Maximum Entropy/Optimal Projection (MEOP) control design synthesis: Optimal quantification of the major design tradeoffs

The underlying philosophy and motivation of the optimal projection/maximum entropy (OP/ME) stochastic modeling and reduced control design methodology for high order systems with parameter uncertainties are discussed. The OP/ME design equations for reduced-order dynamic compensation including the effect of parameter uncertainties are reviewed. The application of the methodology to several Large Space Structures (LSS) problems of representative complexity is illustrated

Following the evolution of glassy states under external perturbations: compression and shear-strain

We consider the adiabatic evolution of glassy states under external perturbations. Although the formalism we use is very general, we focus here on infinite-dimensional hard spheres where an exact analysis is possible. We consider perturbations of the boundary, i.e. compression or (volume preserving) shear-strain, and we compute the response of glassy states to such perturbations: pressure and shear-stress. We find that both quantities overshoot before the glass state becomes unstable at a spinodal point where it melts into a liquid (or yields). We also estimate the yield stress of the glass. Finally, we study the stability of the glass basins towards breaking into sub-basins, corresponding to a Gardner transition. We find that close to the dynamical transition, glasses undergo a Gardner transition after an infinitesimal perturbation.Comment: 4 pages (3 figures) + 24 pages (5 pages) of appendice

New allowed mSUGRA parameter space from variations of the trilinear scalar coupling A0

In minimal Supergravity (mSUGRA) models the lightest supersymmetric particle (assumed to be the lightest neutralino) provides an excellent cold dark matter (CDM) candidate. The supersymmetric parameter space is significantly reduced, if the limits on the CDM relic density, obtained from WMAP data, are used. Assuming a vanishing trilinear scalar coupling A0 and fixed values of tan(beta), these limits result in narrow lines of allowed regions in the m0-m1/2 plane, the so called WMAP strips. In this analysis the trilinear coupling A0 has been varied within +/-4 TeV. A fixed non vanishing A0 value leads to a shift of the WMAP strips in the m0-m1/2 plane.Comment: Typos corrected, Fig.1. updated, references adde

Linearly-Constrained Entropy Maximization Problem with Quadratic Costs and Its Applications to Transportation Planning Problems

Many transportation problems can be formulated as a linearly-constrained convex programming problem whose objective function consists of entropy functions and other cost-related terms. In this paper, we propose an unconstrained convex programming dual approach to solving these problems. In particular, we focus on a class of linearly-constrained entropy maximization problem with quadratic cost, study its Lagrangian dual, and provide a globally convergent algorithm with a quadratic rate of convergence. The theory and algorithm can be readily applied to the trip distribution problem with quadratic cost and many other entropy-based formulations, including the conventional trip distribution problem with linear cost, the entropy-based modal split model, and the decomposed problems of the combined problem of trip distribution and assignment. The efficiency and the robustness of this approach are confirmed by our computational experience

Minimum Relative Entropy for Quantum Estimation: Feasibility and General Solution

We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever necessary, to relax the constraints in order to allow for a physically admissible solution. Building on these results, the variational analysis can be completed ensuring existence and uniqueness of the optimum. The latter can then be computed by standard, efficient standard algorithms for convex optimization, without resorting to approximate methods or restrictive assumptions on its rank.Comment: 9 pages, no figure