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

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

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

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

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

Discovery of the Largest Orbweaving Spider Species: The Evolution of Gigantism in Nephila

More than 41,000 spider species are known with about 400-500 added each year, but for some well-known groups, such as the giant golden orbweavers, Nephila, the last valid described species dates from the 19(th) century. Nephila are renowned for being the largest web-spinning spiders, making the largest orb webs, and are model organisms for the study of extreme sexual size dimorphism (SSD) and sexual biology. Here, we report on the discovery of a new, giant Nephila species from Africa and Madagascar, and review size evolution and SSD in Nephilidae.We formally describe N. komaci sp. nov., the largest web spinning species known, and place the species in phylogenetic context to reconstruct the evolution of mean size (via squared change parsimony). We then test female and male mean size correlation using phylogenetically independent contrasts, and simulate nephilid body size evolution using Monte Carlo statistics.Nephila females increased in size almost monotonically to establish a mostly African clade of true giants. In contrast, Nephila male size is effectively decoupled and hovers around values roughly one fifth of female size. Although N. komaci females are the largest Nephila yet discovered, the males are also large and thus their SSD is not exceptional

Sexual Cannibalism: High Incidence in a Natural Population with Benefits to Females

10 pages, 3 figures.[Background] Sexual cannibalism may be a form of extreme sexual conflict in which females benefit more from feeding on males than mating with them, and males avoid aggressive, cannibalistic females in order to increase net fitness. A thorough understanding of the adaptive significance of sexual cannibalism is hindered by our ignorance of its prevalence in nature. Furthermore, there are serious doubts about the food value of males, probably because most studies that attempt to document benefits of sexual cannibalism to the female have been conducted in the laboratory with non-natural alternative prey. Thus, to understand more fully the ecology and evolution of sexual cannibalism, field experiments are needed to document the prevalence of sexual cannibalism and its benefits to females.[Methodology/Principal Findings] We conducted field experiments with the Mediterranean tarantula (Lycosa tarantula), a burrowing wolf spider, to address these issues. At natural rates of encounter with males, approximately a third of L. tarantula females cannibalized the male. The rate of sexual cannibalism increased with male availability, and females were more likely to kill and consume an approaching male if they had previously mated with another male. We show that females benefit from feeding on a male by breeding earlier, producing 30% more offspring per egg sac, and producing progeny of higher body condition. Offspring of sexually cannibalistic females dispersed earlier and were larger later in the season than spiderlings of non-cannibalistic females.[Conclusions/Significance] In nature a substantial fraction of female L. tarantula kill and consume approaching males instead of mating with them. This behaviour is more likely to occur if the female has mated previously. Cannibalistic females have higher rates of reproduction, and produce higher-quality offspring, than non-cannibalistic females. Our findings further suggest that female L. tarantula are nutrient-limited in nature and that males are high-quality prey. The results of these field experiments support the hypothesis that sexual cannibalism is adaptive to females.This paper has been written under a Ramón y Cajal research contract from the Spanish Ministry of Science and Technology (MCYT) to JML and an I3P-BPD2004-CSIC scholarship to RRB. This work has been funded by MEC grants CGL2004-03153 and CGL2007-60520 to JML, MARG, RRB, CFM and DHW.Peer reviewe

Self Assessment in Insects: Honeybee Queens Know Their Own Strength

Contests mediate access to reproductive opportunities in almost all species of animals. An important aspect of the evolution of contests is the reduction of the costs incurred during intra-specific encounters to a minimum. However, escalated fights are commonly lethal in some species like the honeybee, Apis mellifera. By experimentally reducing honeybee queens' fighting abilities, we demonstrate that they refrain from engaging in lethal contests that typically characterize their reproductive dominance behavior and coexist peacefully within a colony. This suggests that weak queens exploit an alternative reproductive strategy and provides an explanation for rare occurrences of queen cohabitation in nature. Our results further indicate that self-assessment, but not mutual assessment of fighting ability occurs prior to and during the agonistic encounters

Silencing microRNA-134 produces neuroprotective and prolonged seizure-suppressive effects

Temporal lobe epilepsy is a common, chronic neurological disorder characterized by recurrent spontaneous seizures. MicroRNAs (miRNAs) are small, noncoding RNAs that regulate post-transcriptional expression of protein-coding mRNAs, which may have key roles in the pathogenesis of neurological disorders. In experimental models of prolonged, injurious seizures (status epilepticus) and in human epilepsy, we found upregulation of miR-134, a brain-specific, activity-regulated miRNA that has been implicated in the control of dendritic spine morphology. Silencing of miR-134 expression in vivo using antagomirs reduced hippocampal CA3 pyramidal neuron dendrite spine density by 21% and rendered mice refractory to seizures and hippocampal injury caused by status epilepticus. Depletion of miR-134 after status epilepticus in mice reduced the later occurrence of spontaneous seizures by over 90% and mitigated the attendant pathological features of temporal lobe epilepsy. Thus, silencing miR-134 exerts prolonged seizure-suppressant and neuroprotective actions; determining whether these are anticonvulsant effects or are truly antiepileptogenic effects requires additional experimentation