretically justified on a case-by-case basis. An ultimate goal is to find a common cause for allometry of all types and for both living and nonliving systems. The principle I - J = extrem. of Extreme physical information (EPI) is found to provide such a cause. It describes the flow of Fisher information J => I from an attribute value a on the cell level to its exterior observation y. Data y are formed via a system channel function y = f(x,a), with f(x,a) to be found. Extremizing the difference I - J through variation of f(x,a) results in a general allometric law f(x,a)= y = Yx^{a}. Darwinian evolution is presumed to cause a second extremization of I - J, now with respect to the choice of a. The solution is a=+or-n/4, n=0,1,2..., defining the particular powers of biological allometry. Under special circumstances, the model predicts that such biological systems are controlled by but two distinct intracellular information sources. These sources are conjectured to be cellular DNA and cellular transmembrane ion gradient

Fisher's arrow of `time' in cosmological coherent phase space

Fisher's arrow of `time' in a cosmological phase space defined as in quantum optics (i.e., whose points are coherent states) is introduced as follows. Assuming that the phase space evolution of the universe starts from an initial squeezed cosmological state towards a final thermal one, a Fokker-Planck equation for the time-dependent, cosmological Q phase space probability distribution can be written down. Next, using some recent results in the literature, we derive an information arrow of time for the Fisher phase space cosmological entropy based on the Q function. We also mention the application of Fisher's arrow of time to stochastic inflation modelsComment: 10 pages, LaTex, Honorable Mention at GRF-199

Multi-Frequency Synthesis of VLBI Images Using a Generalized Maximum Entropy Method

A new multi-frequency synthesis algorithm for reconstructing images from multi-frequency VLBI data is proposed. The algorithm is based on a generalized maximum-entropy method, and makes it possible to derive an effective spectral correction for images over a broad frequency bandwidth, while simultaneously reconstructing the spectral-index distribution over the source. The results of numerical simulations demonstrating the capabilities of the algorithm are presented.Comment: 17 pages, 8 figure

Reconstructing Images from Projections Using the Maximum-Entropy Method. Numerical Simulations of Low-Aspect Astrotomography

The reconstruction of images from a small number of projections using the maximum-entropy method (MEM) with the Shannon entropy is considered. MEM provides higher-quality image reconstruction for sources with extended components than the Hogbom CLEAN method, which is also used in low-aspect astrotomography. The quality of image reconstruction for sources with mixed structure containing bright, compact features embedded in a comparatively weak, extended base can be further improved using a difference-mapping method, which requires a generalization of MEM for the reconstruction of sign-variable functions.We draw conclusions based on the results of numerical simulations for a number of model radio sources with various morphologies.Comment: 11 pages, 9 figure

Reciprocity relations between ordinary temperature and the Frieden-Soffer's Fisher-temperature

Frieden and Soffer conjectured some years ago the existence of a ``Fisher temperature" T_F that would play, with regards to Fisher's information measure I, the same role that the ordinary temperature T plays vis-a-vis Shannon's logarithmic measure. Here we exhibit the existence of reciprocity relations between T_F and T and provide an interpretation with reference to the meaning of T_F for the canonical ensemble.Comment: 3 pages, no figure

Delocalization and the semiclassical description of molecular rotation

We discuss phase-space delocalization for the rigid rotator within a semiclassical context by recourse to the Husimi distributions of both the linear and the $3D-$anisotropic instances. Our treatment is based upon the concomitant Fisher information measures. The pertinent Wehrl entropy is also investigated in the linear case.Comment: 6 pages, 3 figure

Value of dual testing for identifying tuberculous infection

Setting: A rural community in Chingleput district in Tamil Nadu state in south India. Objective: To determine the value of dual testing with PPD-S and PPD-B for identifying subjects with a tuberculous infection. Design: About 240,000 subjects in rural south India, all of whom were tested initially with PPD-S and PPD-B, were followed up for 15 years, mainly by total population survey once in every 212 years. The incidence of culture-positive tuberculosis was estimated using life-table technique. Results: Among 17,530 subjects with an intermediate reaction (8–11 mm) to PPD-S at intake, 285 with an induration to PPD-S exceeding the induration to PPD-B by at least 2 mm, had a significantly higher incidence of culture-positive tuberculosis than the remaining (154 and 93 per 100,000), and similarly 481 who had an induration of o10mm to PPD-B compared to those with X10mm (131 and 93 per 100,000). These subjects may be regarded as having a tuberculous infection. Infection with non-tuberculous mycobacteria conferred protection of about 30% against the development of tuberculosis over a 15-year period. Conclusion: In subjects with an intermediate reaction (8–11 mm) to PPD-S, dual testing with PPD-B enabled identification of those with a tuberculous infection. Most of the reactions were due to non-tuberculous mycobacteria

A Physical Axiomatic Approach to Schrodinger's Equation

The Schrodinger equation for non-relativistic quantum systems is derived from some classical physics axioms within an ensemble hamiltonian framework. Such an approach enables one to understand the structure of the equation, in particular its linearity, in intuitive terms. Furthermore it allows for a physically motivated and systematic investigation of potential generalisations which are briefly discussed.Comment: Extended version. 14 page