Clustering measure-valued data with Wasserstein barycenters

In this work, learning schemes for measure-valued data are proposed, i.e. data that their structure can be more efficiently represented as probability measures instead of points on $\R^d$, employing the concept of probability barycenters as defined with respect to the Wasserstein metric. Such type of learning approaches are highly appreciated in many fields where the observational/experimental error is significant (e.g. astronomy, biology, remote sensing, etc.) or the data nature is more complex and the traditional learning algorithms are not applicable or effective to treat them (e.g. network data, interval data, high frequency records, matrix data, etc.). Under this perspective, each observation is identified by an appropriate probability measure and the proposed statistical learning schemes rely on discrimination criteria that utilize the geometric structure of the space of probability measures through core techniques from the optimal transport theory. The discussed approaches are implemented in two real world applications: (a) clustering eurozone countries according to their observed government bond yield curves and (b) classifying the areas of a satellite image to certain land uses categories which is a standard task in remote sensing. In both case studies the results are particularly interesting and meaningful while the accuracy obtained is high.Comment: 18 pages, 3 figure

Contingent claim pricing through a continuous time variational bargaining scheme

We consider a variational problem modelling the evolution with time of two probability measures representing the subjective beliefs of a couple of agents engaged in a continuous-time bargaining pricing scheme with the goal of finding a unique price for a contingent claim in a continuous-time financialmarket. This optimization problem is coupled with two finite dimensional portfolio optimization problems, one for each agent involved in the bargaining scheme. Undermild conditions, we prove that the optimization problem under consideration here admits a unique solution, yielding a unique price for the contingent claim.info:eu-repo/semantics/publishedVersio

Microtomographic Analysis of Impact Damage in FRP Composite Laminates: A Comparative Study

With the advancement of testing tools, the ability to characterize mechanical properties of fiber reinforced polymer (FRP) composites under extreme loading scenarios has allowed designers to use these materials in high-level applications more confidently. Conventionally, impact characterization of composite materials is studied via nondestructive techniques such as ultrasonic C-scanning, infrared thermography, X-ray, and acoustography. None of these techniques, however, enable 3D microscale visualization of the damage at different layers of composite laminates. In this paper, a 3D microtomographic technique has been employed to visualize and compare impact damage modes in a set of thermoplastic laminates. The test samples were made of commingled polypropylene (PP) and glass fibers with two different architectures, including the plain woven and unidirectional. Impact testing using a drop-weight tower, followed by postimpact four-point flexural testing and nondestructive tomographic analysis demonstrated a close relationship between the type of fibre architecture and the induced impact damage mechanisms and their extensions

Natural Aging Behaviour Of AA6111 Aluminium

In the continuing drive for weight reduction in new automobile designs, the 6000 series aluminium alloys have emerged as the most promising age-hardenable body sheet material in the automotive industry. Currently, one of the body sheet alloys used for its combination of strength and formability in the (T4) temper is AA6111, an Al-Mg-Si-Cu alloy. The T4 behaviour of AA6111 has been investigated by means of tensile testing, microhardness measurements, differential scanning calorimetry (DSC), scanning electron microscopy (SEM), and X-ray analysis. The results show that AA6111 attains a monotonic strength after approximately 120 h of natural aging. The microstructure consists of an aluminium matrix and angular intermetallic particles containing mainly Al, Fe, Cu, Si and Mn dispersed within the microstructure. The intermetallic particles are found to possess a structural formula of the type AlxFeSi. Compared with other 6xxx series of alloys under the same T4 condition, AA6111 shows superior strength properties. Natural aging is observed to affect the kinetic reaction of AA6111.Dans la campagne continue pour la réduction en poids dans le nouveau modèle d\' automobile, les séries 6000 d\' aluminium en alliage ont émergé comme le matériau de feuille de carrosserie la plus prometteuse endurcirable avec l\'âge dans l\'industrie de l\' automobile. Actuellement, l\' un d\' alliage de feuille de carrosserie utilisé pour sa combinaison de solidité et formabilité dans la trempe (T4) AA6111 un alliage de Al-Mg-Si- Cu. Dans cet article, le comportement T4 de AA6111 a été étudié au moyen de l\'essai de traction, l\'évaluation de microdureté, la calorimétrie de balayage différentiel (CBD), la microscopie électronique à balayage (MEB) et l\'analyse radioscopique. Les résultats montrent que AA6111 atteint une solidité monotone après approximativement 120 h de vieillissement naturel. La microstructure consiste d\'une matrice d\' aluminium et les particules intermétalliques angulaires contenant principalement Al, Fe, Cu, Si, Mn dispersés dans la microstructure. Les particules intermétalliques sont trouvées de posséder une formule structurelle du type Alx Fe Si. Comparé avec d\' autres séries d\' alliage de 6xxx sous la même condition de T4, AA6111 montre les propriétés de solidité supérieure. Les vieillissement naturel est observé d\' influer sur la réaction cinétique de AA6111. Ghana Journal of Science Vol. 47 2007: pp. 91-10

SCENARIOS FOR PRICE DETERMINATION IN INCOMPLETE MARKETS

We study the problem of determination of asset prices in an incomplete market proposing three different but related scenarios, based on utility pricing. One scenario uses a market game approach whereas the other two are based on risk sharing or regret minimizing considerations. Dynamical schemes modeling the convergence of the buyer and seller prices to a unique price are proposed. The case of exponential utilities is treated in detail, in the simplest possible example of an incomplete market, the trinomial model.Incomplete markets, market games, risk sharing, regret, dynamical schemes

Regulating the Environmental Consequences of Preferences for Social Status within an Evolutionary Framework

Taking as given that we are consuming too much and that overconsumption leads to environmental degradation, the present paper examines the regulator's choices between informative advertisement and consumption taxation. We model overconsumption by considering individuals that care about social status apart from the intrinsic utility, derived from direct consumption. We assume that there also exist individuals that care only about their own private consumption and we examine the evolution of preferences through time by allowing individuals to alter their behavior as a result of a learning process, akin to a replicator dynamics type. We consider the regulator's choice of consumption taxation and informative advertisement both in an arbitrary and an optimal control context. In the arbitrary overconsumption control context we find that the regulator could decrease, or even eliminate, the share of status seekers in the population. In the context of optimal overconsumption control, we show that the highest welfare is attained when status seekers are completely eliminated, while the lowest in the case that the entire population consists of status seekers

On Complexities of Impact Simulation of Fiber Reinforced Polymer Composites: A Simplified Modeling Framework

Impact modeling of fiber reinforced polymer composites is a complex and challenging task, in particular for practitioners with less experience in advanced coding and user-defined subroutines. Different numerical algorithms have been developed over the past decades for impact modeling of composites, yet a considerable gap often exists between predicted and experimental observations. In this paper, after a review of reported sources of complexities in impact modeling of fiber reinforced polymer composites, two simplified approaches are presented for fast simulation of out-of-plane impact response of these materials considering four main effects: (a) strain rate dependency of the mechanical properties, (b) difference between tensile and flexural bending responses, (c) delamination, and (d) the geometry of fixture (clamping conditions). In the first approach, it is shown that by applying correction factors to the quasistatic material properties, which are often readily available from material datasheets, the role of these four sources in modeling impact response of a given composite may be accounted for. As a result a rough estimation of the dynamic force response of the composite can be attained. To show the application of the approach, a twill woven polypropylene/glass reinforced thermoplastic composite laminate has been tested under 200 J impact energy and was modeled in Abaqus/Explicit via the built-in Hashin damage criteria. X-ray microtomography was used to investigate the presence of delamination inside the impacted sample. Finally, as a second and much simpler modeling approach it is shown that applying only a single correction factor over all material properties at once can still yield a reasonable prediction. Both advantages and limitations of the simplified modeling framework are addressed in the performed case study

An integrated multiphysics model for friction stir welding of 6061 Aluminum alloy

This article presents a new, combined ‘integrated’- ‘multiphysics’ model of friction stir welding (FSW) where a set of governing equations from non-Newtonian incompressible fluid dynamics, conductive and convective heat transfer, and plain stress solid mechanics have been coupled for calculating the process variables and material behaviour both during and after welding. More specifically, regarding the multiphysics feature, the model is capable of simultaneously predicting the local distribution, location and magnitude of maximum temperature, strain, and strain rate fields around the tool pin during the process; while for the integrated (post-analysis) part, the above predictions have been used to study the microstructure and residual stress field of welded parts within the same developed code. A slip/stick condition between the tool and workpiece, friction and deformation heat source, convection and conduction heat transfer in the workpiece, a solid mechanics-based viscosity definition, and the Zener-Hollomon- based rigid-viscoplastic material properties with solidus cut-off temperature and empirical softening regime have been employed. In order to validate all the predicted variables collectively, the model has been compared to a series of published case studies on individual/limited set of variables, as well as in-house experiments on FSW of aluminum 6061