Optimal Lewenstein-Sanpera Decomposition for some Biparatite Systems

It is shown that for a given bipartite density matrix and by choosing a suitable separable set (instead of product set) on the separable-entangled boundary, optimal Lewenstein-Sanpera (L-S) decomposition can be obtained via optimization for a generic entangled density matrix. Based on this, We obtain optimal L-S decomposition for some bipartite systems such as $2\otimes 2$ and $2\otimes 3$ Bell decomposable states, generic two qubit state in Wootters basis, iso-concurrence decomposable states, states obtained from BD states via one parameter and three parameters local operations and classical communications (LOCC), $d\otimes d$ Werner and isotropic states, and a one parameter $3\otimes 3$ state. We also obtain the optimal decomposition for multi partite isotropic state. It is shown that in all $2\otimes 2$ systems considered here the average concurrence of the decomposition is equal to the concurrence. We also show that for some $2\otimes 3$ Bell decomposable states the average concurrence of the decomposition is equal to the lower bound of the concurrence of state presented recently in [Buchleitner et al, quant-ph/0302144], so an exact expression for concurrence of these states is obtained. It is also shown that for $d\otimes d$ isotropic state where decomposition leads to a separable and an entangled pure state, the average I-concurrence of the decomposition is equal to the I-concurrence of the state. Keywords: Quantum entanglement, Optimal Lewenstein-Sanpera decomposition, Concurrence, Bell decomposable states, LOCC} PACS Index: 03.65.UdComment: 31 pages, Late

hp-adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems

This work is concerned with the derivation of an a posteriori error estimator for Galerkin approximations to nonlinear initial value problems with an emphasis on finite-time existence in the context of blow-up. The structure of the derived estimator leads naturally to the development of both h and hp versions of an adaptive algorithm designed to approximate the blow-up time. The adaptive algorithms are then applied in a series of numerical experiments, and the rate of convergence to the blow-up time is investigated

Transcriptomic Profiling of DNA Damage Response in Patient-Derived Glioblastoma Cells before and after Radiation and Temozolomide Treatment

Glioblastoma is a highly aggressive, invasive and treatment-resistant tumour. The DNA damage response (DDR) provides tumour cells with enhanced ability to activate cell cycle arrest and repair treatment-induced DNA damage. We studied the expression of DDR, its relationship with standard treatment response and patient survival, and its activation after treatment. The transcriptomic profile of DDR pathways was characterised within a cohort of isocitrate dehydrogenase (IDH) wild-type glioblastoma from The Cancer Genome Atlas (TCGA) and 12 patient-derived glioblastoma cell lines. The relationship between DDR expression and patient survival and cell line response to temozolomide (TMZ) or radiation therapy (RT) was assessed. Finally, the expression of 84 DDR genes was examined in glioblastoma cells treated with TMZ and/or RT. Although distinct DDR cluster groups were apparent in the TCGA cohort and cell lines, no significant differences in OS and treatment response were observed. At the gene level, the high expression of ATP23, RAD51C and RPA3 independently associated with poor prognosis in glioblastoma patients. Finally, we observed a substantial upregulation of DDR genes after treatment with TMZ and/or RT, particularly in RT-treated glioblastoma cells, peaking within 24 h after treatment. Our results confirm the potential influence of DDR genes in patient outcome. The observation of DDR genes in response to TMZ and RT gives insight into the global response of DDR pathways after adjuvant treatment in glioblastoma, which may have utility in determining DDR targets for inhibition

Recirculating Flows Involving Short Fiber Suspensions: Numerical Difficulties and Efficient Advanced Micro-Macro Solvers

Numerical modelling of non-Newtonian flows usually involves the coupling between equations of motion characterized by an elliptic character, and the fluid constitutive equation, which defines an advection problem linked to the fluid history. There are different numerical techniques to treat the hyperbolic advection equations. In non-recirculating flows, Eulerian discretizations can give a convergent solution within a short computing time. However, the existence of steady recirculating flow areas induces additional difficulties. Actually, in these flows neither boundary conditions nor initial conditions are known. In this paper we compares different advanced strategies (some of them recently proposed and extended here for addressing complex flows) when they are applied to the solution of the kinetic theory description of a short fiber suspension fluid flows