Super Teichmüller spaces: Punctures and elliptic points

A model for the super Teichmüller space is described and calculated when the super Riemann surfaces no longer have a compact nonsingular body manifold. The bosonic and fermionic dimensions turn out to be the dimensions of the appropriate spaces of automorphic forms, in the case where the body has a finite number of punctures and/or elliptic points.     

2-manifolds of constant curvature, 3-parameter isometry groups and bäcklund transformations

The relationship between the Sine Gordon equation and Riemannian 2-manifolds of constant negative curvature is well known. We point out that it gives rise (locally) to a transitive action of the 3-parameter group SL(2,R) on the manifold. This enables us to elucidate group theoretically the geometry underlying the Bäcklund transformation. The transformation arises by passing from the 2-manifold, a homogeneous space, to 2-submanifolds of SL(2,R) defined by orbits of the solvable subgroup of SL(2,R). A similar approach allows us several other such transformations, for example, transformations linking φ_xx+φ_yy = sinhφ to φ_xx+φ_yy = sinφ and φ_xx+φ_yy = e^2φ to φ_xx+φ_yy = 0.     

Muon spin relaxation measurements of CsC60, RbC60, KC60

Muon spin relaxation (μ⁺SR) measurements of CsC₆₀ and RbC₆₀ have revealed magnetic ordering at 20 K and 15 K respectively, with static internal fields at the muon site of \sim7 G for both samples. No magnetic ordering is seen in KC₆₀ down to 2.5 K. An apparent small increase in muon spin relaxation which had been seen at 70 K in RbC₆₀ is ascribed to an extrinsic effect, originating in muons which stopped in the aluminum sample holder. This revised version was published online in July 2006 with corrections to the Cover Date.     

Optimal economic growth with foreign trade and a learning industry

Ryder (Ref. 1) has developed a simple two-sector macroeconomic model incorporatinglearning by doing as a determinant of the growth of productivity-enhancing experience and its effect on foreign trade. In this paper, optimal foreign trade and capital allocation policies are determined, in the context of the above model, for ranges of the international trade price not considered by Ryder. An extension of Ryder's model to include a dual trade price structure is briefly discussed. A specific numerical example is used to ascertain the configuration of the various features occurring in the extremal fields at different price levels.     

Operation of a conducting PRIZ

The construction and operation of a PRIZ spatial light modulator is reported using semi-transparent electrodes and no insulating layers. Qualitative observations of the dynamic properties of such conducting devices are found to be similar to those reported in the Soviet literature with several exceptions. The devices demonstrated dynamic detection, memory, and oscillatory instability as well as the typical directional filtering and dc suppression of the standard PRIZ which uses insulating layers. This is the first report of a non-Soviet built device of this type.     

MANET Routing with Provably Low Complexity Through Constant Density Clustering and Route Request Broadcast

As mobile ad hoc networks (MANETs) are emerging as important components in critical and large-scale applications, it is crucial to develop MANET routing mechanisms with provably low complexity. In this paper, we give a tutorial overview of the efficient use of elementary node clustering and route request broadcast mechanisms for low-complexity MANET routing. We explain these mechanisms with illustrative examples and discuss their theoretical performance characteristics. We demonstrate that node clustering with constant density and route request broadcasting with a doubling radius technique over the network of cluster leaders can be employed for MANET routing with theoretically proven low complexity. Moreover, we contrast these efficient elementary clustering and route request broadcast mechanisms with clustering and route information accumulation mechanisms in the widely studied AODV and DSR routing protocols and discuss the implications of these various mechanisms for scalable MANET routing.     

Magnetic dilution in the geometrically frustrated SrCr(9p)Ga(12-9p)O19 and the role of local dynamics: A muon spin relaxation study

We investigate the spin dynamics of SrCr(9p)Ga(12-9p)O19 for p below and above the percolation threshold p(c) using muon spin relaxation. Our major findings are as follows: (i) At T-->0 the relaxation rate is T independent and approximately p(3), (ii) the slowing down of spin fluctuation is activated with an energy U, which is also a linear function of p(3) and lim U as p-->0 = 8 K; this energy scale could stem only from a single ion anisotropy, and (iii) the p dependence of the dynamical properties is identical below and above p(c), indicating that they are controlled by local excitation.     

An Adaptive Interacting Wang–Landau Algorithm for Automatic Density Exploration

While statisticians are well-accustomed to performing exploratory analysis in the modeling stage of an analysis, the notion of conducting preliminary general-purpose exploratory analysis in the Monte Carlo stage (or more generally, the model-fitting stage) of an analysis is an area that we feel deserves much further attention. Toward this aim, this article proposes a general-purpose algorithm for automatic density exploration. The proposed exploration algorithm combines and expands upon components from various adaptive Markov chain Monte Carlo methods, with the Wang–Landau algorithm at its heart. Additionally, the algorithm is run on interacting parallel chains—a feature that both decreases computational cost as well as stabilizes the algorithm, improving its ability to explore the density. Performance of this new parallel adaptive Wang–Landau algorithm is studied in several applications. Through a Bayesian variable selection example, we demonstrate the convergence gains obtained with interacting chains. The ability of the algorithm’s adaptive proposal to induce mode-jumping is illustrated through a Bayesian mixture modeling application. Last, through a two-dimensional Ising model, the authors demonstrate the ability of the algorithm to overcome the high correlations encountered in spatial models. Supplemental materials are available online.     

A nonstationary model of newborn EEG

The detection of seizure in the newborn is a critical aspect of neurological research. Current automatic detection techniques are difficult to assess due to the problems associated with acquiring and labelling newborn electroencephalogram (EEG) data. A realistic model for newborn EEG would allow confident development, assessment and comparison of these detection techniques. This paper presents a model for newborn EEG that accounts for its self-similar and nonstationary nature. The model consists of background and seizure submodels. The newborn EEG background model is based on the short-time power spectrum with a time-varying power law. The relationship between the fractal dimension and the power law of a power spectrum is utilized for accurate estimation of the short-time power law exponent. The newborn EEG seizure model is based on a well-known time-frequency signal model. This model addresses all significant time-frequency characteristics of newborn EEG seizure which include; multiple components or harmonics, piecewise linear instantaneous frequency laws and harmonic amplitude modulation. Estimates of the parameters of both models are shown to be random and are modelled using the data from a total of 500 background epochs and 204 seizure epochs. The newborn EEG background and seizure models are validated against real newborn EEG data using the correlation coefficient. The results show that the output of the proposed models have a higher correlation with real newborn EEG than currently accepted models (a 10% and 38% improvement for background and seizure models, respectively).