The existence of an inverse limit of inverse system of measure spaces - a purely measurable case

The existence of an inverse limit of an inverse system of (probability) measure spaces has been investigated since the very beginning of the birth of the modern probability theory. Results from Kolmogorov [10], Bochner [2], Choksi [5], Metivier [14], Bourbaki [3] among others have paved the way of the deep understanding of the problem under consideration. All the above results, however, call for some topological concepts, or at least ones which are closely related topological ones. In this paper we investigate purely measurable inverse systems of (probability) measure spaces, and give a sucient condition for the existence of a unique inverse limit. An example for the considered purely measurable inverse systems of (probability) measure spaces is also given

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Superseded and extended in hep-th/0105110 and hep-th/0208112.Comment: Superseded and extended in hep-th/0105110 and hep-th/020811

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

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

The performance effects of creative imitation on original products: Evidence from lab and field experiments

Research Summary: A market entrant often challenges the incumbent using creative imitation: The entrant creatively combines imitated aspects of the original with its own innovative characteristics to create a distinct offering. Using lab and field experiments to examine creative imitation in China, we find the effects of creative imitations on the originals depend on the creative imitation's quality. We explore the underlying mechanisms, and show that including a low-quality creative imitation in the retail choice set increases satisfaction with and choice of the original, while a moderate-quality creative imitation does the opposite. Moreover, creative imitation affects consumers' satisfaction with the original by influencing whether their experience with the original verifies their expectations. Our paper reveals creative imitation effects to help incumbent firms effectively address them. Managerial Summary: When the incumbent is challenged by an entrant using creative imitation, consumers may react differently to the incumbent, and understanding consumers' reactions allows the incumbent to make better strategic decisions about how to address the challenge. Using lab and field experiments, we investigate creative imitations with two quality levels common in our empirical context, low quality and moderate quality, and examine how and why they differentially affect the originals. We find the presence of a low-quality creative imitation actually increased choice of the original by enhancing consumers' satisfaction with it, while a moderate-quality creative imitation reduced choice of the original by undermining satisfaction with it. Our research suggests the incumbent should address moderate-quality creative imitations' challenges to customer satisfaction, while temporarily tolerating low-quality creative imitations

The differential impact of friendship on cooperative and competitive coordination

Friendship is commonly assumed to reduce strategic uncertainty and enhance tacit coordination. However, this assumption has never been tested across two opposite poles of coordination involving either strategic complementarity or substitutability. We had participants interact with friends or strangers in two classic coordination games: the stag hunt game, which exhibits strategic complementarity and may foster "cooperation", and the entry game, which exhibits strategic substitutability and may foster "competition". Both games capture a frequent trade-off between a potentially high paying but uncertain option and a low paying but safe alternative. We find that, relative to strangers, friends are more likely to choose options involving uncertainty in stag hunt games but the opposite is true in entry games. Furthermore, in stag hunt games, friends "tremble" less between options, coordinate better and earn more, but these advantages are largely decreased or lost in entry games. We further investigate how these effects are modulated by risk attitudes, friendship qualities and interpersonal similarities

Shopping Streets versus Shopping Malls - Determinants of Agglomeration Format Attractiveness from the Customers' Point of View

The decline of shopping streets and the rise of shopping malls have been major trends in European retailing for decades. So far, research has failed to investigate this shift of agglomeration format (AF) patronage from a marketing perspective, including the consumers’ point of view. This paper presents a theoretical comparison of generic similarities and conceptual differences between shopping streets and shopping malls. Based on this comparison the AF-specific characteristics perceived by consumers are compared and discussed with respect to their impact on agglomeration attractiveness. This leads to the development of a conceptual framework which is empirically tested using a web-based survey of almost 1,000 consumers representing a typical urban central European retail market. The relative importance of nine distinctive AF characteristics on attractiveness was analysed using structural equation modelling. The findings proved to be quite similar for both shopping streets and shopping malls; the retail tenant mix and atmosphere had the highest relative importance

Stateful Multi-Client Verifiable Computation

This paper develops a cryptographic protocol for outsourcing arbitrary stateful computation among multiple clients to an untrusted server, while guaranteeing integrity of the data. The clients communicate only with the server and store only a short authenticator to ensure that the server does not cheat. Our contribution is two-fold. First, we extend the recent hash&prove scheme of Fiore et al. (CCS 2016) to stateful computations that support arbitrary updates by the untrusted server, in a way that can be verified by the clients. We use this scheme to generically instantiate authenticated data types. Second, we describe a protocol for multi-client verifiable computation based on an authenticated data type, and prove that it achieves a computational version of fork linearizability. This is the strongest guarantee that can be achieved in the setting where clients do not communicate directly; it ensures correctness and consistency of outputs seen by the clients individually