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

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)

Cosmological solutions and observational constraints on 5-dimensional braneworld cosmology with gravitating Nambu-Goto matching conditions

We investigate the cosmological implications of the recently constructed 5-dimensional braneworld cosmology with gravitating Nambu-Goto matching conditions. Inserting both matter and radiation sectors, we first extract the analytical cosmological solutions. Additionally, we use observational data from Type Ia Supernovae (SNIa) and Baryon Acoustic Oscillations (BAO), along with requirements of Big Bang Nucleosynthesis (BBN), in order to impose constraints on the parameters of the model. We find that the scenario at hand is in very good agreement with observations, and thus a small departure from the standard Randall-Sundrum scenario is allowed.Comment: 22 pages, 5 figures, version published in Phys. Rev. D. arXiv admin note: text overlap with arXiv:1312.429

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

Geographical Coarsegraining of Complex Networks

We perform the renormalization-group-like numerical analysis of geographically embedded complex networks on the two-dimensional square lattice. At each step of coarsegraining procedure, the four vertices on each $2 \times 2$ square box are merged to a single vertex, resulting in the coarsegrained system of the smaller sizes. Repetition of the process leads to the observation that the coarsegraining procedure does not alter the qualitative characteristics of the original scale-free network, which opens the possibility of subtracting a smaller network from the original network without destroying the important structural properties. The implication of the result is also suggested in the context of the recent study of the human brain functional network.Comment: To appear in Phys. Rev. Let