Resampling methods for spatial regression models under a class of stochastic designs

In this paper we consider the problem of bootstrapping a class of spatial regression models when the sampling sites are generated by a (possibly nonuniform) stochastic design and are irregularly spaced. It is shown that the natural extension of the existing block bootstrap methods for grid spatial data does not work for irregularly spaced spatial data under nonuniform stochastic designs. A variant of the blocking mechanism is proposed. It is shown that the proposed block bootstrap method provides a valid approximation to the distribution of a class of M-estimators of the spatial regression parameters. Finite sample properties of the method are investigated through a moderately large simulation study and a real data example is given to illustrate the methodology.Comment: Published at http://dx.doi.org/10.1214/009053606000000551 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A general approach to the sign problem - the factorization method with multiple observables

The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with the partition function whose integrand is not real positive. The basic idea of the factorization method applied on such a system is to control some observables in order to determine and sample efficiently the region of configuration space which gives important contribution to the partition function. We argue that it is crucial to choose appropriately the set of the observables to be controlled in order for the method to work successfully in a general system. This is demonstrated by an explicit example, in which it turns out to be necessary to control more than one observables. Extrapolation to large system size is possible due to the nice scaling properties of the factorized functions, and known results obtained by an analytic method are shown to be consistently reproduced.Comment: 6 pages, 3 figures, (v2) references added (v3) Sections IV, V and VI improved, final version accepted by PR

A Study of the Complex Action Problem in a Simple Model for Dynamical Compactification in Superstring Theory Using the Factorization Method

The IIB matrix model proposes a mechanism for dynamically generating four dimensional space--time in string theory by spontaneous breaking of the ten dimensional rotational symmetry $\textrm{SO}(10)$. Calculations using the Gaussian expansion method (GEM) lend support to this conjecture. We study a simple $\textrm{SO}(4)$ invariant matrix model using Monte Carlo simulations and we confirm that its rotational symmetry breaks down, showing that lower dimensional configurations dominate the path integral. The model has a strong complex action problem and the calculations were made possible by the use of the factorization method on the density of states $\rho_n(x)$ of properly normalized eigenvalues $\tilde\lambda_n$ of the space--time moment of inertia tensor. We study scaling properties of the factorized terms of $\rho_n(x)$ and we find them in agreement with simple scaling arguments. These can be used in the finite size scaling extrapolation and in the study of the region of configuration space obscured by the large fluctuations of the phase. The computed values of $\tilde\lambda_n$ are in reasonable agreement with GEM calculations and a numerical method for comparing the free energy of the corresponding ansatze is proposed and tested.Comment: 7 pages, 4 figures, Talk presented at the XXVIII International Symposium on Lattice Field Theory, Lattice2010, Villasimius, Italy, June 201

Recent Progress of Multiferroic Perovskite Manganites

Many multiferroic materials, with various chemical compositions and crystal structures, have been discovered in the past years. Among these multiferroics, some perovskite manganites with ferroelectricity driven by magnetic orders are of particular interest. In these multiferroic perovskite manganites, not only their multiferroic properties are quite prominent, but also the involved physical mechanisms are very plenty and representative. In this Brief Review, we will introduce some recent theoretical and experimental progress on multiferroic manganites.Comment: 24 pages, 17 figures. A brief revie

Cyclic nucleotide-gated channels: structural basis of ligand efficacy and allosteric modulation

Most working proteins, including metabolic enzymes, transcription regulators, and membrane receptors, transporters, and ion channels, share the property of allosteric coupling. The term 'allosteric' means that these proteins mediate indirect interactions between sites that are physically separated on the protein. In the example of ligand-gated ion channels, the binding of a suitable ligand elicits local conformational changes at the binding site, which are coupled to further conformational changes in regions distant from the binding site. The physical motions finally arrive at the site of biological activity: the ion-permeating pore. The conformational changes that lead from the ligand binding to the actual opening of the pore comprise 'gating'. In 1956, del Castillo and Katz suggested that the competition between different ligands at nicotinic acetylcholine receptors (nAChRs) could be explained by formation of an intermediate, ligand-bound, yet inactive state of the receptor, which separates the active state of the receptor from the initial binding of the ligand (del Castillo & Katz, 1957). This 'binding-then-gating', two-step model went beyond the then-prevailing drug-receptor model that assumes a single bimolecular binding reaction, and paralleled Stephenson's conceptual dichotomy of 'affinity' and 'efficacy' (Stephenson, 1956). In 1965 Monod, Wyman and Changeux presented a simple allosteric model (the MWC model) (Monod et al. 1965) that explained the cooperative binding of oxygen to haemoglobin; it was adopted as an important paradigm for ligand-gated channels soon after its initial formulation (Changeux et al. 1967; Karlin, 1967; Colquhoun, 1973)