Probability distributions of Linear Statistics in Chaotic Cavities and associated phase transitions

We establish large deviation formulas for linear statistics on the $N$ transmission eigenvalues $\{T_i\}$ of a chaotic cavity, in the framework of Random Matrix Theory. Given any linear statistics of interest $A=\sum_{i=1}^N a(T_i)$, the probability distribution $\mathcal{P}_A(A,N)$ of $A$ generically satisfies the large deviation formula $\lim_{N\to\infty}[-2\log\mathcal{P}_A(Nx,N)/\beta N^2]=\Psi_A(x)$, where $\Psi_A(x)$ is a rate function that we compute explicitly in many cases (conductance, shot noise, moments) and $\beta$ corresponds to different symmetry classes. Using these large deviation expressions, it is possible to recover easily known results and to produce new formulas, such as a closed form expression for $v(n)=\lim_{N\to\infty}\mathrm{var}(\mathcal{T}_n)$ (where $\mathcal{T}_n=\sum_{i}T_i^n$) for arbitrary integer $n$. The universal limit $v^\star=\lim_{n\to\infty} v(n)=1/2\pi\beta$ is also computed exactly. The distributions display a central Gaussian region flanked on both sides by non-Gaussian tails. At the junction of the two regimes, weakly non-analytical points appear, a direct consequence of phase transitions in an associated Coulomb gas problem. Numerical checks are also provided, which are in full agreement with our asymptotic results in both real and Laplace space even for moderately small $N$. Part of the results have been announced in [P. Vivo, S.N. Majumdar and O. Bohigas, {\it Phys. Rev. Lett.} {\bf 101}, 216809 (2008)].Comment: 31 pages, 16 figures. To appear in Phys. Rev. B. Added section IVD about comparison with other theories and numerical simulation

Concentrations of some toxic and trace elements in wild boar (Sus scrofa) organs and tissues in different areas of the Province of Viterbo, Central Italy

The aim of the present study was to determine heavy metal reference levels for exposure and risk assessment studies on a local scale. We measured lead (Pb), chromium (Cr), zinc (Zn), copper (Cu) and cadmium (Cd) content in edible tissues and organs of wild boars harvested in dif- ferent areas of the Province of Viterbo, Central Italy. The average levels of cadmium recorded in 75 wild boars were 0.085, 0.079 and 1.052 mg Cd kg–1 wet weight (w.w.) in the liver, muscle and kidney, respectively. The majority of the muscle samples and some of the liver samples contained levels of heavy metal that were over the legal limit [EU Maximum Residue Levels (MRLs)] for pigs. Our data are similar to or lower than the val- ues reported in most of the available literature. For Pb concentration, the average values record- ed were 0.318, 0.126 and 0.298 mg kg–1 w.w. in the liver, muscle and kidney, respectively. The sam- ples that were non-compliant with regulatory limits (MRLs) for pigs were registered only for muscle. Available data on the presence of Pb con- tent in game meat report lower values than ours, most likely because the area around the bullet path was avoided while sampling. The average values of total Cr were 0.141, 0.139 and 0.097 mg kg–1 w.w. in the liver, muscle and kidney, respec- tively. For Zn, the mean values were 49.76, 53.21 and 32.46 mg kg–1 w.w. in the liver, muscle and kidney, respectively. Cu content was 46.12, 12.20 and 5.64 mg Cu kg–1 w.w. in the liver, muscle and kidney, respectively. The results obtained have been validated on the basis of the scarce and inconsistent Italian literature available and on international studies

Lattice model for cold and warm swelling of polymers in water

We define a lattice model for the interaction of a polymer with water. We solve the model in a suitable approximation. In the case of a non-polar homopolymer, for reasonable values of the parameters, the polymer is found in a non-compact conformation at low temperature; as the temperature grows, there is a sharp transition towards a compact state, then, at higher temperatures, the polymer swells again. This behaviour closely reminds that of proteins, that are unfolded at both low and high temperatures.Comment: REVTeX, 5 pages, 2 EPS figure

Optimal low-thrust transfers between libration point orbits

Over the past three decades, ballistic and impulsive trajectories between libration point orbits (LPOs) in the Sun–Earth–Moon system have been investigated to a large extent. It is known that coupling invariant manifolds of LPOs of two different circular restricted three-body problems (i.e., the Sun–Earth and the Earth–Moon systems) can lead to significant mass savings in specific transfers, such as from a low Earth orbit to the Moon’s vicinity. Previous investigations on this issuemainly considered the use of impulsive maneuvers along the trajectory. Here we investigate the dynamical effects of replacing impulsive V’s with low-thrust trajectory arcs to connect LPOs using invariant manifold dynamics. Our investigation shows that the use of low-thrust propulsion in a particular phase of the transfer and the adoption of a more realistic Sun–Earth–Moon four-body model can provide better and more propellant-efficient solution. For this purpose, methods have been developed to compute the invariant tori and their manifolds in this dynamical modelPeer ReviewedPostprint (published version

A unified fluctuation formula for one-cut β\beta-ensembles of random matrices

Using a Coulomb gas approach, we compute the generating function of the covariances of power traces for one-cut $\beta$-ensembles of random matrices in the limit of large matrix size. This formula depends only on the support of the spectral density, and is therefore universal for a large class of models. This allows us to derive a closed-form expression for the limiting covariances of an arbitrary one-cut $\beta$-ensemble. As particular cases of the main result we consider the classical $\beta$-Gaussian, $\beta$-Wishart and $\beta$-Jacobi ensembles, for which we derive previously available results as well as new ones within a unified simple framework. We also discuss the connections between the problem of trace fluctuations for the Gaussian Unitary Ensemble and the enumeration of planar maps.Comment: 16 pages, 4 figures, 3 tables. Revised version where references have been added and typos correcte

Asymptotics of Selberg-like integrals: The unitary case and Newton's interpolation formula

We investigate the asymptotic behavior of the Selberg-like integral $$\frac1{N!}\int_{[0,1]^N}x_1^p\prod_{i<j}(x_i-x_j)^2\prod_ix_i^{a-1}(1-x_i)^{b-1}dx_i$$, as $N\to\infty$ for different scalings of the parameters $a$ and $b$ with $N$. Integrals of this type arise in the random matrix theory of electronic scattering in chaotic cavities supporting $N$ channels in the two attached leads. Making use of Newton's interpolation formula, we show that an asymptotic limit exists and we compute it explicitly

Model for the hydration of non-polar compounds and polymers

We introduce an exactly solvable statistical-mechanical model of the hydration of non-polar compounds, based on grouping water molecules in clusters where hydrogen bonds and isotropic interactions occur; interactions between clusters are neglected. Analytical results show that an effective strengthening of hydrogen bonds in the presence of the solute, together with a geometric reorganization of water molecules, are enough to yield hydrophobic behavior. We extend our model to describe a non-polar homopolymer in aqueous solution, obtaining a clear evidence of both ``cold'' and ``warm'' swelling transitions. This suggests that our model could be relevant to describe some features of protein folding.Comment: REVTeX, 6 pages, 3 figure

Effect of frailty on treatment, hospitalisation and death in patients with chronic heart failure

Background: Frailty is common in patients with chronic heart failure (CHF) and is associated with poor outcomes. The natural history of frail patients with CHF is unknown. Methods: Frailty was assessed using the clinical frailty scale (CFS) in 467 consecutive patients with CHF (67% male, median age 76 years, median NT-proBNP 1156 ng/L) attending a routine follow-up visit. Those with CFS > 4 were classified as frail. We investigated the relation between frailty and treatments, hospitalisation and death in patients with CHF. Results: 206 patients (44%) were frail. Of 291 patients with HF with reduced ejection fraction (HeFREF), those who were frail (N = 117; 40%) were less likely to receive optimal treatment, with many not receiving a renin–angiotensin–aldosterone system inhibitor (frail: 25% vs. non-frail: 4%), a beta-blocker (16% vs. 8%) or a mineralocorticoid receptor antagonist (50% vs 41%). By 1 year, there were 56 deaths and 322 hospitalisations, of which 25 (45%) and 198 (61%), respectively, were due to non-cardiovascular (non-CV) causes. Most deaths (N = 46, 82%) and hospitalisations (N = 215, 67%) occurred in frail patients. Amongst frail patients, 43% of deaths and 64% of hospitalisations were for non-CV causes; 58% of cardiovascular (CV) deaths were due to advancing HF. Among non-frail patients, 50% of deaths and 57% of hospitalisations were for non-CV causes; all CV deaths were due to advancing HF. Conclusion: Frailty in patients with HeFREF is associated with sub-optimal medical treatment. Frail patients are more likely to die or be admitted to hospital, but whether frail or not, many events are non-CV

Large Deviations of the Maximum Eigenvalue in Wishart Random Matrices

We compute analytically the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W=X^T X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value =N/c decreases for large N as $\sim \exp[-\frac{\beta}{2}N^2 \Phi_{-}(\frac{2}{\sqrt{c}}+1;c)]$, where \beta=1,2 correspond respectively to real and complex Wishart matrices, c=N/M < 1 and \Phi_{-}(x;c) is a large deviation function that we compute explicitly. The result for the Anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of constrained Wishart matrices whose eigenvalues are forced to be smaller than a fixed barrier. The numerical simulations are in excellent agreement with the analytical predictions.Comment: Published version. References and appendix adde

Bladder metastases of appendiceal mucinous adenocarcinoma: a case presentation

<p>Abstract</p> <p>Background</p> <p>Appendiceal adenocarcinoma is rare with a frequency of 0.08% of all surgically removed appendices. Few cases of appendiceal carcinoma infiltrating the bladder wall for spatial contiguity have been documented.</p> <p>Case Presentation</p> <p>A case is reported of a 45-years old woman with mucinous cystadenocarcinoma of the appendix with bladder metastasis. Although ultrasonography and voided urinary cytology were negative, abdomen computed tomography (CT) scan and cystoscopy and subsequent pathological examination revealed a mass exclusively located in the anterior wall of the bladder. Histopathology of the transurethral bladder resection revealed a bladder adenocarcinoma [6 cm (at the maximum diameter) × 2,5 cm; approximate weight: 10 gr] with focal mucinous aspects penetrating the muscle and perivisceral fat. Laparotomy evidenced the presence of a solid mass of the appendix (2,5 cm × 3 cm × 2 cm) extending to the loco-regional lymph nodes. Appendectomy and right hemicolectomy, linfoadenectomy and partial cystectomy were performed. The subsequent pathological examination revealed a mucinous cystadenocarcinoma of the appendix with metastatic cells colonising the anterior bladder wall and several colic lymph nodes.</p> <p>Conclusions</p> <p>The rarity of the appendiceal carcinoma invading the urinary bladder and its usual involvement of nearest organs and the posterior bladder wall, led us to describe this case which demonstrates the ability of the appendiceal cancer to metastasize different regions of urinary bladder.</p