Post-Nonlinear Mixtures and Beyond

Although sources in general nonlinear mixturm arc not separable iising only statistical independence, a special and realistic case of nonlinear mixtnres, the post nonlinear (PNL) mixture is separable choosing a suited separating system. Then, a natural approach is based on the estimation of tho separating Bystem parameters by minimizing an indcpendence criterion, like estimated mwce mutual information. This class of methods requires higher (than 2) order statistics, and cannot separate Gaarsian sources. However, use of [weak) prior, like source temporal correlation or nonstationarity, leads to other source separation Jgw rithms, which are able to separate Gaussian sourra, and can even, for a few of them, works with second-order statistics. Recently, modeling time correlated s011rces by Markov models, we propose vcry efficient algorithms hmed on minimization of the conditional mutual information. Currently, using the prior of temporally correlated sources, we investigate the fesihility of inverting PNL mixtures with non-bijectiw non-liacarities, like quadratic functions. In this paper, we review the main ICA and BSS results for riunlinear mixtures, present PNL models and algorithms, and finish with advanced resutts using temporally correlated snu~sm

Longitudinal neurochemical modifications in the aging mouse brain measured in vivo by (1)H magnetic resonance spectroscopy.

Alterations to brain homeostasis during development are reflected in the neurochemical profile determined noninvasively by (1)H magnetic resonance spectroscopy. We determined longitudinal biochemical modifications in the cortex, hippocampus, and striatum of C57BL/6 mice aged between 3 and 24 months . The regional neurochemical profile evolution indicated that aging induces general modifications of neurotransmission processes (reduced GABA and glutamate), primary energy metabolism (altered glucose, alanine, and lactate) and turnover of lipid membranes (modification of choline-containing compounds and phosphorylethanolamine), which are all probably involved in the frequently observed age-related cognitive decline. Interestingly, the neurochemical profile was different in male and female mice, particularly in the levels of taurine that may be under the control of estrogen receptors. These neurochemical profiles constitute the basal concentrations in cortex, hippocampus, and striatum of healthy aging male and female mice.

Energy relaxation in nonlinear one-dimensional lattices

We study energy relaxation in thermalized one-dimensional nonlinear arrays of the Fermi-Pasta-Ulam type. The ends of the thermalized systems are placed in contact with a zero-temperature reservoir via damping forces. Harmonic arrays relax by sequential phonon decay into the cold reservoir, the lower-frequency modes relaxing first. The relaxation pathway for purely anharmonic arrays involves the degradation of higher-energy nonlinear modes into lower-energy ones. The lowest-energy modes are absorbed by the cold reservoir, but a small amount of energy is persistently left behind in the array in the form of almost stationary low-frequency localized modes. Arrays with interactions that contain both a harmonic and an anharmonic contribution exhibit behavior that involves the interplay of phonon modes and breather modes. At long times relaxation is extremely slow due to the spontaneous appearance and persistence of energetic high-frequency stationary breathers. Breather behavior is further ascertained by explicitly injecting a localized excitation into the thermalized arrays and observing the relaxation behavior.

Simulating maize phenology as a function of air temperature with a linear and a nonlinear model

The objective of this study was to adapt a nonlinear model (Wang and Engel - WE) for simulating the phenology of maize (Zea mays L.), and to evaluate this model and a linear one (thermal time), in order to predict developmental stages of a field-grown maize variety. A field experiment, during 2005/2006 and 2006/2007 was conducted in Santa Maria, RS, Brazil, in two growing seasons, with seven sowing dates each. Dates of emergence, silking, and physiological maturity of the maize variety BRS Missões were recorded in six replications in each sowing date. Data collected in 2005/2006 growing season were used to estimate the coefficients of the two models, and data collected in the 2006/2007 growing season were used as independent data set for model evaluations. The nonlinear WE model accurately predicted the date of silking and physiological maturity, and had a lower root mean square error (RMSE) than the linear (thermal time) model. The overall RMSE for silking and physiological maturity was 2.7 and 4.8 days with WE model, and 5.6 and 8.3 days with thermal time model, respectively.

In vivo brain macromolecule signals in healthy and glioblastoma mouse models: (1) H magnetic resonance spectroscopy, post-processing and metabolite quantification at 14.1 T.

In (1) H magnetic resonance spectroscopy, macromolecule signals underlay metabolite signals, and knowing their contribution is necessary for reliable metabolite quantification. When macromolecule signals are measured using an inversion-recovery pulse sequence, special care needs to be taken to correctly remove residual metabolite signals to obtain a pure macromolecule spectrum. Furthermore, since a single spectrum is commonly used for quantification in multiple experiments, the impact of potential macromolecule signal variability, because of regional differences or pathologies, on metabolite quantification has to be assessed. In this study, we introduced a novel method to post-process measured macromolecule signals that offers a flexible and robust way of removing residual metabolite signals. This method was applied to investigate regional differences in the mouse brain macromolecule signals that may affect metabolite quantification when not taken into account. However, since no significant differences in metabolite quantification were detected, it was concluded that a single macromolecule spectrum can be generally used for the quantification of healthy mouse brain spectra. Alternatively, the study of a mouse model of human glioma showed several alterations of the macromolecule spectrum, including, but not limited to, increased mobile lipid signals, which had to be taken into account to avoid significant metabolite quantification errors.

Measurement of the tree root growth using electrical impedance spectroscopy

Abstract

In vivo time-resolved spectroscopy of the human bronchial early cancer autofluorescence.

Time-resolved measurements of tissue autofluorescence (AF) excited at 405 nm were carried out with an optical-fiber-based spectrometer in the bronchi of 11 patients. The objectives consisted of assessing the lifetime as a new tumor/normal (T/N) tissue contrast parameter and trying to explain the origin of the contrasts observed when using AF-based cancer detection imaging systems. No significant change in the AF lifetimes was found. AF bronchoscopy performed in parallel with an imaging device revealed both intensity and spectral contrasts. Our results suggest that the spectral contrast might be due to an enhanced blood concentration just below the epithelial layers of the lesion. The intensity contrast probably results from the thickening of the epithelium in the lesions. The absence of T/N lifetime contrast indicates that the quenching is not at the origin of the fluorescence intensity and spectral contrasts. These lifetimes (6.9 ns, 2.0 ns, and 0.2 ns) were consistent for all the examined sites. The fact that these lifetimes are the same for different emission domains ranging between 430 and 680 nm indicates that there is probably only one dominant fluorophore involved. The measured lifetimes suggest that this fluorophore is elastin.

Endorectal Magnetic Resonance Imaging and Spectroscopy Are Useful for Selecting Candidates for Biopsy among Patients with Persistently Elevated Prostate Specific Antigen

To evaluate the efficacy of endorectal Magnetic Resonance Imaging (MRI) and Magnetic Resonance Spetroscopic Imaging (MRSI) combined with total prostate-specific antigen (tPSA) and free prostate-specific antigen (fPSA) in selecting candidates for biopsy. Subjects and Methods: 246 patients with elevated tPSA (median: 7.81 ng/ml) underwent endorectal MRI and MRSI before Transrectal Ultrasound (TRUS) biopsy (10 peripheral + 2 central cores); patients with positive biopsies were treated with radical intention; those with negative biopsies were followed up and underwent MRSI before each additional biopsy if tPSA rose persistently. Mean follow-up: 27.6 months. We compared MRI, MRSI, tPSA, and fPSA with histopathology by sextant and determined the association between the Gleason score and MRI and MRSI. We determined the most accurate combination to detect prostate cancer (PCa) using receiver operating curves; we estimated the odds ratios (OR) and calculated sensitivity, specificity, and positive and negative predictive values. Results: No difference in tPSA was found between patients with and without PCa (p = 0.551). In the peripheral zone, the risk of PCa increased with MRSI grade; patients with high-grade MRSI had the greatest risk of PCa over time (OR = 328.6); the model including MRI, MRSI, tPSA, and fPSA was more accurate (Area under Curve: AUC = 95.7%) than MRI alone (AUC = 85.1%) or fPSA alone (AUC = 78.1%), but not than MRSI alone (94.5%). In the transitional zone, the model was less accurate (AUC = 84.4%). The association (p = 0.005) between MRSI and Gleason score was significant in both zones. Conclusions: MRSI is useful in patients with elevated tPSA. High-grade MRSI lesions call for repeated biopsies. Men with negative MRSI may forgo further biopsies because a significantly high Gleason lesion is very unlikely

An overview of the metabolic differences between Bradyrhizobium japonicum 110 bacteria and differentiated bacteroids from soybean (Glycine max) root nodules: an in vitro 13C- and 31P-nuclear magnetic resonance spectroscopy study.

Bradyrhizobium japonicum is a symbiotic nitrogen-fixing soil bacteria that induce root nodules formation in legume soybean (Glycine max.). Using (13)C- and (31)P-nuclear magnetic resonance (NMR) spectroscopy, we have analysed the metabolite profiles of cultivated B. japonicum cells and bacteroids isolated from soybean nodules. Our results revealed some quantitative and qualitative differences between the metabolite profiles of bacteroids and their vegetative state. This includes in bacteroids a huge accumulation of soluble carbohydrates such as trehalose, glutamate, myo-inositol and homospermidine as well as Pi, nucleotide pools and intermediates of the primary carbon metabolism. Using this novel approach, these data show that most of the compounds detected in bacteroids reflect the metabolic adaptation of rhizobia to the surrounding microenvironment with its host plant cells.

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.

Stability and adaptability of runner peanut genotypes based on nonlinear regression and AMMI analysis

The objective of this work was to estimate the stability and adaptability of pod and seed yield in runner peanut genotypes based on the nonlinear regression and AMMI analysis. Yield data from 11 trials, distributed in six environments and three harvests, carried out in the Northeast region of Brazil during the rainy season were used. Significant effects of genotypes (G), environments (E), and GE interactions were detected in the analysis, indicating different behaviors among genotypes in favorable and unfavorable environmental conditions. The genotypes BRS Pérola Branca and LViPE‑06 are more stable and adapted to the semiarid environment, whereas LGoPE‑06 is a promising material for pod production, despite being highly dependent on favorable environments.

Chaotic systems with a null conditional Lyapunov exponent under nonlinear driving.

Control of a chaotic system by homogeneous nonlinear driving, when a conditional Lyapunov exponent is zero, may give rise to special and interesting synchronizationlike behaviors in which the response evolves in perfect correlation with the drive. Among them, there are the amplification of the drive attractor and the shift of it to a different region of phase space. In this paper, these synchronizationlike behaviors are discussed, and demonstrated by computer simulation of the Lorentz model [E. N. Lorenz, J. Atmos. Sci. 20 130 (1963)] and the double scroll [T. Matsumoto, L. O. Chua, and M. Komuro, IEEE Trans. CAS CAS-32, 798 (1985)].

Predicting rapeseed oil content with near-infrared spectroscopy

The objective of this work was to establish a calibration equation and to estimate the efficiency of near-infrared reflectance (NIR) spectroscopy for evaluating rapeseed oil content in Southern Brazil. Spectral data from 124 half-sib families were correlated with oil contents determined by the chemical method. The accuracy of the equation was verified by coefficient of determination (R²) of 0.92, error of calibration (SEC) of 0.78, and error of performance (SEP) of 1.22. The oil content of ten genotypes, which were not included in the calibration with NIR, was similar to the one obtained by the standard chemical method. NIR spectroscopy is adequate to differentiate oil content of rapeseed genotypes.

Linear and nonlinear terrain deformation maps from a reduced set of interferometric SAR images

In this paper, an advanced technique for the generation of deformation maps using synthetic aperture radar (SAR) data is presented. The algorithm estimates the linear and nonlinear components of the displacement, the error of the digital elevation model (DEM) used to cancel the topographic terms, and the atmospheric artifacts from a reduced set of low spatial resolution interferograms. The pixel candidates are selected from those presenting a good coherence level in the whole set of interferograms and the resulting nonuniform mesh tessellated with the Delauney triangulation to establish connections among them. The linear component of movement and DEM error are estimated adjusting a linear model to the data only on the connections. Later on, this information, once unwrapped to retrieve the absolute values, is used to calculate the nonlinear component of movement and atmospheric artifacts with alternate filtering techniques in both the temporal and spatial domains. The method presents high flexibility with respect to the required number of images and the baselines length. However, better results are obtained with large datasets of short baseline interferograms. The technique has been tested with European Remote Sensing SAR data from an area of Catalonia (Spain) and validated with on-field precise leveling measurements.

General electromagnetic simulation tool to predict the microwave nonlinear response of planar, arbitrarily-shaped HTS structures

This work describes a simulation tool being developed at UPC to predict the microwave nonlinear behavior of planar superconducting structures with very few restrictions on the geometry of the planar layout. The software is intended to be applicable to most structures used in planar HTS circuits, including line, patch, and quasi-lumped microstrip resonators. The tool combines Method of Moments (MoM) algorithms for general electromagnetic simulation with Harmonic Balance algorithms to take into account the nonlinearities in the HTS material. The Method of Moments code is based on discretization of the Electric Field Integral Equation in Rao, Wilton and Glisson Basis Functions. The multilayer dyadic Green's function is used with Sommerfeld integral formulation. The Harmonic Balance algorithm has been adapted to this application where the nonlinearity is distributed and where compatibility with the MoM algorithm is required. Tests of the algorithm in TM010 disk resonators agree with closed-form equations for both the fundamental and third-order intermodulation currents. Simulations of hairpin resonators show good qualitative agreement with previously published results, but it is found that a finer meshing would be necessary to get correct quantitative results. Possible improvements are suggested.