Vibrational modes of circular free plates under tension

The vibrational frequencies of a plate under tension are given by the eigenvalues $\omega$ of the equation $\Delta^2u-\tau\Delta u=\omega u$. This paper determines the eigenfunctions and eigenvalues of this bi-Laplace problem on the ball under natural (free) boundary conditions. In particular, the fundamental modes --- the eigenfunctions of the lowest nonzero eigenvalue --- are identified and found to have simple angular dependence.Comment: 17 pages. To be submitted for publication shortly

Invasion speeds for structured populations in fluctuating environments

We live in a time where climate models predict future increases in environmental variability and biological invasions are becoming increasingly frequent. A key to developing effective responses to biological invasions in increasingly variable environments will be estimates of their rates of spatial spread and the associated uncertainty of these estimates. Using stochastic, stage-structured, integro-difference equation models, we show analytically that invasion speeds are asymptotically normally distributed with a variance that decreases in time. We apply our methods to a simple juvenile-adult model with stochastic variation in reproduction and an illustrative example with published data for the perennial herb, \emph{Calathea ovandensis}. These examples buttressed by additional analysis reveal that increased variability in vital rates simultaneously slow down invasions yet generate greater uncertainty about rates of spatial spread. Moreover, while temporal autocorrelations in vital rates inflate variability in invasion speeds, the effect of these autocorrelations on the average invasion speed can be positive or negative depending on life history traits and how well vital rates ``remember'' the past

A remark on an overdetermined problem in Riemannian Geometry

Let $(M,g)$ be a Riemannian manifold with a distinguished point $O$ and assume that the geodesic distance $d$ from $O$ is an isoparametric function. Let $\Omega\subset M$ be a bounded domain, with $O \in \Omega$, and consider the problem $\Delta_p u = -1$ in $\Omega$ with $u=0$ on $\partial \Omega$, where $\Delta_p$ is the $p$-Laplacian of $g$. We prove that if the normal derivative $\partial_{\nu}u$ of $u$ along the boundary of $\Omega$ is a function of $d$ satisfying suitable conditions, then $\Omega$ must be a geodesic ball. In particular, our result applies to open balls of $\mathbb{R}^n$ equipped with a rotationally symmetric metric of the form $g=dt^2+\rho^2(t)\,g_S$, where $g_S$ is the standard metric of the sphere.Comment: 8 pages. This paper has been written for possible publication in a special volume dedicated to the conference "Geometric Properties for Parabolic and Elliptic PDE's. 4th Italian-Japanese Workshop", organized in Palinuro in May 201

Visualizing dimensionality reduction of systems biology data

One of the challenges in analyzing high-dimensional expression data is the detection of important biological signals. A common approach is to apply a dimension reduction method, such as principal component analysis. Typically, after application of such a method the data is projected and visualized in the new coordinate system, using scatter plots or profile plots. These methods provide good results if the data have certain properties which become visible in the new coordinate system and which were hard to detect in the original coordinate system. Often however, the application of only one method does not suffice to capture all important signals. Therefore several methods addressing different aspects of the data need to be applied. We have developed a framework for linear and non-linear dimension reduction methods within our visual analytics pipeline SpRay. This includes measures that assist the interpretation of the factorization result. Different visualizations of these measures can be combined with functional annotations that support the interpretation of the results. We show an application to high-resolution time series microarray data in the antibiotic-producing organism Streptomyces coelicolor as well as to microarray data measuring expression of cells with normal karyotype and cells with trisomies of human chromosomes 13 and 21

Front-like entire solutions for monostable reaction-diffusion systems

This paper is concerned with front-like entire solutions for monostable reactiondiffusion systems with cooperative and non-cooperative nonlinearities. In the cooperative case, the existence and asymptotic behavior of spatially independent solutions (SIS) are first proved. Combining a SIS and traveling fronts with different wave speeds and directions, the existence and various qualitative properties of entire solutions are then established using comparison principle. In the non-cooperative case, we introduce two auxiliary cooperative systems and establish some comparison arguments for the three systems. The existence of entire solutions is then proved via the traveling fronts and SIS of the auxiliary systems. Our results are applied to some biological and epidemiological models. To the best of our knowledge, it is the first work to study the entire solutions of non-cooperative reaction-diffusion systems

Dissociable effects of 5-HT2C receptor antagonism and genetic inactivation on perseverance and learned non-reward in an egocentric spatial reversal task

Cognitive flexibility can be assessed in reversal learning tests, which are sensitive to modulation of 5-HT2C receptor (5-HT2CR) function. Successful performance in these tests depends on at least two dissociable cognitive mechanisms which may separately dissipate associations of previous positive and negative valence. The first is opposed by perseverance and the second by learned non-reward. The current experiments explored the effect of reducing function of the 5-HT2CR on the cognitive mechanisms underlying egocentric reversal learning in the mouse. Experiment 1 used the 5-HT2CR antagonist SB242084 (0.5 mg/kg) in a between-groups serial design and Experiment 2 used 5-HT2CR KO mice in a repeated measures design. Animals initially learned to discriminate between two egocentric turning directions, only one of which was food rewarded (denoted CS+, CS−), in a T- or Y-maze configuration. This was followed by three conditions; (1) Full reversal, where contingencies reversed; (2) Perseverance, where the previous CS+ became CS− and the previous CS− was replaced by a novel CS+; (3) Learned non-reward, where the previous CS− became CS+ and the previous CS+ was replaced by a novel CS-. SB242084 reduced perseverance, observed as a decrease in trials and incorrect responses to criterion, but increased learned non-reward, observed as an increase in trials to criterion. In contrast, 5-HT2CR KO mice showed increased perseverance. 5-HT2CR KO mice also showed retarded egocentric discrimination learning. Neither manipulation of 5-HT2CR function affected performance in the full reversal test. These results are unlikely to be accounted for by increased novelty attraction, as SB242084 failed to affect performance in an unrewarded novelty task. In conclusion, acute 5-HT2CR antagonism and constitutive loss of the 5-HT2CR have opposing effects on perseverance in egocentric reversal learning in mice. It is likely that this difference reflects the broader impact of 5HT2CR loss on the development and maintenance of cognitive function

Should Research Ethics Encourage the Production of Cost-Effective Interventions?

This project considers whether and how research ethics can contribute to the provision of cost-effective medical interventions. Clinical research ethics represents an underexplored context for the promotion of cost-effectiveness. In particular, although scholars have recently argued that research on less-expensive, less-effective interventions can be ethical, there has been little or no discussion of whether ethical considerations justify curtailing research on more expensive, more effective interventions. Yet considering cost-effectiveness at the research stage can help ensure that scarce resources such as tissue samples or limited subject popula- tions are employed where they do the most good; can support parallel efforts by providers and insurers to promote cost-effectiveness; and can ensure that research has social value and benefits subjects. I discuss and rebut potential objections to the consideration of cost-effectiveness in research, including the difficulty of predicting effectiveness and cost at the research stage, concerns about limitations in cost-effectiveness analysis, and worries about overly limiting researchers’ freedom. I then consider the advantages and disadvantages of having certain participants in the research enterprise, including IRBs, advisory committees, sponsors, investigators, and subjects, consider cost-effectiveness. The project concludes by qualifiedly endorsing the consideration of cost-effectiveness at the research stage. While incorporating cost-effectiveness considerations into the ethical evaluation of human subjects research will not on its own ensure that the health care system realizes cost-effectiveness goals, doing so nonetheless represents an important part of a broader effort to control rising medical costs

Contribution of Cystine-Glutamate Antiporters to the Psychotomimetic Effects of Phencyclidine

Altered glutamate signaling contributes to a myriad of neural disorders, including schizophrenia. While synaptic levels are intensely studied, nonvesicular release mechanisms, including cystine–glutamate exchange, maintain high steady-state glutamate levels in the extrasynaptic space. The existence of extrasynaptic receptors, including metabotropic group II glutamate receptors (mGluR), pose nonvesicular release mechanisms as unrecognized targets capable of contributing to pathological glutamate signaling. We tested the hypothesis that activation of cystine–glutamate antiporters using the cysteine prodrug N-acetylcysteine would blunt psychotomimetic effects in the rodent phencyclidine (PCP) model of schizophrenia. First, we demonstrate that PCP elevates extracellular glutamate in the prefrontal cortex, an effect that is blocked by N-acetylcysteine pretreatment. To determine the relevance of the above finding, we assessed social interaction and found that N-acetylcysteine reverses social withdrawal produced by repeated PCP. In a separate paradigm, acute PCP resulted in working memory deficits assessed using a discrete trial t-maze task, and this effect was also reversed by N-acetylcysteine pretreatment. The capacity of N-acetylcysteine to restore working memory was blocked by infusion of the cystine–glutamate antiporter inhibitor (S)-4-carboxyphenylglycine into the prefrontal cortex or systemic administration of the group II mGluR antagonist LY341495 indicating that the effects of N-acetylcysteine requires cystine–glutamate exchange and group II mGluR activation. Finally, protein levels from postmortem tissue obtained from schizophrenic patients revealed significant changes in the level of xCT, the active subunit for cystine–glutamate exchange, in the dorsolateral prefrontal cortex. These data advance cystine–glutamate antiporters as novel targets capable of reversing the psychotomimetic effects of PCP

Precise measurement of the W-boson mass with the CDF II detector

We have measured the W-boson mass MW using data corresponding to 2.2/fb of integrated luminosity collected in proton-antiproton collisions at 1.96 TeV with the CDF II detector at the Fermilab Tevatron collider. Samples consisting of 470126 W->enu candidates and 624708 W->munu candidates yield the measurement MW = 80387 +- 12 (stat) +- 15 (syst) = 80387 +- 19 MeV. This is the most precise measurement of the W-boson mass to date and significantly exceeds the precision of all previous measurements combined

X-ray emission from the Sombrero galaxy: discrete sources

We present a study of discrete X-ray sources in and around the bulge-dominated, massive Sa galaxy, Sombrero (M104), based on new and archival Chandra observations with a total exposure of ~200 ks. With a detection limit of L_X = 1E37 erg/s and a field of view covering a galactocentric radius of ~30 kpc (11.5 arcminute), 383 sources are detected. Cross-correlation with Spitler et al.'s catalogue of Sombrero globular clusters (GCs) identified from HST/ACS observations reveals 41 X-rays sources in GCs, presumably low-mass X-ray binaries (LMXBs). We quantify the differential luminosity functions (LFs) for both the detected GC and field LMXBs, whose power-low indices (~1.1 for the GC-LF and ~1.6 for field-LF) are consistent with previous studies for elliptical galaxies. With precise sky positions of the GCs without a detected X-ray source, we further quantify, through a fluctuation analysis, the GC LF at fainter luminosities down to 1E35 erg/s. The derived index rules out a faint-end slope flatter than 1.1 at a 2 sigma significance, contrary to recent findings in several elliptical galaxies and the bulge of M31. On the other hand, the 2-6 keV unresolved emission places a tight constraint on the field LF, implying a flattened index of ~1.0 below 1E37 erg/s. We also detect 101 sources in the halo of Sombrero. The presence of these sources cannot be interpreted as galactic LMXBs whose spatial distribution empirically follows the starlight. Their number is also higher than the expected number of cosmic AGNs (52+/-11 [1 sigma]) whose surface density is constrained by deep X-ray surveys. We suggest that either the cosmic X-ray background is unusually high in the direction of Sombrero, or a distinct population of X-ray sources is present in the halo of Sombrero.Comment: 11 figures, 5 tables, ApJ in pres