Image scoring in ad-hoc networks : an investigation on realistic settings

Encouraging cooperation in distributed Multi-Agent Systems (MAS) remains an open problem. Emergent application domains such as Mobile Ad-hoc Networks (MANETs) are characterised by constraints including sparse connectivity and a lack of direct interaction history. Image scoring, a simple model of reputation proposed by Nowak and Sigmund, exhibits low space and time complexity and promotes cooperation through indirect reciprocity, in which an agent can expect cooperation in the future without repeat interactions with the same partners. The low overheads of image scoring make it a promising technique for ad-hoc networking domains. However, the original investigation of Nowak and Sigmund is limited in that it (i) used a simple idealised setting, (ii) did not consider the effects of incomplete information on the mechanism’s efficacy, and (iii) did not consider the impact of the network topology connecting agents. We address these limitations by investigating more realistic values for the number of interactions agents engage in, and show that incomplete information can cause significant errors in decision making. As the proportion of incorrect decisions rises, the efficacy of image scoring falls and selfishness becomes more dominant. We evaluate image scoring on three different connection topologies: (i) completely connected, which closely approximates Nowak and Sigmund’s original setup, (ii) random, with each pair of nodes connected with a constant probability, and (iii) scale-free, which is known to model a number of real world environments including MANETs

A Classification of Minimal Sets of Torus Homeomorphisms

We provide a classification of minimal sets of homeomorphisms of the two-torus, in terms of the structure of their complement. We show that this structure is exactly one of the following types: (1) a disjoint union of topological disks, or (2) a disjoint union of essential annuli and topological disks, or (3) a disjoint union of one doubly essential component and bounded topological disks. Periodic bounded disks can only occur in type 3. This result provides a framework for more detailed investigations, and additional information on the torus homeomorphism allows to draw further conclusions. In the non-wandering case, the classification can be significantly strengthened and we obtain that a minimal set other than the whole torus is either a periodic orbit, or the orbit of a periodic circloid, or the extension of a Cantor set. Further special cases are given by torus homeomorphisms homotopic to an Anosov, in which types 1 and 2 cannot occur, and the same holds for homeomorphisms homotopic to the identity with a rotation set which has non-empty interior. If a non-wandering torus homeomorphism has a unique and totally irrational rotation vector, then any minimal set other than the whole torus has to be the extension of a Cantor set.Comment: Published in Mathematische Zeitschrift, June 2013, Volume 274, Issue 1-2, pp 405-42

Efficient algorithms for tensor scaling, quantum marginals and moment polytopes

We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our algorithm provides an efficient weak membership oracle for the associated moment polytopes, an important family of implicitly-defined convex polytopes with exponentially many facets and a wide range of applications. These include the entanglement polytopes from quantum information theory (in particular, we obtain an efficient solution to the notorious one-body quantum marginal problem) and the Kronecker polytopes from representation theory (which capture the asymptotic support of Kronecker coefficients). Our algorithm can be applied to succinct descriptions of the input tensor whenever the marginals can be efficiently computed, as in the important case of matrix product states or tensor-train decompositions, widely used in computational physics and numerical mathematics. We strengthen and generalize the alternating minimization approach of previous papers by introducing the theory of highest weight vectors from representation theory into the numerical optimization framework. We show that highest weight vectors are natural potential functions for scaling algorithms and prove new bounds on their evaluations to obtain polynomial-time convergence. Our techniques are general and we believe that they will be instrumental to obtain efficient algorithms for moment polytopes beyond the ones consider here, and more broadly, for other optimization problems possessing natural symmetries

Bench-to-bedside review: Molecular pharmacology and clinical use of inert gases in anesthesia and neuroprotection

In the past decade there has been a resurgence of interest in the clinical use of inert gases. In the present paper we review the use of inert gases as anesthetics and neuroprotectants, with particular attention to the clinical use of xenon. We discuss recent advances in understanding the molecular pharmacology of xenon and we highlight specific pharmacological targets that may mediate its actions as an anesthetic and neuroprotectant. We summarize recent in vitro and in vivo studies on the actions of helium and the other inert gases, and discuss their potential to be used as neuroprotective agents

Isoperimetric Inequalities for Minimal Submanifolds in Riemannian Manifolds: A Counterexample in Higher Codimension

For compact Riemannian manifolds with convex boundary, B.White proved the following alternative: Either there is an isoperimetric inequality for minimal hypersurfaces or there exists a closed minimal hypersurface, possibly with a small singular set. There is the natural question if a similar result is true for submanifolds of higher codimension. Specifically, B.White asked if the non-existence of an isoperimetric inequality for k-varifolds implies the existence of a nonzero, stationary, integral k-varifold. We present examples showing that this is not true in codimension greater than two. The key step is the construction of a Riemannian metric on the closed four-dimensional ball B with the following properties: (1) B has strictly convex boundary. (2) There exists a complete nonconstant geodesic. (3) There does not exist a closed geodesic in B.Comment: 11 pages, We changed the title and added a section that exhibits the relation between our example and the question posed by Brian White concerning isoperimetric inequalities for minimal submanifold

Supporting cooperation and coordination in open multi-agent systems

Cooperation and coordination between agents are fundamental processes for increasing aggregate and individual benefit in open Multi-Agent Systems (MAS). The increased ubiquity, size, and complexity of open MAS in the modern world has prompted significant research interest in the mechanisms that underlie cooperative and coordinated behaviour. In open MAS, in which agents join and leave freely, we can assume the following properties: (i) there are no centralised authorities, (ii) agent authority is uniform, (iii) agents may be heterogeneously owned and designed, and may consequently have con icting intentions and inconsistent capabilities, and (iv) agents are constrained in interactions by a complex connecting network topology. Developing mechanisms to support cooperative and coordinated behaviour that remain effective under these assumptions remains an open research problem. Two of the major mechanisms by which cooperative and coordinated behaviour can be achieved are (i) trust and reputation, and (ii) norms and conventions. Trust and reputation, which support cooperative and coordinated behaviour through notions of reciprocity, are effective in protecting agents from malicious or selfish individuals, but their capabilities can be affected by a lack of information about potential partners and the impact of the underlying network structure. Regarding conventions and norms, there are still a wide variety of open research problems, including: (i) manipulating which convention or norm a population adopts, (ii) how to exploit knowledge of the underlying network structure to improve mechanism efficacy, and (iii) how conventions might be manipulated in the middle and latter stages of their lifecycle, when they have become established and stable. In this thesis, we address these issues and propose a number of techniques and theoretical advancements that help ensure the robustness and efficiency of these mechanisms in the context of open MAS, and demonstrate new techniques for manipulating convention emergence in large, distributed populations. Specfically, we (i) show that gossiping of reputation information can mitigate the detrimental effects of incomplete information on trust and reputation and reduce the impact of network structure, (ii) propose a new model of conventions that accounts for limitations in existing theories, (iii) show how to manipulate convention emergence using small groups of agents inserted by interested parties, (iv) demonstrate how to learn which locations in a network have the greatest capacity to in uence which convention a population adopts, and (v) show how conventions can be manipulated in the middle and latter stages of the convention lifecycle

Strictly Toral Dynamics

This article deals with nonwandering (e.g. area-preserving) homeomorphisms of the torus $\mathbb{T}^2$ which are homotopic to the identity and strictly toral, in the sense that they exhibit dynamical properties that are not present in homeomorphisms of the annulus or the plane. This includes all homeomorphisms which have a rotation set with nonempty interior. We define two types of points: inessential and essential. The set of inessential points $ine(f)$ is shown to be a disjoint union of periodic topological disks ("elliptic islands"), while the set of essential points $ess(f)$ is an essential continuum, with typically rich dynamics (the "chaotic region"). This generalizes and improves a similar description by J\"ager. The key result is boundedness of these "elliptic islands", which allows, among other things, to obtain sharp (uniform) bounds of the diffusion rates. We also show that the dynamics in $ess(f)$ is as rich as in $\mathbb{T}^2$ from the rotational viewpoint, and we obtain results relating the existence of large invariant topological disks to the abundance of fixed points.Comment: Incorporates suggestions and corrections by the referees. To appear in Inv. Mat

Novel methods of fabrication and metrology of superconducting nanostructures

As metrology extends toward the nanoscale, a number of potential applications and new challenges arise. By combining photolithography with focused ion beam and/or electron beam methods, superconducting quantum interference devices (SQUIDs) with loop dimensions down to 200 nm and superconducting bridge dimensions of the order 80 nm have been produced. These SQUIDs have a range of potential applications. As an illustration, we describe a method for characterizing the effective area and the magnetic penetration depth of a structured superconducting thin film in the extreme limit, where the superconducting penetration depth $lambda$ is much greater than the film thickness and is comparable with the lateral dimensions of the device