A Matrix Hyperbolic Cosine Algorithm and Applications

In this paper, we generalize Spencer's hyperbolic cosine algorithm to the matrix-valued setting. We apply the proposed algorithm to several problems by analyzing its computational efficiency under two special cases of matrices; one in which the matrices have a group structure and an other in which they have rank-one. As an application of the former case, we present a deterministic algorithm that, given the multiplication table of a finite group of size $n$, it constructs an expanding Cayley graph of logarithmic degree in near-optimal O(n^2 log^3 n) time. For the latter case, we present a fast deterministic algorithm for spectral sparsification of positive semi-definite matrices, which implies an improved deterministic algorithm for spectral graph sparsification of dense graphs. In addition, we give an elementary connection between spectral sparsification of positive semi-definite matrices and element-wise matrix sparsification. As a consequence, we obtain improved element-wise sparsification algorithms for diagonally dominant-like matrices.Comment: 16 pages, simplified proof and corrected acknowledging of prior work in (current) Section

The neutron radii of Lead and neutron stars

A new relation between the neutron skin of a heavy nucleus and the radius of a neutron star is proposed: the larger the neutron skin of the nucleus the larger the radius of the star. Relativistic models that reproduce a variety of ground-state observables can not determine uniquely the neutron skin of a heavy nucleus. Thus, a large range of neutron skins is generated by supplementing the models with nonlinear couplings between isoscalar and isovector mesons. We illustrate how the correlation between the neutron skin and the radius of the star can be used to place important constraints on the equation of state and how it may help elucidate the existence of a phase transition in the interior of the neutron star.Comment: 4 pages including 4 encapsulated postscript figure

A lattice NRQCD calculation of the B0−Bˉ0B^0-\bar{B}^0 mixing parameter B_B

We present a lattice calculation of the B meson B-parameter B_B using the NRQCD action. The heavy quark mass dependence is explicitly studied over a mass range between m_b and 4m_b with the $O(1/m_Q)$ and $O(1/m_Q^2)$ actions. We find that the ratios of lattice matrix elements $/^2$ and $/^2$, which contribute to B_B through mixing, have significant $1/m_Q$ dependence while that of the leading operator $/^2$ has little $1/m_Q$ effect. The combined result for B_B(m_b) has small but non-zero mass dependence, and the B_B(m_b) becomes smaller by 10% with the 1/m_Q correction compared to the static result. Our result in the quenched approximation at \beta=5.9 is B_{B_d}(5 GeV) = 0.75(3)(12), where the first error is statistical and the second is a systematic uncertainty.Comment: 20 pages, 11 figures, uses REVTeX, typos correcte

Random Series and Discrete Path Integral methods: The Levy-Ciesielski implementation

We perform a thorough analysis of the relationship between discrete and series representation path integral methods, which are the main numerical techniques used in connection with the Feynman-Kac formula. First, a new interpretation of the so-called standard discrete path integral methods is derived by direct discretization of the Feynman-Kac formula. Second, we consider a particular random series technique based upon the Levy-Ciesielski representation of the Brownian bridge and analyze its main implementations, namely the primitive, the partial averaging, and the reweighted versions. It is shown that the n=2^k-1 subsequence of each of these methods can also be interpreted as a discrete path integral method with appropriate short-time approximations. We therefore establish a direct connection between the discrete and the random series approaches. In the end, we give sharp estimates on the rates of convergence of the partial averaging and the reweighted Levy-Ciesielski random series approach for sufficiently smooth potentials. The asymptotic rates of convergence are found to be O(1/n^2), in agreement with the rates of convergence of the best standard discrete path integral techniques.Comment: 20 pages, 4 figures; the two equations before Eq. 14 are corrected; other typos are remove

The Stroop revisited: a meta-analysis of interference control in AD/HD

Background: An inhibition deficit, including poor interference control, has been implicated as one of the core deficits in AD/HD. Interference control is clinically measured by the Stroop Colour-Word Task. The aim of this meta-analysis was to investigate the strength of an interference deficit in AD/HD as measured by the Stroop Colour-Word Task and to assess the role of moderating variables that could explain the results. These moderating variables included: methods of calculating the interference score, comorbid reading and psychiatric disorders, AD/HD-subtypes, gender, age, intellectual functioning, medication, and sample size. Methods: Seventeen independent studies were located including 1395 children, adolescents, and young adults, in the age range of 6-27 years. A meta-analysis was conducted to assess the effect sizes for the scores on the word and the colour card as well as the interference score. Results: Children with AD/HD performed more poorly on all three dependent variables. The effect sizes for word reading (d = .49) and colour naming (d = .58) were larger and more homogeneous than the effect size for the interference score (d = .35). The method used to calculate the interference score strongly influenced the findings for this measure. When interference control was calculated as the difference between the score on the colour card minus the score on the colour-word card, no differences were found between AD/HD groups and normal control groups. Discussion: The Stroop Colour-Word Task, in standard form, does not provide strong evidence for a deficit in interference control in AD/HD. However, the Stroop Colour-Word Task may not be a valid measure of interference control in AD/HD and alternative methodologies may be needed to test this aspect of the inhibitory deficit model in AD/HD. © Association for Child Psychology Psychiatry, 2004

Prevalence of Frailty in European Emergency Departments (FEED): an international flash mob study

Introduction Current emergency care systems are not optimized to respond to multiple and complex problems associated with frailty. Services may require reconfiguration to effectively deliver comprehensive frailty care, yet its prevalence and variation are poorly understood. This study primarily determined the prevalence of frailty among older people attending emergency care. Methods This cross-sectional study used a flash mob approach to collect observational European emergency care data over a 24-h period (04 July 2023). Sites were identified through the European Task Force for Geriatric Emergency Medicine collaboration and social media. Data were collected for all individuals aged 65 + who attended emergency care, and for all adults aged 18 + at a subset of sites. Variables included demographics, Clinical Frailty Scale (CFS), vital signs, and disposition. European and national frailty prevalence was determined with proportions with each CFS level and with dichotomized CFS 5 + (mild or more severe frailty). Results Sixty-two sites in fourteen European countries recruited five thousand seven hundred eighty-five individuals. 40% of 3479 older people had at least mild frailty, with countries ranging from 26 to 51%. They had median age 77 (IQR, 13) years and 53% were female. Across 22 sites observing all adult attenders, older people living with frailty comprised 14%. Conclusion 40% of older people using European emergency care had CFS 5 + . Frailty prevalence varied widely among European care systems. These differences likely reflected entrance selection and provide windows of opportunity for system configuration and workforce planning