1,110 research outputs found
Random Matrix approach to collective behavior and bulk universality in protein dynamics
Covariance matrices of amino acid displacements, commonly used to
characterize the large-scale movements of proteins, are investigated through
the prism of Random Matrix Theory. Bulk universality is detected in the local
spacing statistics of noise-dressed eigenmodes, which is well described by a
Brody distribution with parameter . This finding, supported by
other consistent indicators, implies a novel quantitative criterion to single
out the collective degrees of freedom of the protein from the majority of
high-energy, localized vibrations.Comment: 4 pages, 7 figure
Compact smallest eigenvalue expressions in Wishart-Laguerre ensembles with or without fixed-trace
The degree of entanglement of random pure states in bipartite quantum systems
can be estimated from the distribution of the extreme Schmidt eigenvalues. For
a bipartition of size M\geq N, these are distributed according to a
Wishart-Laguerre ensemble (WL) of random matrices of size N x M, with a
fixed-trace constraint. We first compute the distribution and moments of the
smallest eigenvalue in the fixed trace orthogonal WL ensemble for arbitrary
M\geq N. Our method is based on a Laplace inversion of the recursive results
for the corresponding orthogonal WL ensemble by Edelman. Explicit examples are
given for fixed N and M, generalizing and simplifying earlier results. In the
microscopic large-N limit with M-N fixed, the orthogonal and unitary WL
distributions exhibit universality after a suitable rescaling and are therefore
independent of the constraint. We prove that very recent results given in terms
of hypergeometric functions of matrix argument are equivalent to more explicit
expressions in terms of a Pfaffian or determinant of Bessel functions. While
the latter were mostly known from the random matrix literature on the QCD Dirac
operator spectrum, we also derive some new results in the orthogonal symmetry
class.Comment: 25 pag., 4 fig - minor changes, typos fixed. To appear in JSTA
The Index Distribution of Gaussian Random Matrices
We compute analytically, for large N, the probability distribution of the
number of positive eigenvalues (the index N_{+}) of a random NxN matrix
belonging to Gaussian orthogonal (\beta=1), unitary (\beta=2) or symplectic
(\beta=4) ensembles. The distribution of the fraction of positive eigenvalues
c=N_{+}/N scales, for large N, as Prob(c,N)\simeq\exp[-\beta N^2 \Phi(c)] where
the rate function \Phi(c), symmetric around c=1/2 and universal (independent of
), is calculated exactly. The distribution has non-Gaussian tails, but
even near its peak at c=1/2 it is not strictly Gaussian due to an unusual
logarithmic singularity in the rate function.Comment: 4 pages Revtex, 4 .eps figures include
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Bump start needed: linking guidelines, policy and practice in promoting physical activity during and beyond pregnancy
First paragraph: There is compelling evidence that regular physical activity (PA) during pregnancy benefits both mother and baby.1 2 Notably, physical and psychological benefits are evident in the literature, such as marked reductions in the development of gestational diabetes and hypertensive disorders, alongside improvements in depressive symptoms and cardiorespiratory fitness.1 2 The evidence base has been reflected by recent policy initiatives, for example, in 2017 (relaunched in 2019), the UK‘s chief medical officers (CMOs) published PA guidelines for pregnant women, which made substantial strides in unifying and translating the evidence into recommendations.1 The CMO guidelines are aimed at supporting health professionals to provide consistent, evidence-based PA messages to women throughout pregnancy.1 Recently, the Chartered Institute for the Management of Sport and Physical Activity have updated their professional standards for working with antenatal and postnatal clients to align with these CMO guidelines.3 However, not all women have access to professionals with this level of expertise and training, potentially limiting the impact of the CMO guidelines
Distributions of Conductance and Shot Noise and Associated Phase Transitions
For a chaotic cavity with two indentical leads each supporting N channels, we
compute analytically, for large N, the full distribution of the conductance and
the shot noise power and show that in both cases there is a central Gaussian
region flanked on both sides by non-Gaussian tails. The distribution is weakly
singular at the junction of Gaussian and non-Gaussian regimes, a direct
consequence of two phase transitions in an associated Coulomb gas problem.Comment: 5 pages, 3 figures include
Spectra of Empirical Auto-Covariance Matrices
We compute spectra of sample auto-covariance matrices of second order
stationary stochastic processes. We look at a limit in which both the matrix
dimension and the sample size used to define empirical averages
diverge, with their ratio kept fixed. We find a remarkable scaling
relation which expresses the spectral density of sample
auto-covariance matrices for processes with dynamical correlations as a
continuous superposition of appropriately rescaled copies of the spectral
density for a sequence of uncorrelated random
variables. The rescaling factors are given by the Fourier transform
of the auto-covariance function of the stochastic process. We also obtain a
closed-form approximation for the scaling function
. This depends on the shape parameter , but
is otherwise universal: it is independent of the details of the underlying
random variables, provided only they have finite variance. Our results are
corroborated by numerical simulations using auto-regressive processes.Comment: 4 pages, 2 figure
Number statistics for -ensembles of random matrices: applications to trapped fermions at zero temperature
Let be the probability that a
-ensemble of random matrices with confining potential
has eigenvalues inside an interval of the real
line. We introduce a general formalism, based on the Coulomb gas technique and
the resolvent method, to compute analytically for large . We show that this probability scales for large
as , where is the Dyson index of the
ensemble. The rate function , independent of ,
is computed in terms of single integrals that can be easily evaluated
numerically. The general formalism is then applied to the classical
-Gaussian (), -Wishart () and
-Cauchy () ensembles. Expanding the rate function
around its minimum, we find that generically the number variance exhibits a non-monotonic behavior as a function of the size
of the interval, with a maximum that can be precisely characterized. These
analytical results, corroborated by numerical simulations, provide the full
counting statistics of many systems where random matrix models apply. In
particular, we present results for the full counting statistics of zero
temperature one-dimensional spinless fermions in a harmonic trap.Comment: 34 pages, 19 figure
Overcoming the risk of inaction from emissions uncertainty in smallholder agriculture
The potential for improving productivity and increasing the resilience of smallholder agriculture, while also contributing to climate change mitigation, has recently received considerable political attention (Beddington et al 2012). Financial support for improving smallholder agriculture could come from performance-based funding including sale of carbon credits or certified commodities, payments for ecosystem services, and nationally appropriate mitigation action (NAMA) budgets, as well as more traditional sources of development and environment finance. Monitoring the greenhouse gas fluxes associated with changes to agricultural practice is needed for performance-based mitigation funding, and efforts are underway to develop tools to quantify mitigation achieved and assess trade-offs and synergies between mitigation and other livelihood and environmental priorities (Olander 2012)
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