Computational science and re-discovery: open-source implementations of ellipsoidal harmonics for problems in potential theory

We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their substantial value for problems ranging in scale from molecules to the entire solar system. In this article, we suggest two possible reasons for the paucity relative to spherical harmonics. The first is essentially historical---ellipsoidal harmonics developed during the late 19th century and early 20th, when it was found that only the lowest-order harmonics are expressible in closed form. Each higher-order term requires the solution of an eigenvalue problem, and tedious manual computation seems to have discouraged applications and theoretical studies. The second explanation is practical: even with modern computers and accurate eigenvalue algorithms, expansions in ellipsoidal harmonics are significantly more challenging to compute than those in Cartesian or spherical coordinates. The present implementations reduce the "barrier to entry" by providing an easy and free way for the community to begin using ellipsoidal harmonics in actual research. We demonstrate our implementation using the specific and physiologically crucial problem of how charged proteins interact with their environment, and ask: what other analytical tools await re-discovery in an era of inexpensive computation?Comment: 25 pages, 3 figure

The role of inertia for the rotation of a nearly spherical particle in a general linear flow

We analyse the angular dynamics of a neutrally buoyant nearly spherical particle immersed in a steady general linear flow. The hydrodynamic torque acting on the particle is obtained by means of a reciprocal theorem, regular perturbation theory exploiting the small eccentricity of the nearly spherical particle, and assuming that inertial effects are small, but finite.Comment: 7 pages, 1 figur

Reduced habituation of auditory evoked potentials indicate cortical hyper-excitability in Fragile X Syndrome

Sensory hypersensitivities are common, clinically distressing features of Fragile X Syndrome (FXS). Preclinical evidence suggests this abnormality may result from synaptic hyper-excitability in sensory systems. This model predicts reduced sensory habituation to repeated stimulus presentation. Fourteen adolescents and adults with FXS and 15 age-matched controls participated in a modified auditory gating task using trains of 4 identical tones during dense array electroencephalography (EEG). Event-related potential and single trial time–frequency analyses revealed decreased habituation of the N1 event-related potential response in FXS, and increased gamma power coupled with decreases in gamma phase-locking during the early-stimulus registration period. EEG abnormalities in FXS were associated with parent reports of heightened sensory sensitivities and social communication deficits. Reduced habituation and altered gamma power and phase-locking to auditory cues demonstrated here in FXS patients parallels preclinical findings with Fmr1 KO mice. Thus, the EEG abnormalities seen in FXS patients support the model of neocortical hyper-excitability in FXS, and may provide useful translational biomarkers for evaluating novel treatment strategies targeting its neural substrate

Two-Center Integrals for r_{ij}^{n} Polynomial Correlated Wave Functions

All integrals needed to evaluate the correlated wave functions with polynomial terms of inter-electronic distance are included. For this form of the wave function, the integrals needed can be expressed as a product of integrals involving at most four electrons

A resting EEG study of neocortical hyperexcitability and altered functional connectivity in fragile X syndrome

(A) Scalp topographies of “local coupling”, showing correlations in each electrode between relative power of activity in the theta, and lower and upper alpha power bands and gamma power for male FXS and male healthy control participants, with significant group differences presented in the bottom row (p < 0.05, corrected), with dark blue reflecting no group difference. (B) Mean and standard error of correlations for all electrodes showing group differences as are plotted in A. * denotes correlations of spectral power in theta and upper alpha bands with gamma band power that are significantly different from zero based on the results of permutation analyses at p < 0.05. (TIF 4297 kb

Ordinary morality does not imply atheism

Many theist as well as many atheist philosophers have maintained that if God exists, then every instance of undeserved, unwanted suffering ultimately benefits the sufferer. Recently, several authors have argued that this implication of theism conflicts with ordinary morality. I show that these arguments all rest on a common mistake. Defenders of these arguments overlook the role of merely potential instances of suffering in determining our moral obligations toward suffering

Thirty Years After Michael E. Porter: What Do We Know About Business Exit?

Although a business exit is an important corporate change initiative, the buyer’s side seems to be more appealing to management researchers than the seller’s because acquisitions imply growth, i.e., success. Yet from an optimistic viewpoint, business exit can effectively create value for the selling company. In this paper we attempt to bring the relevance of the seller’s side back into our consciousness by asking: What do we know about business exit? We start our exploration with Porter (1976), focusing on literature that investigates the antecedents of, barriers to, and outcomes of business exit. We also include studies from related fields such as finance and economics.1 Through this research we determine three clusters of findings: factors promoting business exit, exit barriers, and exit outcomes. Overall, it is the intention of this paper to highlight the importance of business exit for research and practice. Knowing what we know about business exits and their high financial value we should bear in mind that exit need not mean failure but a new beginning for a corporation

Hormonal Signal Amplification Mediates Environmental Conditions during Development and Controls an Irreversible Commitment to Adulthood

Many animals can choose between different developmental fates to maximize fitness. Despite the complexity of environmental cues and life history, different developmental fates are executed in a robust fashion. The nematode Caenorhabditis elegans serves as a powerful model to examine this phenomenon because it can adopt one of two developmental fates (adulthood or diapause) depending on environmental conditions. The steroid hormone dafachronic acid (DA) directs development to adulthood by regulating the transcriptional activity of the nuclear hormone receptor DAF-12. The known role of DA suggests that it may be the molecular mediator of environmental condition effects on the developmental fate decision, although the mechanism is yet unknown. We used a combination of physiological and molecular biology techniques to demonstrate that commitment to reproductive adult development occurs when DA levels, produced in the neuroendocrine XXX cells, exceed a threshold. Furthermore, imaging and cell ablation experiments demonstrate that the XXX cells act as a source of DA, which, upon commitment to adult development, is amplified and propagated in the epidermis in a DAF-12 dependent manner. This positive feedback loop increases DA levels and drives adult programs in the gonad and epidermis, thus conferring the irreversibility of the decision. We show that the positive feedback loop canalizes development by ensuring that sufficient amounts of DA are dispersed throughout the body and serves as a robust fate-locking mechanism to enforce an organism-wide binary decision, despite noisy and complex environmental cues. These mechanisms are not only relevant to C. elegans but may be extended to other hormonal-based decision-making mechanisms in insects and mammals

A Discrete Time Model for the Analysis of Medium-Throughput C. elegans Growth Data

BACKGROUND: As part of a program to predict the toxicity of environmental agents on human health using alternative methods, several in vivo high- and medium-throughput assays are being developed that use C. elegans as a model organism. C. elegans-based toxicological assays utilize the COPAS Biosort flow sorting system that can rapidly measure size, extinction (EXT) and time-of-flight (TOF), of individual nematodes. The use of this technology requires the development of mathematical and statistical tools to properly analyze the large volumes of biological data. METHODOLOGY/PRINCIPAL FINDINGS: Findings A Markov model was developed that predicts the growth of populations of C. elegans. The model was developed using observations from a 60 h growth study in which five cohorts of 300 nematodes each were aspirated and measured every 12 h. Frequency distributions of log(EXT) measurements that were made when loading C. elegans L1 larvae into 96 well plates (t = 0 h) were used by the model to predict the frequency distributions of the same set of nematodes when measured at 12 h intervals. The model prediction coincided well with the biological observations confirming the validity of the model. The model was also applied to log(TOF) measurements following an adaptation. The adaptation accounted for variability in TOF measurements associated with potential curling or shortening of the nematodes as they passed through the flow cell of the Biosort. By providing accurate estimates of frequencies of EXT or TOF measurements following varying growth periods, the model was able to estimate growth rates. Best model fits showed that C. elegans did not grow at a constant exponential rate. Growth was best described with three different rates. Microscopic observations indicated that the points where the growth rates changed corresponded to specific developmental events: the L1/L2 molt and the start of oogenesis in young adult C. elegans. CONCLUSIONS: Quantitative analysis of COPAS Biosort measurements of C. elegans growth has been hampered by the lack of a mathematical model. In addition, extraneous matter and the inability to assign specific measurements to specific nematodes made it difficult to estimate growth rates. The present model addresses these problems through a population-based Markov model

Mapping adipose and muscle tissue expression quantitative trait loci in African Americans to identify genes for type 2 diabetes and obesity

Relative to European Americans, type 2 diabetes (T2D) is more prevalent in African Americans (AAs). Genetic variation may modulate transcript abundance in insulin-responsive tissues and contribute to risk; yet published studies identifying expression quantitative trait loci (eQTLs) in African ancestry populations are restricted to blood cells. This study aims to develop a map of genetically regulated transcripts expressed in tissues important for glucose homeostasis in AAs, critical for identifying the genetic etiology of T2D and related traits. Quantitative measures of adipose and muscle gene expression, and genotypic data were integrated in 260 non-diabetic AAs to identify expression regulatory variants. Their roles in genetic susceptibility to T2D, and related metabolic phenotypes were evaluated by mining GWAS datasets. eQTL analysis identified 1,971 and 2,078 cis-eGenes in adipose and muscle, respectively. Cis-eQTLs for 885 transcripts including top cis-eGenes CHURC1, USMG5, and ERAP2, were identified in both tissues. 62.1% of top cis-eSNPs were within ±50kb of transcription start sites and cis-eGenes were enriched for mitochondrial transcripts. Mining GWAS databases revealed association of cis-eSNPs for more than 50 genes with T2D (e.g. PIK3C2A, RBMS1, UFSP1), gluco-metabolic phenotypes, (e.g. INPP5E, SNX17, ERAP2, FN3KRP), and obesity (e.g. POMC, CPEB4). Integration of GWAS meta-analysis data from AA cohorts revealed the most significant association for cis-eSNPs of ATP5SL and MCCC1 genes, with T2D and BMI, respectively. This study developed the first comprehensive map of adipose and muscle tissue eQTLs in AAs (publically accessible at https://mdsetaa.phs.wakehealth.edu) and identified genetically-regulated transcripts for delineating genetic causes of T2D, and related metabolic phenotypes