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The Historicity of Economic Sciences: The Main Epistemological Ruptures
No full textThe object of this work is threefold: it consists (a) in explaining and justifying, based on Foucault's concept of episteme, the epistemological foundations from which Classical Economics, Keynesian Economics and Neoclassical Economics were built; (b) in studying the nature of the epistemological ruptures that allow differentiating these schools; and (c) in defining the degree of incommensurability of these different paradigms. In the first part, I will define the main epistemological tools that allow studying the birth and evolution of science. In the second part, I will study the nature of the epistemological ruptures that characterize these evolutions and these different schools
Étude comparative d'algorithmes d'apprentissage artificiel pour la reconnaissance faciale
No full textBackground: The fundamental need for authentication and identification of humans using their physiological, behavioral or biological characteristics, continues to be applied extensively to secure localities, property, financial transactions, etc. Biometric systems based on face characteristics, continue to attract the attention of researchers, major public and private services. In the literature, many methods have been deployed by different authors. The best performance must be found in order to be able to recommend the most effective method. So, the main objective of thisarticle is to make a comparative study of different existing techniques.Methods: A biometric system is generally composed of four stages: acquisition of facial images, preprocessing, extraction of characteristics and finally classification. In this work, the focus is on machine learning algorithms for classification. These algorithms are: Support Vector Machines (SVM), Artificial Neural Networks (ANN), K-Nearest Neighbors (KNN), Random Forests (RF), Logistic Regression (LR), Naive Bayesian Classification (NB: Naive Bayes’ Classifiers) and deep learning techniques such as Convolutional Neural Networks (CNN). The comparison criterion is the average performance, calculated using three performance measures: recognition rate, confusion matrix, and the Area Under Receiver Operating Characteristic (ROC) curve.Results: Based on this criterion, the performance comparison of selected machine learning algorithms, shows that CNN is the best, with an average performance of 100.00% On ORL face database. However, on the YALE database, classical algorithms such as artificial neural networks have obtained the best performances, the highest being a rate of 100%.Discussion: Deep learning techniques are very efficient in image classification as proven by the results on the ORL database. However, their inefficiency on YALE face database is due to the small size of this database which is inappropriate for some deep learning algorithms. But this weakness can be corrected by image augmentation techniques. The comparison of these results with existing state-of-the-art methods is nearly the same. Authors achieved performances of 94.82%, 95.79%, 96.15%, 96.44%, 97.27%, 98.52% and 98.95% for NB, KNN, RF, LR, ANN, SVM and CNN classifiers, respectively. Finally, in depth discussion, it is concluded that between all these approaches which are useful in face recognition, the CNN is the best classification algorithm
Variable binding and substitution for (nameless) dummies
No full textBy abstracting over well-known properties of De Bruijn's representation withnameless dummies, we design a new theory of syntax with variable binding andcapture-avoiding substitution. We propose it as a simpler alternative to Fiore,Plotkin, and Turi's approach, with which we establish a strong formal link. Wealso show that our theory easily incorporates simple types and equationsbetween terms
Agency, functionalism, and all that. A Sraffian view
No full textFormer contributions examined the approach to institutions and economic history that can be derived from the classical and Marxian 'surplus approach' as particularly recovered by Piero Sraffa (1951) and Pierangelo Garegnani (1960). The present paper deals with the allegation levelled against historical materialism-and consequently against the surplus approach to institutions-of organicism or functionalism. Organicism is said to look at individuals as passive vectors functionally serving in various capabilities the reproduction and destiny of society as a whole. In this way human agency in the operation and change of society is excluded or at least restrained. Methodological individualism is the traditional alternative supported both by neoclassical and by (some) Marxist schools. The literature over the 'agency versus structure' determination of human behaviour in social and human sciences is immense. I will therefore limit myself to some episodes that may however provide enough food for thought on this field. I shall defend a functionalist view of society while giving space to individual intentional action and aspirations, albeit informed by historical conditioning circumstances. Historical reconstruction of the objective and subjective features of the economic formations under examination, rather than the empty and a-historical study of individual choices, unrelated to the social context, looks like the way to go. Agency must be historically contextualised
Integrable maps in 4D and modified Volterra lattices
No full textIn recent work, we presented the construction of a family of differenceequations associated with the Stieltjes continued fraction expansion of acertain function on a hyperelliptic curve of genus . As well as proving thateach such discrete system is an integrable map in the Liouville sense, we alsoshowed it to be an algebraic completely integrable system. In the discretesetting, the latter means that the generic level set of the invariants is anaffine part of an abelian variety, in this case the Jacobian of thehyperelliptic curve, and each iteration of the map corresponds to a translationby a fixed vector on the Jacobian. In addition, we demonstrated that, bycombining the discrete integrable dynamics with the flow of one of thecommuting Hamiltonian vector fields, these maps provide genus algebro-geometric solutions of the infinite Volterra lattice, which justifiednaming them Volterra maps, denoted . The original motivation behind our work was the fact that, in the particularcase , we could recover an example of an integrable symplectic map in fourdimensions found by Gubbiotti, Joshi, Tran and Viallet, who classifiedbirational maps in 4D admitting two invariants (first integrals) with aparticular degree structure, by considering recurrences of fourth order with acertain symmetry. Hence, in this particular case, the map yieldsgenus two solutions of the Volterra lattice. The purpose of this note is topoint out how two of the other 4D integrable maps obtained in theclassification of Gubbiotti et al. correspond to genus two solutions of twodifferent forms of the modified Volterra lattice, being related via aMiura-type transformation to the Volterra map . We dedicate this work to a dear friend and colleague, Decio Levi
Sigma model instantons and singular tau function
No full textThe generating series for the instanton contribution to Green functions ofthe sigma model was found in the works of Schwarz, Fateev and Frolov. Weshow that this series can be written as a formal tau function of the two-sidedtwo-component KP hierarchy. We call it formal singular tau function becausethis tau function is a sum where each term is the infrared and ultravioletdivergent one exactly as the series found by the mentioned authors. However onecan regularize this singluar tau function and to obtain regular observables.This is because observables contains ratious of mentioned divergentexpressions. Thus, we enladge the families of tau functions to work with.Comment: 8 page
Deciding Equations in the Time Warp Algebra
No full textJoin-preserving maps on the discrete time scale , referred to astime warps, have been proposed as graded modalities that can be used toquantify the growth of information in the course of program execution. The setof time warps forms a simple distributive involutive residuated lattice --called the time warp algebra -- that is equipped with residual operationsrelevant to potential applications. In this paper, we show that although thetime warp algebra generates a variety that lacks the finite model property, itnevertheless has a decidable equational theory. We also describe animplementation of a procedure for deciding equations in this algebra, writtenin the OCaml programming language, that makes use of the Z3 theorem prover
A new discretization of the Euler equation via the finite operator theory
No full textWe propose a novel discretization procedure for the classical Euler equation, based on the theory of Galois differential algebras and the finite operator calculus developed by G.C. Rota and collaborators. This procedure allows us to define algorithmically a new discrete model which inherits from the continuous Euler equation a class of exact solutions
Conjectures analogous to the Collatz conjecture
No full textIn this paper we introduce some conjectures analogous to the well-known Collatz conjecture
B\"{a}cklund transformations as integrable discretization. The geometric approach
No full textWe present interpretation of known results in the theory of discreteasymptotic and discrete conjugate nets from the "discretization by B\"{a}cklundtransformations" point of view. We collect both classical formulas of XIXthcentury differential geometry of surfaces and their transformations, and morerecent results from geometric theory of integrable discrete equations. We firstpresent transformations of hyperbolic surfaces within the context of theMoutard equation and Weingarten congruences. The permutability property of thetransformations provides a way to construct integrable discrete analogs of theasymptotic nets for such surfaces. Then after presenting the theory ofconjugate nets and their transformations we apply the principle thatB\"{a}cklund transformations provide integrable discretization to obtain knownresults on the discrete conjugate nets. The same approach gives, via theRibaucour transformations, discrete integrable analogs of orthogonal conjugatenets.Comment: 18 pages, 4 figures; dedication added, typos corrected (v2). This article is part of an OCNMP Special Issue in Memory of Professor Decio Lev