Probably Approximately Correct Nash Equilibrium Learning

We consider a multi-agent noncooperative game with agents' objective functions being affected by uncertainty. Following a data driven paradigm, we represent uncertainty by means of scenarios and seek a robust Nash equilibrium solution. We treat the Nash equilibrium computation problem within the realm of probably approximately correct (PAC) learning. Building upon recent developments in scenario-based optimization, we accompany the computed Nash equilibrium with a priori and a posteriori probabilistic robustness certificates, providing confidence that the computed equilibrium remains unaffected (in probabilistic terms) when a new uncertainty realization is encountered. For a wide class of games, we also show that the computation of the so called compression set - a key concept in scenario-based optimization - can be directly obtained as a byproduct of the proposed solution methodology. Finally, we illustrate how to overcome differentiability issues, arising due to the introduction of scenarios, and compute a Nash equilibrium solution in a decentralized manner. We demonstrate the efficacy of the proposed approach on an electric vehicle charging control problem.Comment: Preprint submitted to IEEE Transactions on Automatic Contro

Feasibility study and design concept for an orbiting ice-penetrating radar sounder to characterize in three-dimensions the Europan ice mantle down to (and including) any ice/ocean interface

This report presents a radar sounding model based on the range of current working hypotheses for the nature of Europa's icy shell.Institute for Geophysic

Mechanical behavior of osteoporotic bone at sub-lamellar length scales

Osteoporosis is a disease known to promote bone fragility but the effect on the mechanical properties of bone material, which is independent of geometric effects, is particularly unclear. To address this problem, micro-beams of osteoporotic bone were prepared using focused ion beam (FIB) microscopy and mechanically tested in compression using an atomic force microscope (AFM) while observing using in situ electron microscopy. This experimental approach was shown to be effective at measuring the subtle changes in the mechanical properties of bone material required to evaluate the effects of osteoporosis. Osteoporotic bone material was found to have lower elastic modulus and increased strain to failure when compared to healthy bone material, while the strength of osteoporotic and healthy bone was similar. A mechanism is suggested based on these results and previous literature that indicates degradation of the organic material in osteoporosis bone is responsible for resultant mechanical properties

A Sparse Bayesian Estimation Framework for Conditioning Prior Geologic Models to Nonlinear Flow Measurements

We present a Bayesian framework for reconstruction of subsurface hydraulic properties from nonlinear dynamic flow data by imposing sparsity on the distribution of the solution coefficients in a compression transform domain

Characterization of the frequency of extreme events by the Generalized Pareto Distribution

Based on recent results in extreme value theory, we use a new technique for the statistical estimation of distribution tails. Specifically, we use the Gnedenko-Pickands-Balkema-de Haan theorem, which gives a natural limit law for peak-over-threshold values in the form of the Generalized Pareto Distribution (GPD). Useful in finance, insurance, hydrology, we investigate here the earthquake energy distribution described by the Gutenberg-Richter seismic moment-frequency law and analyze shallow earthquakes (depth h < 70 km) in the Harvard catalog over the period 1977-2000 in 18 seismic zones. The whole GPD is found to approximate the tails of the seismic moment distributions quite well above moment-magnitudes larger than mW=5.3 and no statistically significant regional difference is found for subduction and transform seismic zones. We confirm that the b-value is very different in mid-ocean ridges compared to other zones (b=1.50=B10.09 versus b=1.00=B10.05 corresponding to a power law exponent close to 1 versus 2/3) with a very high statistical confidence. We propose a physical mechanism for this, contrasting slow healing ruptures in mid-ocean ridges with fast healing ruptures in other zones. Deviations from the GPD at the very end of the tail are detected in the sample containing earthquakes from all major subduction zones (sample size of 4985 events). We propose a new statistical test of significance of such deviations based on the bootstrap method. The number of events deviating from the tails of GPD in the studied data sets (15-20 at most) is not sufficient for determining the functional form of those deviations. Thus, it is practically impossible to give preference to one of the previously suggested parametric families describing the ends of tails of seismic moment distributions.Comment: pdf document of 21 pages + 2 tables + 20 figures (ps format) + one file giving the regionalizatio

The friction force mouse-pad and the forearm muscles efforts (preliminary results)

The objective of the article is to evaluate the impact of the friction force mouse-pad in the contraction level of the forearm muscles M. extensor carpi ulnaris, M. extensor digitorum M. extensor carpi radialis longus.A standard protocol of mouse movements was performed involving horizontal, vertical and diagonal mouse displacements drag-and-drop type. The operators were instructed to execute the protocol with their normal working speed. The movements protocol were performed by each subject (n=17) with three selected pairs mouse-pad, classified as low, medium and high friction force pairs. The mean time to execute the protocol with each mouse was ~138s. Mean values of ~13%MVE and ~17%MVE were found in the M. extensor carpi ulnaris and in the M. extensor digitorum respectively when performing the movements’ protocol. A 8.1% increase in %MVE was observed in the M. extensor digitorum and a 9.4% increase in %MVE was observed in the M. extensor carpi ulnaris when the high friction force pair was operated, relatively to the low friction force pair (pComputer mouse, Forearm muscles, EMG, Drag-and-drop, Friction force mouse-pad

Impact-induced acceleration by obstacles

We explore a surprising phenomenon in which an obstruction accelerates, rather than decelerates, a moving flexible object. It has been claimed that the right kind of discrete chain falling onto a table falls \emph{faster} than a free-falling body. We confirm and quantify this effect, reveal its complicated dependence on angle of incidence, and identify multiple operative mechanisms. Prior theories for direct impact onto flat surfaces, which involve a single constitutive parameter, match our data well if we account for a characteristic delay length that must impinge before the onset of excess acceleration. Our measurements provide a robust determination of this parameter. This supports the possibility of modeling such discrete structures as continuous bodies with a complicated constitutive law of impact that includes angle of incidence as an input.Comment: small changes and corrections, added reference