Homotopy Method for the Large, Sparse, Real Nonsymmetric Eigenvalue Problem

A homotopy method to compute the eigenpairs, i.e., the eigenvectors and eigenvalues, of a given real matrix A1 is presented. From the eigenpairs of some real matrix A0, the eigenpairs of A(t) ≡ (1 − t)A0 + tA1 are followed at successive "times" from t = 0 to t = 1 using continuation. At t = 1, the eigenpairs of the desired matrix A1 are found. The following phenomena are present when following the eigenpairs of a general nonsymmetric matrix: • bifurcation, • ill conditioning due to nonorthogonal eigenvectors, • jumping of eigenpaths. These can present considerable computational difficulties. Since each eigenpair can be followed independently, this algorithm is ideal for concurrent computers. The homotopy method has the potential to compete with other algorithms for computing a few eigenvalues of large, sparse matrices. It may be a useful tool for determining the stability of a solution of a PDE. Some numerical results will be presented

The dynamics of laser droplet generation

We propose an experimental setup allowing for the characterization of laser droplet generation in terms of the underlying dynamics, primarily showing that the latter is deterministically chaotic by means of nonlinear time series analysis methods. In particular, we use a laser pulse to melt the end of a properly fed vertically placed metal wire. Due to the interplay of surface tension, gravity force and light-metal interaction, undulating pendant droplets are formed at the molten end, which eventually completely detach from the wire as a consequence of their increasing mass. We capture the dynamics of this process by employing a high-speed infrared camera, thereby indirectly measuring the temperature of the wire end and the pendant droplets. The time series is subsequently generated as the mean value over the pixel intensity of every infrared snapshot. Finally, we employ methods of nonlinear time series analysis to reconstruct the phase space from the observed variable and test it against determinism and stationarity. After establishing that the observed laser droplet generation is a deterministic and dynamically stationary process, we calculate the spectra of Lyapunov exponents. We obtain a positive largest Lyapunov exponent and a negative divergence, i.e., sum of all the exponents, thus indicating that the observed dynamics is deterministically chaotic with an attractor as solution in the phase space. In addition to characterizing the dynamics of laser droplet generation, we outline industrial applications of the process and point out the significance of our findings for future attempts at mathematical modeling.Comment: 7 two-column pages, 8 figures; accepted for publication in Chaos [supplementary material available at http://www.matjazperc.com/chaos/laser.html

On Modeling Clustering Indexes of BT-Like Systems

Abstract—In this paper, we explore the “clustering ” phenomenon in BT-like systems. A high clustering implies peers have a high tendency to exchange information with peers of the similar bandwidth type. We first show the clustering does exist in BT-like systems. Although high clustering is desirable for file sharing application, it may not be appropriate for multimedia streaming applications. We provide analytical models to calculate the clustering index and illustrate how one can control the clustering index for different P2P applications. I

Numerical Study of the Behaviour of Wall Shear Stress in Pulsatile Stenotic Flows

This paper presents a numerical study of pulsatile flow through an axisymmetric stenosed artery. Numerical calculations of the incompressible Navier-Stokes equations were carried out in an axisymmetric geometry to investigate how the wall shear stress (WSS) is affected by varying levels of stenosis contractions and pulse periods (reduced velocity). It is found that the distribution and strength of the WSS is closely correlated with the position of the vortex ring formed at the stenosis. Each vortex ring generates high WSS at the stenosis walls and this high WSS propagate downstream with the vortex ring. As the vortex ring convects downstream, it loses its strength due to viscous effects and WSS decreases in magnitude. In general, the strength of the vortex ring increases with increasing stenosis levels which leads to higher WSS values on the walls. The effect of smaller pulse period is to reduce the distance between the vortex rings, thus increasing the spatial variation of WSS along the stenosed artery

A Neuroanatomical Signature for Schizophrenia Across Different Ethnic Groups

Schizophrenia is a disabling clinical syndrome found across the world. While the incidence and clinical expression of this illness are strongly influenced by ethnic factors, it is unclear whether patients from different ethnicities show distinct brain deficits. In this multicentre study, we used structural Magnetic Resonance Imaging to investigate neuroanatomy in 126 patients with first episode schizophrenia who came from 4 ethnically distinct cohorts (White Caucasians, African-Caribbeans, Japanese, and Chinese). Each patient was individually matched with a healthy control of the same ethnicity, gender, and age (±1 year). We report a reduction in the gray matter volume of the right anterior insula in patients relative to controls (P < .05 corrected); this reduction was detected in all 4 ethnic groups despite differences in psychopathology, exposure to antipsychotic medication and image acquisition sequence. This finding provides evidence for a neuroanatomical signature of schizophrenia expressed above and beyond ethnic variations in incidence and clinical expression. In light of the existing literature, implicating the right anterior insula in bipolar disorder, depression, addiction, obsessive-compulsive disorder, and anxiety, we speculate that the neuroanatomical deficit reported here may represent a transdiagnostic feature of Axis I disorders

Effect of next-nearest neighbor coupling on the optical spectra in bilayer graphene

We investigate the dependence of the optical conductivity of bilayer graphene (BLG) on the intra- and inter-layer interactions using the most complete model to date. We show that the next nearest-neighbor intralayer coupling introduces new features in the low-energy spectrum that are highly sensitive to sample doping, changing significantly the ``universal'' conductance. Further, its interplay with interlayer couplings leads to an anisotropy in conductance in the ultraviolet range. We propose that experimental measurement of the optical conductivity of intrinsic and doped BLG will provide a good benchmark for the relative importance of intra- and inter-layer couplings at different doping levels.Comment: 5 pages, 5 figure

Quantitative multidimensional phenotypes improve genetic analysis of laterality traits

The UK Medical Research Council and Wellcome (Grant ref: 217065/Z/19/Z) and the University of Bristol provide core support for ALSPAC. This publication is the work of the authors and SP and JS will serve as guarantors for the analysis of the ALSPAC data presented in this paper. GWAS data were generated by Sample Logistics and Genotyping Facilities at Wellcome Sanger Institute and LabCorp (Laboratory Corporation of America) using support from 23andMe. Support to the genetic analysis was provided by the St Andrews Bioinformatics Unit funded by the Wellcome Trust [grant 105621/Z/14/Z]. The Hong Kong sample was funded through a Collaborative Research Fund from the Hong Kong Special Administrative Region Research Grants Council (CUHK8/CRF/13G, and C4054-17WF). JS is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, 418445085) and supported by the Wellcome Trust [Institutional Strategic Support fund, Grant number 204821/Z/16/Z]. SP is funded by the Royal Society (UF150663).Handedness is the most commonly investigated lateralised phenotype and is usually measured as a binary left/right category. Its links with psychiatric and neurodevelopmental disorders prompted studies aimed at understanding the underlying genetics, while other measures and side preferences have been less studied. We investigated the heritability of hand, as well as foot, and eye preference by assessing parental effects (n ≤ 5028 family trios) and SNP-based heritability (SNP-h2, n ≤ 5931 children) in the Avon Longitudinal Study of Parents and Children (ALSPAC). An independent twin cohort from Hong Kong (n = 358) was used to replicate results from structural equation modelling (SEM). Parental left-side preference increased the chance of an individual to be left-sided for the same trait, with stronger maternal than paternal effects for footedness. By regressing out the effects of sex, age, and ancestry, we transformed laterality categories into quantitative measures. The SNP-h2 for quantitative handedness and footedness was 0.21 and 0.23, respectively, which is higher than the SNP-h2 reported in larger genetic studies using binary handedness measures. The heritability of the quantitative measure of handedness increased (0.45) compared to a binary measure for writing hand (0.27) in the Hong Kong twins. Genomic and behavioural SEM identified a shared genetic factor contributing to handedness, footedness, and eyedness, but no independent effects on individual phenotypes. Our analysis demonstrates how quantitative multidimensional laterality phenotypes are better suited to capture the underlying genetics than binary traits.Publisher PDFPeer reviewe

Photo-disintegration cross section measurements on 186^{186}W, 187^{187}Re and 188^{188}Os: Implications for the Re-Os cosmochronology

Cross sections of the $^{186}$W, $^{187}$Re, $^{188}$Os($\gamma,n$) reactions were measured using quasi-monochromatic photon beams from laser Compton scattering (LCS) with average energies from 7.3 to 10.9 MeV. The results are compared with the predictions of Hauser-Feshbach statistical calculations using four different sets of input parameters. In addition, the inverse neutron capture cross sections were evaluated by constraining the model parameters, especially the $E1$ strength function, on the basis of the experimental data. The present experiment helps to further constrain the correction factor $F_{\sigma}$ for the neutron capture on the 9.75 keV state in $^{187}$Os. Implications of $F_{\sigma}$ to the Re-Os cosmochronology are discussed with a focus on the uncertainty in the estimate of the age of the Galaxy.Comment: 11 page