Transient Bimodality and Catastrophic Jumps in Innovation Diffusion

A new phenomenon in innovation diffusion that exhibits a transient bimodality familiar in physical sciences is predicted in this paper for the first time on the basis of an extended Bass model. This accounts for the population heterogeneity, with the parameters characterizing the ldquoword of mouthrdquo and ldquomass mediardquo processes as random. A theoretical framework based on a nonlinear random differential equation is thus introduced to develop a stochastic model for new product diffusion with parametric uncertainty. The analytical investigation of the model establishes the existence of transient bimodality, which manifests through a cusp catastrophe. Illustrations based on analytical and simulation studies are presented. Empirical validation of the proposed model based on well-known data sets where the Bass model is known to fit very well has been carried out.     

Effects of distributed delays on the stability of structures under seismic excitation and multiplicative noise

The effect of seismic excitation and multiplicative noise (arising from environmental fluctuations) on the stability of a single degree of freedom system with distributed delays are investigated. The system is modelled in the form of a stochastic integro-differential equation interpreted in Stratonovich sense. Both deterministic stability and stochastic moment stability are examined for the system in the absence of seismic excitation. The model is also extended to incorporate effects of symmetric nonlinearity. The simulation of stochastic linear and nonlinear systems is carried out by resorting to numerical techniques for the solution of stochastic differential equations. Part of the work was done during the visit of the second author to the Jawaharal Nehru University, New Delhi in December 1993, for which the authors would like to thank the University.     

A stochastic approximation approach to active queue management

Recently, a dynamic adaptive queue management with random dropping (AQMRD) scheme has been developed to capture the time-dependent variation of average queue size by incorporating the rate of change of average queue size as a parameter. A major issue with AQMRD is the choice of parameters. In this paper, a novel online stochastic approximation based optimization scheme is proposed to dynamically tune the parameters of AQMRD and which is also applicable for other active queue management (AQM) algorithms. Our optimization scheme significantly improves the throughput, average queue size, and loss-rate in relation to other AQM schemes.     

Power law behavior in IF model with random excitatory and inhibitory rates

A new mechanism is proposed to generate power law behavior in interspike interval (ISI) distribution when a collection of neurons group together and fire together. Employing superstatistical framework, the mechanism requires a population of neurons which is characterized by randomly distributed excitatory and inhibitory rates. The distribution of these rates is characterized by independent gamma variates. The effect of randomness in the rates exhibits power law behavior in first passage time of the integrate and fire (IF) model. Extensive Monte Carlo simulation studies of the underlying stochastic differential equation (SDE) are carried out which also depict asymptotically power law behavior for ISI distribution for an ensemble of IF neurons.     

Bimodal packet distribution in loss systems using maximum Tsallis entropy principle

A theoretical model of loss system is proposed and analysed within the framework of maximum Tsallis entropy principle. The study provides an explicit expression for state probability distribution of packets in presence of long-range dependent traffic. The unimodal state probability distribution corresponding to well-known Erlang?s loss formula is recovered for Tsallis entropy parameter q = 1. As the parameter q is lowered from unity, it is shown that the state probability distribution makes a transition from unimodal to bimodal. The emergence of bimodality can be regarded as a consequence of long-range dependence. The implication of the model in the design of loss systems is discussed.     

Rationales for Bradford's law

Two models of the mechanism responsible for the distribution of scientific papers in an area over periodicals are given. Empirical distributions following Bradford's law are shown to agree quite closely with a lognormal distribution. This distribution arises, in one model, by taking the probability of a paper being published in a particular journal as the product of many independent factors. It can also arise, according to an alternative mechanism. by random subdivision of the papers in a field over the journals. The mechanisms are compared with other models in the literature.     

Maximum entropy and discretization of probability distributions

Using gaussian quadrature we can find m concentrations of probability that replace the density function of a random variable X and match 2m - 1 of its moments. This reduces a probabilistic analysis to m deterministic ones. Even small values of m provide excellent accuracy in many practical circumstances. When fewer than 2m - 1 moments are known there is arbitrariness in the choice of the concentrations, which is overcome by resorting to the maximum entropy formalism. Its use is here systematized for the case in which αXb and we know N moments of the density of X, so that calculation of N - 1 integrals suffices for finding the density function and any number of its moments. The approach is illustrated for m = 2 and 3, N = 2, 3, α = 0, B = ∞ and graphs are provided for finding the equivalent concentrations.     

On the Applicability of Average Channel Capacity in Log-Normal Fading Environment

The statistical characterization of channel capacity in slow fading environment modeled by log-normal probability density function is considered. The probability density function of channel capacity is found to be positively skewed and significantly departs from bell shaped curve for higher values of σ _dB . The computation of first two moments of channel capacity provides a measure for relative fluctuation in terms of coefficient of variation (CV). It is noted that the value of CV is quite high in lower range of SNR and starts declining with increasing SNR. This may question the applicability of average channel capacity as a performance measure in slow fading scenario and accordingly a more appropriate measure is based on outage capacity. A simple procedure based on three-point estimate is outlined to obtain the approximate expression for higher order moments of channel capacity and they are found to be in excellent agreement with exact results.     

On identifying marker genes from gene expression data in a neural framework through online feature analysis

Many attempts have been made to analyze gene expression data. Typical goals of such analysis include discovery of subclasses, designing predictors/classifiers for diseases, identifying marker genes, and trying to get a deeper understanding of underlying biological process. Success of each of these tasks strongly depends on the features used to solve the problem. The high dimensional nature of expression profiles makes the task very difficult. Consequently, many researchers have used some feature selection criteria to reduce the dimensionality of the problem. These approaches are off‐line in nature, as feature selection is done in a separate phase from the system design phase. These approaches ignore the fact that utility of features depends on both the problem that is solved and the tool that is used to solve the problem. We here propose to use a novel neural scheme that picks up the necessary features on‐line when the system learns the classification task. Because it considers all the features at one go, it does not miss any subtle combination of these features. We demonstrate the effectiveness of our on‐line feature selection (OFS) scheme to distinguish between acute myeloid leukemia (AML) and acute lymphoblastic leukemia (ALL) cancer expression data set. Our scheme could identify only five genes that can produce results as good as or even better than what is reported in the literature on this data set. It identifies an important marker gene that alone has a very good discriminating power. This analysis method is quite general in nature and can be effectively used in other areas of bioinformatics. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 453–467, 2006.     

q-Exponential product-form solution of packet distribution in queueing networks: maximization of Tsallis entropy

A maximum Tsallis entropy solution is presented to examine the effect of long-range dependence (LRD) of packet traffic on network of queues. An important finding is that usual product form solution of queueing networks does not hold. However, it is possible to preserve the product like structure in terms of q-product of q-exponential functions. A special case is considered when normalized q-expectation values of first moment and queue utilization at each node are available as the constraint. The joint state probability distribution is shown to depict asymptotically power law behavior.