A Trace Formula for Products of Diagonal Matrix Elements in Chaotic Systems

We derive a trace formula for $\sum_n A_{nn}B_{nn}...\delta(E-E_n)$, where $A_{nn}$ is the diagonal matrix element of the operator $A$ in the energy basis of a chaotic system. The result takes the form of a smooth term plus periodic-orbit corrections; each orbit is weighted by the usual Gutzwiller factor times $A_p B_p ...$, where $A_p$ is the average of the classical observable $A$ along the periodic orbit $p$. This structure for the orbit corrections was previously proposed by Main and Wunner (chao-dyn/9904040) on the basis of numerical evidence.Comment: 8 pages; analysis made more rigorous in the revised versio

Numerical simul tion of droplet impact erosion : dang van fatigue approach

The aim of this work is to understand the erosion mechanism caused by repeated water droplets impingement on a metallic structure, and then perform numerical simulations of the damage. When a high velocity water droplet with small diameter impacts a rigid surface, interaction is driven by inertial effects. Upon impact, the “water-hammer” pressure appears by inertial effect at the center of the contact though the maximum pressure occurs on the envelope of the contact area. Lateral jetting occurs by compression when the wave front travelling inside droplet overtakes the contact area. Concerning the structure, erosion is due to fatigue crack- ing. First, material grains are weakened during an “incubation” phase. After a large number of impacts, micro-cracks emerge and lead to ejection or fracture of grains, what is called “am- plification” phase. Numerical simulation including rigid solid allows to locate the most loaded zones of the area, by observing the pressure and mainly the impulse. A 2-way coupling compu- tation with fluid-structure interaction at macroscopic scale allows to confirm the fatigue-based mechanism by observing the hydrostatic stress. Finally, erosion program developed with Dang Van criterion provides the location of the most eroded zones of the structure during a loading cycle. They locate at the edge of jetting zone, which shows the influence of microjets in the erosion mechanism

Patient satisfaction and survey response in 717 hospital surveys in Switzerland: a cross-sectional study.

The association between patient satisfaction and survey response is only partly understood. In this study, we describe the association between average satisfaction and survey response rate across hospital surveys, and model the association between satisfaction and propensity to respond for individual patients. Secondary analysis of patient responses (166'014 respondents) and of average satisfaction scores and response rates obtained in 717 annual patient satisfaction surveys conducted between 2011 and 2015 at 164 Swiss hospitals. The satisfaction score was the average of 5 items scored between 0 and 10. The association between satisfaction and response propensity in individuals was modeled as the function that predicted best the observed response rates across surveys. Among the 717 surveys, response rates ranged from 16.1 to 80.0% (pooled average 49.8%), and average satisfaction scores ranged from 8.36 to 9.79 (pooled mean 9.15). At the survey level, the mean satisfaction score and response rate were correlated (r = 0.61). This correlation held for all subgroups of surveys, except for the 5 large university hospitals. The estimated individual response propensity function was "J-shaped": the probability of responding was lowest (around 20%) for satisfaction scores between 3 and 7, increased sharply to about 70% for those maximally satisfied, and increased slightly for the least satisfied. Average satisfaction scores projected for 100% participation were lower than observed average scores. The most satisfied patients were the most likely to participate in a post-hospitalization satisfaction survey. This tendency produces an upward bias in observed satisfaction scores, and a positive correlation between average satisfaction and response rate across surveys

Block circulant matrices with circulant blocks, weil sums and mutually unbiased bases, II. The prime power case

In our previous paper \cite{co1} we have shown that the theory of circulant matrices allows to recover the result that there exists $p+1$ Mutually Unbiased Bases in dimension $p$, $p$ being an arbitrary prime number. Two orthonormal bases $\mathcal B, \mathcal B'$ of $\mathbb C^d$ are said mutually unbiased if $\forall b\in \mathcal B, \forall b' \in \mathcal B'$ one has that $$| b\cdot b'| = \frac{1}{\sqrt d}$$ ($b\cdot b'$ hermitian scalar product in $\mathbb C^d$). In this paper we show that the theory of block-circulant matrices with circulant blocks allows to show very simply the known result that if $d=p^n$ ($p$ a prime number, $n$ any integer) there exists $d+1$ mutually Unbiased Bases in $\mathbb C^d$. Our result relies heavily on an idea of Klimov, Munoz, Romero \cite{klimuro}. As a subproduct we recover properties of quadratic Weil sums for $p\ge 3$, which generalizes the fact that in the prime case the quadratic Gauss sums properties follow from our results

Coherent States Expectation Values as Semiclassical Trajectories

We study the time evolution of the expectation value of the anharmonic oscillator coordinate in a coherent state as a toy model for understanding the semiclassical solutions in quantum field theory. By using the deformation quantization techniques, we show that the coherent state expectation value can be expanded in powers of $\hbar$ such that the zeroth-order term is a classical solution while the first-order correction is given as a phase-space Laplacian acting on the classical solution. This is then compared to the effective action solution for the one-dimensional \f^4 perturbative quantum field theory. We find an agreement up to the order \l\hbar, where \l is the coupling constant, while at the order \l^2 \hbar there is a disagreement. Hence the coherent state expectation values define an alternative semiclassical dynamics to that of the effective action. The coherent state semiclassical trajectories are exactly computable and they can coincide with the effective action trajectories in the case of two-dimensional integrable field theories.Comment: 20 pages, no figure

Bispectral and spectral entropy indices at propofol-induced loss of consciousness in young and elderly patients

Background Bispectral (BIS) and state/response entropy (SE/RE) indices have been widely used to estimate depth of anaesthesia and sedation. In adults, independent of age, adequate and safe depth of anaesthesia for surgery is usually assumed when these indices are between 40 and 60. Since the EEG is changing with increasing age, we investigated the impact of advanced age on BIS, SE, and RE indices during induction. Methods BIS and SE/RE indices were recorded continuously in elderly (≥65 yr) and young (≤40 yr) surgical patients who received propofol until loss of consciousness (LOC) using stepwise increasing effect-site concentrations. LOC was defined as an observer assessment of alertness/sedation score <2, corresponding to the absence of response to mild prodding or shaking. Results We analysed 35 elderly [average age, 78 yr (range, 67-96)] and 34 young [35 (19-40)] patients. At LOC, all indices were significantly higher in elderly compared with young patients: BISLOC, median 70 (range, 58-91) vs 58 (40-70); SELOC, 71 (31-88) vs 55.5 (23-79); and RELOC, 79 (35-96) vs 59 (25-80) (P<0.001 for all comparisons). With all three monitors, only a minority of elderly patients lost consciousness within a 40-60 index range: two (5.7%) with BIS and RE each, and seven (20%) with SE. In young patients, the respective numbers were 20 (58.8%) for BIS, 13 (38.2%) for SE, and nine (26.5%) for RE. Conclusions In adults undergoing propofol induction, BIS, SE, and RE indices at LOC are significantly affected by ag

Coherent-State Approach to Two-dimensional Electron Magnetism

We study in this paper the possible occurrence of orbital magnetim for two-dimensional electrons confined by a harmonic potential in various regimes of temperature and magnetic field. Standard coherent state families are used for calculating symbols of various involved observables like thermodynamical potential, magnetic moment, or spatialdistribution of current. Their expressions are given in a closed form and the resulting Berezin-Lieb inequalities provide a straightforward way to study magnetism in various limit regimes. In particular, we predict a paramagnetic behaviour in the thermodynamical limit as well as in the quasiclassical limit under a weak field. Eventually, we obtain an exact expression for the magnetic moment which yields a full description of the phase diagram of the magnetization.Comment: 21 pages, 6 figures, submitted to PR

Whole brain radiotherapy with a conformational external beam radiation boost for lung cancer patients with 1-3 brain metastasis: a multi institutional study

BACKGROUND: To determine the outcome of patients with brain metastasis (BM) from lung cancer treated with an external beam radiotherapy boost (RTB) after whole brain radiotherapy (WBRT). METHODS: A total of 53 BM patients with lung cancer were treated sequentially with WBRT and RTB between 1996 and 2008 according to our institutional protocol. Mean age was 58.8 years. The median KPS was 90. Median recursive partitioning analysis (RPA) and graded prognostic assessment (GPA) grouping were 2 and 2.5, respectively. Surgery was performed on 38 (71%) patients. The median number of BM was 1 (range, 1-3). Median WBRT and RTB combined dose was 39 Gy (range, 37.5-54). Median follow-up was 12.0 months. RESULTS: During the period of follow-up, 37 (70%) patients died. The median overall survival (OS) was 14.5 months. Only 13 patients failed in the brain. The majority of patients (n = 29) failed distantly. The 1-year OS, -local control, extracranial failure rates were 61.2%, 75.2% and 60.8%, respectively. On univariate analysis, improved OS was found to be significantly associated with total dose (&lt; or = 39 Gy vs. &gt; 39 Gy; p &lt; 0.01), age &lt; 65 (p &lt; 0.01), absence of extracranial metastasis (p &lt; 0.01), GPA &gt; or = 2.5 (p = 0.01), KPS &gt; or = 90 (p = 0.01), and RPA &lt; 2 (p = 0.04). On multivariate analysis, total dose (p &lt; 0.01) and the absence of extracranial metastasis (p = 0.03) retained statistical significance. CONCLUSIONS: The majority of lung cancer patients treated with WBRT and RTB progressed extracranially. There might be a subgroup of younger patients with good performance status and no extracranial disease who may benefit from dose escalation after WBRT to the metastatic site