Understanding software size distribution is critical to software cost estimation using COCOMO model and design of reliable production function model. This paper proposes and validates a theoretical framework based on the maximization of Shannon entropy to learn component size distribution of software systems when partial information about the moments is given. Specification of appropriate moment constraints either in the form of shifted geometric mean or arithmetic mean or both geometric and arithmetic means are considered. The models are validated using 30 real datasets. The analysis reveals that software systems where component sizes depict power-law behavior are governed by shifted geometric mean whereas those systems in which component size distribution shows exponential behavior are described by arithmetic mean. Another type of software system is also considered where the component size distribution is found to depict gamma distribution. Such systems are characterized by specification of both arithmetic and geometric means. The study underlines that the use of modern object-oriented programming languages adheres to power-law distribution indicating the existence of team synergies leading to substantial containment of software costs when compared to the use of traditional procedural programming languages.

Bit error rate (BER) and channel capacity are two important metrics to assess the performance of free‐space optical communication (FSOC) systems. Due to the fading of the optical signal owing to the atmospheric effects, these two quantities behave as random variables. Most of the studies in this direction have focused on the calculation of only the average of these quantities. However, since the complete information about a random variable is encoded in its distribution, it is more informative to examine the latter itself. In this work, the authors derive exact probability density function (PDF) expressions for the BER and the channel capacity for an arbitrary irradiance model. In particular, they investigate these exact results for log‐normal, gamma‐gamma, and K distributions. For the BER analysis, they focus on the binary phase shift keying and quadrature phase shift keying modulation schemes. The authors' analytical reults are found to be in conformity with Monte Carlo simulations. The exact PDFs of the BER and the channel capacity reveal that there are several instances when the average is unable to capture the actual behaviour of these quantities, and therefore one must be careful in drawing conclusions based on the first moment only.

A new approximate expression for the probability density function (pdf) of K‐distribution is proposed. The approximate pdf is found to be in good agreement with the exact analytical closed‐form expression over the desired range of scintillation index lying between 2 and 3. Employing the proposed pdf, the expression in respect of two of the QoS measures of fade probability and bit error rate (BER) valid under various modulation schemes is given. Using the generalised expression of BER, plots under ON–OFF keying and binary phase shift keying modulation schemes are shown. The resulting expressions provide a better understanding in contrast to the exact results obtained in terms of Meijer G functions. Numerical computations are carried out to demonstrate the efficacy of approximate results.

We consider a stochastic differential equation (SDE) model of slotted Aloha with the retransmission probability as the associated parameter. We formulate the problem in both (a) the finite horizon and (b) the infinite horizon average cost settings. We apply the algorithm of for the first setting, while for the second, we adapt a related algorithm from that was originally developed in the simulation optimization framework. In the first setting, we obtain an optimal parameter trajectory that prescribes the parameter to use at any given instant while in the second setting, we obtain an optimal time-invariant parameter. Our algorithms are seen to exhibit good performance.

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.

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.

Abstract For studying performance characteristics of radio channels, the knowledge about the probability density function (pdf) of fading–shadowing effects is essential. K‐distribution corresponding to Rayleigh–gamma distribution (RGD) is widely used to approximate a more realistic Rayleigh–lognormal distribution (RLD) which does not have a closed form expression. A new composite Rayleigh‐inverse Gaussian distribution (RIGD), an alternative to K‐distribution, is analyzed with regards to its suitability and effectiveness in radio channels. Detailed investigations are made to study the performance characteristics of RIGD and K‐distribution (RGD) in terms of Kullback–Leibler (KL) measure of divergence. Based on these investigations, it is found that RIGD is better suited for capturing fading–shadowing aspects of radio channels instead of K‐distribution. Copyright © 2006 John Wiley & Sons, Ltd.

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.