Primordial Perturbations from Multifield Inflation with Nonminimal Couplings

Realistic models of particle physics include many scalar fields. These fields generically have nonminimal couplings to the Ricci curvature scalar, either as part of a generalized Einstein theory or as necessary counterterms for renormalization in curved background spacetimes. We develop a gauge-invariant formalism for calculating primordial perturbations in models with multiple nonminimally coupled fields. We work in the Jordan frame (in which the nonminimal couplings remain explicit) and identify two distinct sources of entropy perturbations for such models. One set of entropy perturbations arises from interactions among the multiple fields. The second set arises from the presence of nonminimal couplings. Neither of these varieties of entropy perturbations will necessarily be suppressed in the long-wavelength limit, and hence they can amplify the curvature perturbation, $\zeta$, even for modes that have crossed outside the Hubble radius. Models that overproduce long-wavelength entropy perturbations endanger the close fit between predicted inflationary spectra and empirical observations.Comment: 16 pages, no figures. References added to match published versio

Grover's search with faults on some marked elements

Grover's algorithm is a quantum query algorithm solving the unstructured search problem of size $N$ using $O(\sqrt{N})$ queries. It provides a significant speed-up over any classical algorithm \cite{Gro96}. The running time of the algorithm, however, is very sensitive to errors in queries. It is known that if query may fail (report all marked elements as unmarked) the algorithm needs $\Omega(N)$ queries to find a marked element \cite{RS08}. \cite{AB+13} have proved the same result for the model where each marked element has its own probability to be reported as unmarked. We study the behavior of Grover's algorithm in the model where the search space contains both faulty and non-faulty marked elements. We show that in this setting it is indeed possible to find one of non-faulty marked items in $O(\sqrt{N})$ queries. We also analyze the limiting behavior of the algorithm for a large number of steps and show the existence and the structure of limiting state $\rho_{lim}$.Comment: 17 pages, 6 figure

Volumes of polytopes in spaces of constant curvature

We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a solution for Seidel problem on the volume of non-Euclidean tetrahedron. Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmagupta formula for the area of such quadrilateral. We also present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference

Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry

A new method to obtain trigonometry for the real spaces of constant curvature and metric of any (even degenerate) signature is presented. The method encapsulates trigonometry for all these spaces into a single basic trigonometric group equation. This brings to its logical end the idea of an absolute trigonometry, and provides equations which hold true for the nine two-dimensional spaces of constant curvature and any signature. This family of spaces includes both relativistic and non-relativistic homogeneous spacetimes; therefore a complete discussion of trigonometry in the six de Sitter, minkowskian, Newton--Hooke and galilean spacetimes follow as particular instances of the general approach. Any equation previously known for the three classical riemannian spaces also has a version for the remaining six spacetimes; in most cases these equations are new. Distinctive traits of the method are universality and self-duality: every equation is meaningful for the nine spaces at once, and displays explicitly invariance under a duality transformation relating the nine spaces. The derivation of the single basic trigonometric equation at group level, its translation to a set of equations (cosine, sine and dual cosine laws) and the natural apparition of angular and lateral excesses, area and coarea are explicitly discussed in detail. The exposition also aims to introduce the main ideas of this direct group theoretical way to trigonometry, and may well provide a path to systematically study trigonometry for any homogeneous symmetric space.Comment: 51 pages, LaTe

Algorithms and software for areal surface texture function parameters

Software for the evaluation of areal surface texture function parameters is described. Definitions of the parameters, expressed in terms of the inverse areal material ratio function, are provided along with details of the numerical algorithms employed in the software to implement calculations to evaluate approximations to the parameters according to those definitions. Results obtained using the software to process a number of data sets representing different surfaces are compared with those returned by proprietary software for surface texture measurement. Differences in the results, arising from different choices being made when implementing the steps in the parameter evaluation process, are discussed

Textbook accounts of the rules of indices with rational exponents

The rules of indices, e.g. anbn = (ab)n, are a particularly important part of elementary algebra. This paper reports results from a textbook analysis which examined how the shift from integer to rational exponents in the rules of indices is discussed in school textbooks. The analysis also considered related issues, such as notation and the introduction of complex numbers. A selection of popular textbooks from the period 1800–2000 was examined and the nature of the justification given for the extension of meaning to rational indices considered. In both the definition and computational rules, when extending the domain of n in an to rational numbers the (potential) contraction of the domain of a to positive numbers was often quietly ignored. A wide variety of approaches are used in choosing what is to be a definition, what is to follow, and how this is justified. The difference between computational rules for practical algebraic manipulation and a formal definition was often blurred.<br/

Computer-Aided Lead Optimization: Improved Small-Molecule Inhibitor of the Zinc Endopeptidase of Botulinum Neurotoxin Serotype A

Optimization of a serotype-selective, small-molecule inhibitor of botulinum neurotoxin serotype A (BoNTA) endopeptidase is a formidable challenge because the enzyme-substrate interface is unusually large and the endopeptidase itself is a large, zinc-binding protein with a complex fold that is difficult to simulate computationally. We conducted multiple molecular dynamics simulations of the endopeptidase in complex with a previously described inhibitor (Kiapp of 7±2.4 µM) using the cationic dummy atom approach. Based on our computational results, we hypothesized that introducing a hydroxyl group to the inhibitor could improve its potency. Synthesis and testing of the hydroxyl-containing analog as a BoNTA endopeptidase inhibitor showed a twofold improvement in inhibitory potency (Kiapp of 3.8±0.8 µM) with a relatively small increase in molecular weight (16 Da). The results offer an improved template for further optimization of BoNTA endopeptidase inhibitors and demonstrate the effectiveness of the cationic dummy atom approach in the design and optimization of zinc protease inhibitors

A deletion in GDF7 is associated with a heritable forebrain commissural malformation concurrent with ventriculomegaly and interhemispheric cysts in cats

Publisher Copyright: © 2020 by the authors.An inherited neurologic syndrome in a family of mixed-breed Oriental cats has been characterized as forebrain commissural malformation, concurrent with ventriculomegaly and interhemispheric cysts. However, the genetic basis for this autosomal recessive syndrome in cats is unknown. Forty-three cats were genotyped on the Illumina Infinium Feline 63K iSelect DNA Array and used for analyses. Genome-wide association studies, including a sib-transmission disequilibrium test and a case-control association analysis, and homozygosity mapping, identified a critical region on cat chromosome A3. Short-read whole genome sequencing was completed for a cat trio segregating with the syndrome. A homozygous 7 bp deletion in growth differentiation factor 7 (GDF7) (c.221_227delGCCGCGC [p.Arg74Profs]) was identified in affected cats, by comparison to the 99 Lives Cat variant dataset, validated using Sanger sequencing and genotyped by fragment analyses. This variant was not identified in 192 unaffected cats in the 99 Lives dataset. The variant segregated concordantly in an extended pedigree. In mice, GDF7 mRNA is expressed within the roof plate when commissural axons initiate ventrally-directed growth. This finding emphasized the importance of GDF7 in the neurodevelopmental process in the mammalian brain. A genetic test can be developed for use by cat breeders to eradicate this variant.Peer reviewe

Werewolf, there wolf : Variants in hairless associated with hypotrichia and roaning in the lykoi cat breed

Publisher Copyright: © 2020 by the authors. Licensee MDPI, Basel, Switzerland.A variety of cat breeds have been developed via novelty selection on aesthetic, dermatological traits, such as coat colors and fur types. A recently developed breed, the lykoi (a.k.a. werewolf cat), was bred from cats with a sparse hair coat with roaning, implying full color and all white hairs. The lykoi phenotype is a form of hypotrichia, presenting as a significant reduction in the average numbers of follicles per hair follicle group as compared to domestic shorthair cats, a mild to severe perifollicular to mural lymphocytic infiltration in 77% of observed hair follicle groups, and the follicles are often miniaturized, dilated, and dysplastic. Whole genome sequencing was conducted on a single lykoi cat that was a cross between two independently ascertained lineages. Comparison to the 99 Lives dataset of 194 non‐lykoi cats suggested two variants in the cat homolog for Hairless (HR) (HR lysine demethylase and nuclear receptor corepressor) as candidate causal gene variants. The lykoi cat was a compound heterozygote for two loss of function variants in HR, an exon 3 c.1255_1256dupGT (chrB1:36040783), which should produce a stop codon at amino acid 420 (p.Gln420Serfs*100) and, an exon 18 c.3389insGACA (chrB1:36051555), which should produce a stop codon at amino acid position 1130 (p.Ser1130Argfs*29). Ascertainment of 14 additional cats from founder lineages from Canada, France and different areas of the USA identified four additional loss of function HR variants likely causing the highly similar phenotypic hair coat across the diverse cats. The novel variants in HR for cat hypotrichia can now be established between minor differences in the phenotypic presentations.Peer reviewe