210 research outputs found
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, , 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 using 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 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
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 .Comment: 17 pages, 6 figure
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
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 and . 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
Equilibrium configurations of fluids and their stability in higher dimensions
We study equilibrium shapes, stability and possible bifurcation diagrams of
fluids in higher dimensions, held together by either surface tension or
self-gravity. We consider the equilibrium shape and stability problem of
self-gravitating spheroids, establishing the formalism to generalize the
MacLaurin sequence to higher dimensions. We show that such simple models, of
interest on their own, also provide accurate descriptions of their general
relativistic relatives with event horizons. The examples worked out here hint
at some model-independent dynamics, and thus at some universality: smooth
objects seem always to be well described by both ``replicas'' (either
self-gravity or surface tension). As an example, we exhibit an instability
afflicting self-gravitating (Newtonian) fluid cylinders. This instability is
the exact analogue, within Newtonian gravity, of the Gregory-Laflamme
instability in general relativity. Another example considered is a
self-gravitating Newtonian torus made of a homogeneous incompressible fluid. We
recover the features of the black ring in general relativity.Comment: 42 pages, 11 Figures, RevTeX4. Accepted for publication in Classical
and Quantum Gravity. v2: Minor corrections and references adde
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 ”M) 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 ”M) 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
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