A fully adaptive numerical approximation for a two-dimensional epidemic model with nonlinear cross-diffusion

An epidemic model is formulated by a reactionâeuro"diffusion system where the spatial pattern formation is driven by cross-diffusion. The reaction terms describe the local dynamics of susceptible and infected species, whereas the diffusion terms account for the spatial distribution dynamics. For both self-diffusion and cross-diffusion, nonlinear constitutive assumptions are suggested. To simulate the pattern formation two finite volume formulations are proposed, which employ a conservative and a non-conservative discretization, respectively. An efficient simulation is obtained by a fully adaptive multiresolution strategy. Numerical examples illustrate the impact of the cross-diffusion on the pattern formation.

Simple-sugar meals target GLUT2 at enterocyte apical membranes to improve sugar absorption: a study in GLUT2-null mice.

The physiological significance of the presence of GLUT2 at the food-facing pole of intestinal cells is addressed by a study of fructose absorption in GLUT2-null and control mice submitted to different sugar diets. Confocal microscopy localization, protein and mRNA abundance, as well as tissue and membrane vesicle uptakes of fructose were assayed. GLUT2 was located in the basolateral membrane of mice fed a meal devoid of sugar or containing complex carbohydrates. In addition, the ingestion of a simple sugar meal promoted the massive recruitment of GLUT2 to the food-facing membrane. Fructose uptake in brush-border membrane vesicles from GLUT2-null mice was half that of wild-type mice and was similar to the cytochalasin B-insensitive component, i.e. GLUT5-mediated uptake. A 5 day consumption of sugar-rich diets increased fructose uptake fivefold in wild-type tissue rings when it only doubled in GLUT2-null tissue. GLUT5 was estimated to contribute to 100 % of total uptake in wild-type mice fed low-sugar diets, falling to 60 and 40 % with glucose and fructose diets respectively; the complement was ensured by GLUT2 activity. The results indicate that basal sugar uptake is mediated by the resident food-facing SGLT1 and GLUT5 transporters, whose mRNA abundances double in long-term dietary adaptation. We also observe that a large improvement of intestinal absorption is promoted by the transient recruitment of food-facing GLUT2, induced by the ingestion of a simple-sugar meal. Thus, GLUT2 and GLUT5 could exert complementary roles in adapting the absorption capacity of the intestine to occasional or repeated loads of dietary sugars.

Fast low-specific absorption rate B0 -mapping along projections at high field using two-dimensional radiofrequency pulses.

PURPOSE: At 7 Tesla (T), conventional static field (B0 ) projection mapping techniques, e.g., FASTMAP, FASTESTMAP, lead to elevated specific absorption rates (SAR), requiring longer total acquisition times (TA). In this work, the series of adiabatic pulses needed for slab selection in FASTMAP is replaced by a single two-dimensional radiofrequency (2D-RF) pulse to minimize TA while ensuring equal shimming performance. METHODS: Spiral gradients and 2D-RF pulses were designed to excite thin slabs in the small tip angle regime. The corresponding selection profile was characterized in phantoms and in vivo. After optimization of the shimming protocol, the spectral linewidths obtained after 2D localized shimming were compared with conventional techniques and published values from (Emir et al NMR Biomed 2012;25:152-160) in six different brain regions. RESULTS: Results on healthy volunteers show no significant difference (P > 0.5) between the spectroscopic linewidths obtained with the adiabatic (TA = 4 min) and the new low-SAR and time-efficient FASTMAP sequence (TA = 42 s). The SAR can be reduced by three orders of magnitude and TA accelerated six times without impact on the shimming performances or quality of the resulting spectra. CONCLUSION: Multidimensional pulses can be used to minimize the RF energy and time spent for automated shimming using projection mapping at high field. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc.

Integration of local-scale hydrological and regional-scale geophysical based on a nonlinear Bayesian sequential simulation approach

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending the corresponding approaches to the regional scale represents a major, and as-of-yet largely unresolved, challenge. To address this problem, we have developed a downscaling procedure based on a non-linear Bayesian sequential simulation approach. The basic objective of this algorithm is to estimate the value of the sparsely sampled hydraulic conductivity at non-sampled locations based on its relation to the electrical conductivity, which is available throughout the model space. The in situ relationship between the hydraulic and electrical conductivities is described through a non-parametric multivariate kernel density function. This method is then applied to the stochastic integration of low-resolution, re- gional-scale electrical resistivity tomography (ERT) data in combination with high-resolution, local-scale downhole measurements of the hydraulic and electrical conductivities. Finally, the overall viability of this downscaling approach is tested and verified by performing and comparing flow and transport simulation through the original and the downscaled hydraulic conductivity fields. Our results indicate that the proposed procedure does indeed allow for obtaining remarkably faithful estimates of the regional-scale hydraulic conductivity structure and correspondingly reliable predictions of the transport characteristics over relatively long distances.

Nonlinear analysis of human physical activity patterns in health and disease.

The reliable and objective assessment of chronic disease state has been and still is a very significant challenge in clinical medicine. An essential feature of human behavior related to the health status, the functional capacity, and the quality of life is the physical activity during daily life. A common way to assess physical activity is to measure the quantity of body movement. Since human activity is controlled by various factors both extrinsic and intrinsic to the body, quantitative parameters only provide a partial assessment and do not allow for a clear distinction between normal and abnormal activity. In this paper, we propose a methodology for the analysis of human activity pattern based on the definition of different physical activity time series with the appropriate analysis methods. The temporal pattern of postures, movements, and transitions between postures was quantified using fractal analysis and symbolic dynamics statistics. The derived nonlinear metrics were able to discriminate patterns of daily activity generated from healthy and chronic pain states.

Stimulus statistics shape oscillations in nonlinear recurrent neural networks.

Rhythmic activity plays a central role in neural computations and brain functions ranging from homeostasis to attention, as well as in neurological and neuropsychiatric disorders. Despite this pervasiveness, little is known about the mechanisms whereby the frequency and power of oscillatory activity are modulated, and how they reflect the inputs received by neurons. Numerous studies have reported input-dependent fluctuations in peak frequency and power (as well as couplings across these features). However, it remains unresolved what mediates these spectral shifts among neural populations. Extending previous findings regarding stochastic nonlinear systems and experimental observations, we provide analytical insights regarding oscillatory responses of neural populations to stimulation from either endogenous or exogenous origins. Using a deceptively simple yet sparse and randomly connected network of neurons, we show how spiking inputs can reliably modulate the peak frequency and power expressed by synchronous neural populations without any changes in circuitry. Our results reveal that a generic, non-nonlinear and input-induced mechanism can robustly mediate these spectral fluctuations, and thus provide a framework in which inputs to the neurons bidirectionally regulate both the frequency and power expressed by synchronous populations. Theoretical and computational analysis of the ensuing spectral fluctuations was found to reflect the underlying dynamics of the input stimuli driving the neurons. Our results provide insights regarding a generic mechanism supporting spectral transitions observed across cortical networks and spanning multiple frequency bands.

alphaENaC-mediated lithium absorption promotes nephrogenic diabetes insipidus.

Lithium-induced nephrogenic diabetes insipidus (NDI) is accompanied by polyuria, downregulation of aquaporin 2 (AQP2), and cellular remodeling of the collecting duct (CD). The amiloride-sensitive epithelial sodium channel (ENaC) is a likely candidate for lithium entry. Here, we subjected transgenic mice lacking αENaC specifically in the CD (knockout [KO] mice) and littermate controls to chronic lithium treatment. In contrast to control mice, KO mice did not markedly increase their water intake. Furthermore, KO mice did not demonstrate the polyuria and reduction in urine osmolality induced by lithium treatment in the control mice. Lithium treatment reduced AQP2 protein levels in the cortex/outer medulla and inner medulla (IM) of control mice but only partially reduced AQP2 levels in the IM of KO mice. Furthermore, lithium induced expression of H(+)-ATPase in the IM of control mice but not KO mice. In conclusion, the absence of functional ENaC in the CD protects mice from lithium-induced NDI. These data support the hypothesis that ENaC-mediated lithium entry into the CD principal cells contributes to the pathogenesis of lithium-induced NDI.

Alveolar epithelial CNGA1 channels mediate cGMP-stimulated, amiloride-insensitive, lung liquid absorption.

Impairment of lung liquid absorption can lead to severe respiratory symptoms, such as those observed in pulmonary oedema. In the adult lung, liquid absorption is driven by cation transport through two pathways: a well-established amiloride-sensitive Na(+) channel (ENaC) and, more controversially, an amiloride-insensitive channel that may belong to the cyclic nucleotide-gated (CNG) channel family. Here, we show robust CNGA1 (but not CNGA2 or CNGA3) channel expression principally in rat alveolar type I cells; CNGA3 was expressed in ciliated airway epithelial cells. Using a rat in situ lung liquid clearance assay, CNG channel activation with 1 mM 8Br-cGMP resulted in an approximate 1.8-fold stimulation of lung liquid absorption. There was no stimulation by 8Br-cGMP when applied in the presence of either 100 μM L: -cis-diltiazem or 100 nM pseudechetoxin (PsTx), a specific inhibitor of CNGA1 channels. Channel specificity of PsTx and amiloride was confirmed by patch clamp experiments showing that CNGA1 channels in HEK 293 cells were not inhibited by 100 μM amiloride and that recombinant αβγ-ENaC were not inhibited by 100 nM PsTx. Importantly, 8Br-cGMP stimulated lung liquid absorption in situ, even in the presence of 50 μM amiloride. Furthermore, neither L: -cis-diltiazem nor PsTx affected the β(2)-adrenoceptor agonist-stimulated lung liquid absorption, but, as expected, amiloride completely ablated it. Thus, transport through alveolar CNGA1 channels, located in type I cells, underlies the amiloride-insensitive component of lung liquid reabsorption. Furthermore, our in situ data highlight the potential of CNGA1 as a novel therapeutic target for the treatment of diseases characterised by lung liquid overload.

Robust Nonlinear Mapping of Soil Contamination Using Support Regression

Spatial data analysis mapping and visualization is of great importance in various fields: environment, pollution, natural hazards and risks, epidemiology, spatial econometrics, etc. A basic task of spatial mapping is to make predictions based on some empirical data (measurements). A number of state-of-the-art methods can be used for the task: deterministic interpolations, methods of geostatistics: the family of kriging estimators (Deutsch and Journel, 1997), machine learning algorithms such as artificial neural networks (ANN) of different architectures, hybrid ANN-geostatistics models (Kanevski and Maignan, 2004; Kanevski et al., 1996), etc. All the methods mentioned above can be used for solving the problem of spatial data mapping. Environmental empirical data are always contaminated/corrupted by noise, and often with noise of unknown nature. That's one of the reasons why deterministic models can be inconsistent, since they treat the measurements as values of some unknown function that should be interpolated. Kriging estimators treat the measurements as the realization of some spatial randomn process. To obtain the estimation with kriging one has to model the spatial structure of the data: spatial correlation function or (semi-)variogram. This task can be complicated if there is not sufficient number of measurements and variogram is sensitive to outliers and extremes. ANN is a powerful tool, but it also suffers from the number of reasons. of a special type ? multiplayer perceptrons ? are often used as a detrending tool in hybrid (ANN+geostatistics) models (Kanevski and Maignank, 2004). Therefore, development and adaptation of the method that would be nonlinear and robust to noise in measurements, would deal with the small empirical datasets and which has solid mathematical background is of great importance. The present paper deals with such model, based on Statistical Learning Theory (SLT) - Support Vector Regression. SLT is a general mathematical framework devoted to the problem of estimation of the dependencies from empirical data (Hastie et al, 2004; Vapnik, 1998). SLT models for classification - Support Vector Machines - have shown good results on different machine learning tasks. The results of SVM classification of spatial data are also promising (Kanevski et al, 2002). The properties of SVM for regression - Support Vector Regression (SVR) are less studied. First results of the application of SVR for spatial mapping of physical quantities were obtained by the authorsin for mapping of medium porosity (Kanevski et al, 1999), and for mapping of radioactively contaminated territories (Kanevski and Canu, 2000). The present paper is devoted to further understanding of the properties of SVR model for spatial data analysis and mapping. Detailed description of the SVR theory can be found in (Cristianini and Shawe-Taylor, 2000; Smola, 1996) and basic equations for the nonlinear modeling are given in section 2. Section 3 discusses the application of SVR for spatial data mapping on the real case study - soil pollution by Cs137 radionuclide. Section 4 discusses the properties of the modelapplied to noised data or data with outliers.