Quantum Markov Model for Data from Shafir-Tversky Experiments in Cognitive Psychology

2009 ◽  
Vol 16 (04) ◽  
pp. 371-385 ◽  
Author(s):  
Luigi Accardi ◽  
Andrei Khrennikov ◽  
Masanori Ohya
Keyword(s):  
Cognitive Psychology ◽  
Markov Model ◽  
Detailed Balance ◽  
Quantum Probability ◽  
Point Of View ◽  
Von Neumann ◽  
Detailed Balance Condition ◽  
Psychology And Economics ◽  
Sure Thing Principle ◽  
Neumann Model

We analyze, from the point of view of quantum probability, statistical data from two interesting experiments, done by Shafir and Tversky [1, 2] in the domain of cognitive psychology. These are gambling experiments of Prisoner Dilemma type. They have important consequences for economics, especially for the justification of the Savage "Sure Thing Principle" [3] (implying that agents of the market behave rationally). Data from these experiments were astonishing, both from the viewpoint of cognitive psychology and economics and probability theory. Players behaved irrationally. Moreover, all attempts to generate these data by using classical Markov model were unsuccessful. In this note we show (by inventing a simple statistical test — generalized detailed balance condition) that these data are non-Kolmogorovian. We also show that it is neither quantum (i.e., it cannot be described by Dirac-von Neumann model). We proceed towards a quantum Markov model for these data.

scholarly journals INTRODUCTION TO THE SPECIAL ISSUE OF ECONOMICS AND PHILOSOPHY ON AMBIGUITY AVERSION

2009 ◽  
Vol 25 (3) ◽  
pp. 247-248 ◽  
Author(s):  
Giacomo Bonanno ◽  
Martin van Hees ◽  
Christian List ◽  
Bertil Tungodden
Keyword(s):  
Decision Making ◽  
Expected Utility ◽  
Ambiguity Aversion ◽  
Point Of View ◽  
Special Issue ◽  
Von Neumann ◽  
Descriptive Theory ◽  
Sure Thing Principle ◽  
New Literature ◽  
Theoretical Side

The paradigm for modelling decision-making under uncertainty has undoubtedly been the theory of Expected Utility, which was first developed by von Neumann and Morgenstern (1944) and later extended by Savage (1954) to the case of subjective uncertainty. The inadequacy of the theory of Subjective Expected Utility (SEU) as a descriptive theory was soon pointed out in experiments, most famously by Allais (1953) and Ellsberg (1961). The observed departures from SEU noticed by Allais and Ellsberg became known as “paradoxes”. The Ellsberg paradox gave rise, several years later, to a new literature on decision-making under ambiguity. The theoretical side of this literature was pioneered by Schmeidler (1989). This literature views the departures from SEU in situations similar to those discussed by Ellsberg as rational responses to ambiguity. The rationality is “recovered” by relaxing Savage's Sure-Thing principle and adding an ambiguity-aversion postulate. Thus the ambiguity-aversion literature takes a normative point of view and does consider Ellsberg-type choices as behavioural “anomalies”.

A Wasserstein-type Distance to Measure Deviation from Equilibrium of Quantum Markov Semigroups

2013 ◽  
Vol 20 (02) ◽  
pp. 1350009 ◽  
Author(s):  
Julián Agredo
Keyword(s):  
Von Neumann Algebra ◽  
Separable Hilbert Space ◽  
Optimal Transport ◽  
Detailed Balance ◽  
Wasserstein Distance ◽  
Markov Semigroup ◽  
Bounded Operators ◽  
Von Neumann ◽  
Detailed Balance Condition ◽  
Quantum Markov Semigroup

In this paper we define a distance W between states in the non-commutative von Neumann algebra [Formula: see text] of bounded operators on a separable Hilbert space [Formula: see text], in order to measure deviations from equilibrium using a rate ep W(·). The restriction of W to the diagonal subalgebra of [Formula: see text] coincides with the Wasserstein distance used in optimal transport. Moreover, if ρ is a normal invariant state of a quantum Markov semigroup [Formula: see text], then ep W(ρ) = 0 if and only if a detailed balance condition holds.

On the validity of hilbert's nullstellensatz, artin's theorem, and related results in grothendieck toposes

1988 ◽  
Vol 53 (4) ◽  
pp. 1177-1187
Author(s):  
W. A. MacCaull
Keyword(s):  
Intuitionistic Logic ◽  
Main Idea ◽  
Rational Functions ◽  
Completeness Theorem ◽  
Point Of View ◽  
Polynomial Rings ◽  
Von Neumann ◽  
Ordered Fields ◽  
Von Neumann Regular ◽  
Theoretic Point

Using formally intuitionistic logic coupled with infinitary logic and the completeness theorem for coherent logic, we establish the validity, in Grothendieck toposes, of a number of well-known, classically valid theorems about fields and ordered fields. Classically, these theorems have proofs by contradiction and most involve higher order notions. Here, the theorems are each given a first-order formulation, and this form of the theorem is then deduced using coherent or formally intuitionistic logic. This immediately implies their validity in arbitrary Grothendieck toposes. The main idea throughout is to use coherent theories and, whenever possible, find coherent formulations of formulas which then allow us to call upon the completeness theorem of coherent logic. In one place, the positive model-completeness of the relevant theory is used to find the necessary coherent formulas.The theorems here deal with polynomials or rational functions (in s indeterminates) over fields. A polynomial over a field can, of course, be represented by a finite string of field elements, and a rational function can be represented by a pair of strings of field elements. We chose the approach whereby results on polynomial rings are reduced to results about the base field, because the theory of polynomial rings in s indeterminates over fields, although coherent, is less desirable from a model-theoretic point of view. Ultimately we are interested in the models.This research was originally motivated by the works of Saracino and Weispfenning [SW], van den Dries [Dr], and Bunge [Bu], each of whom generalized some theorems from algebraic geometry or ordered fields to (commutative, von Neumann) regular rings (with unity).

The problem of measuring the quantity of output in the input–output model by W. Leontief in modeling the trends in economic reproduction of nations and regions

2021 ◽  
Vol 19 (8) ◽  
pp. 1568-1592
Author(s):  
Nikolai I. KURYSHEV
Keyword(s):  
Input Output ◽  
Von Neumann ◽  
Output Matrix ◽  
Production And Consumption ◽  
Production Quantity ◽  
Mathematical Analyses ◽  
Neumann Model ◽  
Product Output ◽  
The Relationship ◽  
Cost Characteristics

Subject. This article deals with the problem of constructing a Leontief's input–output matrix. Objectives. The article aims to determine the rules for constructing a Leontief's input–output matrix on the basis of data on production time and quantity of product output. Methods. For the study, I used the methods of logical and mathematical analyses. Results. The article formulates the rules for constructing a Leontief's input–output matrix, taking into account differences in the time of production, quantity of output, as well as the conditions for the reproduction of the resources expended. It summarizes these rules for the J. von Neumann model. Conclusions. The proposed approach to the analysis of the material mechanism of economic reproduction defines the relationship between the quantitative and cost characteristics of the production and consumption of products and resources. This relationship opens up new opportunities for the application of input–output models to create simple and accurate algorithms for identifying and predicting the macroeconomic trends.

What is a “difficult poem”? Towards a definition

2008 ◽  
Vol 37 (2) ◽  
Author(s):  
Iris Yaron
Keyword(s):  
Cognitive Psychology ◽  
Text Comprehension ◽  
Point Of View ◽  
Modern Poetry ◽  
Communicative Acts ◽  
The Subject ◽  
Poetic Texts ◽  
The One ◽  
The Way

AbstractModern poetry developed and transformed difficulty into a prominent aesthetic norm of poetry. The abundance of difficult poetic texts necessitates a study of the corpus. After differentiating between the way difficulty is perceived in poetry and in other communicative acts, I present the approach that I have adopted for the purpose of studying difficult poetry. In contrast to other studies which have examined difficulty from the author's perspective and, as a consequence, described factors that cause textual difficulty, I propose to examine the subject from the reader's point of view. The reader, after all, is the one who feels or does not feel the difficulty. The concept ‘difficult poem’ is necessarily interdisciplinary and the question of what is “difficult” involves cognitive psychology and its models of text comprehension. Following a discussion of these domains, I present the “definition” that I propose for the ‘difficult poem’.

scholarly journals Revisit on the thermodynamic stability of Hořava–Lifshitz black hole

2018 ◽  
Vol 27 (04) ◽  
pp. 1850048
Author(s):  
Xudong Meng ◽  
Ruihong Wang
Keyword(s):  
Black Hole ◽  
Thermodynamic Properties ◽  
Thermodynamic Stability ◽  
Detailed Balance ◽  
De Sitter ◽  
Thermodynamic Variable ◽  
Detailed Balance Condition ◽  
First Law Of Thermodynamics ◽  
Balance Condition ◽  
Lifshitz Black Hole

We study the thermodynamic properties of the black hole derived in Hořava–Lifshitz (HL) gravity without the detailed-balance condition. The parameter [Formula: see text] in the HL black hole plays the same role as that of the electric charge in the Reissner–Nordström-anti-de Sitter (RN-AdS) black hole. By analogy, we treat the parameter [Formula: see text] as the thermodynamic variable and obtain the first law of thermodynamics for the HL black hole. Although the HL black hole and the RN-AdS black hole have the similar mass and temperature, due to their very different entropy, the two black holes have very different thermodynamic properties. By calculating the heat capacity and the free energy, we analyze the thermodynamic stability of the HL black hole.

The First Generation of Computers

2019 ◽  
pp. 117-142
Author(s):  
Giuseppe Primiero
Keyword(s):  
First Generation ◽  
Point Of View ◽  
Historical Evolution ◽  
Universal Model ◽  
Von Neumann ◽  
Model Of Computation ◽  
Von Neumann Architecture

This chapter starts with the analysis of the engineering foundation of computing which, proceeding in parallelwith themathematical foundation, led to the design and creation of physical computingmachines. It illustrates the historical evolution of the first generation of computing and their technical foundation, known as the von Neumann architecture. Fromthe conceptual point of view, the chapter clarifies the relation between the universal model of computation and the construction of an all-purpose machine.

On a Generalized Von Neumann Model

1965 ◽  
Vol 6 (1) ◽  
pp. 115 ◽  
Author(s):  
Hanjiro Haga ◽  
Mikiro Otsuki
Keyword(s):  
Von Neumann ◽  
Neumann Model

TWO-PHOTON ABSORPTION AND EMISSION PROCESS

2005 ◽  
Vol 08 (04) ◽  
pp. 573-591 ◽  
Author(s):  
FRANCO FAGNOLA ◽  
ROBERTO QUEZADA
Keyword(s):  
Detailed Balance ◽  
Photon Absorption ◽  
Positive Temperature ◽  
Stationary States ◽  
Emission Process ◽  
Absorption And Emission ◽  
Detailed Balance Condition ◽  
Two Photon Absorption ◽  
Two Photon ◽  
Invariant States

We analyze the two-photon absorption and emission process and characterize the stationary states at zero and positive temperature. We show that entangled stationary states exist only at zero temperature and, at positive temperature, there exists infinitely many commuting invariant states satisfying the detailed balance condition.

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