Steady states in a structured epidemic model with Wentzell boundary condition

We introduce a nonlinear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen load. The class of uninfected individuals constitutes a special compartment that carries mass, hence the model is equipped with generalized Wentzell (or dynamic) boundary conditions. Our model is intended to describe the spread of infection of a vertically transmitted disease, for example Wolbachia in a mosquito population. Therefore the (infinite dimensional) nonlinearity arises in the recruitment term. First we establish global existence of solutions and the Principle of Linearised Stability for our model. Then, in our main result, we formulate simple conditions, which guarantee the existence of non-trivial steady states of the model. Our method utilizes an operator theoretic framework combined with a fixed point approach. Finally, in the last section we establish a sufficient condition for the local asymptotic stability of the positive steady state

Systematic Improvement of Classical Nucleation Theory

We reconsider the applicability of classical nucleation theory (CNT) to the calculation of the free energy of solid cluster formation in a liquid and its use to the evaluation of interface free energies from nucleation barriers. Using two different freezing transitions (hard spheres and NaCl) as test cases, we first observe that the interface-free-energy estimates based on CNT are generally in error. As successive refinements of nucleation-barrier theory, we consider corrections due to a non-sharp solid-liquid interface and to a non-spherical cluster shape. Extensive calculations for the Ising model show that corrections due to a non-sharp and thermally fluctuating interface account for the barrier shape with excellent accuracy. The experimental solid nucleation rates that are measured in colloids are better accounted for by these non-CNT terms, whose effect appears to be crucial in the interpretation of data and in the extraction of the interface tension from them.Comment: 20 pages (text + supplementary material

Investigating photoexcitation-induced mitochondrial damage by chemotherapeutic corroles using multimode optical imaging

We recently reported that a targeted, brightly fluorescent gallium corrole (HerGa) is highly effective for breast tumor detection and treatment. Unlike structurally similar porphryins, HerGa exhibits tumor-targeted toxicity without the need for photoexcitation. We have now examined whether photoexcitation further modulates HerGa toxicity, using multimode optical imaging of live cells, including two-photon excited fluorescence, differential interference contrast (DIC), spectral, and lifetime imaging. Using two-photon excited fluorescence imaging, we observed that light at specific wavelengths augments the HerGa-mediated mitochondrial membrane potential disruption of breast cancer cells in situ. In addition, DIC, spectral, and fluorescence lifetime imaging enabled us to both validate cell damage by HerGa photoexcitation and investigate HerGa internalization, thus allowing optimization of light dose and timing. Our demonstration of HerGa phototoxicity opens the way for development of new methods of cancer intervention using tumor-targeted corroles

Optimal distribution of phosphorus compounds in multi-layered natural fabric reinforced biocomposites

Flame retardancy and mechanical performance of multi-layered biocomposites, consisting of polylactic acid (PLA) matrix films and plain-woven flax fabrics as reinforcement, were investigated. Full factorial design (32) was applied to evaluate the effects of the distribution of P and N containing compounds between the matrix and the fibrous carrier. Composition property correlations of the composite constituents (i.e. flax fabrics treated in aqueous solutions of diammonium phosphate and urea with differing ratio and concentrations and matrix films with 0 to 20 wt% ammonium polyphosphate based intumescent flame retardant content) were determined by thermogravimetric analyses and open flame tests. Positive interaction between the composite constituents was revealed for green composites consisting of various combinations of treated fabrics and intumescent PLA systems. The biocomposites flame retarded with a combined approach, i.e. with a balanced distribution of P containing additives between the phases, were found to gain improved mechanical performance and fire retardancy. It was confirmed by tensile testing and electron microscopy as well as by UL-94, limiting oxygen index and cone calorimeter tests. As a conclusion, interpretation is given for the optimum found

Cosmetics Alter Biologically-Based Factors of Beauty: Evidence from Facial Contrast

The use of cosmetics by women seems to consistently increase their attractiveness. What factors of attractiveness do cosmetics alter to achieve this? Facial contrast is a known cue to sexual dimorphism and youth, and cosmetics exaggerate sexual dimorphisms in facial contrast. Here, we demonstrate that the luminance contrast pattern of the eyes and eyebrows is consistently sexually dimorphic across a large sample of faces, with females possessing lower brow contrasts than males, and greater eye contrast than males. Red-green and yellow-blue color contrasts were not found to differ consistently between the sexes. We also show that women use cosmetics not only to exaggerate sexual dimorphisms of brow and eye contrasts, but also to increase contrasts that decline with age. These findings refine the notion of facial contrast, and demonstrate how cosmetics can increase attractiveness by manipulating factors of beauty associated with facial contrast

DNA uptake into nuclei: Numerical and analytical results

The dynamics of polymer translocation through a pore has been the subject of recent theoretical and experimental works. We have considered theoretical estimates and performed computer simulations to understand the mechanism of DNA uptake into the cell nucleus, a phenomenon experimentally investigated by attaching a small bead to the free end of the double helix and pulling this bead with the help of an optical trap. The experiments show that the uptake is monotonous and slows down when the remaining DNA segment becomes very short. Numerical and analytical studies of the entropic repulsion between the DNA filament and the membrane wall suggest a new interpretation of the experimental observations. Our results indicate that the repulsion monotonically decreases as the uptake progresses. Thus, the DNA is pulled in (i) either by a small force of unknown origin, and then the slowing down can be interpreted only statistically; (ii) or by a strong but slow ratchet mechanism, which would naturally explain the observed monotonicity, but then the slowing down requires additional explanations. Only further experiments can unambiguously distinguish between these two mechanisms.Comment: 12 pages, 6 figures, submitted to J. Phys. Cond. Ma

Escape rate from a metastable state weakly interacting with a heat bath driven by an external noise

Based on a system-reservoir model, where the reservoir is driven by an external stationary, Gaussian noise with arbitrary decaying correlation function, we study the escape rate from a metastable state in the energy diffusion regime. For the open system we derive the Fokker-Planck equation in the energy space and subsequently calculate the generalized non-Markovian escape rate from a metastable well in the energy diffusion domain. By considering the dynamics in a model cubic potential we show that the results obtained from numerical simulation are in good agreement with the theoretical prediction. It has been also shown numerically that the well known turnover feature can be restored from our model.Comment: 11 pages, 2 figure

Weighted network modules

The inclusion of link weights into the analysis of network properties allows a deeper insight into the (often overlapping) modular structure of real-world webs. We introduce a clustering algorithm (CPMw, Clique Percolation Method with weights) for weighted networks based on the concept of percolating k-cliques with high enough intensity. The algorithm allows overlaps between the modules. First, we give detailed analytical and numerical results about the critical point of weighted k-clique percolation on (weighted) Erdos-Renyi graphs. Then, for a scientist collaboration web and a stock correlation graph we compute three-link weight correlations and with the CPMw the weighted modules. After reshuffling link weights in both networks and computing the same quantities for the randomised control graphs as well, we show that groups of 3 or more strong links prefer to cluster together in both original graphs.Comment: 19 pages, 7 figure

Interpersonal distance theory of autism and its implication for cognitive assessment, therapy, and daily life

The interpersonal distance (IPD) theory provides a novel approach to studying autism spectrum disorder (ASD). In this article, we present recent findings on the neurobiological underpinnings of IPD regulation that are distinct in individuals with ASD. We also discuss the potential influence of environmental factors on IPD. We suggest that different IPD regulation may have implications for cognitive performance in experimental and diagnostic settings, may influence the effectiveness of training and therapy, and may play a role in the typical forms of social communication and leisure activities chosen by autistic individuals. We argue that reconsidering the results of ASD research through the lens of IPD would lead to a different interpretation of previous findings. Finally, we propose a methodological approach to study this phenomenon systematically