Related papers: A Quantum Model for the Ellsberg and Machina Parad…
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…
This article is devoted to the study of which appears as the most famous paradoxes of quantum theory (Schrodinger cat, EPR argument and Aspect experiments, delayed choice experiments and retrocausality problems). Through these experiments,…
Any attempt to introduce probabilities into quantum mechanics faces difficulties due to the mathematical structure of Hilbert space, as reflected in Birkhoff and von Neumann's proposal for a quantum logic. The (consistent or decoherent)…
We begin with a brief summary of issues encountered involving causality in quantum theory, placing careful emphasis on the assumptions involved in results such as the EPR paradox and Bell's inequality. We critique some solutions to the…
Quantum game theory, whatever opinions may be held due to its abstract physical formalism, have already found various applications even outside the orthodox physics domain. In this paper we introduce the concept of a quantum auction, its…
At the zero lower bound, the New Keynesian model predicts that output and inflation collapse to implausibly low levels, and that government spending and forward guidance have implausibly large effects. To resolve these anomalies, we…
Shafer's theory of belief and the Bayesian theory of probability are two alternative and mutually inconsistent approaches toward modelling uncertainty in artificial intelligence. To help reduce the conflict between these two approaches,…
We give a general formulation of the utility maximization problem under nondominated model uncertainty in discrete time and show that an optimal portfolio exists for any utility function that is bounded from above. In the unbounded case,…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
Actual realisations of EPR experiments do {\em not} demonstrate non-locality. A model is presented that should enable non-specialists as well as specialists to understand how easy it is to find realistic explanations for the observations.…
Machine learning models are used for pattern recognition analysis of big data, without direct human intervention. The task of unsupervised learning is to find the probability distribution that would best describe the available data, and…
The Einstein-Podolsky-Rosen (EPR) paradox was presented as an argument that quantum mechanics is an incomplete description of physical reality. However, the premises on which the argument is based are falsifiable by Bell experiments. In…
Demonstrating quantum advantage in machine learning tasks requires navigating a complex landscape of proposed models and algorithms. To bring clarity to this search, we introduce a framework that connects the structure of parametrized…
Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum…
Building learning models frequently requires evaluating numerous intermediate models. Examples include models considered during feature selection, model structure search, and parameter tunings. The evaluation of an intermediate model…
This text is addressed to mathematicians who are interested in generalized functions and unbounded operators on a Hilbert space. We expose in detail (in a "formal way" - as done by Heisenberg and Pauli - i.e. without mathematical…
We propose a novel framework for the quantum geometry of expectation values over arbitrary sets of operators and establish a link between this geometry and the eigenstates of Hamiltonian families generated by these operators. We show that…
Since the advent of quantum mechanics we have mainly been concerned with its predictions from the perspective of an external observer. This is in strong contrast to the theory of general relativity, where the physics is governed by the…
The random utility model, a cornerstone in economics, is axiomatized by Falmagne (1978) and McFadden and Richter (1990) with the assumption that if a menu is observable, the choice frequencies of all alternatives are also observable.…
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…