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

Scallop swimming kinematics and muscle performance: modelling the effects of "within-animal" variation in temperature sensitivity

Escape behaviour was investigated in Queen scallops (Aequipecten opercularis) acclimated to 5, 10 or 15 degrees C and tested at their acclimation temperature. Scallops are active molluscs, able to escape from predators by jet-propelled swimming using a striated muscle working in opposition to an elastic hinge ligament. The first cycle of the escape response was recorded using high-speed video ( 250 Hz) and whole-animal velocity and acceleration determined. Muscle shortening velocity, force and power output were calculated using measurements of valve movement and jet area, and a simple biomechanical model. The average shortening speed of the adductor muscle had a Q(10) of 2.04, significantly reducing the duration of the jetting phase of the cycle with increased temperature. Muscle lengthening velocity and the overall duration of the clap cycle were changed little over the range 5 - 15 degrees C, as these parameters were controlled by the relatively temperature-insensitive, hinge ligament. Improvements in the average power output of the adductor muscle over the first clap cycle ( 222 vs. 139 W kg(-1) wet mass at 15 and 5 degrees C respectively) were not translated into proportional increases in overall swimming velocity, which was only 32% higher at 15 degrees C ( 0.37m s(-1)) than 5 degrees C (0.28 m s(-1))

Measuring measurement

Measurement connects the world of quantum phenomena to the world of classical events. It plays both a passive role, observing quantum systems, and an active one, preparing quantum states and controlling them. Surprisingly - in the light of the central status of measurement in quantum mechanics - there is no general recipe for designing a detector that measures a given observable. Compounding this, the characterization of existing detectors is typically based on partial calibrations or elaborate models. Thus, experimental specification (i.e. tomography) of a detector is of fundamental and practical importance. Here, we present the realization of quantum detector tomography: we identify the optimal positive-operator-valued measure describing the detector, with no ancillary assumptions. This result completes the triad, state, process, and detector tomography, required to fully specify an experiment. We characterize an avalanche photodiode and a photon number resolving detector capable of detecting up to eight photons. This creates a new set of tools for accurately detecting and preparing non-classical light.Comment: 6 pages, 4 figures,see video abstract at http://www.quantiki.org/video_abstracts/0807244

Individual rules for trail pattern formation in Argentine ants (Linepithema humile)

We studied the formation of trail patterns by Argentine ants exploring an empty arena. Using a novel imaging and analysis technique we estimated pheromone concentrations at all spatial positions in the experimental arena and at different times. Then we derived the response function of individual ants to pheromone concentrations by looking at correlations between concentrations and changes in speed or direction of the ants. Ants were found to turn in response to local pheromone concentrations, while their speed was largely unaffected by these concentrations. Ants did not integrate pheromone concentrations over time, with the concentration of pheromone in a 1 cm radius in front of the ant determining the turning angle. The response to pheromone was found to follow a Weber's Law, such that the difference between quantities of pheromone on the two sides of the ant divided by their sum determines the magnitude of the turning angle. This proportional response is in apparent contradiction with the well-established non-linear choice function used in the literature to model the results of binary bridge experiments in ant colonies (Deneubourg et al. 1990). However, agent based simulations implementing the Weber's Law response function led to the formation of trails and reproduced results reported in the literature. We show analytically that a sigmoidal response, analogous to that in the classical Deneubourg model for collective decision making, can be derived from the individual Weber-type response to pheromone concentrations that we have established in our experiments when directional noise around the preferred direction of movement of the ants is assumed.Comment: final version, 9 figures, submitted to Plos Computational Biology (accepted

Vaccines against toxoplasma gondii : challenges and opportunities

Development of vaccines against Toxoplasma gondii infection in humans is of high priority, given the high burden of disease in some areas of the world like South America, and the lack of effective drugs with few adverse effects. Rodent models have been used in research on vaccines against T. gondii over the past decades. However, regardless of the vaccine construct, the vaccines have not been able to induce protective immunity when the organism is challenged with T. gondii, either directly or via a vector. Only a few live, attenuated T. gondii strains used for immunization have been able to confer protective immunity, which is measured by a lack of tissue cysts after challenge. Furthermore, challenge with low virulence strains, especially strains with genotype II, will probably be insufficient to provide protection against the more virulent T. gondii strains, such as those with genotypes I or II, or those genotypes from South America not belonging to genotype I, II or III. Future studies should use animal models besides rodents, and challenges should be performed with at least one genotype II T. gondii and one of the more virulent genotypes. Endpoints like maternal-foetal transmission and prevention of eye disease are important in addition to the traditional endpoint of survival or reduction in numbers of brain cysts after challenge

A haplotype of polymorphisms in ASE-1, RAI and ERCC1 and the effects of tobacco smoking and alcohol consumption on risk of colorectal cancer: a danish prospective case-cohort study

<p>Abstract</p> <p>Background</p> <p>Single nucleotide polymorphisms (SNPs) are the most frequent type of genetic variation in the human genome, and are of interest for the study of susceptibility to and protection from diseases. The haplotype at chromosome 19q13.2-3 encompassing the three SNPs <it>ASE-1 </it>G-21A, <it>RAI </it>IVS1 A4364G and <it>ERCC1 </it>Asn118Asn have been associated with risk of breast cancer and lung cancer. Haplotype carriers are defined as the homozygous carriers of <it>RAI </it>IVS1 A4364G^A, <it>ERCC1 </it>Asn118Asn^Tand <it>ASE-1 </it>G-21A^G. We aimed to evaluate whether the three polymorphisms and the haplotype are associated to risk of colorectal cancer, and investigated gene-environment associations between the polymorphisms and the haplotype and smoking status at enrolment, smoking duration, average smoking intensity and alcohol consumption, respectively, in relation to risk of colorectal cancer.</p> <p>Methods</p> <p>Associations between the three individual polymorphisms, the haplotype and risk of colorectal cancer were examined, as well as gene-environment interaction, in a Danish case-cohort study including 405 cases and a comparison group of 810 persons. Incidence rate ratio (IRR) were estimated by the Cox proportional hazards model stratified according to gender, and two-sided 95% confidence intervals (CI) and p-values were calculated based on robust estimates of the variance-covariance matrix and Wald's test of the Cox regression parameter.</p> <p>Results</p> <p>No consistent associations between the three individual polymorphisms, the haplotype and risk of colorectal cancer were found. No statistically significant interactions between the genotypes and the lifestyle exposures smoking or alcohol consumption were observed.</p> <p>Conclusion</p> <p>Our results suggest that the <it>ASE-1 </it>G-21A, <it>RAI </it>IVS1 A4364G and <it>ERCC1 </it>Asn118Asn polymorphisms and the previously identified haplotype are not associated with risk of colorectal cancer. We found no evidence of gene-environment interaction between the three polymorphisms and the haplotype and smoking intensity and alcohol consumption, respectively, in relation to the risk of colorectal cancer.</p

Neutrino-electron scattering in noncommutative space

Neutral particles can couple with the $U(1)$ gauge field in the adjoint representation at the tree level if the space-time coordinates are noncommutative (NC). Considering neutrino-photon coupling in the NC QED framework, we obtain the differential cross section of neutrino-electron scattering. Similar to the magnetic moment effect, one of the NC terms is proportional to $\frac 1 T$, where $T$ is the electron recoil energy. Therefore, this scattering provides a chance to achieve a stringent bound on the NC scale in low energy by improving the sensitivity to the smaller electron recoil energy.Comment: 12 pages, 2 figure

Esophageal perforation in South of Sweden: Results of surgical treatment in 125 consecutive patients

<p>Abstract</p> <p>Background</p> <p>For many years there has been a debate as to which is the method of choice in treating patients with esophageal perforation. The literature consists mainly of small case series. Strategies for aiding patients struck with this disease is changing as new and less traumatic treatment options are developing. We studied a relatively large consecutive material of esophageal perforations in an effort to evaluate prognostic factors, diagnostic efforts and treatment strategy in these patients.</p> <p>Methods</p> <p>125 consecutive patients treated at the University Hospital of Lund from 1970 to 2006 were studied retrospectively. Prognostic factors were evaluated using the Cox proportional hazards model.</p> <p>Results</p> <p>Pre-operative ASA score was the only factor that significantly influenced outcome. Neck incision for cervical perforation (n = 8) and treatment with a covered stent with or without open drainage for a thoracic perforation (n = 6) had the lowest mortality. Esophageal resection (n = 8) had the highest mortality. A CAT scan or an oesophageal X-ray with oral contrast were the most efficient diagnostic tools. The preferred treatment strategy changed over the course of the study period, from a more aggressive surgical approach towards using covered stents to seal the perforation.</p> <p>Conclusion</p> <p>Pre-operative ASA score was the only factor that significantly influenced outcome in this study. Treatment strategies are changing as less traumatic options have become available. Sealing an esophageal perforation with a covered stent, in combination with open or closed drainage when necessary, is a promising treatment strategy.</p