Search results for " Statistical"
showing 10 items of 1649 documents
Similarity Solutions and Collapse in the Attractive Gross-Pitaevskii Equation
2000
We analyse a generalised Gross-Pitaevskii equation involving a paraboloidal trap potential in $D$ space dimensions and generalised to a nonlinearity of order $2n+1$. For {\em attractive} coupling constants collapse of the particle density occurs for $Dn\ge 2$ and typically to a $\delta$-function centered at the origin of the trap. By introducing a new dynamical variable for the spherically symmetric solutions we show that all such solutions are self-similar close to the center of the trap. Exact self-similar solutions occur if, and only if, $Dn=2$, and for this case of $Dn=2$ we exhibit an exact but rather special D=1 analytical self-similar solution collapsing to a $\delta$-function which …
Statistical Mechanics of the Integrable Models
1987
There is an infinity of classically integrable models. The only ones we can consider here, and these only briefly, are: the sine-Gordon (s-G) model $${\phi _{{\rm{xx}}}}{}^ - {\phi _{{\rm{tt}}}} = {{\rm{m}}^2}\sin \phi ,$$ (1.1) the sinh-Gordon (sinh-G) model $${\phi _{{\rm{xx}}}}{}^ - {\phi _{{\rm{tt}}}} = {{\rm{m}}^2}\sinh \phi ,$$ (1.2) and the repulsive and attractive non-linear Schrodinger (NLS) models $${}^ - {\rm{i}}{\phi _{\rm{t}}} = {\phi _{{\rm{xx}}}}{}^ - 2{\rm{c}}\phi {\left| \phi \right|^2}.$$ (1.3) The “attractive” NLS has real coupling constant c 0; φ is complex. In (1.1) and (1.2) m is a mass (ħ = c = 1) and φ is real. These 4 integrable models are in one space and one time …
Quantum and Classical Statistical Mechanics of the Non-Linear Schrödinger, Sinh-Gordon and Sine-Gordon Equations
1985
We are going to describe our work on the quantum and classical statistical mechanics of some exactly integrable non-linear one dimensional systems. The simplest is the non-linear Schrodinger equation (NLS) $$i{\psi _t} = - {\psi _{XX}} + 2c{\psi ^ + }\psi \psi $$ (1) where c, the coupling constant, is positive. The others are the sine- and sinh-Gordon equations (sG and shG) $${\phi _{xx}} - {\phi _{tt}} = {m^2}\sin \phi $$ (1.2) $${\phi _{xx}} - {\phi _{tt}} = {m^2}\sinh \phi $$ (1.3)
Domain Wall Renormalization Group Study of XY Model with Quenched Random Phase Shifts
2002
The XY model with quenched random disorder is studied by a zero temperature domain wall renormalization group method in 2D and 3D. Instead of the usual phase representation we use the charge (vortex) representation to compute the domain wall, or defect, energy. For the gauge glass corresponding to the maximum disorder we reconfirm earlier predictions that there is no ordered phase in 2D but an ordered phase can exist in 3D at low temperature. However, our simulations yield spin stiffness exponents $\theta_{s} \approx -0.36$ in 2D and $\theta_{s} \approx +0.31$ in 3D, which are considerably larger than previous estimates and strongly suggest that the lower critical dimension is less than thr…
Energy landscape properties studied using symbolic sequences
2006
We investigate a classical lattice system with $N$ particles. The potential energy $V$ of the scalar displacements is chosen as a $\phi ^4$ on-site potential plus interactions. Its stationary points are solutions of a coupled set of nonlinear equations. Starting with Aubry's anti-continuum limit it is easy to establish a one-to-one correspondence between the stationary points of $V$ and symbolic sequences $\bm{\sigma} = (\sigma_1,...,\sigma_N)$ with $\sigma_n=+,0,-$. We prove that this correspondence remains valid for interactions with a coupling constant $\epsilon$ below a critical value $\epsilon_c$ and that it allows the use of a ''thermodynamic'' formalism to calculate statistical prope…
Measuring Spatiotemporal Dependencies in Bivariate Temporal Random Sets with Applications to Cell Biology
2008
Analyzing spatiotemporal dependencies between different types of events is highly relevant to many biological phenomena (e.g., signaling and trafficking), especially as advances in probes and microscopy have facilitated the imaging of dynamic processes in living cells. For many types of events, the segmented areas can overlap spatially and temporally, forming random clumps. In this paper, we model the binary image sequences of two different event types as a realization of a bivariate temporal random set and propose a nonparametric approach to quantify spatial and spatiotemporal interrelations using the pair correlation, cross-covariance, and the Ripley K functions. Based on these summary st…
Diagnostic accuracy of adding copeptin to cardiac troponin for non-ST-elevation myocardial infarction: A systematic review and meta-analysis.
2018
Introduction This study aimed to determine the diagnostic accuracy of adding copeptin to cardiac troponin (cTn) on admission to the emergency department (ED) for non-ST elevation myocardial infarction (NSTEMI) compared to cTn alone. Materials and methods A literature search of MEDLINE, EMBASE, and the Cochrane Library was performed (search date: April 13, 2018). Primary studies were included if they accurately reported on patients with symptoms suggestive of acute myocardial infarction and measured both cTn alone and cTn with copeptin upon admission to the ED. The patients with evidence of ST elevation myocardial infarction were excluded. To assess the risk of bias for the included studies,…
Applying univariate vs. multivariate statistics to investigate therapeutic efficacy in (pre)clinical trials: A Monte Carlo simulation study on the ex…
2020
BackgroundSmall sample sizes combined with multiple correlated endpoints pose a major challenge in the statistical analysis of preclinical neurotrauma studies. The standard approach of applying univariate tests on individual response variables has the advantage of simplicity of interpretation, but it fails to account for the covariance/correlation in the data. In contrast, multivariate statistical techniques might more adequately capture the multi-dimensional pathophysiological pattern of neurotrauma and therefore provide increased sensitivity to detect treatment effects.ResultsWe systematically evaluated the performance of univariate ANOVA, Welch's ANOVA and linear mixed effects models ver…
Testing Measurement Invariance Across Spanish and English Versions of the Physical Self-Description Questionnaire : An Application of Exploratory Str…
2014
Test of measurement invariance across translated versions of questionnaires is a critical prerequisite to comparing scores on the different versions. In this study, we used exploratory structural equation modeling (ESEM) as an alternative approach to evaluate the measurement invariance of the Spanish version of the Physical Self-Description Questionnaire (PSDQ). The two versions were administered to large samples of Australian and Spanish adolescents. First, we compared the CFA and ESEM approaches and showed that ESEM fitted the data much better and resulted in substantially more differentiated factors. We then tested measurement invariance with a 13-model ESEM taxonomy. Results justified u…
Cross-Cultural Validity of the Physical Self-Description Questionnaire: Comparison of Factor Structures in Australia, Spain, and Turkey
2002
Abstract We evaluated the cross-cultural generalizability of the factor structure for the Physical Self-Description Questionnaire (PSDQ) using confirmatory factor analysis. The factor structure was reasonably invariant over large samples of responses by Australian, Spanish, and Turkish students. Consistent with a priori predictions, the factor structures based on Australian and Spanish high school students were somewhat more similar to each other than to those based on Turkish university students, but these differences were small. Psychometric, theoretical, cross-cultural, and practical considerations support the PSDQ's usefulness in a variety of research and applied settings. The study als…