Self-interacting scalar field cosmologies: unified exact solutions and symmetries

We investigate a mechanism that generates exact solutions of scalar field cosmologies in a unified way. The procedure investigated here permits to recover almost all known solutions, and allows one to derive new solutions as well. In particular, we derive and discuss one novel solution defined in terms of the Lambert function. The solutions are organised in a classification which depends on the choice of a generating function which we have denoted by x(phi) that reflects the underlying thermodynamics of the model. We also analyse and discuss the existence of form-invariance dualities between solutions. A general way of defining the latter in an appropriate fashion for scalar fields is put forward.

On the spectra of certain integro-differential-delay problems with applications in neurodynamics

We investigate the spectrum of certain integro-differential-delay equations (IDDEs) which arise naturally within spatially distributed, nonlocal, pattern formation problems. Our approach is based on the reformulation of the relevant dispersion relations with the use of the Lambert function. As a particular application of this approach, we consider the case of the Amari delay neural field equation which describes the local activity of a population of neurons taking into consideration the finite propagation speed of the electric signal. We show that if the kernel appearing in this equation is symmetric around some point a= 0 or consists of a sum of such terms, then the relevant dispersion relation yields spectra with an infinite number of branches, as opposed to finite sets of eigenvalues considered in previous works. Also, in earlier works the focus has been on the most rightward part of the spectrum and the possibility of an instability driven pattern formation. Here, we numerically survey the structure of the entire spectra and argue that a detailed knowledge of this structure is important within neurodynamical applications. Indeed, the Amari IDDE acts as a filter with the ability to recognise and respond whenever it is excited in such a way so as to resonate with one of its rightward modes, thereby amplifying such inputs and dampening others. Finally, we discuss how these results can be generalised to the case of systems of IDDEs.

A Closed-Form Solution for the Optimal Time Evolution of an Exponentially Decaying Signal with Thermal Noise

The signal-to-noise ratio of a monoexponentially decaying signal exhibits a maximum at an evolution time of approximately 1.26 T-2. It has previously been thought that there is no closed-form solution to express this maximum. We report in this note that this maximum can be represented in a specific, analytical closed form in terms of the negative real branch of an inverse function known as the Lambert W function. The Lambert function is finding increasing use in the solution of problems in a variety of areas in the physical sciences. (C) 2014 Wiley Periodicals, Inc.

Explicit Expressions for Solar Panel Equivalent Circuit Parameters Based on Analytical Formulation and the Lambert W-Function

Due to the high dependence of photovoltaic energy efficiency on environmental conditions (temperature, irradiation...), it is quite important to perform some analysis focusing on the characteristics of photovoltaic devices in order to optimize energy production, even for small-scale users. The use of equivalent circuits is the preferred option to analyze solar cells/panels performance. However, the aforementioned small-scale users rarely have the equipment or expertise to perform large testing/calculation campaigns, the only information available for them being the manufacturer datasheet. The solution to this problem is the development of new and simple methods to define equivalent circuits able to reproduce the behavior of the panel for any working condition, from a very small amount of information. In the present work a direct and completely explicit method to extract solar cell parameters from the manufacturer datasheet is presented and tested. This method is based on analytical formulation which includes the use of the Lambert W-function to turn the series resistor equation explicit. The presented method is used to analyze commercial solar panel performance (i.e., the current-voltage–I-V–curve) at different levels of irradiation and temperature. The analysis performed is based only on the information included in the manufacturer’s datasheet.

Explicit expressions for solar panel equivalent circuit parameters based on analytical formulation and the Lambert W - Function

Due to the high dependence of photovoltaic energy efficiency on environmental conditions (temperature, irradiation...), it is quite important to perform some analysis focusing on the characteristics of photovoltaic devices in order to optimize energy production, even for small-scale users. The use of equivalent circuits is the preferred option to analyze solar cells/panels performance. However, the aforementioned small-scale users rarely have the equipment or expertise to perform large testing/calculation campaigns, the only information available for them being the manufacturer datasheet. The solution to this problem is the development of new and simple methods to define equivalent circuits able to reproduce the behavior of the panel for any working condition, from a very small amount of information. In the present work a direct and completely explicit method to extract solar cell parameters from the manufacturer datasheet is presented and tested. This method is based on analytical formulation which includes the use of the Lambert W-function to turn the series resistor equation explicit. The presented method is used to analyze the performance (i.e., the I - V curve) of a commercial solar panel at different levels of irradiation and temperature. The analysis performed is based only on the information included in the manufacturer's datasheet.

Integration of genome-wide association studies with biological knowledge identifies six novel genes related to kidney function.

In conducting genome-wide association studies (GWAS), analytical approaches leveraging biological information may further understanding of the pathophysiology of clinical traits. To discover novel associations with estimated glomerular filtration rate (eGFR), a measure of kidney function, we developed a strategy for integrating prior biological knowledge into the existing GWAS data for eGFR from the CKDGen Consortium. Our strategy focuses on single nucleotide polymorphism (SNPs) in genes that are connected by functional evidence, determined by literature mining and gene ontology (GO) hierarchies, to genes near previously validated eGFR associations. It then requires association thresholds consistent with multiple testing, and finally evaluates novel candidates by independent replication. Among the samples of European ancestry, we identified a genome-wide significant SNP in FBXL20 (P = 5.6 × 10(-9)) in meta-analysis of all available data, and additional SNPs at the INHBC, LRP2, PLEKHA1, SLC3A2 and SLC7A6 genes meeting multiple-testing corrected significance for replication and overall P-values of 4.5 × 10(-4)-2.2 × 10(-7). Neither the novel PLEKHA1 nor FBXL20 associations, both further supported by association with eGFR among African Americans and with transcript abundance, would have been implicated by eGFR candidate gene approaches. LRP2, encoding the megalin receptor, was identified through connection with the previously known eGFR gene DAB2 and extends understanding of the megalin system in kidney function. These findings highlight integration of existing genome-wide association data with independent biological knowledge to uncover novel candidate eGFR associations, including candidates lacking known connections to kidney-specific pathways. The strategy may also be applicable to other clinical phenotypes, although more testing will be needed to assess its potential for discovery in general.

Urotensin-II System in Genetic Control of Blood Pressure and Renal Function.

Urotensin-II controls ion/water homeostasis in fish and vascular tone in rodents. We hypothesised that common genetic variants in urotensin-II pathway genes are associated with human blood pressure or renal function. We performed family-based analysis of association between blood pressure, glomerular filtration and genes of the urotensin-II pathway (urotensin-II, urotensin-II related peptide, urotensin-II receptor) saturated with 28 tagging single nucleotide polymorphisms in 2024 individuals from 520 families; followed by an independent replication in 420 families and 7545 unrelated subjects. The expression studies of the urotensin-II pathway were carried out in 97 human kidneys. Phylogenetic evolutionary analysis was conducted in 17 vertebrate species. One single nucleotide polymorphism (rs531485 in urotensin-II gene) was associated with adjusted estimated glomerular filtration rate in the discovery cohort (p = 0.0005). It showed no association with estimated glomerular filtration rate in the combined replication resource of 8724 subjects from 6 populations. Expression of urotensin-II and its receptor showed strong linear correlation (r = 0.86, p<0.0001). There was no difference in renal expression of urotensin-II system between hypertensive and normotensive subjects. Evolutionary analysis revealed accumulation of mutations in urotensin-II since the divergence of primates and weaker conservation of urotensin-II receptor in primates than in lower vertebrates. Our data suggest that urotensin-II system genes are unlikely to play a major role in genetic control of human blood pressure or renal function. The signatures of evolutionary forces acting on urotensin-II system indicate that it may have evolved towards loss of function since the divergence of primates.

The 3' half of the mouse mammary tumor virus orf gene is not sufficient for its superantigen function in transgenic mice.

The Mouse Mammary Tumor Virus (MMTV) long terminal repeat contains an open reading frame (orf) of 960 nucleotides encoding a 36 kDa polypeptide with a putative transmembrane domain and five N-glycosylation sites in the N-terminal part of the protein. Transgenic mice bearing either the complete or the 3' terminal half of the orf sequence of MMTV-GR under the control of the SV40 promoter were raised. As shown previously by FACS analysis transgenic mice which express the complete orf gene have a significant deletion of V beta 14 expressing T cells at 6 weeks of age. Here we show that no clonal deletion of V beta 14 bearing T cells takes place in transgenic mice that contain orf sequences from the fifth ATG to the termination codon. The pattern of tissues expressing the truncated transgene was studied by the Polymerase Chain Reaction (PCR) and was very similar to the one obtained in the V beta 14 deleting animals. These data suggest that the amino-terminal portion of the ORF protein (pORF) is required for a superantigen function, while our previous data indicated that determinants from the carboxy-terminus play an important role for TCR V beta specificity.

Genome-wide association study of kidney function decline in individuals of European descent.

Genome-wide association studies (GWASs) have identified multiple loci associated with cross-sectional eGFR, but a systematic genetic analysis of kidney function decline over time is missing. Here we conducted a GWAS meta-analysis among 63,558 participants of European descent, initially from 16 cohorts with serial kidney function measurements within the CKDGen Consortium, followed by independent replication among additional participants from 13 cohorts. In stage 1 GWAS meta-analysis, single-nucleotide polymorphisms (SNPs) at MEOX2, GALNT11, IL1RAP, NPPA, HPCAL1, and CDH23 showed the strongest associations for at least one trait, in addition to the known UMOD locus, which showed genome-wide significance with an annual change in eGFR. In stage 2 meta-analysis, the significant association at UMOD was replicated. Associations at GALNT11 with Rapid Decline (annual eGFR decline of 3 ml/min per 1.73 m(2) or more), and CDH23 with eGFR change among those with CKD showed significant suggestive evidence of replication. Combined stage 1 and 2 meta-analyses showed significance for UMOD, GALNT11, and CDH23. Morpholino knockdowns of galnt11 and cdh23 in zebrafish embryos each had signs of severe edema 72 h after gentamicin treatment compared with controls, but no gross morphological renal abnormalities before gentamicin administration. Thus, our results suggest a role in the deterioration of kidney function for the loci GALNT11 and CDH23, and show that the UMOD locus is significantly associated with kidney function decline.Kidney International advance online publication, 10 December 2014; doi:10.1038/ki.2014.361.

Genetic associations at 53 loci highlight cell types and biological pathways relevant for kidney function.

Reduced glomerular filtration rate defines chronic kidney disease and is associated with cardiovascular and all-cause mortality. We conducted a meta-analysis of genome-wide association studies for estimated glomerular filtration rate (eGFR), combining data across 133,413 individuals with replication in up to 42,166 individuals. We identify 24 new and confirm 29 previously identified loci. Of these 53 loci, 19 associate with eGFR among individuals with diabetes. Using bioinformatics, we show that identified genes at eGFR loci are enriched for expression in kidney tissues and in pathways relevant for kidney development and transmembrane transporter activity, kidney structure, and regulation of glucose metabolism. Chromatin state mapping and DNase I hypersensitivity analyses across adult tissues demonstrate preferential mapping of associated variants to regulatory regions in kidney but not extra-renal tissues. These findings suggest that genetic determinants of eGFR are mediated largely through direct effects within the kidney and highlight important cell types and biological pathways.

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

Relationship Between Orofacial Function, Dentofacial Morphology, And Bite Force In Young Subjects.

The aim was to evaluate the relationship between orofacial function, dentofacial morphology, and bite force in young subjects. Three hundred and sixteen subjects were divided according to dentition stage (early, intermediate, and late mixed and permanent dentition). Orofacial function was screened using the Nordic Orofacial Test-Screening (NOT-S). Orthodontic treatment need, bite force, lateral and frontal craniofacial dimensions and presence of sleep bruxism were also assessed. The results were submitted to descriptive statistics, normality and correlation tests, analysis of variance, and multiple linear regression to test the relationship between NOT-S scores and the studied independent variables. The variance of NOT-S scores between groups was not significant. The evaluation of the variables that significantly contributed to NOT-S scores variation showed that age and presence of bruxism related to higher NOT-S total scores, while the increase in overbite measurement and presence of closed lip posture related to lower scores. Bite force did not show a significant relationship with scores of orofacial dysfunction. No significant correlations between craniofacial dimensions and NOT-S scores were observed. Age and sleep bruxism were related to higher NOT-S scores, while the increase in overbite measurement and closed lip posture contributed to lower scores of orofacial dysfunction.

Impaired Compensatory Beta-cell Function And Growth In Response To High-fat Diet In Ldl Receptor Knockout Mice.

In this study, we investigated the effect of low density lipoprotein receptor (LDLr) deficiency on gap junctional connexin 36 (Cx36) islet content and on the functional and growth response of pancreatic beta-cells in C57BL/6 mice fed a high-fat (HF) diet. After 60 days on regular or HF diet, the metabolic state and morphometric islet parameters of wild-type (WT) and LDLr-/- mice were assessed. HF diet-fed WT animals became obese and hypercholesterolaemic as well as hyperglycaemic, hyperinsulinaemic, glucose intolerant and insulin resistant, characterizing them as prediabetic. Also they showed a significant decrease in beta-cell secretory response to glucose. Overall, LDLr-/- mice displayed greater susceptibility to HF diet as judged by their marked cholesterolaemia, intolerance to glucose and pronounced decrease in glucose-stimulated insulin secretion. HF diet induced similarly in WT and LDLr-/- mice, a significant decrease in Cx36 beta-cell content as revealed by immunoblotting. Prediabetic WT mice displayed marked increase in beta-cell mass mainly due to beta-cell hypertrophy/replication. Nevertheless, HF diet-fed LDLr-/- mice showed no significant changes in beta-cell mass, but lower islet-duct association (neogenesis) and higher beta-cell apoptosis index were seen as compared to controls. The higher metabolic susceptibility to HF diet of LDLr-/- mice may be explained by a deficiency in insulin secretory response to glucose associated with lack of compensatory beta-cell expansion.