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Shiv Nadar University

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. © 1976-2012 IEEE.

World University root node

Computer Science and Engineering

(SoE) School of Engineering

Fulltext

IEEE Transactions on Software Engineering

Learning Component Size Distributions for Software Cost Estimation: Models Based on Arithmetic and Shifted Geometric Means Rules

Wireless channel characteristics are random in nature. Consideration of shadowing and fading effect in the channel is necessary so as to capture the behavior of signal variation at the receiving end. The composite effect of the phenomenon is prominent in applications where receiving nodes are deployed in deep faded region with shadowed signal propagation. This becomes more important as the average power of the signal becomes random due to fading and shadowing effects. This effect is more prominent to capture the random behavior of the channel one has to adopt the probabilistic framework by using probability distributions. The Rayleigh–lognormal distribution (RLD), useful in characterizing fading and shadowing aspects of wireless communication channel, has a complex integral having no closed form. Noting that inverse Gaussian distribution closely approximates lognormal distribution, a better approximation is proposed by generalized inverse Gaussian distribution (GIGD). While different combination of compound probability distribution is capable of capturing the behavior of the channel, no such compound distributions work for the complete range of channel variations. Thus, the probability density function of the resulting Rayleigh–generalized inverse Gaussian distribution (RGIGD), besides having a closed form and being analytically tractable, is a more appropriate substitute for RLD. Based on Kullback–Leibler (K–L) measure to assess closeness of two probability distributions, it is found that the proposed RGIGD distribution is closer to the original RLD than other distributions, viz. RGD, RIGD. Further, the proposed distribution can be considered to provide a solution for a large range variation in the sense that RGD and RIGD become its special cases and yields more realistic values of quality of service parameters along with flexibility of covering a wide range of the signal variations through its special cases. © 2021, Shiraz University.

Iranian Journal of Science and Technology - Transactions of Electrical Engineering

Composite Channel Model for Wireless Propagation with Wide-Range Signal Variation Using Rayleigh–Generalized Inverse Gaussian Distribution

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. © The Institution of Engineering and Technology 2019

Physics

(SoNS) School of Natural Sciences

IET Communications

Exact distributions for bit error rate and channel capacity in free-space optical communication

A theoretical model based on the generalized neuronal model with distributed delay (GNMDD) is proposed to generate multimodal/bimodal inter-spike interval (ISI) distribution. The distributed delay is assumed to be general in the sense that it is a linear combination of gamma distributed weak and strong memory kernels. It is found that the expected membrane potential in the subthreshold regime exhibits damped oscillatory behavior. This causes the ISI pattern to become bimodal/multimodal. Furthermore, the effect of external damped oscillatory current in the GNMDD model is investigated. Based on extensive simulation study of a set of coupled stochastic differential equations in the presence of a threshold, a vast amount of spiking data are generated. Using the non-parametric modeling approach, the optimal bin width of the histogram is obtained by using the Freedman-Diaconis rule. It is to be noted that, with the increasing amplitude of the damped oscillatory current, the multimodal ISI distribution changes to unimodal ISI distribution when the magnitude of external current reaches a critical value. It is found that the entropy also shows a sudden transition around the critical point. This phenomenon is akin to a phase transition. © 2018 IEEE.

IEEE Transactions on Nanobioscience

Suppression of multimodality in Inter-Spike interval distribution: Role of external damped oscillatory input

A theoretical investigation is presented that characterizes the emerging sub-threshold membrane potential and inter-spike interval (ISI) distributions of an ensemble of IF neurons that group together and fire together. The squared-noise intensity σ2 of the ensemble of neurons is treated as a random variable to account for the electrophysiological variations across population of nearly identical neurons. Employing superstatistical framework, both ISI distribution and sub-threshold membrane potential distribution of neuronal ensemble are obtained in terms of generalized K-distribution. The resulting distributions exhibit asymptotic behavior akin to stretched exponential family. Extensive simulations of the underlying SDE with random σ2 are carried out. The results are found to be in excellent agreement with the analytical results. The analysis has been extended to cover the case corresponding to independent random fluctuations in drift in addition to random squared-noise intensity. The novelty of the proposed analytical investigation for the ensemble of IF neurons is that it yields closed form expressions of probability distributions in terms of generalized K-distribution. Based on a record of spiking activity of thousands of neurons, the findings of the proposed model are validated. The squared-noise intensity σ2 of identified neurons from the data is found to follow gamma distribution. The proposed generalized K-distribution is found to be in excellent agreement with that of empirically obtained ISI distribution of neuronal ensemble. © 2018 Elsevier B.V.

BioSystems

Characterizing ISI and sub-threshold membrane potential distributions: Ensemble of IF neurons with random squared-noise intensity

<p>A new analytical approximate expression for K distribution is proposed by expanding it in terms of orthogonal associated Laguerre polynomial. The expansion is truncated after first three terms, which yields a fairly close approximation to K distribution. The advantage of the proposed approximation is that the analytical closed form expression for bit error rate can be easily derived. KL measure is used to show the accuracy of the proposed approximation. The proposed approximate probability density function and bit error rate work well within the desired range of the channel parameter α, which is 1 &lt; α &lt; 2 and corresponds to the scintillation index value ranging from 2 to 3. We have also demonstrated the utility of our approximation for other quality of service metric such as fade probability. © 2009-2012 IEEE.</p>