In the field of economic analysis, computability in the formation of economic hypotheses is seen as the way forward. In this book, Professor Velupillai implements a theoretical research program along these lines. Choice theory, learning rational expectations equlibria, the persistence of adaptive behaviour, arithmetical games, aspects of production theory, and economic dynamics are given recursion theoretic interpretations. These interpretations lead to new kinds of questions being posed by the economic theorist. In particular, recurison theoretic decision problems replace standard optimisation (...) paradigms in economic analysis. Economic theoretic questions, posed recursion-theoretically, lead to answers that are ambiguous: undecidable choices, uncomputable learning processes, and algorithmically unplayable games become standard answers. Professor Velupillai argues that a recursion theoretic formalisation of economic analysisComputable Economicsmakes the subject intrinsically inductive and computational. (shrink)

First published in 2013. Routledge is an imprint of Taylor & Francis, an informa company.

The New Economic Windows Series, derived from Massimo Salzano's ideas and work, incorporates material from textbooks, monographs and conference proceedings that deals with both the theoretical and applied aspects of various sub-disciplines ...

The book contains thirty original articles dealing with important aspects of theoretical as well as applied economic theory. While the principal focus is on: the computational and algorithmic nature of economic dynamics; individual as well as collective decision process and rational behavior, some contributions emphasize also the importance of classical recursion theory and constructive mathematics for dynamical systems, business cycles theories, growth theories, and others are in the area of history of thought, methodology and behavioural economics. The contributors range from (...) Nobel Laureates to the promising new generation of innovative thinkers. This volume is also a Festschrift in honour of Professor Kumaraswamy Vela Velupillai, the founder of Computable Economics, a growing field of research where important results stemming from classical recursion theory and constructive mathematics are applied to economic theory. The aim and hope is to provide new tools for economic modelling. This book will be of particular appeal to postgraduate students and scholars in one or more of the following fields: computable economics, business cycles, macroeconomics, growth theories, methodology, behavioural economics, financial economics, experimental and agent based economics. It might be also of importance to those interested on the general theme of algorithmic foundations for social sciences. (shrink)

Computation and Simulation have always played a role in economics – whether it be pure economic theory or any variant of applied, especially policy-oriented, macro- and microeconomics or what has increasingly come to be called empirical or experimental economics. Computations and simulations are also intrinsically dynamic. This triptych – computation, simulation and dynamic – is given natural foundations, mainly as a result of developments in the mathematics underpinnings in the potentials of computing, using digital technology. A running theme in this (...) essay is the recognition that, increasingly, the development of economic theory seems to go hand in hand with advances in the theory and practice of computing, which is, in turn, a catalyst for the move away from too much reliance on any kind of mathematics for the formalisation of economic entities that is inconsistent with the mathematical, methodological and epistemological foundations of the theory of computation. (shrink)

This article introduces the notion of duplex elements of the finite rings and corresponding neutrosophic rings. The authors establish duplex ring Dup(R) and neutrosophic duplex ring Dup(R)I)) by way of various illustrations. The tables of different duplicities are constructed to reveal the comparison between rings Dup(Zn), Dup(Dup(Zn)) and Dup(Dup(Dup(Zn ))) for the cyclic ring Zn . The proposed duplicity structures have several algebraic systems with dissimilar consequences. Author’s characterize finite rings with R + R is different from the duplex ring (...) Dup(R). However, this characterization supports that R + R = Dup(R) for some well known rings, namely zero rings and finite fields. (shrink)

Speaker recognition under mismatched conditions is a challenging task. Speech signal is nonlinear and nonstationary, and therefore, difficult to analyze under realistic conditions. Also, in real conditions, the nature of the noise present in speech data is not known a priori. In such cases, the performance of speaker identification or speaker verification degrades considerably under realistic conditions. Any SR system uses a voice activity detector as the front-end subsystem of the whole system. The performance of most VADs deteriorates at the (...) front end of the SR task or system under degraded conditions or in realistic conditions where noise plays a major role. Recently, speech data analysis and processing using Norden E. Huang’s empirical mode decomposition combined with Hilbert transform, commonly referred to as Hilbert–Huang transform, has become an emerging trend. EMD is an a posteriori, adaptive, data analysis tool used in time domain that is widely accepted by the research community. Recently, speech data analysis and speech data processing for speech recognition and SR tasks using EMD have been increasing. EMD-based VAD has become an important adaptive subsystem of the SR system that mostly mitigates the effect of mismatch between the training and the testing phase. Recently, we have developed a VAD algorithm using a zero-frequency filter-assisted peaking resonator and EMD. In this article, the efficacy of an EMD-based VAD algorithm is studied at the front end of a text-independent language-independent SI task for the speaker’s data collected in three languages at five different places, such as home, street, laboratory, college campus, and restaurant, under realistic conditions using EDIROL-R09 HR, a 24-bit wav/mp3 recorder. The performance of this proposed SI task is compared against the traditional energy-based VAD in terms of percentage identification rate. In both cases, widely accepted Mel frequency cepstral coefficients are computed by employing frame processing from the extracted voiced speech regions using the respective VAD techniques from the realistic speech utterances, and are used as a feature vector for speaker modeling using popular Gaussian mixture models. The experimental results showed that the proposed SI task with the VAD algorithm using ZFFPR and EMD at its front end performs better than the SI task with short-term energy-based VAD when used at its front end, and is somewhat encouraging. (shrink)

. Speaker recognition has been an active research area for many years. Methods to represent and quantify information embedded in speech signal are termed as features of the signal. The features are obtained, modeled and stored for further reference when the system is to be tested. Decision whether to accept or reject speakers are taken based on parameters of the data modeling techniques. Real world offers various degradations to the signal that hamper the signal quality. The degradations may be due (...) to ambient background noise, reverberation or multispeaker scenario. This paper presents a survey of various feature extraction, data modeling methods, metrics that are used to take the decisions and methods that can be used to preprocess the degraded data that have been used to perform the task of speaker recognition. (shrink)

This article presents an overview of the single-channel dereverberation methods suitable for distant speech recognition application. The dereverberation methods are mainly classified based on the domain of enhancement of speech signal captured by a distant microphone. Many single-channel speech enhancement methods focus on either denoising or dereverberating the distorted speech signal. There are very few methods that consider both noise and reverberation effects. Such methods are discussed under a multistage approach in this article. The article concludes with a hypothesis that (...) the methods that do not require an a priori reverberation impulse response is desirable in varying the environmental conditions for DSR applications such as intelligent home and office environments, humanoid robots, and automobiles rather than the methods that require an a priori reverberation impulse response. (shrink)

The performance of most of the state-of-the-art speaker recognition systems deteriorates under degraded conditions, owing to mismatch between the training and testing sessions. This study focuses on the front end of the speaker verification system to reduce the mismatch between training and testing. An adaptive voice activity detection algorithm using zero-frequency filter assisted peaking resonator was integrated into the front end of the SV system. The performance of this proposed SV system was studied under degraded conditions with 50 selected speakers (...) from the NIST 2003 database. The degraded condition was simulated by adding different types of noises to the original speech utterances. The different types of noises were chosen from the NOISEX-92 database to simulate degraded conditions at signal-to-noise ratio levels from 0 to 20 dB. In this study, widely used 39-dimension Mel frequency cepstral coefficient features were used, and Gaussian mixture model–universal background model was used for speaker modeling. The proposed system’s performance was studied against the energy-based VAD used as the front end of the SV system. The proposed SV system showed some encouraging results when EMD-based VAD was used at its front end. (shrink)

In this article, a new adaptive data-driven strategy for voice activity detection using empirical mode decomposition is proposed. Speech data are decomposed using an a posteriori, adaptive, data-driven EMD in the time domain to yield a set of physically meaningful intrinsic mode functions. Each IMF preserves the nonlinear and nonstationary property of the speech utterance. Among a set of IMFs, the IMF that contains source information dominantly called characteristic IMF can be identified and extracted by designing a zero-frequency filter-assisted peaking (...) resonator. The detected CIMF is used to compute energy using short-term processing. Choosing proper threshold, voiced regions in speech utterances are detected using frame energy. The proposed framework has been studied on both clean speech utterance and noisy speech utterance. The proposed method is used for voice activity detection in the presence of white noise and shows encouraging result in the presence of white noise up to 0 dB. (shrink)

Jean-Paul Fitoussi needs no introduction as one of the world's foremost Macroeconomists of his generation. This celebration of his work includes contributions from Nobel Prize - winning economists Robert W. Clower and Robert Solow as well as Olivier Blanchard and leading economic theorist, Edmond Malinvaud.

Kumaraswamy Vela Velupillai [74] presents a constructivist perspective on the foundations of mathematical economics, praising the views of Feynman in developing path integrals and Dirac in developing the delta function. He sees their approach as consistent with the Bishop constructive mathematics and considers its view on the Bolzano-Weierstrass, Hahn-Banach, and intermediate value theorems, and then the implications of these arguments for such “crown jewels” of mathematical economics as the existence of general equilibrium and the second welfare theorem. He also (...) relates these ideas to the weakening of certain assumptions to allow for more general results as shown by Rosser [51] in his extension of Gödel’s incompleteness theorem in his opening section. This paper considers these arguments in reverse order, moving from the matters of economics applications to the broader issue of constructivist mathematics, concluding by considering the views of Rosser on these matters, drawing both on his writings and on personal conversations with him. (shrink)

Due to the advance computer technology, the use of probability distributions has been raised up to solve the real life problems. These applications are found in reliability engineering, computer sciences, economics, psychology, survival analysis, and some others. This study offers a new probability model called Marshall–Olkin Extended Gumbel Type-II which can model various shapes of the failure rate function. The proposed distribution is capable to model increasing, decreasing, reverse J-shaped, and upside down bathtub shapes of the failure rate function. Various (...) statistical properties of the proposed distribution are derived such as alternate expressions for the density and distribution function, special cases of MOEGT-II distribution, quantile function, Lorenz curve, and Bonferroni curve. Estimation of the unknown parameters is carried out by the method of maximum likelihood. A simulation study is conducted using three different iterative methods with different samples of sizes n. The usefulness and potentiality of the MOEGT-II distribution have been shown using three real life data sets. The MOEGT-II distribution has been demonstrated as better fit than Exponentiated Gumbel Type-II, Marshall–Olkin Gumbel Type-II, Gumbel Type-II, Marshall–Olkin–Frechet, Frechet, Burr III, Log Logistic, Beta Inverse Weibull, and Kumaraswamy Inverse Weibull distributions. (shrink)

“The ‘fallacy of composition’ that drives a felicitous wedge between micro and macro, between the individual and the aggregate, and gives rise to emergent phenomena in economics, non-algorithmic ways – as conjectured originally by John Stuart Mill…, George Herbert Lewes … , and codified by Lloyd Morgan … in his popular Gifford Lectures - may yet be tamed by unconventional models of computation.” --K. Vela Velupillai (2008, p. 21).