Dissipation effect in the double-well Bose-Einstein Condensate

Dynamics of the double-well Bose-Einstein condensate subject to energy dissipation is studied by solving a reduced one-dimensional time-dependent Gross-Pitaevskii equation numerically. We first reproduce the phase space diagram of the system without dissipation systematically, and then calculate evolutionary trajectories of dissipated systems. It is clearly shown that the dissipation can drive the system to evolve gradually from the $\pi$-mode quantum macroscopic self-trapping state, a state with relatively higher energy, to the lowest energy stationary state in which particles distribute equally in the two wells. The average phase and phase distribution in each well are discussed as well. We show that the phase distribution varies slowly in each well but may exhibit abrupt changes near the barrier. This sudden change occurs at the minimum position in particle density profile. We also note that the average phase in each well varies much faster with time than the phase difference between two wells.Comment: 7 pages, 7 figures, to be published in Euro. Phys. J.

Optimal Reinsurance-Investment Problem for an Insurer and a Reinsurer with Jump-Diffusion Process

The optimal reinsurance-investment strategies considering the interests of both the insurer and reinsurer are investigated. The surplus process is assumed to follow a jump-diffusion process and the insurer is permitted to purchase proportional reinsurance from the reinsurer. Applying dynamic programming approach and dual theory, the corresponding Hamilton-Jacobi-Bellman equations are derived and the optimal strategies for exponential utility function are obtained. In addition, several sensitivity analyses and numerical illustrations in the case with exponential claiming distributions are presented to analyze the effects of parameters about the optimal strategies

An Interval of No-Arbitrage Prices in Financial Markets with Volatility Uncertainty

In financial markets with volatility uncertainty, we assume that their risks are caused by uncertain volatilities and their assets are effectively allocated in the risk-free asset and a risky stock, whose price process is supposed to follow a geometric G-Brownian motion rather than a classical Brownian motion. The concept of arbitrage is used to deal with this complex situation and we consider stock price dynamics with no-arbitrage opportunities. For general European contingent claims, we deduce the interval of no-arbitrage price and the clear results are derived in the Markovian case

Case Report: Kaposiform hemangioendothelioma with PIK3CA mutation successfully treated with sirolimus

Kaposiform hemangioendothelioma (KHE) is an extremely rare, locally aggressive vascular neoplasm. The etiopathogenesis of KHE is still poorly understood. In the present study, we found a new mutation in KHE (c.685delA, p.Thr229fs). The KHE patient with the PIK3CA mutation showed complete regression after sirolimus treatment. We propose that the presence of the PIK3CA mutation in KHE may correlate with good response to sirolimus

High-intensity corneal collagen crosslinking with riboflavin and UVA in rat cornea

<div><p>Corneal collagen cross-linking (CXL) halts human corneal ectasias progression by increasing stromal mechanical stiffness. Although some reports describe that this procedure is effective in dealing with some infectious and immunologic corneal thinning diseases, there is a need for more animal models whose corneal thickness more closely resemble those occurring in these patients. To meet this need, we describe here high-intensity protocols that are safe and effective for obtaining CXL in rat corneas. Initially, a range of potentially effective UVA doses were evaluated based on their effectiveness in increasing tissue enzymatic resistance to dissolution. At UVA doses higher than a threshold level of 0.54 J/cm², resistance to enzymatic digestion increased relative to that in non-irradiated corneas. Based on the theoretical threshold CXL dose, a CXL regimen was established in which the UVA tissue irradiance was 9 mW/cm², which was delivered at doses of either 2.16, 2.7 or 3.24 J/cm². Their dose dependent effects were evaluated on ocular surface morphological integrity, keratocyte apoptotic frequency, tissue thickness and endothelial cell layer density. Doses of 2.16 and 2.7 J/cm² transiently decreased normal corneal transparency and increased thickness. These effects were fully reversed after 14 days. In contrast, 3.24 J/cm² had more irreversible side effects. Three days after treatment, apoptotic frequency in the CXL-2.16 group was lower than that at higher doses. Endothelial cell losses remained evident only in the CXL-3.24 group at 42 days posttreatment. Stromal fiber thickening was evident in all the CXL-treated groups. We determined both the threshold UVA dose using the high-intensity CXL procedure and identified an effective dose range that provides optimal CXL with minimal transient side effects in the rat cornea. These results may help to provide insight into how to improve the CXL outcome in patients afflicted with a severe corneal thinning disease.</p></div

Differential effects of CXL treatment on clinical signs.

<p>(A) Representative slit lamp images showing differences between the 4 different groups on day 7 after CXL-treatment. (B) Time dependent changes in inflammatory index among the 4 groups from day 1 to 42 (Data are presented as Mean ±(SEM, CXL groups versus control group; n = 6, **p < 0.01).</p

CXL-induced changes in stromal and endothelium ultrastructure on day 7.

<p>The stroma had a compacted collagenous matrix (Left arrow) containing degenerative changes in keratocytes across the stroma in all CXL-treated groups (Middle arrow). No such defects were detected in the posterior stroma and endothelium of the CXL-2.16 group (n = 3).</p

CXL-induced apoptosis and keratocyte density.

<p>(A) Apoptosis of the rat keratocytes (green, positive TUNEL staining) are present in the CXL-treated areas and control cornea on day 3. The control cornea had a normal DAPI staining pattern. In the cross-linked corneas, some keratocyte were apoptotic. Apparent endothelial layer damage was detected in the CXL-3.24 group. (B) Significant difference was evident between keratocyte density in CXL-treated and control corneas on day 3. The keratocyte counts significantly decreased in the CXL-2.7 and 3.24 groups compared with the CXL-2.16 group (### p < 0.01 versus CXL-treated groups, *** p < 0.001 versus control group, respectively; Data are presented as Mean ± SEM, n = 3. scale bars = 50 μm).</p