We simulate blood flow in patient-specific cerebral arteries. The complicated geometry in the human brain makes the problem challenging. We use a fully unstructured three dimensional mesh to cover the artery, and Galerkin/least-squares finite element method to discretize the incompressible Navier-Stokes equations, that are employed to model the blood flow, and the resulting large sparse nonlinear system of equations is solved by a Newton-Krylov-Schwarz algorithm. From the computed flow fields, we are able to understand certain behavior of the blood flow of this particular patient before and after a stenosis is surgically removed. We also report the robustness and parallel performance of the domain decomposition based algorithm.

Largescale multiple testing with correlated test statistics arises frequently in much scientific research. Incorporating correlation information in approximating the false discovery proportion (FDP) has attracted increasing attention in recent years. When the covariance matrix of test statistics is known, Fan and his colleagues provided an accurate approximation of the FDP under arbitrary dependence structure and some sparsity assumption. However, the covariance matrix is often unknown in many applications and such dependence information must be estimated before approximating the FDP. The estimation accuracy can greatly affect the FDP approximation. In the current paper, we study theoretically the effect of unknown dependence on the testing procedure and establish a general framework such that the FDP can be well approximated. The effects of unknown dependence on approximating the FDP are in the

Recently, the Little Dragon Two and Poly-Dragon multivariate based public-key cryptosystems were proposed as efficient and secure schemes. In particular, the inventors of the two schemes claim that Little Dragon Two and Poly-Dragon resist algebraic cryptanalysis. In this paper, we show that MXL2, an algebraic attack method based on the XL algorithm and Ding’s concept of Mutants, is able to break Little Dragon Two with keys of length up to 229 bits and Poly-Dragon with keys of length up to 299. This contradicts the security claim for the proposed schemes and demonstrates the strength of MXL2 and the Mutant concept. This strength is further supported by experiments that show that in attacks on both schemes the MXL2 algorithm outperforms the Magma’s implementation of F4.

Let$L$be a formally selfadjoint differential operator and$p$a real-valued function, both on$a$≤$x$<∞. The deficiency indices are the numbers of solutions of$Lu$=λ$pu$for Im λ>0 and for Im λ<0 which have a certain regularity at$x$=∞. (A) If$p(x)$≥0 this regularity means that the integral of$p(x)$│$u$│^{2}converges at infinity. (B) If$p$changes its sign for arbitrarily large values of$x$but$L$has a positive definite Dirichlet integral it is natural to relate the regularity to this integral. Weyl’s classical study of the deficiency indices is reviewed for (A) with the help of elementary theory of quadratic forms. Individual bounds are found for the deficiency indices also when$L$is of odd order. It is then indicated how the method carriers over to (B).

We extend the idea of crossvalidation to choose the smoothing parameters of the double-kernel local linear regression for estimating a conditional density. Our selection rule optimises the estimated conditional density function by minimising the integrated squared error. We also discuss three other bandwidth selection rules, an ad hoc method used by Fan et al. (1996), a bootstrap method of Hall et al. (1999) for bandwidth selection in the estimation of conditional distribution functions, modified by Bashtannyk &amp; Hyndman (2001) to cover conditional density functions, and finally a simple approach proposed by Hyndman &amp; Yao (2002). The performance of the new approach is compared with these three methods by simulation studies, and our method performs outstandingly well. The method is illustrated by an application to estimating the transition density and the Value-at-Risk of treasury-bill data.