Relational Hidden Variables and Non-Locality

We use a simple relational framework to develop the key notions and results on hidden variables and non-locality. The extensive literature on these topics in the foundations of quantum mechanics is couched in terms of probabilistic models, and properties such as locality and no-signalling are formulated probabilistically. We show that to a remarkable extent, the main structure of the theory, through the major No-Go theorems and beyond, survives intact under the replacement of probability distributions by mere relations.Comment: 42 pages in journal style. To appear in Studia Logic

Deconfinement and the Hagedorn Transition in String Theory

Superseded and extended in hep-th/0105110 and hep-th/0208112.Comment: Superseded and extended in hep-th/0105110 and hep-th/020811

Non-Zero Sum Games for Reactive Synthesis

In this invited contribution, we summarize new solution concepts useful for the synthesis of reactive systems that we have introduced in several recent publications. These solution concepts are developed in the context of non-zero sum games played on graphs. They are part of the contributions obtained in the inVEST project funded by the European Research Council.Comment: LATA'16 invited pape

Limits on models of the ultrahigh energy cosmic rays based on topological defects

An erratum exists for this article. Please see the description link below for details.Using the propagation of ultrahigh energy nucleons, photons, and electrons in the universal radiation backgrounds, we obtain limits on the luminosity of topological defect scenarios for the origin of the highest energy cosmic rays. The limits are set as a function of the mass of the X particles emitted by the cosmic strings or other defects, the cosmological evolution of the topological defects, and the strength of the extragalactic magnetic fields. The existing data on the cosmic ray spectrum and on the isotropic 100 MeV gamma-ray background limit significantly the parameter space in which topological defects can generate the flux of the highest energy cosmic rays, and rule out models with the standard X-particle mass of 10¹⁶GeV and higher.R. J. Protheroe and Todor Stane

The Intrinsic Quantum Nature of Nash Equilibrium Mixtures

Every undergraduate textbook in game theory has a chapter discussing the difficulty to interpret the mixed Nash equilibrium strategies. Unlike the usual suggested interpretations made in those textbooks, here we prove that these randomised strategies neither imply that players use some coin flips to make their decisions, nor that the mixtures represent the uncertainty of each player about the others' actions.Instead, the paper demonstrates a fundamental connection between the Nash equilibrium 'randomised' or 'mixed' strategies of classical game theory and the pure quantum states of quantum theory in physics. This link has some key consequences for the meaning of randomised strategies:In the main theorem, I prove that in every mixed Nash equilibrium, each player state of knowledge about his/her own future rational choices is represented by a pure quantum state. This indicates that prior making his/her actual choice, each player must be in a quantum superposition over her/his possible rational choices (in the support of his probability measure). This result notably permits to show that the famous 'indifference condition' that must be satisfied by each player in an equilibrium is actually the condition that ensures each player is in a 'rational epistemic state of ignorance' about her/his own future choice of an action

Relativistic theories of interacting fields and fluids

We investigate divergence-type theories (DTT) describing the dissipative interaction between a field and a fluid. We look for theories which, under equilibrium conditions, reduce to the theory of a Klein-Gordon scalar field and a perfect fluid. We show that the requirements of causality and positivity of entropy production put non-trivial constarints to the structure of the interaction terms. These theories provide a basis for the phenomonological study of the reheating period.Comment: 17 pages, no figures, minor corrections mad

Respecting the deal: how to manage co-opetitive actors in open innovation

Platforms like E-bay allow product seekers and providers to meet and exchange goods. On the same way in open innovation, as defined by Chesbrough, an enterprise can collect ideas from outside the company. But on E-bay, the seeker can return the product if it does not correspond to the expectations, since E-bay is the third-party actor in charge of assuring that the agreement between seekers and providers will be respected. So who does provide the same service for what concerns open innovation, where specifications might not fully defined? In this paper we shall describe the business model of an organizational structure to support the elicitation and respect of agreements between actors, who have conflicting interests but that gain from cooperating together. The concepts of the model will be illustrated to derive a set of propositions and a simple example will illustrate one of its possible instantiations. The description of our first evaluation phase shall find place at the end

The Sheaf-Theoretic Structure Of Non-Locality and Contextuality

We use the mathematical language of sheaf theory to give a unified treatment of non-locality and contextuality, in a setting which generalizes the familiar probability tables used in non-locality theory to arbitrary measurement covers; this includes Kochen-Specker configurations and more. We show that contextuality, and non-locality as a special case, correspond exactly to obstructions to the existence of global sections. We describe a linear algebraic approach to computing these obstructions, which allows a systematic treatment of arguments for non-locality and contextuality. We distinguish a proper hierarchy of strengths of no-go theorems, and show that three leading examples --- due to Bell, Hardy, and Greenberger, Horne and Zeilinger, respectively --- occupy successively higher levels of this hierarchy. A general correspondence is shown between the existence of local hidden-variable realizations using negative probabilities, and no-signalling; this is based on a result showing that the linear subspaces generated by the non-contextual and no-signalling models, over an arbitrary measurement cover, coincide. Maximal non-locality is generalized to maximal contextuality, and characterized in purely qualitative terms, as the non-existence of global sections in the support. A general setting is developed for Kochen-Specker type results, as generic, model-independent proofs of maximal contextuality, and a new combinatorial condition is given, which generalizes the `parity proofs' commonly found in the literature. We also show how our abstract setting can be represented in quantum mechanics. This leads to a strengthening of the usual no-signalling theorem, which shows that quantum mechanics obeys no-signalling for arbitrary families of commuting observables, not just those represented on different factors of a tensor product.Comment: 33 pages. Extensively revised, new results included. Published in New Journal of Physic