scholarly journals Mathematical Structure and Empirical Content

2021 ◽  
Author(s):  
Michael E Miller
Keyword(s):  
Mathematical Structure ◽  
Empirical Content

The Empirical Content of Adaptive Models

2004 ◽  
Author(s):  
Jon Bendor ◽  
Daniel Diermeier ◽  
Michael M. Ting
Keyword(s):  
Empirical Content ◽  
Adaptive Models

La otredad: ¿real o inventada? El caso de las brujas

1999 ◽  
pp. 21-33
Author(s):  
Elia Nathan Bravo
Keyword(s):  
Early Modern ◽  
Social Inequalities ◽  
Strict Sense ◽  
Empirical Content ◽  
Extreme Situation ◽  
Modern Times ◽  
The Witch ◽  
Early Modern Times ◽  
The One ◽  
In Virtue Of

The purpose of this paper is two-fold. On the one hand, it offers a general analysis of stigmas (a person has one when, in virtue of its belonging to a certain group, such as that of women, homosexuals, etc., he or she is subjugated or persecuted). On the other hand, I argue that stigmas are “invented”. More precisely, I claim that they are not descriptive of real inequalities. Rather, they are socially created, or invented in a lax sense, in so far as the real differences to which they refer are socially valued or construed as negative, and used to justify social inequalities (that is, the placing of a person in the lower positions within an economic, cultural, etc., hierarchy), or persecutions. Finally, I argue that in some cases, such as that of the witch persecution of the early modern times, we find the extreme situation in which a stigma was invented in the strict sense of the word, that is, it does not have any empirical content.

The Inner Rational Agent

2018 ◽  
Author(s):  
Robert Sugden
Keyword(s):  
Human Agency ◽  
Welfare Economics ◽  
Rational Agent ◽  
Empirical Content ◽  
Normative Economics ◽  
Normative Analysis ◽  
True Preference ◽  
Implicit Model ◽  
The World ◽  
Psychological Foundation

Chapter 4 reviews ‘behavioural welfare economics’—the approach to normative analysis that is favoured by most behavioural economists. This approach assumes that people have context-independent ‘true’ or ‘latent’ preferences which, because of psychologically-induced errors, are not always revealed in actual choices. Behavioural welfare economics aims to reconstruct latent preferences by identifying and removing the effects of error on decisions, and to design policies to satisfy those preferences. Its implicit model of human agency is of an ‘inner rational agent’ that interacts with the world through an imperfect psychological ‘shell’. I argue that there is no satisfactory evidence to support this model, and no credible psychological foundation for it. Since the concept of true preference has no empirical content, the idea that such preferences can be reconstructed is a mirage. Normative economics needs to be more radical in giving up rationality assumptions.

scholarly journals Understanding mathematics of Grover’s algorithm

2021 ◽  
Vol 20 (5) ◽  
Author(s):  
Paweł J. Szabłowski
Keyword(s):  
Phase Change ◽  
Unitary Operator ◽  
Mathematical Structure ◽  
Complex Numbers ◽  
Unitary Operators ◽  
Grover’S Algorithm ◽  
Great Probability ◽  
Grover's Algorithm ◽  
One Step ◽  
The One

AbstractWe analyze the mathematical structure of the classical Grover’s algorithm and put it within the framework of linear algebra over the complex numbers. We also generalize it in the sense, that we are seeking not the one ‘chosen’ element (sometimes called a ‘solution’) of the dataset, but a set of m such ‘chosen’ elements (out of $$n>m)$$ n > m ) . Besides, we do not assume that the so-called initial superposition is uniform. We assume also that we have at our disposal an oracle that ‘marks,’ by a suitable phase change $$\varphi $$ φ , all these ‘chosen’ elements. In the first part of the paper, we construct a unique unitary operator that selects all ‘chosen’ elements in one step. The constructed operator is uniquely defined by the numbers $$\varphi $$ φ and $$\alpha $$ α which is a certain function of the coefficients of the initial superposition. Moreover, it is in the form of a composition of two so-called reflections. The result is purely theoretical since the phase change required to reach this heavily depends on $$\alpha $$ α . In the second part, we construct unitary operators having a form of composition of two or more reflections (generalizing the constructed operator) given the set of orthogonal versors. We find properties of these operations, in particular, their compositions. Further, by considering a fixed, ‘convenient’ phase change $$\varphi ,$$ φ , and by sequentially applying the so-constructed operator, we find the number of steps to find these ‘chosen’ elements with great probability. We apply this knowledge to study the generalizations of Grover’s algorithm ($$m=1,\phi =\pi $$ m = 1 , ϕ = π ), which are of the form, the found previously, unitary operators.

scholarly journals Universal Synthesizer of Mueller Matrices Based on the Symmetry Properties of the Enpolarizing Ellipsoid

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 983
Author(s):  
José J. Gil ◽  
Ignacio San José
Keyword(s):  
Mathematical Structure ◽  
Mueller Matrix ◽  
Morphological Properties ◽  
Nondestructive Analysis ◽  
Structural Decomposition ◽  
Symmetry Properties ◽  
Mueller Matrices ◽  
Scattering Measurement ◽  
The Way

Polarimetry is today a widely used and powerful tool for nondestructive analysis of the structural and morphological properties of a great variety of material samples, including aerosols and hydrosols, among many others. For each given scattering measurement configuration, absolute Mueller polarimeters provide the most complete polarimetric information, intricately encoded in the 16 parameters of the corresponding Mueller matrix. Thus, the determination of the mathematical structure of the polarimetric information contained in a Mueller matrix constitutes a topic of great interest. In this work, besides a structural decomposition that makes explicit the role played by the diattenuation-polarizance of a general depolarizing medium, a universal synthesizer of Muller matrices is developed. This is based on the concept of an enpolarizing ellipsoid, whose symmetry features are directly linked to the way in which the polarimetric information is organized.

scholarly journals A new variational approach for the thermodynamic topology optimization of hyperelastic structures

2020 ◽  
Author(s):  
Philipp Junker ◽  
Daniel Balzani
Keyword(s):  
Topology Optimization ◽  
Variational Approach ◽  
Large Deformations ◽  
Mathematical Structure ◽  
Detailed Model ◽  
Novel Approach ◽  
Extremal Principles ◽  
Model Derivation ◽  
Numerical Discretization ◽  
Total Structure

AbstractWe present a novel approach to topology optimization based on thermodynamic extremal principles. This approach comprises three advantages: (1) it is valid for arbitrary hyperelastic material formulations while avoiding artificial procedures that were necessary in our previous approaches for topology optimization based on thermodynamic principles; (2) the important constraints of bounded relative density and total structure volume are fulfilled analytically which simplifies the numerical implementation significantly; (3) it possesses a mathematical structure that allows for a variety of numerical procedures to solve the problem of topology optimization without distinct optimization routines. We present a detailed model derivation including the chosen numerical discretization and show the validity of the approach by simulating two boundary value problems with large deformations.

scholarly journals The dissipative approach to quantum field theory: conceptual foundations and ontological implications

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Andrea Oldofredi ◽  
Hans Christian Öttinger
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Nonequilibrium Thermodynamics ◽  
Particle Creation ◽  
Mathematical Structure ◽  
Alternative Formulation ◽  
Quantum Field ◽  
Conceptual Foundations ◽  
Particle Creation And Annihilation

AbstractMany attempts have been made to provide Quantum Field Theory with conceptually clear and mathematically rigorous foundations; remarkable examples are the Bohmian and the algebraic perspectives respectively. In this essay we introduce the dissipative approach to QFT, a new alternative formulation of the theory explaining the phenomena of particle creation and annihilation starting from nonequilibrium thermodynamics. It is shown that DQFT presents a rigorous mathematical structure, and a clear particle ontology, taking the best from the mentioned perspectives. Finally, after the discussion of its principal implications and consequences, we compare it with the main Bohmian QFTs implementing a particle ontology.

Fundamentals of generalized rigidity matrices for multi-layered media

1983 ◽  
Vol 73 (3) ◽  
pp. 749-763
Author(s):  
Maurice A. Biot
Keyword(s):  
Plane Strain ◽  
Initial Stress ◽  
Three Dimensional ◽  
Layered Media ◽  
Mathematical Structure ◽  
Irreversible Thermodynamics ◽  
Initial Stresses ◽  
General Context ◽  
Viscoelastic Media ◽  
Linear Irreversible Thermodynamics

abstract Rigidity matrices for multi-layered media are derived for isotropic and orthotropic layers by a simple direct procedure which brings to light their fundamental mathematical structure. The method was introduced many years ago by the author in the more general context of dynamics and stability of multi-layers under initial stress. Other earlier results are also briefly recalled such as the derivation of three-dimensional solutions from plane strain modes, the effect of initial stresses, gravity, and couple stresses for thinly laminated layers. The extension of the same mathematical structure and symmetry to viscoelastic media is valid as a consequence of fundamental principles in linear irreversible thermodynamics.

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