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

Linear Versus Nonlinear Methods for Detecting Magnetospheric and Ionospheric Current Systems Patterns

Abstract There is a growing interest in the development of models and methods of analysis aimed to recognize in the geomagnetic field signals the different contributions coming from the various sources both internal and external to the Earth. Many models describing the geomagnetic field of internal and external origin have been developed. Here, we investigate the possibility to recognize in the magnetic field of external origin the different contributions coming from external sources. We consider the measurements of the vertical component of the geomagnetic field recorded by the European Space Agency (ESA) Swarm A and B satellites at low and mid latitudes during a geomagnetically quiet period. We apply two different methods of analysis: a linear method, that is, the empirical orthogonal function (EOF), and a nonlinear one, that is, the multivariate empirical mode decomposition (MEMD). Due to the high nonlinear behavior of the different external contributions to the magnetic signal the MEMD seems to recognize better than EOF the main intrinsic modes capable of describing the different magnetic spatial structures embedded in the analyzed signal. By applying the MEMD only five modes and a residue are necessary to recognize the different contributions coming from the external sources in the magnetic signal against the 26 modes that are necessary in the case of the EOF. This study is an example of the potential of the MEMD to give new insights into the analysis of the geomagnetic field of external origin and to separate the ionospheric signal from the magnetospheric one in a simple and rapid way

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

Critical time-step size analysis and mass scaling by ghost-penalty for immersogeometric explicit dynamics

In this article, we study the effect of small-cut elements on the critical time-step size in an immersogeometric context. We analyze different formulations for second-order (membrane) and fourth-order (shell-type) equations, and derive scaling relations between the critical time-step size and the cut-element size for various types of cuts. In particular, we focus on different approaches for the weak imposition of Dirichlet conditions: by penalty enforcement and with Nitsche's method. The stability requirement for Nitsche's method necessitates either a cut-size dependent penalty parameter, or an additional ghost-penalty stabilization term is necessary. Our findings show that both techniques suffer from cut-size dependent critical time-step sizes, but the addition of a ghost-penalty term to the mass matrix serves to mitigate this issue. We confirm that this form of `mass-scaling' does not adversely affect error and convergence characteristics for a transient membrane example, and has the potential to increase the critical time-step size by orders of magnitude. Finally, for a prototypical simulation of a Kirchhoff-Love shell, our stabilized Nitsche formulation reduces the solution error by well over an order of magnitude compared to a penalty formulation at equal time-step size

Numerical approximation of the generalized regularized long wave equation using Petrov–Galerkin finite element method

The generalized regularized long wave (GRLW) equation has been developed to model a variety of physical phenomena such as ion-acoustic and magnetohydro dynamic waves in plasma,nonlinear transverse waves in shallow water and phonon packets in nonlinear crystals. This paper aims to develop andanalyze a powerful numerical scheme for the nonlinear GRLWequation by Petrov–Galerkin method in which the elementshape functions are cubic and weight functions are quadratic B-splines. The proposed method is implemented to three ref-erence problems involving propagation of the single solitarywave, interaction of two solitary waves and evolution of solitons with the Maxwellian initial condition. The variational for-mulation and semi-discrete Galerkin scheme of the equation are firstly constituted. We estimate rate of convergence of such an approximation. Using Fourier stability analysis of thelinearized scheme we show that the scheme is uncondition-ally stable. To verify practicality and robustness of the new scheme error norms L2, L∞ and three invariants I1, I2,and I3 are calculated. The computed numerical results are compared with other published results and confirmed to be precise and effective

Global MYCN Transcription Factor Binding Analysis in Neuroblastoma Reveals Association with Distinct E-Box Motifs and Regions of DNA Hypermethylation

BACKGROUND: Neuroblastoma, a cancer derived from precursor cells of the sympathetic nervous system, is a major cause of childhood cancer related deaths. The single most important prognostic indicator of poor clinical outcome in this disease is genomic amplification of MYCN, a member of a family of oncogenic transcription factors. METHODOLOGY: We applied MYCN chromatin immunoprecipitation to microarrays (ChIP-chip) using MYCN amplified/non-amplified cell lines as well as a conditional knockdown cell line to determine the distribution of MYCN binding sites within all annotated promoter regions. CONCLUSION: Assessment of E-box usage within consistently positive MYCN binding sites revealed a predominance for the CATGTG motif (p\u3c0.0016), with significant enrichment of additional motifs CATTTG, CATCTG, CAACTG in the MYCN amplified state. For cell lines over-expressing MYCN, gene ontology analysis revealed enrichment for the binding of MYCN at promoter regions of numerous molecular functional groups including DNA helicases and mRNA transcriptional regulation. In order to evaluate MYCN binding with respect to other genomic features, we determined the methylation status of all annotated CpG islands and promoter sequences using methylated DNA immunoprecipitation (MeDIP). The integration of MYCN ChIP-chip and MeDIP data revealed a highly significant positive correlation between MYCN binding and DNA hypermethylation. This association was also detected in regions of hemizygous loss, indicating that the observed association occurs on the same homologue. In summary, these findings suggest that MYCN binding occurs more commonly at CATGTG as opposed to the classic CACGTG E-box motif, and that disease associated over expression of MYCN leads to aberrant binding to additional weaker affinity E-box motifs in neuroblastoma. The co-localization of MYCN binding and DNA hypermethylation further supports the dual role of MYCN, namely that of a classical transcription factor affecting the activity of individual genes, and that of a mediator of global chromatin structure

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.

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

Simplifying the Representation of Radiance from Multiple Emitters

International audienceIn recent work radiance function properties and discontinuity meshing have been used to construct high quality interpolants representing radiance. Such approaches do not consider the combined effect of multiple sources and thus perform unnecessary discontinuity meshing calculations and often construct interpolants with too fine subdivision. In this research we present an extended structured sampling algorithm that treats scenes with shadows and multiple sources. We then introduce an algorithm which simplifies the mesh based on the interaction of multiple sources. For unoccluded regions an a posteriori simplification technique is used. For regions in shadow, we first compute the maximal umbral/penumbral and penumbral/light boundaries. This construction facilitates the determination of whether full discontinuity meshing is required or whether it can be avoided due to the illumination from another source. An estimate of the error caused by potential simplification is used for this decision. Thus full discontinuitymesh calculation is only incurred in regions where it is necessary resulting in a more compact representation of radiance

Parity conserving gamma asymmetry in n-p radiative capture

The importance of n-p radiative capture, utilizing polarized cold neutrons, as a means of measuring the weak pion coupling constant is reviewed. Parity conserving processes of the form k_gamma*[s_n,k_n] can contribute to the s_n*k_gamma photon asymmetry in any such experiment, if the apparatus is not perfectly symmetric. For an incident laboratory neutron energy of 0.003 eV a value of A^{PC}_{gamma}=0.67*10^{-8} is obtained for two different potential models (Argonne AV14 and Nijmegen Reid93). Serving as an extreme test case, the Reid soft core potential yields 0.61*10^{-8}, close to the result of the contemporary forces. Implications for extracting the weak pion coupling constant and for monitoring the beam polarization are discussed.Comment: 8 page