Optimization as a design strategy. Considerations based on building simulation-assisted experiments about problem decomposition

In this article the most fundamental decomposition-based optimization method - block coordinate search, based on the sequential decomposition of problems in subproblems - and building performance simulation programs are used to reason about a building design process at micro-urban scale and strategies are defined to make the search more efficient. Cyclic overlapping block coordinate search is here considered in its double nature of optimization method and surrogate model (and metaphore) of a sequential design process. Heuristic indicators apt to support the design of search structures suited to that method are developed from building-simulation-assisted computational experiments, aimed to choose the form and position of a small building in a plot. Those indicators link the sharing of structure between subspaces ("commonality") to recursive recombination, measured as freshness of the search wake and novelty of the search moves. The aim of these indicators is to measure the relative effectiveness of decomposition-based design moves and create efficient block searches. Implications of a possible use of these indicators in genetic algorithms are also highlighted.Comment: 48 pages. 12 figures, 3 table

WIMP astronomy and particle physics with liquid-noble and cryogenic direct-detection experiments

Once weakly-interacting massive particles (WIMPs) are unambiguously detected in direct-detection experiments, the challenge will be to determine what one may infer from the data. Here, I examine the prospects for reconstructing the local speed distribution of WIMPs in addition to WIMP particle-physics properties (mass, cross sections) from next-generation cryogenic and liquid-noble direct-detection experiments. I find that the common method of fixing the form of the velocity distribution when estimating constraints on WIMP mass and cross sections means losing out on the information on the speed distribution contained in the data and may lead to biases in the inferred values of the particle-physics parameters. I show that using a more general, empirical form of the speed distribution can lead to good constraints on the speed distribution. Moreover, one can use Bayesian model-selection criteria to determine if a theoretically-inspired functional form for the speed distribution (such as a Maxwell-Boltzmann distribution) fits better than an empirical model. The shape of the degeneracy between WIMP mass and cross sections and their offset from the true values of those parameters depends on the hypothesis for the speed distribution, which has significant implications for consistency checks between direct-detection and collider data. In addition, I find that the uncertainties on theoretical parameters depends sensitively on the upper end of the energy range used for WIMP searches. Better constraints on the WIMP particle-physics parameters and speed distribution are obtained if the WIMP search is extended to higher energy (~ 1 MeV).Comment: 25 pages, 27 figures, matches published versio

Alternatives with stronger convergence than coordinate-descent iterative LMI algorithms

In this note we aim at putting more emphasis on the fact that trying to solve non-convex optimization problems with coordinate-descent iterative linear matrix inequality algorithms leads to suboptimal solutions, and put forward other optimization methods better equipped to deal with such problems (having theoretical convergence guarantees and/or being more efficient in practice). This fact, already outlined at several places in the literature, still appears to be disregarded by a sizable part of the systems and control community. Thus, main elements on this issue and better optimization alternatives are presented and illustrated by means of an example.Comment: 3 pages. Main experimental results reproducible from files available on http://www.mathworks.com/matlabcentral/fileexchange/33219 This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Rapid Computation of Thermodynamic Properties Over Multidimensional Nonbonded Parameter Spaces using Adaptive Multistate Reweighting

We show how thermodynamic properties of molecular models can be computed over a large, multidimensional parameter space by combining multistate reweighting analysis with a linear basis function approach. This approach reduces the computational cost to estimate thermodynamic properties from molecular simulations for over 130,000 tested parameter combinations from over a thousand CPU years to tens of CPU days. This speed increase is achieved primarily by computing the potential energy as a linear combination of basis functions, computed from either modified simulation code or as the difference of energy between two reference states, which can be done without any simulation code modification. The thermodynamic properties are then estimated with the Multistate Bennett Acceptance Ratio (MBAR) as a function of multiple model parameters without the need to define a priori how the states are connected by a pathway. Instead, we adaptively sample a set of points in parameter space to create mutual configuration space overlap. The existence of regions of poor configuration space overlap are detected by analyzing the eigenvalues of the sampled states' overlap matrix. The configuration space overlap to sampled states is monitored alongside the mean and maximum uncertainty to determine convergence, as neither the uncertainty or the configuration space overlap alone is a sufficient metric of convergence. This adaptive sampling scheme is demonstrated by estimating with high precision the solvation free energies of charged particles of Lennard-Jones plus Coulomb functional form. We also compute entropy, enthalpy, and radial distribution functions of unsampled parameter combinations using only the data from these sampled states and use the free energies estimates to examine the deviation of simulations from the Born approximation to the solvation free energy

Sensitivity plots for WIMP direct detection using the annual modulation signature

Annual modulation due to the Earth's motion around the Sun is a well known signature of the expected WIMP signal induced in a solid state underground detector. In the present letter we discuss the prospects of this technique on statistical grounds, introducing annual-modulation sensitivity plots for the WIMP-nucleon scalar cross section for different materials and experimental conditions. The highest sensitivity to modulation is found in the WIMP mass interval 10 GeV< m_W < 130 GeV, the actual upper limit depending from the choice of the astrophysical parameters, while the lowest values of the explorable WIMP-nucleon elastic cross-sections fall in most cases within one order of magnitude of the sensitivities of present direct detection WIMP searches.Comment: 24 pages, ReVTeX, 9 figures, submitted to Astroparticle Physic

The TDNNS method for Reissner-Mindlin plates

A new family of locking-free finite elements for shear deformable Reissner-Mindlin plates is presented. The elements are based on the "tangential-displacement normal-normal-stress" formulation of elasticity. In this formulation, the bending moments are treated as separate unknowns. The degrees of freedom for the plate element are the nodal values of the deflection, tangential components of the rotations and normal-normal components of the bending strain. Contrary to other plate bending elements, no special treatment for the shear term such as reduced integration is necessary. The elements attain an optimal order of convergence