Alsophis antiguae

Number of Pages: 3Integrative BiologyGeological Science

Asymptotic Exit Location Distributions in the Stochastic Exit Problem

Consider a two-dimensional continuous-time dynamical system, with an attracting fixed point $S$. If the deterministic dynamics are perturbed by white noise (random perturbations) of strength $\epsilon$, the system state will eventually leave the domain of attraction $\Omega$ of $S$. We analyse the case when, as $\epsilon\to0$, the exit location on the boundary $\partial\Omega$ is increasingly concentrated near a saddle point $H$ of the deterministic dynamics. We show that the asymptotic form of the exit location distribution on $\partial\Omega$ is generically non-Gaussian and asymmetric, and classify the possible limiting distributions. A key role is played by a parameter $\mu$, equal to the ratio $|\lambda_s(H)|/\lambda_u(H)$ of the stable and unstable eigenvalues of the linearized deterministic flow at $H$. If $\mu<1$ then the exit location distribution is generically asymptotic as $\epsilon\to0$ to a Weibull distribution with shape parameter $2/\mu$, on the $O(\epsilon^{\mu/2})$ length scale near $H$. If $\mu>1$ it is generically asymptotic to a distribution on the $O(\epsilon^{1/2})$ length scale, whose moments we compute. The asymmetry of the asymptotic exit location distribution is attributable to the generic presence of a `classically forbidden' region: a wedge-shaped subset of $\Omega$ with $H$ as vertex, which is reached from $S$, in the $\epsilon\to0$ limit, only via `bent' (non-smooth) fluctuational paths that first pass through the vicinity of $H$. We deduce from the presence of this forbidden region that the classical Eyring formula for the small-$\epsilon$ exponential asymptotics of the mean first exit time is generically inapplicable.Comment: This is a 72-page Postscript file, about 600K in length. Hardcopy requests to [email protected] or [email protected]

Transdifferentiation from cornea to lens in Xenopus laevis depends on BMP signalling and involves upregulation of Wnt signalling

<p>Abstract</p> <p>Background</p> <p>Surgical removal of the lens from larval <it>Xenopus laevis </it>results in a rapid transdifferention of central corneal cells to form a new lens. The trigger for this process is understood to be an induction event arising from the unprecedented exposure of the cornea to the vitreous humour that occurs following lens removal. The molecular identity of this trigger is unknown.</p> <p>Results</p> <p>Here, we have used a functional transgenic approach to show that BMP signalling is required for lens regeneration and a microarray approach to identify genes that are upregulated specifically during this process. Analysis of the array data strongly implicates Wnt signalling and the Pitx family of transcription factors in the process of cornea to lens transdifferentiation. Our analysis also captured several genes associated with congenital cataract in humans. Pluripotency genes, in contrast, were not upregulated, supporting the idea that corneal cells transdifferentiate without returning to a stem cell state. Several genes from the array were expressed in the forming lens during embryogenesis. One of these, <it>Nipsnap1</it>, is a known direct target of BMP signalling.</p> <p>Conclusions</p> <p>Our results strongly implicate the developmental Wnt and BMP signalling pathways in the process of cornea to lens transdifferentiation (CLT) in <it>Xenopus</it>, and suggest direct transdifferentiation between these two anterior eye tissues.</p

The spectrum of a Hermitian matrix sum

AbstractAn announcement by Lidskii, (B.V. Lidskii, Functional Anal. Appl. 10 (1982) 76–77 (Russian), 139–140 (English)), claimed to establish the explicit description of the spectrum of a Hermitian matrix sum in the form conjectured by Horn (A. Horn, Pacific J. Math. 16 (1962) 225–241), but no supporting proof has been published. This paper begins an analysis of the claim, and is the first step towards bridging the distance between the elementary methods of Horn's (1962) paper and the partial solution of the same problem using noncommutative harmonic analysis by Dooley et al. (I. Dooley, R. Repka, N. Wildberger, Lin. Mult. Alg. 36 (1993) 79–102). The methods of Horn/Lidskii lead to combinatorial issues of independent interest

Optical and Electrochemical Properties of Multi-layer Polyelectrolyte Thin Films Incorporating Spherical, Gold Colloid Nanomaterials

Polyelectrolyte multilayer (PEM) films incorporating various types of spherical, gold nanomaterials (NMs) were investigated to assess the existence of electrochemical and/or optical signal enhancement effects directly attributable to embedded NMs and the relationship of these effects to film structure and composition. Specifically, electrostatically assembled films of cationic poly-L-lysine (PLL) and anionic poly(4-styrene sulfonate) (PSS) incorporating one of four types of spherical, gold colloid NMs were constructed on 3-(aminopropyl)trimethoxysilane (3-APTMS)-modified glass substrates for optical studies or 11-mercaptoundecanoic (MUA)-modified gold electrodes for electrochemical studies. The NMs inserted into the PEM films include citrate-stabilized gold nanoparticles, thioctic acid-stabilized gold nanoparticles (TAS-NPs), MUA-modified monolayer protected gold clusters, and hollow gold nanoshells (Au-NSs). Optical sensitivity of the NM-embedded films, in terms of absorbance, surface plasmon band shifts, and the dependence of these optical responses on film thickness, varied depending on the type of NM within the film (e.g., TAS-NPs versus Au-NSs) but exhibited no corresponding electrochemical effects in the diffusional voltammetry of a ferricyanide redox probe. While not correlated to optical responses, the increased Faradaic current achieved during voltammetry at NM-embedded PEM films suggested that electrochemical effects of NMs were less dependent on the type of NMs and were, instead, more related to their location within the film and the electrostatic interactions built into the interfacial chemistry of the films. These results should prove useful for developing strategies constructing thin films with NMs that are specifically designed for optical or electrochemical sensing, taking full advantage of the signal enhancements provided by individual types of NMs

Discovery of Northern Fur Seals (Callorhinus ursinus) Breeding on Bogoslof Island Southeastern Bering Sea

A small group of northern fur seals (Callorhinus ursinus) including one male with two females, each with a small pup, and two lone males were discovered on Bogoslof Island, Alaska in the Bering Sea on 20 July 1980. This is the first evidence of breeding on Bogoslof, or on any island in the eastern Bering Sea other than the Pribilof Islands. We suggest that these fur seals require breeding islands adjacent to the continental shelf break where they are supported by the pelagic food web characteristic of the oceanic and outer shelf domains.Key words: fur seal, Callorhinus ursinus, Steller sea lion, Eumetopias jubatus, Aleutian Islands, Bering SeaMots cl&eacute;s: otarie &agrave; fourrure, Callorhinus ursinus, otarie, Eumetopias jubatus, &icirc;les Al&eacute;outiennes, mer de B&eacute;rin

Conformations of N-Heterocyclic Carbene Ligands in Ruthenium Complexes Relevant to Olefin Metathesis

The structure of ruthenium-based olefin metathesis catalyst 3 and model π-complex 5 in solution and in the solid state are reported. The N-tolyl ligands, due to their lower symmetry than the traditional N-mesityl substituents, complicate this analysis, but ultimately provide explanation for the enhanced reactivity of 3 relative to standard catalyst 2. The tilt of the N-tolyl ring provides additional space near the ruthenium center, which is consistent with the enhanced reactivity of 3 toward sterically demanding substrates. Due to this tilt, the more sterically accessible face bears the two methyl substituents of the N-aryl rings. These experimental studies are supported by computational studies of these complexes by DFT. The experimental data provides a means to validate the accuracy of the B3LYP and M06 functionals. B3LYP provides geometries that match X-ray crystal structural data more closely, though it leads to slightly less (0.5 kcal mol^(−1)) accuracy than M06 most likely because it underestimates attractive noncovalent interactions

Polyelectrolyte-Linked Film Assemblies of Nanoparticles and Nanoshells: Growth, Stability, and Optical Properties

Multi-layer films of nanoparticles and nanoshells featuring various polymeric linkage molecules have been assembled and their optical properties characterized. The growth dynamics, including molecular weight effects, and stability of the various nanoparticle film constructions, using both single polymer as well as combinations of alternating charge polyelectrolytes as linking mechanisms, are presented. The polymeric linkers studied include poly-L-lysine, poly-L-arginine, poly(allylamine hydrochloride), and polyamidoamine dendrimers. Significantly air stable films were achieved with the use of multi-layered polymeric bridges between the nanoparticles and nanoshells. Optical sensitivity normally observed with these nanomaterials in solution was observed for their corresponding film geometries, with the nanoshell films exhibiting a markedly higher ability to report their local dielectric environment

Note and Comment

Epithetical Jurisprudence and the Annexation of Fixtures - If we begin with all the facts of a controversy and proceed inductively to determine the rights of the parties litigant, we thus arrive at a jurisprudence of rights, whereas, if we reason deductively from a rule, a definition, or a maxim of law to its application in the facts of our case, we can at best attain only a jurisprudence of rules, which has been so aptly characterized as an epithetical jurisprudence. The subject of fixtures is one in which we have great difficulty in applying the inductive method because the courts have been slower in approaching the subject scientifically in this field of the law than in others