149 research outputs found
Geodesic distances on density matrices
We find an upper bound for geodesic distances associated to monotone
Riemannian metrics on positive definite matrices and density matrices.Comment: 10 page
On the characterisation of paired monotone metrics
Hasegawa and Petz introduced the notion of dual statistically monotone
metrics. They also gave a characterisation theorem showing that
Wigner-Yanase-Dyson metrics are the only members of the dual family. In this
paper we show that the characterisation theorem holds true under more general
hypotheses.Comment: 12 pages, to appear on Ann. Inst. Stat. Math.; v2: changes made to
conform to accepted version, title changed as wel
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Multiplicative cascade models for fine spatial downscaling of rainfall: parameterization with rain gauge data
Capturing the spatial distribution of high-intensity rainfall over short-time intervals is critical for accurately assessing the efficacy of urban stormwater drainage systems. In a stochastic simulation framework, one method of generating realistic rainfall fields is by multiplicative random cascade (MRC) models. Estimation of MRC model parameters has typically relied on radar imagery or, less frequently, rainfall fields interpolated from dense rain gauge networks. However, such data are not always available. Furthermore, the literature is lacking estimation procedures for spatially incomplete datasets. Therefore, we proposed a simple method of calibrating an MRC model when only data from a moderately dense network of rain gauges is available, rather than from the full rainfall field. The number of gauges needs only be sufficient to adequately estimate the variance in the ratio of the rain rate at the rain gauges to the areal average rain rate across the entire spatial domain. In our example for Warsaw, Poland, we used 25 gauges over an area of approximately 1600 km(2). MRC models calibrated using the proposed method were used to downscale 15-min rainfall rates from a 20 by 20 km area to the scale of the rain gauge capture area. Frequency distributions of observed and simulated 15-min rainfall at the gauge scale were very similar. Moreover, the spatial covariance structure of rainfall rates, as characterized by the semivariogram, was reproduced after allowing the probability density function of the random cascade generator to vary with spatial scale.Keywords: Time, Multicomponent decomposition, Fields, Simulation, Disaggregation, Mesoscale rainfall, Scale universal multifractals, Stochastic model
Metric adjusted skew information: Convexity and restricted forms of superadditivity
We give a truly elementary proof of the convexity of metric adjusted skew
information following an idea of Effros. We extend earlier results of weak
forms of superadditivity to general metric adjusted skew informations.
Recently, Luo and Zhang introduced the notion of semi-quantum states on a
bipartite system and proved superadditivity of the Wigner-Yanase-Dyson skew
informations for such states. We extend this result to general metric adjusted
skew informations. We finally show that a recently introduced extension to
parameter values of the WYD-information is a special case of
(unbounded) metric adjusted skew information.Comment: An error in the literature is pointed ou
A Rigorous Proof of Fermi Liquid Behavior for Jellium Two-Dimensional Interacting Fermions
Using the method of continuous constructive renormalization group around the
Fermi surface, it is proved that a jellium two-dimensional interacting system
of Fermions at low temperature remains analytic in the coupling constant
for where is some numerical constant
and is the temperature. Furthermore in that range of parameters, the first
and second derivatives of the self-energy remain bounded, a behavior which is
that of Fermi liquids and in particular excludes Luttinger liquid behavior. Our
results prove also that in dimension two any transition temperature must be
non-perturbative in the coupling constant, a result expected on physical
grounds. The proof exploits the specific momentum conservation rules in two
dimensions.Comment: 4 pages, no figure
Extended scaling relations for planar lattice models
It is widely believed that the critical properties of several planar lattice
models, like the Eight Vertex or the Ashkin-Teller models, are well described
by an effective Quantum Field Theory obtained as formal scaling limit. On the
basis of this assumption several extended scaling relations among their indices
were conjectured. We prove the validity of some of them, among which the ones
by Kadanoff, [K], and by Luther and Peschel, [LP].Comment: 32 pages, 7 fi
Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems
We report the results of certain integrations of quantum-theoretic interest,
relying, in this regard, upon recently developed parameterizations of Boya et
al of the n x n density matrices, in terms of squared components of the unit
(n-1)-sphere and the n x n unitary matrices. Firstly, we express the normalized
volume elements of the Bures (minimal monotone) metric for n = 2 and 3,
obtaining thereby "Bures prior probability distributions" over the two- and
three-state systems. Then, as an essential first step in extending these
results to n > 3, we determine that the "Hall normalization constant" (C_{n})
for the marginal Bures prior probability distribution over the
(n-1)-dimensional simplex of the n eigenvalues of the n x n density matrices
is, for n = 4, equal to 71680/pi^2. Since we also find that C_{3} = 35/pi, it
follows that C_{4} is simply equal to 2^{11} C_{3}/pi. (C_{2} itself is known
to equal 2/pi.) The constant C_{5} is also found. It too is associated with a
remarkably simple decompositon, involving the product of the eight consecutive
prime numbers from 2 to 23.
We also preliminarily investigate several cases, n > 5, with the use of
quasi-Monte Carlo integration. We hope that the various analyses reported will
prove useful in deriving a general formula (which evidence suggests will
involve the Bernoulli numbers) for the Hall normalization constant for
arbitrary n. This would have diverse applications, including quantum inference
and universal quantum coding.Comment: 14 pages, LaTeX, 6 postscript figures. Revised version to appear in
J. Phys. A. We make a few slight changes from the previous version, but also
add a subsection (III G) in which several variations of the basic problem are
newly studied. Rather strong evidence is adduced that the Hall constants are
related to partial sums of denominators of the even-indexed Bernoulli
numbers, although a general formula is still lackin
Functional Integral Construction of the Thirring model: axioms verification and massless limit
We construct a QFT for the Thirring model for any value of the mass in a
functional integral approach, by proving that a set of Grassmann integrals
converges, as the cutoffs are removed and for a proper choice of the bare
parameters, to a set of Schwinger functions verifying the Osterwalder-Schrader
axioms. The corresponding Ward Identities have anomalies which are not linear
in the coupling and which violate the anomaly non-renormalization property.
Additional anomalies are present in the closed equation for the interacting
propagator, obtained by combining a Schwinger-Dyson equation with Ward
Identities.Comment: 55 pages, 9 figure
Pharmacoeconomic analysis of adjuvant oral capecitabine vs intravenous 5-FU/LV in Dukes' C colon cancer: the X-ACT trial
Oral capecitabine (Xeloda<sup>®</sup>) is an effective drug with favourable safety in adjuvant and metastatic colorectal cancer. Oxaliplatin-based therapy is becoming standard for Dukes' C colon cancer in patients suitable for combination therapy, but is not yet approved by the UK National Institute for Health and Clinical Excellence (NICE) in the adjuvant setting. Adjuvant capecitabine is at least as effective as 5-fluorouracil/leucovorin (5-FU/LV), with significant superiority in relapse-free survival and a trend towards improved disease-free and overall survival. We assessed the cost-effectiveness of adjuvant capecitabine from payer (UK National Health Service (NHS)) and societal perspectives. We used clinical trial data and published sources to estimate incremental direct and societal costs and gains in quality-adjusted life months (QALMs). Acquisition costs were higher for capecitabine than 5-FU/LV, but higher 5-FU/LV administration costs resulted in 57% lower chemotherapy costs for capecitabine. Capecitabine vs 5-FU/LV-associated adverse events required fewer medications and hospitalisations (cost savings £3653). Societal costs, including patient travel/time costs, were reduced by >75% with capecitabine vs 5-FU/LV (cost savings £1318), with lifetime gain in QALMs of 9 months. Medical resource utilisation is significantly decreased with capecitabine vs 5-FU/LV, with cost savings to the NHS and society. Capecitabine is also projected to increase life expectancy vs 5-FU/LV. Cost savings and better outcomes make capecitabine a preferred adjuvant therapy for Dukes' C colon cancer. This pharmacoeconomic analysis strongly supports replacing 5-FU/LV with capecitabine in the adjuvant treatment of colon cancer in the UK
FoxO1 Haploinsufficiency Protects Against High-Fat Diet–Induced Insulin Resistance With Enhanced Peroxisome Proliferator–Activated Receptor γ Activation in Adipose Tissue
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