A note on the penalty parameter in Nitsche's method for unfitted boundary value problems

Nitsche's method is a popular approach to implement Dirichlet-type boundary conditions in situations where a strong imposition is either inconvenient or simply not feasible. The method is widely applied in the context of unfitted finite element methods. From the classical (symmetric) Nitsche's method it is well-known that the stabilization parameter in the method has to be chosen sufficiently large to obtain unique solvability of discrete systems. In this short note we discuss an often used strategy to set the stabilization parameter and describe a possible problem that can arise from this. We show that in specific situations error bounds can deteriorate and give examples of computations where Nitsche's method yields large and even diverging discretization errors

Condition number analysis and preconditioning of the finite cell method

The (Isogeometric) Finite Cell Method - in which a domain is immersed in a structured background mesh - suffers from conditioning problems when cells with small volume fractions occur. In this contribution, we establish a rigorous scaling relation between the condition number of (I)FCM system matrices and the smallest cell volume fraction. Ill-conditioning stems either from basis functions being small on cells with small volume fractions, or from basis functions being nearly linearly dependent on such cells. Based on these two sources of ill-conditioning, an algebraic preconditioning technique is developed, which is referred to as Symmetric Incomplete Permuted Inverse Cholesky (SIPIC). A detailed numerical investigation of the effectivity of the SIPIC preconditioner in improving (I)FCM condition numbers and in improving the convergence speed and accuracy of iterative solvers is presented for the Poisson problem and for two- and three-dimensional problems in linear elasticity, in which Nitche's method is applied in either the normal or tangential direction. The accuracy of the preconditioned iterative solver enables mesh convergence studies of the finite cell method

Robust and parallel scalable iterative solutions for large-scale finite cell analyses

The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a wide range of geometrical models can be performed. Application of the finite cell method, and other immersed methods, to large real-life and industrial problems is often limited due to the conditioning problems associated with these methods. These conditioning problems have caused researchers to resort to direct solution methods, which signifi- cantly limit the maximum size of solvable systems. Iterative solvers are better suited for large-scale computations than their direct counterparts due to their lower memory requirements and suitability for parallel computing. These benefits can, however, only be exploited when systems are properly conditioned. In this contribution we present an Additive-Schwarz type preconditioner that enables efficient and parallel scalable iterative solutions of large-scale multi-level hp-refined finite cell analyses.Comment: 32 pages, 17 figure

Widespread dysregulation of MiRNAs by MYCN amplification and chromosomal imbalances in neuroblastoma: association of miRNA expression with survival

MiRNAs regulate gene expression at a post-transcriptional level and their dysregulation can play major roles in the pathogenesis of many different forms of cancer, including neuroblastoma, an often fatal paediatric cancer originating from precursor cells of the sympathetic nervous system. We have analyzed a set of neuroblastoma (n = 145) that is broadly representative of the genetic subtypes of this disease for miRNA expression (430 loci by stem-loop RT qPCR) and for DNA copy number alterations (array CGH) to assess miRNA involvement in disease pathogenesis. The tumors were stratified and then randomly split into a training set (n = 96) and a validation set (n = 49) for data analysis. Thirty-seven miRNAs were significantly over-or under-expressed in MYCN amplified tumors relative to MYCN single copy tumors, indicating a potential role for the MYCN transcription factor in either the direct or indirect dysregulation of these loci. In addition, we also determined that there was a highly significant correlation between miRNA expression levels and DNA copy number, indicating a role for large-scale genomic imbalances in the dysregulation of miRNA expression. In order to directly assess whether miRNA expression was predictive of clinical outcome, we used the Random Forest classifier to identify miRNAs that were most significantly associated with poor overall patient survival and developed a 15 miRNA signature that was predictive of overall survival with 72.7% sensitivity and 86.5% specificity in the validation set of tumors. We conclude that there is widespread dysregulation of miRNA expression in neuroblastoma tumors caused by both over-expression of the MYCN transcription factor and by large-scale chromosomal imbalances. MiRNA expression patterns are also predicative of clinical outcome, highlighting the potential for miRNA mediated diagnostics and therapeutics

Integrating personality research and animal contest theory: aggressiveness in the green swordtail <i>Xiphophorus helleri</i>

&lt;p&gt;Aggression occurs when individuals compete over limiting resources. While theoretical studies have long placed a strong emphasis on context-specificity of aggression, there is increasing recognition that consistent behavioural differences exist among individuals, and that aggressiveness may be an important component of individual personality. Though empirical studies tend to focus on one aspect or the other, we suggest there is merit in modelling both within-and among-individual variation in agonistic behaviour simultaneously. Here, we demonstrate how this can be achieved using multivariate linear mixed effect models. Using data from repeated mirror trials and dyadic interactions of male green swordtails, &lt;i&gt;Xiphophorus helleri&lt;/i&gt;, we show repeatable components of (co)variation in a suite of agonistic behaviour that is broadly consistent with a major axis of variation in aggressiveness. We also show that observed focal behaviour is dependent on opponent effects, which can themselves be repeatable but were more generally found to be context specific. In particular, our models show that within-individual variation in agonistic behaviour is explained, at least in part, by the relative size of a live opponent as predicted by contest theory. Finally, we suggest several additional applications of the multivariate models demonstrated here. These include testing the recently queried functional equivalence of alternative experimental approaches, (e. g., mirror trials, dyadic interaction tests) for assaying individual aggressiveness.&lt;/p&gt

Basis Functions for Linear-Scaling First-Principles Calculations

In the framework of a recently reported linear-scaling method for density-functional-pseudopotential calculations, we investigate the use of localized basis functions for such work. We propose a basis set in which each local orbital is represented in terms of an array of `blip functions'' on the points of a grid. We analyze the relation between blip-function basis sets and the plane-wave basis used in standard pseudopotential methods, derive criteria for the approximate equivalence of the two, and describe practical tests of these criteria. Techniques are presented for using blip-function basis sets in linear-scaling calculations, and numerical tests of these techniques are reported for Si crystal using both local and non-local pseudopotentials. We find rapid convergence of the total energy to the values given by standard plane-wave calculations as the radius of the linear-scaling localized orbitals is increased.Comment: revtex file, with two encapsulated postscript figures, uses epsf.sty, submitted to Phys. Rev.

A Fast Gradient Approximation for Nonlinear Blind Signal Processing

When dealing with nonlinear blind processing algorithms (deconvolution or post-nonlinear source separation), complex mathematical estimations must be done giving as a result very slow algorithms. This is the case, for example, in speech processing, spike signals deconvolution or microarray data analysis. In this paper, we propose a simple method to reduce computational time for the inversion of Wiener systems or the separation of post-nonlinear mixtures, by using a linear approximation in a minimum mutual information algorithm. Simulation results demonstrate that linear spline interpolation is fast and accurate, obtaining very good results (similar to those obtained without approximation) while computational time is dramatically decreased. On the other hand, cubic spline interpolation also obtains similar good results, but due to its intrinsic complexity, the global algorithm is much more slow and hence not useful for our purpose