Fluctuation, time-correlation function and geometric Phase

We establish a fluctuation-correlation theorem by relating the quantum fluctuations in the generator of the parameter change to the time integral of the quantum correlation function between the projection operator and force operator of the ``fast'' system. By taking a cue from linear response theory we relate the quantum fluctuation in the generator to the generalised susceptibility. Relation between the open-path geometric phase, diagonal elements of the quantum metric tensor and the force-force correlation function is provided and the classical limit of the fluctuation-correlation theorem is also discussed.Comment: Latex, 12 pages, no figures, submitted to J. Phys. A: Math & Ge

Bounding Helly numbers via Betti numbers

We show that very weak topological assumptions are enough to ensure the existence of a Helly-type theorem. More precisely, we show that for any non-negative integers $b$ and $d$ there exists an integer $h(b,d)$ such that the following holds. If $\mathcal F$ is a finite family of subsets of $\mathbb R^d$ such that $\tilde\beta_i\left(\bigcap\mathcal G\right) \le b$ for any $\mathcal G \subsetneq \mathcal F$ and every $0 \le i \le \lceil d/2 \rceil-1$ then $\mathcal F$ has Helly number at most $h(b,d)$. Here $\tilde\beta_i$ denotes the reduced $\mathbb Z_2$-Betti numbers (with singular homology). These topological conditions are sharp: not controlling any of these $\lceil d/2 \rceil$ first Betti numbers allow for families with unbounded Helly number. Our proofs combine homological non-embeddability results with a Ramsey-based approach to build, given an arbitrary simplicial complex $K$, some well-behaved chain map $C_*(K) \to C_*(\mathbb R^d)$.Comment: 29 pages, 8 figure

L^{2}-restriction bounds for eigenfunctions along curves in the quantum completely integrable case

We show that for a quantum completely integrable system in two dimensions,the $L^{2}$-normalized joint eigenfunctions of the commuting semiclassical pseudodifferential operators satisfy restriction bounds ofthe form $\int_{\gamma} |\phi_{j}^{\hbar}|^2 ds = {\mathcal O}(|\log \hbar|)$ for generic curves $\gamma$ on the surface. We also prove that the maximal restriction bounds of Burq-Gerard-Tzvetkov are always attained for certain exceptional subsequences of eigenfunctions.Comment: Correct some typos and added some more detail in section

(Re)constructing Dimensions

Compactifying a higher-dimensional theory defined in R^{1,3+n} on an n-dimensional manifold {\cal M} results in a spectrum of four-dimensional (bosonic) fields with masses m^2_i = \lambda_i, where - \lambda_i are the eigenvalues of the Laplacian on the compact manifold. The question we address in this paper is the inverse: given the masses of the Kaluza-Klein fields in four dimensions, what can we say about the size and shape (i.e. the topology and the metric) of the compact manifold? We present some examples of isospectral manifolds (i.e., different manifolds which give rise to the same Kaluza-Klein mass spectrum). Some of these examples are Ricci-flat, complex and K\"{a}hler and so they are isospectral backgrounds for string theory. Utilizing results from finite spectral geometry, we also discuss the accuracy of reconstructing the properties of the compact manifold (e.g., its dimension, volume, and curvature etc) from measuring the masses of only a finite number of Kaluza-Klein modes.Comment: 23 pages, 3 figures, 2 references adde

Approach to ergodicity in quantum wave functions

According to theorems of Shnirelman and followers, in the semiclassical limit the quantum wavefunctions of classically ergodic systems tend to the microcanonical density on the energy shell. We here develop a semiclassical theory that relates the rate of approach to the decay of certain classical fluctuations. For uniformly hyperbolic systems we find that the variance of the quantum matrix elements is proportional to the variance of the integral of the associated classical operator over trajectory segments of length $T_H$, and inversely proportional to $T_H^2$, where $T_H=h\bar\rho$ is the Heisenberg time, $\bar\rho$ being the mean density of states. Since for these systems the classical variance increases linearly with $T_H$, the variance of the matrix elements decays like $1/T_H$. For non-hyperbolic systems, like Hamiltonians with a mixed phase space and the stadium billiard, our results predict a slower decay due to sticking in marginally unstable regions. Numerical computations supporting these conclusions are presented for the bakers map and the hydrogen atom in a magnetic field.Comment: 11 pages postscript and 4 figures in two files, tar-compressed and uuencoded using uufiles, to appear in Phys Rev E. For related papers, see http://www.icbm.uni-oldenburg.de/icbm/kosy/ag.htm

Travelers With Cutaneous Leishmaniasis Cured Without Systemic Therapy

Guidelines recommend wound care and/or local therapy as first-line treatment for cutaneous leishmaniasis. An analysis of a referral treatment program in 135 travelers showed that this approach was feasible in 62% of patients, with positive outcome in 83% of evaluable patient

How reproducible are methods to measure the dynamic viscoelastic properties of poroelastic media?

There is a considerable number of research publications on the acoustical properties of porous media with an elastic frame. A simple search through the Web of Science™ (last accessed 21 March 2018) suggests that there are at least 819 publications which deal with the acoustics of poroelastic media. A majority of these researches require accurate knowledge of the elastic properties over a broad frequency range. However, the accuracy of the measurement of the dynamic elastic properties of poroelastic media has been a contentious issue. The novelty of this paper is that it studies the reproducibility of some popular experimental methods which are used routinely to measure the key elastic properties such as the dynamic Young's modulus, loss factor and Poisson ratio of poroelastic media. In this paper, fourteen independent sets of laboratory measurements were performed on specimens of the same porous materials. The results from these measurements suggest that the reproducibility of this type of experimental method is poor. This work can be helpful to suggest improvements which can be developed to harmonize the way the elastic properties of poroelastic media are measured worldwide

Simple scoring system to predict in-hospital mortality after surgery for infective endocarditis

BACKGROUND: Aspecific scoring systems are used to predict the risk of death postsurgery in patients with infective endocarditis (IE). The purpose of the present study was both to analyze the risk factors for in-hospital death, which complicates surgery for IE, and to create a mortality risk score based on the results of this analysis. METHODS AND RESULTS: Outcomes of 361 consecutive patients (mean age, 59.1\ub115.4 years) who had undergone surgery for IE in 8 European centers of cardiac surgery were recorded prospectively, and a risk factor analysis (multivariable logistic regression) for in-hospital death was performed. The discriminatory power of a new predictive scoring system was assessed with the receiver operating characteristic curve analysis. Score validation procedures were carried out. Fifty-six (15.5%) patients died postsurgery. BMI >27 kg/m2 (odds ratio [OR], 1.79; P=0.049), estimated glomerular filtration rate 55 mm Hg (OR, 1.78; P=0.032), and critical state (OR, 2.37; P=0.017) were independent predictors of in-hospital death. A scoring system was devised to predict in-hospital death postsurgery for IE (area under the receiver operating characteristic curve, 0.780; 95% CI, 0.734-0.822). The score performed better than 5 of 6 scoring systems for in-hospital death after cardiac surgery that were considered. CONCLUSIONS: A simple scoring system based on risk factors for in-hospital death was specifically created to predict mortality risk postsurgery in patients with IE

Identifiability and estimation of pharmacokinetic parameters for the ligands of the macrophage mannose receptor

The aim of this paper is numerical estimation of pharmacokinetic parameters of the ligands of the macrophage mannose receptor, without knowing a priori the values of these parameters. However, it first requires a model identifiability analysis, which is done by applying an algorithm implemented in a symbolic computation language. It is shown that this step can lead to a direct numerical estimation algorithm. In this way, a first estimate is computed from noisy simulated observations without a priori parameter values. Then the resulting parameter estimate is improved by using the classical least-squares method