Finding the smallest eigenvalue by the inverse Monte Carlo method with refinement

Finding the smallest eigenvalue of a given square matrix A of order n is computationally very intensive problem. The most popular method for this problem is the Inverse Power Method which uses LU-decomposition and forward and backward solving of the factored system at every iteration step. An alternative to this method is the Resolvent Monte Carlo method which uses representation of the resolvent matrix [I -qA](-m) as a series and then performs Monte Carlo iterations (random walks) on the elements of the matrix. This leads to great savings in computations, but the method has many restrictions and a very slow convergence. In this paper we propose a method that includes fast Monte Carlo procedure for finding the inverse matrix, refinement procedure to improve approximation of the inverse if necessary, and Monte Carlo power iterations to compute the smallest eigenvalue. We provide not only theoretical estimations about accuracy and convergence but also results from numerical tests performed on a number of test matrices.

An uncollected poem and the 'Madrid Journal' by Bernard Spencer

Derwent May introduces Peter Robinson’s discovery of a lost Bernard Spencer poem and diary.

Nuclear Dbf2-related protein kinases (NDRs) in isolated cardiac myocytes and the myocardium: activation by cellular stresses and by phosphoprotein serine-/threonine-phosphatase inhibitors

The nuclear Dbf2-related protein kinases 1 and 2 (NDR1/2) are closely-related AGC family kinases that are strongly conserved through evolution. In mammals, they are activated inter alia by phosphorylation of an hydrophobic domain threonine-residue [NDR1(Thr-444)/NDR2(Thr-442)] by an extrinsic protein kinase followed by autophosphorylation of a catalytic domain serine-residue [NDR1(Ser-281)/NDR2(Ser-282)]. We examined NDR1/2 expression and regulation in primary cultures of neonatal rat cardiac myocytes and in perfused adult rat hearts. In myocytes, transcripts for NDR2, but not NDR1, were induced by the hypertrophic agonist, endothelin-1. NDR1(Thr-444) and NDR2(Thr-442) were rapidly phosphorylated (maximal in 15-30 min) in myocytes exposed to some phosphoprotein Ser-/Thr-phosphatase 1/2 inhibitors (calyculin A, okadaic acid) and, to a lesser extent, by hyperosmotic shock, low concentrations of H(2)O(2), or chelerythrine. In myocytes adenovirally-transduced to express FLAG-NDR2 (which exhibited a mainly-cytoplasmic localisation), the same agents increased FLAG-NDR2 activity as assessed by in vitro protein kinase assays, indicative of FLAG-NDR2(Ser-282/Thr-442) phosphorylation. Calyculin A-induced phosphorylation of NDR1(Thr-444)/NDR2(Thr-442) and activation of FLAG-NDR2 were inhibited by staurosporine, but not by other protein kinase inhibitors tested. In ex vivo rat hearts, NDR1(Thr-444)/NDR2(Thr-442) were phosphorylated in response to ischaemia-reperfusion or calyculin A. From a pathological viewpoint, we conclude that activities of NDR1 and NDR2 are responsive to cytotoxic stresses in heart preparations and this may represent a previously-unidentified response to myocardial ischaemia in vivo.

Radiometric analysis of the light coupled by optimally cut plastic optical fiber amplitude modulating reflectance displacement sensors

A radiometric analysis of the light coupled by optical fiber amplitude modulating extrinsic-type reflectance displacement sensors is presented. Uncut fiber sensors show the largest range but a smaller responsivity. Single cut fiber sensors exhibit an improvement in responsivity at the expense of range. A further increase in responsivity as well as a reduction in the operational range is obtained when the double cut sensor configuration is implemented. The double cut configuration is particularly suitable in applications where feedback action is applied to the moving reflector surface. © 2000 American Institute of Physics.

Minimising the latency induced by consistency control, within a large scale multi-user distributed virtual reality system

Where users are interacting in a distributed virtual environment, the actions of each user must be observed by peers with sufficient consistency and within a limited delay so as not to be detrimental to the interaction. The consistency control issue may be split into three parts: update control; consistent enactment and evolution of events; and causal consistency. The delay in the presentation of events, termed latency, is primarily dependent on the network propagation delay and the consistency control algorithms. The latency induced by the consistency control algorithm, in particular causal ordering, is proportional to the number of participants. This paper describes how the effect of network delays may be reduced and introduces a scalable solution that provides sufficient consistency control while minimising its effect on latency. The principles described have been developed at Reading over the past five years. Similar principles are now emerging in the simulation community through the HLA standard. This paper attempts to validate the suggested principles within the schema of distributed simulation and virtual environments and to compare and contrast with those described by the HLA definition documents.

Comment on "Tropospheric temperature response to stratospheric ozone recovery in the 21st century" by Hu et al. (2011)

Abstract. In a recent paper Hu et al. (2011) suggest that the recovery of stratospheric ozone during the first half of this century will significantly enhance free tropospheric and surface warming caused by the anthropogenic increase of greenhouse gases, with the effects being most pronounced in Northern Hemisphere middle and high latitudes. These surprising results are based on a multi-model analysis of CMIP3 model simulations with and without prescribed stratospheric ozone recovery. Hu et al. suggest that in order to properly quantify the tropospheric and surface temperature response to stratospheric ozone recovery, it is necessary to run coupled atmosphere-ocean climate models with stratospheric ozone chemistry. The results of such an experiment are presented here, using a state-of-the-art chemistry-climate model coupled to a three-dimensional ocean model. In contrast to Hu et al., we find a much smaller Northern Hemisphere tropospheric temperature response to ozone recovery, which is of opposite sign. We suggest that their result is an artifact of the incomplete removal of the large effect of greenhouse gas warming between the two different sets of models.

Toward monitoring the tropospheric temperature by means of a general circulation model

The recent global tropospheric temperature trend can be reproduced by climate models that are forced only by observed sea surface temperature (SST) anomalies. In this study, simulations with the Hamburg climate model (ECHAM) are compared to temperatures from microwave sounding units (MSU) and to reanalyses from the European Centre for Medium-Range Weather Forecasts. There is overall agreement of observed and simulated tropospheric temperature anomalies in many regions, in particular in the tropics and over the oceans, which lack conventional observing systems. This provides the opportunity to link physically different quantities, such as surface observations or analyses (SST) and satellite soundings (MSU) by means of a general circulation model. The proposed method can indicate inconsistencies between MSU temperatures and SSTs and has apparently done so. Differences between observed and simulated tropospheric temperature anomalies can partly be attributed to stratospheric aerosol variations due to major volcanic eruptions.

Some results from an intercomparison of the climates simulated by 14 atmospheric general circulation models

Some climatological information from 14 atmospheric general circulation models is presented and compared in order to assess the ability of a broad group of models to simulate current climate. The quantities considered are cross sections of temperature, zonal wind, and meridional stream function together with latitudinal distributions of mean sea level pressure and precipitation rate. The nature of the deficiencies in the simulated climates that are common to all models and those which differ among models is investigated; the general improvement in the ability of models to simulate certain aspects of the climate is shown; consideration is given to the effect of increasing resolution on simulated climate; and approaches to understanding and reducing model deficiencies are discussed. The information presented here is a subset of a more voluminous compilation which is available in report form (Boer et al., 1991). This report contains essentially the same text, but results from all 14 models are presented together with additional results in the form of geographical distributions of surface variables and certain difference statistics.

An intercomparison of the climates simulated by 14 atmospheric general circulation models

Climatological information from fourteen atmospheric general circulation models is presented and compared in order to assess the ability of a broad group of models to simulate current climate. The quantities considered are cross sections of temperature, zonal wind and meridional stream function together with latitudinal distributions of mean sea-level pressure and precipitation rate. The nature of the deficiencies in the simulated climates that are common to all models and those which differ among models is investigated, general improvement in the ability of models to simulate certain aspects of the climate is shown, consideration is given to the effect of increasing resolution on simulated climate and approaches to the understanding and reduction of model deficiencies are discussed.