A pedagogical introduction to the replica method for fragile glasses

In this note I present a simplified version of the recent computation (Mezard and Parisi 1998, 1999) of the properties of glasses in the low temperature phase in the framework of the replica theory, using an extension of the tools used in liquid theory. I will only consider here the case of the internal energy at T=0, which can be studied in a simple way without introducing replicas.Comment: 7 pages, 1 figure Talk given at Andalo, March 1999; minor errors have been correcte

Accurate estimate of the relic density and the kinetic decoupling in non-thermal dark matter models

Non-thermal dark matter generation is an appealing alternative to the standard paradigm of thermal WIMP dark matter. We reconsider non-thermal production mechanisms in a systematic way, and develop a numerical code for accurate computations of the dark matter relic density. We discuss in particular scenarios with long-lived massive states decaying into dark matter particles, appearing naturally in several beyond the standard model theories, such as supergravity and superstring frameworks. Since non-thermal production favors dark matter candidates with large pair annihilation rates, we analyze the possible connection with the anomalies detected in the lepton cosmic-ray flux by Pamela and Fermi. Concentrating on supersymmetric models, we consider the effect of these non-standard cosmologies in selecting a preferred mass scale for the lightest supersymmetric particle as dark matter candidate, and the consequent impact on the interpretation of new physics discovered or excluded at the LHC. Finally, we examine a rather predictive model, the G2-MSSM, investigating some of the standard assumptions usually implemented in the solution of the Boltzmann equation for the dark matter component, including coannihilations. We question the hypothesis that kinetic equilibrium holds along the whole phase of dark matter generation, and the validity of the factorization usually implemented to rewrite the system of coupled Boltzmann equation for each coannihilating species as a single equation for the sum of all the number densities. As a byproduct we develop here a formalism to compute the kinetic decoupling temperature in case of coannihilating particles, which can be applied also to other particle physics frameworks, and also to standard thermal relics within a standard cosmology

Optimal Dynamic Procurement Policies for a Storable Commodity with L\'evy Prices and Convex Holding Costs

In this paper we study a continuous time stochastic inventory model for a commodity traded in the spot market and whose supply purchase is affected by price and demand uncertainty. A firm aims at meeting a random demand of the commodity at a random time by maximizing total expected profits. We model the firm's optimal procurement problem as a singular stochastic control problem in which controls are nondecreasing processes and represent the cumulative investment made by the firm in the spot market (a so-called stochastic "monotone follower problem"). We assume a general exponential L\'evy process for the commodity's spot price, rather than the commonly used geometric Brownian motion, and general convex holding costs. We obtain necessary and sufficient first order conditions for optimality and we provide the optimal procurement policy in terms of a "base inventory" process; that is, a minimal time-dependent desirable inventory level that the firm's manager must reach at any time. In particular, in the case of linear holding costs and exponentially distributed demand, we are also able to obtain the explicit analytic form of the optimal policy and a probabilistic representation of the optimal revenue. The paper is completed by some computer drawings of the optimal inventory when spot prices are given by a geometric Brownian motion and by an exponential jump-diffusion process. In the first case we also make a numerical comparison between the value function and the revenue associated to the classical static "newsvendor" strategy.Comment: 28 pages, 3 figures; improved presentation, added new results and section

Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible Investment under Limited Resources

In this paper we study a continuous time, optimal stochastic investment problem under limited resources in a market with N firms. The investment processes are subject to a time-dependent stochastic constraint. Rather than using a dynamic programming approach, we exploit the concavity of the profit functional to derive some necessary and sufficient first order conditions for the corresponding Social Planner optimal policy. Our conditions are a stochastic infinite-dimensional generalization of the Kuhn-Tucker Theorem. The Lagrange multiplier takes the form of a nonnegative optional random measure on [0,T] which is flat off the set of times for which the constraint is binding, i.e. when all the fuel is spent. As a subproduct we obtain an enlightening interpretation of the first order conditions for a single firm in Bank (2005). In the infinite-horizon case, with operating profit functions of Cobb-Douglas type, our method allows the explicit calculation of the optimal policy in terms of the `base capacity' process, i.e. the unique solution of the Bank and El Karoui representation problem (2004).Comment: 25 page

Elimination of Spurious Ambiguity in Transition-Based Dependency Parsing

We present a novel technique to remove spurious ambiguity from transition systems for dependency parsing. Our technique chooses a canonical sequence of transition operations (computation) for a given dependency tree. Our technique can be applied to a large class of bottom-up transition systems, including for instance Nivre (2004) and Attardi (2006)

Visual SLAM for flying vehicles

The ability to learn a map of the environment is important for numerous types of robotic vehicles. In this paper, we address the problem of learning a visual map of the ground using flying vehicles. We assume that the vehicles are equipped with one or two low-cost downlooking cameras in combination with an attitude sensor. Our approach is able to construct a visual map that can later on be used for navigation. Key advantages of our approach are that it is comparably easy to implement, can robustly deal with noisy camera images, and can operate either with a monocular camera or a stereo camera system. Our technique uses visual features and estimates the correspondences between features using a variant of the progressive sample consensus (PROSAC) algorithm. This allows our approach to extract spatial constraints between camera poses that can then be used to address the simultaneous localization and mapping (SLAM) problem by applying graph methods. Furthermore, we address the problem of efficiently identifying loop closures. We performed several experiments with flying vehicles that demonstrate that our method is able to construct maps of large outdoor and indoor environments. © 2008 IEEE

Masonry cross vaults: an overview of the historical developments

The cross vault represents one of the most diffused and fascinating structural typologies of the European architectural heritage. Its history began almost two thousand years ago and reached a widespread use during the Middle Ages with the outstanding gothic cathedrals. Without any proper scientific support but only using trial-and-error methods, considering each building as a scaled specimen of a new one to be built, the ancient workmanship achieved a proper competence represented by the so-called rules of thumb. However, despite this long-lasting history, it is only from the eighteenth centuries that scholars have tried to tackle the problem of analytically describing its structural behaviour. In this regard, the first part of the present study is devoted to the evolution of cross vaults from the geometrical and constructive standpoint, whereas the second one describes the historical advancements of its structural behaviour, until the development of modern limit analysis

Optimization of force-limiting seismic devices connecting structural subsystems

This paper is focused on the optimum design of an original force-limiting floor anchorage system for the seismic protection of reinforced concrete (RC) dual wall-frame buildings. This protection strategy is based on the interposition of elasto-plastic links between two structural subsystems, namely the lateral force resisting system (LFRS) and the gravity load resisting system (GLRS). The most efficient configuration accounting for the optimal position and mechanical characteristics of the nonlinear devices is obtained numerically by means of a modified constrained differential evolution algorithm. A 12-storey prototype RC dual wall-frame building is considered to demonstrate the effectiveness of the seismic protection strategy