Institutions

About Us

Help

Gaeilge
0
1000
Home
Browse
Advanced Search
Search History
Marked List
Statistics
A
A
A
Author(s)
Institution
Publication types
Funder
Year
Limited By:
Author = Velupillai, K. Vela;
8 items found
Sort by
Title
Author
Item type
Date
Institution
Peer review status
Language
Order
Ascending
Descending
25
50
100
per page
Bibtex
CSV
EndNote
RefWorks
RIS
XML
Displaying Results 1  8 of 8 on page 1 of 1
Marked
Mark
A Stochastic Complexity Perspective of Induction in Economics and Inference in Dynamics
(2010)
Velupillai, K. Vela
A Stochastic Complexity Perspective of Induction in Economics and Inference in Dynamics
(2010)
Velupillai, K. Vela
Abstract:
Rissanen's fertile and pioneering minimum description length principle (MDL) has been viewed from the point of view of statistical estimation theory, information theory, as stochastic complexity theory  i.e., a computable approximation of Kolomogorov Complexity  or Solomonoff's recursion theoretic induction principle or as analogous to Kolmogorov's sufficient statistics. All these  and many more  interpretations are valid, interesting and fertile. In this paper I view it from two points of view: those of an algorithmic economist and a dynamical system theorist. From these points of view I suggest, first, a recasting of Jevon's sceptical vision of induction in the light of MDL; and a complexity interpretation of an undecidable question in dynamics.
http://hdl.handle.net/10379/984
Marked
Mark
Advanced Computational Complexity Theory from an Elementary Standpoint
(2010)
Velupillai, K. Vela
Advanced Computational Complexity Theory from an Elementary Standpoint
(2010)
Velupillai, K. Vela
Abstract:
A computable economist's view of the world of computational complexity theory is described. This means the model of computation underpinning theories of computational complexity plays a central role. The emergence of computational complexity theories from diverse traditions is emphasised. The unifications that emerged in the modern era was codified by means of the notions of efficiency of computations, nondeterministric computations, completeness, reducibility and verifiability  all three of the latter concepts had their origins on what may be called 'Post's Program for Research for Higher Recursion Theory'. The recent real model of computation as a basis for studying computational complexity in the domain of the reals is also presented and discussed, albeit critically. A brief sceptical section on algorithmic complexity theory is included in an appendix.
http://hdl.handle.net/10379/952
Marked
Mark
Production of Commodities by Means of Commodities in a Mathematical Mode
(2010)
Velupillai, K. Vela
Production of Commodities by Means of Commodities in a Mathematical Mode
(2010)
Velupillai, K. Vela
Abstract:
The claim in this paper is that Sraffa employed a rigorous logic of mathematical reasoning in his book, Production of Commodities by Means of Commodities (PCC), in such a mode that all existence proofs were constructive. This is the kind of mathematics that was prevalent at the beginning of the 19th century, which was dominated by the concrete, the constructive and the algorithmic. It is, therefore, completely consistent with the economics of the 19th century, which was the fulcrum around which the economics of PCC is centred.
http://hdl.handle.net/10379/1073
Marked
Mark
Rereading Jevons's Principles of ScienceInduction Redux
(2010)
Velupillai, K. Vela
Rereading Jevons's Principles of ScienceInduction Redux
(2010)
Velupillai, K. Vela
Abstract:
In this paper I try to substantiate the thesis that Jevons may have been too harsh on the vices of induction and generously optimistic about the virtues of deduction, as discussed, primarily, in his magnum opus, The Principles of Science. With this aim in mind the paper attempts to suggest (modern), recursion theoretic, theoretical technologies that could reduce and, under conditions that I claim would be acceptable to Jevons, even eliminate the inductive indeterminacies that he had emphasised.
http://hdl.handle.net/10379/981
Marked
Mark
Reappraising FixPoint Formalizations of Rational Expectations Equilibria
(2010)
Velupillai, K. Vela
Reappraising FixPoint Formalizations of Rational Expectations Equilibria
(2010)
Velupillai, K. Vela
Abstract:
The paper begins with a brief introduction to the origins of the tradition of formalizing the determination of a rational expectations equilibrium using topological fix points. It is then suggested that fidelity to the twin economic conceptual bases of rational expectations  selfreference and infinite regress  are not encapsulated in the topological formalism. To remedy this defect, a recursion theoretic formalism for modelling rational expectations equilibria is developed.
http://hdl.handle.net/10379/1104
Marked
Mark
Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics
(2010)
Velupillai, K. Vela
Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics
(2010)
Velupillai, K. Vela
Abstract:
It is natural to claim, as I do in this paper, that the emergence of nonconstructivities in economics is entirely due to the formalizations of economics by means of 'classical' mathematics. I have made similar claims for the emergence of uncomputabilities and undecidabilities in economics in earlier writings. Here, on the other hand, I want to suggest a way of confronting uncomputabilities, and remedying nonconstructivities, in economics, and turning them into a positive force for modelling, for example, endogenous growth, as suggested by Stefano Zambelli. In between, a case is made for economics to take seriously the kind of mathematical modelling fostered by Feynman and Dirac, in particular the way they developed the path integral and the ? function, respectively. A sketch of a 'research program' in mathematical economics, analogous to the way GÃ¶del thought incompleteness and its perplexities should be interpreted and resolved, is also outlined in the concl...
http://hdl.handle.net/10379/982
Marked
Mark
Variations on the Theme of Conning in Mathematical Economics
(2010)
Velupillai, K. Vela
Variations on the Theme of Conning in Mathematical Economics
(2010)
Velupillai, K. Vela
Abstract:
The mathematization of economics is almost exclusively in terms of the mathematics of real analysis which, in turn, is founded on set theory (and the axiom of choice) and orthodox mathematical logic. In this paper I try to point out that this kind of mathematization is replete with economic infelicities. The attempt to extract these infelicities is in terms of three main examples: dynamics, policy and rational expectations and learning. The focus is on the role and reliance on standard fixed point theorems in orthodox mathematical economics.
http://hdl.handle.net/10379/1070
Marked
Mark
Varieties of Mathematics in Economics
(2009)
Velupillai, K. Vela
Varieties of Mathematics in Economics
(2009)
Velupillai, K. Vela
Abstract:
Real analysis, founded on the ZermeloFraenkel axioms, buttressed by the axiom of choice, is the dominant variety of mathematics utilized in the formalization of economic theory. The accident of history that led to this dominance is not inevitable, especially in an age when the digital computer seems to be ubiquitous in research, teaching and learning. At least three other varieties of mathematics have come to be used in the formalization of mathematics in more recent years. These other varieties, I claim, are more consistent with the intrinsic nature and ontology of economic concepts. In this paper I discuss aspects of the way real analysis dominates the mathematical formalizations of economic theory and the prospects for overcoming this dominance.
http://hdl.handle.net/10379/328
Displaying Results 1  8 of 8 on page 1 of 1
Bibtex
CSV
EndNote
RefWorks
RIS
XML
Year
2010 (7)
2009 (1)
built by Enovation Solutions