Riccati-parameter solutions of nonlinear second-order ODEs

It has been proven by Rosu and Cornejo-Perez in 2005 that for some nonlinear second-order ODEs it is a very simple task to find one particular solution once the nonlinear equation is factorized with the use of two first-order differential operators. Here, it is shown that an interesting class of parametric solutions is easy to obtain if the proposed factorization has a particular form, which happily turns out to be the case in many problems of physical interest. The method that we exemplify with a few explicitly solved cases consists in using the general solution of the Riccati equation, which contributes with one parameter to this class of parametric solutions. For these nonlinear cases, the Riccati parameter serves as a `growth' parameter from the trivial null solution up to the particular solution found through the factorization procedureComment: 5 pages, 3 figures, change of title and more tex

Nonlinear Bias and the Convective Fisher Equation

We combine random walks, growth and decay, and convection, in a Monte Carlo simulation to model 1D interface dynamics with fluctuations. The continuum limit corresponds to the deterministic Fisher equation with convection. We find qualitatively the same type of asymmetry, as well as velocity difference, for interface profiles moving in opposite directions. However a transition apparent in the mean-field (continuum) limit is not found in the Monte Carlo simulation.Comment: 2.5 pages (texed) with 4 postscript figures, TeX 3.14t

Noninvasive Determination of Epidermal and Stratum Corneum Thickness in vivo Using Two-Photon Microscopy and Optical Coherence Tomography: Impact of Body Area, Age, and Gender

Background: High-resolution images of the epidermis are important to understand the transdermal penetration and changes in epidermal components. Both ex vivo and in vivo technologies are available to picture the epidermal thickness (ET). So far, the illustration of the stratum corneum (SC) has not been possible without artifacts. Objective: Precision in vivo measurement of the ET and SC, duly considering the impact of location on the body, age, and gender. Methods: In this pilot study on 20 skin-healthy subjects aged 18-66 years, the ET was imaged by two-photon microscopy (2PM) and optical coherence tomography (OCT), and the SC by using 2PM at five different body sites. Results: On solar-exposed body areas, both the epidermis and SC are thicker compared to solar-protected areas (p < 0.05), the epidermis at the gluteal region being the thickest (p < 0.05). The ET decreases with age (p < 0.05). Males show a thicker epidermis than females (p < 0.05). Conclusion: 2PM provides a noninvasive method for imaging the epidermis and especially the SC in vivo and is optimally suited for the application of histological criteria

Near streambed flow shapes microbial guilds within and across trophic levels in fluvial biofilms

Flow is an important physical driver of biofilm communities. Here, we tested the effects of the near bed flows in two mountainous stream reaches on the structure of biofilm microbial guilds (autotrophs, heterotrophic bacteria, and heterotrophic protists) within and across trophic levels. Near bed flow velocity and turbulent kinetic energy were important physical drivers for structuring the communities within and across guilds of the multitrophic fluvial biofilms. The effects of flow were nested in a seasonal and spatial (across-streams) context. Changes in physicochemical factors (temperature, light, dissolved carbon, and nutrients) along the reaches were alike in both streams suggesting that environmental boundary conditions at larger temporal scales were responsible for the seasonal differences of biofilm communities, whereas locally microbial diversity was shaped by near bed flow. Typically, the abundance of autotrophs increased with flow, indicating that biofilms shifted toward increasing autotrophy with increasing shear forces. Filamentous autotrophs seemed to provide protected habitats from the shear forces for smaller sized bacteria. Heterotrophic protist abundance decreased with flow leading to decreasing grazer to prey ratio. Bacteria thus benefitted from a reduction in grazing pressure at faster flowing, more turbulent sites. Our results suggest that near bed flow can impact the magnitude and direction of matter fluxes through the microbial food web and possibly affect ecosystem functioning of fluvial biofilms

A Singular Perturbation Analysis for \\Unstable Systems with Convective Nonlinearity

We use a singular perturbation method to study the interface dynamics of a non-conserved order parameter (NCOP) system, of the reaction-diffusion type, for the case where an external bias field or convection is present. We find that this method, developed by Kawasaki, Yalabik and Gunton for the time-dependant Ginzburg-Landau equation and used successfully on other NCOP systems, breaks down for our system when the strength of bias/convection gets large enough.Comment: 5 pages, PostScript forma

Wind farm facilities in Germany kill noctule bats from near and far

Over recent years, it became widely accepted that alternative, renewable energy may come at some risk for wildlife, for example, when wind turbines cause large numbers of bat fatalities. To better assess likely populations effects of wind turbine related wildlife fatalities, we studied the geographical origin of the most common bat species found dead below German wind turbines, the noctule bat (Nyctalus noctula). We measured stable isotope ratios of non-exchangeable hydrogen in fur keratin to separate migrants from local individuals, used a linear mixed-effects model to identify temporal, spatial and biological factors explaining the variance in measured stable isotope ratios and determined the geographical breeding provenance of killed migrants using isoscape origin models. We found that 72% of noctule bat casualties (n = 136) were of local origin, while 28% were long-distance migrants. These findings highlight that bat fatalities at German wind turbines may affect both local and distant populations. Our results indicated a sex and age-specific vulnerability of bats towards lethal accidents at turbines, i.e. a relatively high proportion of killed females were recorded among migratory individuals, whereas more juveniles than adults were recorded among killed bats of local origin. Migratory noctule bats were found to originate from distant populations in the Northeastern parts of Europe. The large catchment areas of German wind turbines and high vulnerability of female and juvenile noctule bats call for immediate action to reduce the negative cross-boundary effects of bat fatalities at wind turbines on local and distant populations. Further, our study highlights the importance of implementing effective mitigation measures and developing species and scale-specific conservation approaches on both national and international levels to protect source populations of bats. The efficacy of local compensatory measures appears doubtful, at least for migrant noctule bats, considering the large geographical catchment areas of German wind turbines for this species

Fitting a 3D Morphable Model to Edges: A Comparison Between Hard and Soft Correspondences

We propose a fully automatic method for fitting a 3D morphable model to single face images in arbitrary pose and lighting. Our approach relies on geometric features (edges and landmarks) and, inspired by the iterated closest point algorithm, is based on computing hard correspondences between model vertices and edge pixels. We demonstrate that this is superior to previous work that uses soft correspondences to form an edge-derived cost surface that is minimised by nonlinear optimisation.Comment: To appear in ACCV 2016 Workshop on Facial Informatic

Copula Eigenfaces with Attributes: Semiparametric Principal Component Analysis for a Combined Color, Shape and Attribute Model

Principal component analysis is a ubiquitous method in parametric appearance modeling for describing dependency and variance in datasets. The method requires the observed data to be Gaussian-distributed. We show that this requirement is not fulfilled in the context of analysis and synthesis of facial appearance. The model mismatch leads to unnatural artifacts which are severe to human perception. As a remedy, we use a semiparametric Gaussian copula model, where dependency and variance are modeled separately. This model enables us to use arbitrary Gaussian and non-Gaussian marginal distributions. Moreover, facial color, shape and continuous or categorical attributes can be analyzed in an unified way. Accounting for the joint dependency between all modalities leads to a more specific face model. In practice, the proposed model can enhance performance of principal component analysis in existing pipelines: The steps for analysis and synthesis can be implemented as convenient pre- and post-processing steps

A Closest Point Proposal for MCMC-based Probabilistic Surface Registration

We propose to view non-rigid surface registration as a probabilistic inference problem. Given a target surface, we estimate the posterior distribution of surface registrations. We demonstrate how the posterior distribution can be used to build shape models that generalize better and show how to visualize the uncertainty in the established correspondence. Furthermore, in a reconstruction task, we show how to estimate the posterior distribution of missing data without assuming a fixed point-to-point correspondence. We introduce the closest-point proposal for the Metropolis-Hastings algorithm. Our proposal overcomes the limitation of slow convergence compared to a random-walk strategy. As the algorithm decouples inference from modeling the posterior using a propose-and-verify scheme, we show how to choose different distance measures for the likelihood model. All presented results are fully reproducible using publicly available data and our open-source implementation of the registration framework