For the continuum and discrete elastic equations, we derive exact artificial boundary conditions (ABCs), often referred to as transparent boundary conditions, that can be applied at a planar interface below which there are no forces. Solution of the elasticity equations can then be performed using this interface as an artificial boundary, often with greatly reduced computational effort, but without loss of accuracy. A general solvability requirement is presented for the existence of an artificial boundary operator for discrete systems (such as discrete elasticity) on an unbounded (semi-infinite) domain. The solvability requirement is validated by introducing a sum-of-exponentials ansatz for the solution below the artificial boundary. We also derive a new expression for the total energy for the system, involving only the region above the artificial boundary. Numerical examples are provided to confirm and illustrate the accuracy and effectiveness of the results.

Abstract. Using the vector field method, we find a more general condition than finite type that implies a local regularity result for the ∂-Neumann operator. In our result, it is possible for an analytic disk to be on the part of the boundary where we have local regularity. 1.

Motivation: Genes are typically expressed in modular manners in biological processes. Recent studies reflect such features in analyzing gene expression patterns by directly scoring gene sets. Gene annotations have been used to define the gene sets, which have served to reveal specific biological themes from expression data. However, current annotations have limited analytical power, because they are classified by single categories providing only unary information for the gene sets.

Results: Here we propose a method for discovering composite biological themes from expression data. We intersected two annotated gene sets from different categories of Gene Ontology (GO). We then scored the expression changes of all the single and intersected sets. In this way, we were able to uncover, for example, a gene set with the molecular function F and the cellular component C that showed significant expression change, while the changes in individual gene sets were not significant. We provided an exemplary analysis for HIV-1 immune response. In addition, we tested the method on 20 public datasets where we found many ‘filtered’ composite terms the number of which reached ∼34% (a strong criterion, 5% significance) of the number of significant unary terms on average. By using composite annotation, we can derive new and improved information about disease and biological processes from expression data.

Availability: We provide a web application (ADGO: ) for the analysis of differentially expressed gene sets with composite GO annotations. The user can analyze Affymetrix and dual channel array (spotted cDNA and spotted oligo microarray) data for four species: human, mouse, rat and yeast.

We prove that the Steiner ratio for hyperbolic surfaces is 1/2.

In this paper, we construct a new exotic smooth 4-manifold X which is homeomorphic, but not diffeomorphic, to CP2#13 (CP) over bar (2). Moreover the manifold X has vanishing Seiberg-Witten invariants for all Spin(c)-structures of X and has no symplectic structure.

Second-order partial differential equations have been studied as a useful tool for noise
removal. The Perona?Malik model [P. Perona, Malik, Scale space and edge detection
using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intell. 12 (1990) 629?
639] has an edge preserving property but have sometimes the undesirable red effect.
In this paper, we propose improved models by combining Catte? et al.s model [F. Catte,
P.L. Lions, J.M. Morel, T. Coll, Image selective smoothing and edge detection by nonlinear
diffusion, SIAM J. Numer. Anal. 129 (1992) 182?193] with fourth-order terms. We
prove the existence and uniqueness of the proposed models. Then, we show numerical
evidence of the power of resolution of these models with respect to other known models
as the Perona?Malik model, the Catte? et al.s model, the modified total variation model
by Chan et al. [T. Chan, A. Marquina, P. Mulet, Second order differential functionals in
total variation-based image restoration. Available from : http:www.math.ucla.edu chan, etc.

Numerical solutions of exact controllability problems for linear and semilinear wave equations with distributed controls are studied. Exact controllability problems can be solved by the corresponding optimal control problems. The optimal control problem is reformulated as a system of equations (an optimality system) that consists of an initial value problem for the underlying (linear or semilinear) wave equation and a terminal value problem for the adjoint wave equation. The discretized optimality system is solved by a shooting method. The convergence properties of the numerical shooting method in the context of exact controllability are illustrated through computational experiments.