An adaptive Metropolis-Hastings scheme: sampling and optimization

We propose an adaptive Metropolis-Hastings algorithm in which sampled data are used to update the proposal distribution. We use the samples found by the algorithm at a particular step to form the information-theoretically optimal mean-field approximation to the target distribution, and update the proposal distribution to be that approximatio. We employ our algorithm to sample the energy distribution for several spin-glasses and we demonstrate the superiority of our algorithm to the conventional MH algorithm in sampling and in annealing optimization.Comment: To appear in Europhysics Letter

Geometric Aspects of the Moduli Space of Riemann Surfaces

This is a survey of our recent results on the geometry of moduli spaces and Teichmuller spaces of Riemann surfaces appeared in math.DG/0403068 and math.DG/0409220. We introduce new metrics on the moduli and the Teichmuller spaces of Riemann surfaces with very good properties, study their curvatures and boundary behaviors in great detail. Based on the careful analysis of these new metrics, we have a good understanding of the Kahler-Einstein metric from which we prove that the logarithmic cotangent bundle of the moduli space is stable. Another corolary is a proof of the equivalences of all of the known classical complete metrics to the new metrics, in particular Yau's conjectures in the early 80s on the equivalences of the Kahler-Einstein metric to the Teichmuller and the Bergman metric.Comment: Survey article of our recent results on the subject. Typoes corrrecte

Hybrid Local-Order Mechanism for Inversion Symmetry Breaking

Using classical Monte Carlo simulations, we study a simple statistical mechanical model of relevance to the emergence of polarisation from local displacements on the square and cubic lattices. Our model contains two key ingredients: a Kitaev-like orientation-dependent interaction between nearest neighbours, and a steric term that acts between next-nearest neighbours. Taken by themselves, each of these two ingredients is incapable of driving long-range symmetry breaking, despite the presence of a broad feature in the corresponding heat capacity functions. Instead each component results in a "hidden" transition on cooling to a manifold of degenerate states, the two manifolds are different in the sense that they reflect distinct types of local order. Remarkably, their intersection---\emph{i.e.} the ground state when both interaction terms are included in the Hamiltonian---supports a spontaneous polarisation. In this way, our study demonstrates how local ordering mechanisms might be combined to break global inversion symmetry in a manner conceptually similar to that operating in the "hybrid" improper ferroelectrics. We discuss the relevance of our analysis to the emergence of spontaneous polarisation in well-studied ferroelectrics such as BaTiO$_3$ and KNbO$_3$.Comment: 8 pages, 8 figure

SQG-Differential Evolution for difficult optimization problems under a tight function evaluation budget

In the context of industrial engineering, it is important to integrate efficient computational optimization methods in the product development process. Some of the most challenging simulation-based engineering design optimization problems are characterized by: a large number of design variables, the absence of analytical gradients, highly non-linear objectives and a limited function evaluation budget. Although a huge variety of different optimization algorithms is available, the development and selection of efficient algorithms for problems with these industrial relevant characteristics, remains a challenge. In this communication, a hybrid variant of Differential Evolution (DE) is introduced which combines aspects of Stochastic Quasi-Gradient (SQG) methods within the framework of DE, in order to improve optimization efficiency on problems with the previously mentioned characteristics. The performance of the resulting derivative-free algorithm is compared with other state-of-the-art DE variants on 25 commonly used benchmark functions, under tight function evaluation budget constraints of 1000 evaluations. The experimental results indicate that the new algorithm performs excellent on the 'difficult' (high dimensional, multi-modal, inseparable) test functions. The operations used in the proposed mutation scheme, are computationally inexpensive, and can be easily implemented in existing differential evolution variants or other population-based optimization algorithms by a few lines of program code as an non-invasive optional setting. Besides the applicability of the presented algorithm by itself, the described concepts can serve as a useful and interesting addition to the algorithmic operators in the frameworks of heuristics and evolutionary optimization and computing

Forward estimation of movement state in posterior parietal cortex

During goal-directed movements, primates are able to rapidly and accurately control an online trajectory despite substantial delay times incurred in the sensorimotor control loop. To address the problem of large delays, it has been proposed that the brain uses an internal forward model of the arm to estimate current and upcoming states of a movement, which are more useful for rapid online control. To study online control mechanisms in the posterior parietal cortex (PPC), we recorded from single neurons while monkeys performed a joystick task. Neurons encoded the static target direction and the dynamic movement angle of the cursor. The dynamic encoding properties of many movement angle neurons reflected a forward estimate of the state of the cursor that is neither directly available from passive sensory feedback nor compatible with outgoing motor commands and is consistent with PPC serving as a forward model for online sensorimotor control. In addition, we found that the space–time tuning functions of these neurons were largely separable in the angle–time plane, suggesting that they mostly encode straight and approximately instantaneous trajectories

Independent Loop Invariants for 2+1 Gravity

We identify an explicit set of complete and independent Wilson loop invariants for 2+1 gravity on a three-manifold $M=\R\times\Sigma^g$, with $\Sigma^g$ a compact oriented Riemann surface of arbitrary genus $g$. In the derivation we make use of a global cross section of the $PSU(1,1)$-principal bundle over Teichm\"uller space given in terms of Fenchel-Nielsen coordinates.Comment: 11pp, 2 figures (postscript, compressed and uu-encoded), TeX, Pennsylvania State University, CGPG-94/7-

Spectral isolation of naturally reductive metrics on simple Lie groups

We show that within the class of left-invariant naturally reductive metrics $\mathcal{M}_{\operatorname{Nat}}(G)$ on a compact simple Lie group $G$, every metric is spectrally isolated. We also observe that any collection of isospectral compact symmetric spaces is finite; this follows from a somewhat stronger statement involving only a finite part of the spectrum.Comment: 19 pages, new title and abstract, revised introduction, new result demonstrating that any collection of isospectral compact symmetric spaces must be finite, to appear Math Z. (published online Dec. 2009

Computational core and fixed-point organisation in Boolean networks

In this paper, we analyse large random Boolean networks in terms of a constraint satisfaction problem. We first develop an algorithmic scheme which allows to prune simple logical cascades and under-determined variables, returning thereby the computational core of the network. Second we apply the cavity method to analyse number and organisation of fixed points. We find in particular a phase transition between an easy and a complex regulatory phase, the latter one being characterised by the existence of an exponential number of macroscopically separated fixed-point clusters. The different techniques developed are reinterpreted as algorithms for the analysis of single Boolean networks, and they are applied to analysis and in silico experiments on the gene-regulatory networks of baker's yeast (saccaromices cerevisiae) and the segment-polarity genes of the fruit-fly drosophila melanogaster.Comment: 29 pages, 18 figures, version accepted for publication in JSTA

The vein-banding disease syndrome: A synergistic reaction between grapevine viroids and fanleaf virus

Viroid-free Vitis vinifera cultivars Cabernet Sauvignon and Sauvignon blanc were established in controlled field trials in California to evaluate the relationship between grapevine viroids and fanleaf virus for induction of the vein-banding disease. Vein-banding symptoms were observed only on vines which contained the three principal grapevine viroids, grapevine yellow speckle viroids (GYSVd-1, GYSVd-2), and hop stunt viroid (HSVd-g), as well as grapevine fanleaf virus (GFLV). Sauvignon blanc vines which contained the single viroid, HSVd-g, and GFLV were non-symptomatic indicating an absence of a correlation between HSVd-g and the vein-banding disease. The intensity of vein-banding symptoms was directly correlated with an enhanced titer of GYSVd-1 and GYSVd-2. Vein-banding and yellow speckle symptomatic as well as non-symptomatic vines in Italy contained two viroids, GYSVd-1 and HSVd-g. However, symptomatic vines displayed a higher titer of GYSVd-1 than non-symptomatic materials and vein-banding symptomatic vines were GFLV infected. These data experimentally demonstrate that expression of the vein-banding disease is induced by an unique synergistic reaction between a viroid, GYSVd-1 and a virus, GFLV

A local families index formula for d-bar operators on punctured Riemann surfaces

Using heat kernel methods developed by Vaillant, a local index formula is obtained for families of d-bar operators on the Teichmuller universal curve of Riemann surfaces of genus g with n punctures. The formula also holds on the moduli space M{g,n} in the sense of orbifolds where it can be written in terms of Mumford-Morita-Miller classes. The degree two part of the formula gives the curvature of the corresponding determinant line bundle equipped with the Quillen connection, a result originally obtained by Takhtajan and Zograf.Comment: 47 page