The age of Professor Narmadeshwar Jha

Professor Narmadeshwar Jha was a noted scholar on History of Economic Thought that took its shape under the influence of Alfred Marshall. His widely referred book - The Age of Marshall: Aspects of British Economic Thought, 1890-1915 – was written under the supervision of Professor A.J. Brown of Leeds (UK) and published with a commendatory foreword written by Sir Dennis H. Robertson. Professor Jha devised a methodology to conduct research in the history of economic ideas. This brief paper presents Professor Jha as a teacher, economist and scholar.History of Economic Thought; Bhagalpur University; Bihar; India; Alfred Marshall; Institutional Economics; Will to economize; Rabindranath Tagore; Dennis H. Robertson; A. J. Brown; University of Leeds (UK)

A note on least squares fitting of signal waveforms

Signal waveforms are very fast dampening oscillatory time series composed of exponential functions. The regular least squares fitting techniques are often unstable when used to fit exponential functions to such signal waveforms since such functions are highly correlated. Of late, some attempts have been made to estimate the parameters of such functions by Monte Carlo based search/random walk algorithms. In this study we use the Differential Evaluation based method of least squares to fit the exponential functions and obtain much more accurate results.Signal waveform; exponential functions; Differential Evolution; Global optimization; Nonlinear Least Squares; Monte Carlo; Curve fitting; parameter estimation; Random Walk; Search methods; Fortran

Possibilities of quality enhancement in higher education by intensive use of information technology

Quality of higher education is a multi-dimensional concept. It lies in effectiveness of transmitting knowledge and skill; the authenticity, content, coverage and depth of information; availability of reading/teaching materials; help in removing obstacles to learning; applicability of knowledge in solving the real life problems; fruitfulness of knowledge in personal and social domains; convergence of content and variety of knowledge over space (countries and regions) and different sections of the people; cost-effectiveness and administrative efficiency. Information technology has progressed very fast in the last three decades; it has produced equipments at affordable cost and it has now made their wider application feasible. This technology has made search, gathering, dissemination, storing, retrieval, transmission and reception of knowledge easier, cheaper and faster. Side by side, a vast virtual library vying with the library in prints has emerged and continues growing rapidly. One may hold that the e-libraries are the libraries of tomorrow when the libraries in prints will be the antiques or the archival objects of the past. This paper discusses in details how information technology can be applied to enhance the quality of higher education at affordable cost. It also discusses the major obstacles to optimal utilization of information technology and measures to remove them.Information Technology; Quality in Higher Education; e-library; e-book; e-journal

Performance of Differential Evolution and Particle Swarm Methods on Some Relatively Harder Multi-modal Benchmark Functions

This paper aims at comparing the performance of the Differential Evolution (DE) and the Repulsive Particle Swarm (RPS) methods of global optimization. To this end, some relatively difficult test functions have been chosen. Among these test functions, some are new while others are well known in the literature. We use DE method with the exponential crossover scheme as well as with no crossover (only probabilistic replacement). Our findings suggest that DE (with the exponential crossover scheme) mostly fails to find the optimum in case of the functions under study. Of course, it succeeds in case of some functions (perm#2, zero-sum) for very small dimension, but begins to falter as soon as the dimension is increased. In case of DCS function, it works well up to dimension = 5. When we use no crossover (only probabilistic replacement) we obtain better results in case of several of the functions under study. In case of Perm#1, Perm#2, Zero-sum, Kowalik, Hougen and Power-sum functions, a remarkable advantage is there. Whether crossover or no crossover, DE falters when the optimand function has some element of randomness. This is indicated by the functions: Yao-Liu#7, Fletcher-Powell, and “New function#2”. DE has no problems in optimizing the “New function #1”. But the “New function #2” proves to be a hard nut. However, RPS performs much better for such stochastic functions. When the Fletcher-Powell function is optimized with non-stochastic c vector, DE works fine. But as soon as c is stochastic, it becomes unstable. Thus, it may be observed that an introduction of stochasticity into the decision variables (or simply added to the function as in Yao-Liu#7) interferes with the fundamentals of DE, which works through attainment of better and better (in the sense of Pareto improvement) population at each successive iteration. The paper concludes: (1) for different types of problems, different schemes of crossover (including none) may be suitable or unsuitable, (2) Stochasticity entering into the optimand function may make DE unstable, but RPS may function well.Differential Evolution; Repulsive Particle Swarm; Global optimization; non-convex functions; Fortran; computer program; benchmark; test; Stochastic functions; Fletcher-Powell; Kowalik; Hougen; Power-sum; Perm; Zero-sum; New functions; Bukin function

A Brief History of Production Functions

This paper gives an outline of evolution of the concept and econometrics of production function, which was one of the central apparatus of neo-classical economics. It shows how the famous Cobb-Douglas production function was indeed invented by von Thunen and Wicksell, how the CES production function was formulated, how the elasticity of substitution was made a variable and finally how Sato’s function incorporated biased technical changes. It covers almost all specifications proposed during 1950-1975, and further the LINEX production functions and incorporation of energy as an input. The paper in divided into (1) single product functions, (2) joint product functions, and (3) aggregate production functions. It also discusses the ‘capital controversy’ and its impacts.Production function; Cobb-Douglas; CES; Transcendental; translog; Zellner-Revankar; VES; Bruno; Kadiyala; Diewert; Kummel; Mundlak; Engineering production function; Multi-output; joint product; Data Envelopment; Household production function; Humbug production function; capital controversy; Cambridge controversy

NLINLS: a Differential Evolution based nonlinear least squares Fortran 77 program

This paper provides the list of Fortran 77 codes of nonlinear least squares using Differential Evolution as the minimizer algorithm. It has been tested on a number of difficult nonlinear least squares problems (taken from NIST, USA including CPC-X Software challenge problems). Help on how to use the program also is provided.Nonlinear least squares; Differential Evolution; Fortran 77

On construction of robust composite indices by linear aggregation

In this paper we construct thirteen different types of composite indices by linear combination of indicator variables (with and without outliers/data corruption). Weights of different indicator variables are obtained by maximization of the sum of squared (and, alternatively, absolute) correlation coefficients of the composite indices with the constituent indicator variables. Seven different types of correlation are used: Karl Pearson, Spearman, Signum, Bradley, Shevlyakov, Campbell and modified Campbell. Composite indices have also been constructed by maximization of the minimal correlation. We find that performance of indices based on robust measures of correlation such as modified Campbell and Spearman, as well as that of the maxi-min based method, is excellent. Using these methods we obtain composite indices that are autochthonously sensitive and allochthonously robust. This paper also justifies a use of simple mean-based composite indices, often used in construction of human development index.Composite index; linear aggregation; principal components; robust correlation; Spearman, Signum; Bradley; Shevlyakov; Campbell; Hampel; outliers; mutilation of data

Estimation under Multicollinearity: Application of Restricted Liu and Maximum Entropy Estimators to the Portland Cement Dataset

A high degree of multicollinearity among the explanatory variables severely impairs estimation of regression coefficients by the Ordinary Least Squares. Several methods have been suggested to ameliorate the deleterious effects of multicollinearity. In this paper we aim at comparing the Restricted Liu estimates of regression coefficients with those obtained by applying the Maximum Entropy Leuven (MEL) family of estimators on the widely analyzed dataset on Portland cement. This dataset has been obtained from an experimental investigation of the heat evolved during the setting and hardening of Portland cements of varied composition and the dependence of this heat on the percentage of four compounds in the clinkers from which the cement was produced. The relevance of the relationship between the heat evolved and the chemical processes undergone while setting takes place is best stated in the words of Woods et al.: "This property is of interest in the construction of massive works as dams, in which the great thickness severely hinder the outflow of the heat. The consequent rise in temperature while the cement is hardening may result in contractions and cracking when the eventual cooling to the surrounding temperature takes place." Two alternative models have been formulated, the one with an intercept term (non-homogenous) that exhibits a very high degree of multicollinearity and the other with no intercept term (extended homogenous) that characterizes perfect multicollinearity. Our findings suggest that several members of the MEL family of estimators outperform the OLS and the Restricted Liu estimators. The MEL estimators perform well even when perfect multicollinearity is there. A few of them may outperform the Minimum Norm LS (OLS+) estimator. Since the MEL estimators do not seek extra information from the analyst, they are easy to apply. Therefore, one may rely on the MEL estimators for obtaining the coefficients of a linear regression model under the conditions of severe (including perfect) multicollinearity among the explanatory variables.Multicollinearity; Estimator; Restricted Liu; Maximum Entropy Leuven estimator; MEL family; Modular Maximum Entropy Leuven estimator; Least Absolute Deviation; Minimum Norm Least Squares; Moore-Penrose inverse; Portland cement dataset

Repulsive Particle Swarm Method on Some Difficult Test Problems of Global Optimization

In this paper we test a particular variant of the (Repulsive) Particle Swarm method on some rather difficult global optimization problems. A number of these problems are collected from the extant literature and a few of them are newly introduced. First, we introduce the Particle Swarm method of global optimization and its variant called the 'Repulsive Particle Swarm' (RPS) method. Then we endow the particles with some stronger local search abilities - much like tunneling - so that each particle can make a search in its neighborhood to optimize itself. Next, we introduce the test problems, the existing as well as the new ones. We also give plots of some of these functions to help appreciation of the optimization problem. Finally, we present the results of the RPS optimization exercise and compare the results with those obtained by using the Genetic algorithm (GA)and/or Simulated annealing (SA) method. We append the (Fortran) computer program that we have developed and used in this exercise. Our findings indicate that neither the RPS nor the GA/SA method can assuredly find the optimum of an arbitrary function. In case of the Needle-eye and the Corana functions both methods perform equally well while in case of Bukin's 6th function both yield the values of decision variables far away from the right ones. In case of zero-sum function, GA performs better than the RPS. In case of the Perm #2 function, both of the methods fail when the dimension grows larger. In several cases, GA falters or fails while RPS succeeds. In case of N#1 through N#5 and the ANNs XOR functions the RPS performs better than the Genetic algorithm. It is needed that we find out some criteria to classify the problems that suit (or does not suit) a particular method. This classification will highlight the comparative advantages of using a particular method for dealing with a particular class of problems.Repulsive Particle Swarm; Global optimization; non-convex functions; Bounded rationality; local optima; Bukin; Corana; Rcos; Freudenstein Roth; Goldenstein Price; ANNs XOR; Perm; Power sum; Zero sum; Needle-eye; Genetic algorithms; variants; Fortran; computer program; benchmark; test

Median as a weighted arithmetic mean of all sample observations

It is generally held that median does not use all sample observations. However, median may be expressed as a weighted arithmetic mean of all sample observations. Some Monte Carlo studies have been conducted to show that the method works perfectly well.