Deterministic SR in a Piecewise Linear Chaotic Map

The phenomenon of Stochastic Resonance (SR) is observed in a completely deterministic setting - with thermal noise being replaced by one-dimensional chaos. The piecewise linear map investigated in the paper shows a transition from symmetry-broken to symmetric chaos on increasing a system parameter. In the latter state, the chaotic trajectory switches between the two formerly disjoint attractors, driven by the map's inherent dynamics. This chaotic switching rate is found to `resonate' with the frequency of an externally applied periodic perturbation (multiplicative or additive). By periodically modulating the parameter at a specific frequency $\omega$, we observe the existence of resonance where the response of the system (in terms of the residence-time distribution) is maximum. This is a clear indication of SR-like behavior in a chaotic system.Comment: 6 pages LaTex, 4 figure

Economic Inequality: Is it Natural?

Mounting evidences are being gathered suggesting that income and wealth distribution in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas in equilibrium, but also deviating significantly for high income groups. Application of physics models seem to provide illuminating ideas and understanding, complimenting the observations.Comment: 7 pages, 2 eps figs, 2 boxes with text and 2 eps figs; Popular review To appear in Current Science; typos in refs and text correcte

Sudoku Squares as Experimental Designs

Sudoku is a popular combinatorial puzzle. We give a brief overview of some mathematical features of a Sudoku square. Then we focus on interpreting Sudoku squares as experimental designs in order to meet a practical need

A characterization of Dirichlet distributions

AbstractJ. N. Darroch and D. Ratcliff (J. Amer. Statist. Assoc. 66 (1971), 641–643) have given a characterization of the Dirichlet distributions based on the properties of independence of various functions of the random variables (X1, X2, …, Xk) having a joint continuous distribution over the k-dimensional simplex: 0 ≤ x1 ≤ Σ xi ≤ 1. In this paper we provide a further characterization of this family of distributions essentially based on the properties of linear regression. Some extra conditions have been imposed and these are indeed indispensable

Design Issues for Generalized Linear Models: A Review

Generalized linear models (GLMs) have been used quite effectively in the modeling of a mean response under nonstandard conditions, where discrete as well as continuous data distributions can be accommodated. The choice of design for a GLM is a very important task in the development and building of an adequate model. However, one major problem that handicaps the construction of a GLM design is its dependence on the unknown parameters of the fitted model. Several approaches have been proposed in the past 25 years to solve this problem. These approaches, however, have provided only partial solutions that apply in only some special cases, and the problem, in general, remains largely unresolved. The purpose of this article is to focus attention on the aforementioned dependence problem. We provide a survey of various existing techniques dealing with the dependence problem. This survey includes discussions concerning locally optimal designs, sequential designs, Bayesian designs and the quantile dispersion graph approach for comparing designs for GLMs.Comment: Published at http://dx.doi.org/10.1214/088342306000000105 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org