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.

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.

Scan statistics analysis of forest fire clusters

Spatio-temporal clusters in 1997?2003 fire sequences of Tuscany region (central Italy) have been identified and analysed by using the scan statistic, a method which was devised to evidence clusters in epidemiology. Results showed that the method is reliable to find clusters of events and to evaluate their significance via Monte Carlo replication. The evaluation of the presence of spatial and temporal patterns in fire occurrence and their significance could have a great impact in forthcoming studies on fire occurrences prediction.

Multisensor change detection with nonlinear canonical correlation

The analysis of multi-modal and multi-sensor images is nowadays of paramount importance for Earth Observation (EO) applications. There exist a variety of methods that aim at fusing the different sources of information to obtain a compact representation of such datasets. However, for change detection existing methods are often unable to deal with heterogeneous image sources and very few consider possible nonlinearities in the data. Additionally, the availability of labeled information is very limited in change detection applications. For these reasons, we present the use of a semi-supervised kernel-based feature extraction technique. It incorporates a manifold regularization accounting for the geometric distribution and jointly addressing the small sample problem. An exhaustive example using Landsat 5 data illustrates the potential of the method for multi-sensor change detection.

Target Molecular Size and Sodium Dodecyl Sulfate-Polyacrylamide Gel Electrophoresis Analysis of the ATP-and Pyrophosphate-Dependent Proton Pumps from Maize Root Tonoplast.

Tonoplast-enriched membranes were prepared from maize (Zea mays L. cv LG 11) primary roots, using sucrose nonlinear gradients. The functional molecular size of the tonoplast ATP-and PPi-dependent proton pumps were analyzed by radiation inactivation. Glucose-6-phosphate dehydrogenase (G6PDH) was added as an internal standard. Frozen samples (-196 degrees C) of the membranes were irradiated with (60)Co for different periods of time. After thawing the samples, the activities of G6PDH, ATPase, and PPase were tested. By applying target theory, the functional sizes of the ATPase and PPase in situ were found to be around 540 and 160 kilodaltons, respectively. The two activities were solubilized and separated by gel filtration chromatography. The different polypeptides copurifying with the two pumps were analyzed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis. Two bands (around 59 and 65 kilodaltons) were associated with the ATPase activity, whereas a double band (around 40 kilodaltons) was recovered with the PPase activity.

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.

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.

Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

Modelling body mass index and endometrial cancer risk in a pooled-analysis of three case-control studies.

OBJECTIVE: To quantify the relation between body mass index (BMI) and endometrial cancer risk, and to describe the shape of such a relation. DESIGN: Pooled analysis of three hospital-based case-control studies. SETTING: Italy and Switzerland. POPULATION: A total of 1449 women with endometrial cancer and 3811 controls. METHODS: Multivariate odds ratios (OR) and 95% confidence intervals (95% CI) were obtained from logistic regression models. The shape of the relation was determined using a class of flexible regression models. MAIN OUTCOME MEASURE: The relation of BMI with endometrial cancer. RESULTS: Compared with women with BMI 18.5 to <25 kg/m(2) , the odds ratio was 5.73 (95% CI 4.28-7.68) for women with a BMI ≥35 kg/m(2) . The odds ratios were 1.10 (95% CI 1.09-1.12) and 1.63 (95% CI 1.52-1.75) respectively for an increment of BMI of 1 and 5 units. The relation was stronger in never-users of oral contraceptives (OR 3.35, 95% CI 2.78-4.03, for BMI ≥30 versus <25 kg/m(2) ) than in users (OR 1.22, 95% CI 0.56-2.67), and in women with diabetes (OR 8.10, 95% CI 4.10-16.01, for BMI ≥30 versus <25 kg/m(2) ) than in those without diabetes (OR 2.95, 95% CI 2.44-3.56). The relation was best fitted by a cubic model, although after the exclusion of the 5% upper and lower tails, it was best fitted by a linear model. CONCLUSIONS: The results of this study confirm a role of elevated BMI in the aetiology of endometrial cancer and suggest that the risk in obese women increases in a cubic nonlinear fashion. The relation was stronger in never-users of oral contraceptives and in women with diabetes. TWEETABLE ABSTRACT: Risk of endometrial cancer increases with elevated body weight in a cubic nonlinear fashion.