An estimate on the fractal dimension of attractors of gradient-like dynamical systems

This paper is dedicated to estimate the fractal dimension of exponential global attractors of some generalized gradient-like semigroups in a general Banach space in terms of the maximum of the dimension of the local unstable manifolds of the isolated invariant sets, Lipschitz properties of the semigroup and the rate of exponential attraction. We also generalize this result for some special evolution processes, introducing a concept of Morse decomposition with pullback attractivity. Under suitable assumptions, if (A, A*) is an attractor-repeller pair for the attractor A of a semigroup {T(t) : t >= 0}, then the fractal dimension of A can be estimated in terms of the fractal dimension of the local unstable manifold of A*, the fractal dimension of A, the Lipschitz properties of the semigroup and the rate of the exponential attraction. The ingredients of the proof are the notion of generalized gradient-like semigroups and their regular attractors, Morse decomposition and a fine analysis of the structure of the attractors. As we said previously, we generalize this result for some evolution processes using the same basic ideas. (C) 2012 Elsevier Ltd. All rights reserved.

Electronic Properties of Water in Liquid Environment. A Sequential QM/MM Study Using the Free Energy Gradient Method

There is a continuous search for theoretical methods that are able to describe the effects of the liquid environment on molecular systems. Different methods emphasize different aspects, and the treatment of both the local and bulk properties is still a great challenge. In this work, the electronic properties of a water molecule in liquid environment is studied by performing a relaxation of the geometry and electronic distribution using the free energy gradient method. This is made using a series of steps in each of which we run a purely molecular mechanical (MM) Monte Carlo Metropolis simulation of liquid water and subsequently perform a quantum mechanical/molecular mechanical (QM/MM) calculation of the ensemble averages of the charge distribution, atomic forces, and second derivatives. The MP2/aug-cc-pV5Z level is used to describe the electronic properties of the QM water. B3LYP with specially designed basis functions are used for the magnetic properties. Very good agreement is found for the local properties of water, such as geometry, vibrational frequencies, dipole moment, dipole polarizability, chemical shift, and spin-spin coupling constants. The very good performance of the free energy method combined with a QM/MM approach along with the possible limitations are briefly discussed.

The importance of plant life form on spatial associations along a subtropical coastal dune gradient

Questions Does the spatial association between isolated adult trees and understorey plants change along a gradient of sand dunes? Does this association depend on the life form of the understorey plant? Location Coastal sand dunes, southeast Brazil. Methods We recorded the occurrence of understorey plant species in 100 paired 0.25 m2 plots under adult trees and in adjacent treeless sites along an environmental gradient from beach to inland. Occurrence probabilities were modelled as a function of the fixed variables of the presence of a neighbour, distance from the seashore and life form, and a random variable, the block (i.e. the pair of plots). Generalized linear mixed models (GLMM) were fitted in a backward step-wise procedure using Akaike's information criterion (AIC) for model selection. Results The occurrence of understorey plants was affected by the presence of an adult tree neighbour, but the effect varied with the life form of the understorey species. Positive spatial association was found between isolated adult neighbour and young trees, whereas a negative association was found for shrubs. Moreover, a neutral association was found for lianas, whereas for herbs the effect of the presence of an adult neighbour ranged from neutral to negative, depended on the subgroup considered. The strength of the negative association with forbs increased with distance from the seashore. However, for the other life forms, the associational pattern with adult trees did not change along the gradient. Conclusions For most of the understorey life forms there is no evidence that the spatial association between isolated adult trees and understorey plants changes with the distance from the seashore, as predicted by the stress gradient hypothesis, a common hypothesis in the literature about facilitation in plant communities. Furthermore, the positive spatial association between isolated adult trees and young trees identified along the entire gradient studied indicates a positive feedback that explains the transition from open vegetation to forest in subtropical coastal dune environments.

Use of passive diffusion sampling method for defining NO2 concentrations gradient in São Paulo, Brazil

Abstract Background Air pollution in São Paulo is constantly being measured by the State of Sao Paulo Environmental Agency, however there is no information on the variation between places with different traffic densities. This study was intended to identify a gradient of exposure to traffic-related air pollution within different areas in São Paulo to provide information for future epidemiological studies. Methods We measured NO2 using Palmes' diffusion tubes in 36 sites on streets chosen to be representative of different road types and traffic densities in São Paulo in two one-week periods (July and August 2000). In each study period, two tubes were installed in each site, and two additional tubes were installed in 10 control sites. Results Average NO2 concentrations were related to traffic density, observed on the spot, to number of vehicles counted, and to traffic density strata defined by the city Traffic Engineering Company (CET). Average NO2concentrations were 63μg/m3 and 49μg/m3 in the first and second periods, respectively. Dividing the sites by the observed traffic density, we found: heavy traffic (n = 17): 64μg/m3 (95% CI: 59μg/m3 – 68μg/m3); local traffic (n = 16): 48μg/m3 (95% CI: 44μg/m3 – 52μg/m3) (p < 0.001). Conclusion The differences in NO2 levels between heavy and local traffic sites are large enough to suggest the use of a more refined classification of exposure in epidemiological studies in the city. Number of vehicles counted, traffic density observed on the spot and traffic density strata defined by the CET might be used as a proxy for traffic exposure in São Paulo when more accurate measurements are not available.

Iterative regularization methods for ill-posed problems

This Ph.D thesis focuses on iterative regularization methods for regularizing linear and nonlinear ill-posed problems. Regarding linear problems, three new stopping rules for the Conjugate Gradient method applied to the normal equations are proposed and tested in many numerical simulations, including some tomographic images reconstruction problems. Regarding nonlinear problems, convergence and convergence rate results are provided for a Newton-type method with a modified version of Landweber iteration as an inner iteration in a Banach space setting.

High gradient magnetic separation (HGMS) of erythrocytes infected with plasmodium falciparum

This thesis was undertaken to explore possible applications of high gradient magnetic separation (HGMS) for the separation of RBCs infected with Plasmodium falciparum, with the dual aim of establishing a novel and superior method for isolating late-stage infected cells, and of obtaining synchronized cell cultures.rnThe presented work presents protocols for HGMS of parasitized RBCs that fulfil these aims. Late-stage parasitized cell can be isolated essentially devoid of contamination with non-infected and ring-stage infected cells. Such an easy method for a highly quantitative and qualitative purification has not yet been reported. Synchronous cultures can be obtained both following depletion of late-stage infected cells, and following isolation of the latter. The quality of synchronization cultures matches that of sorbitol lysis, the current standard method for malaria culture synchronization. An advantage of HGMS is the avoidance of osmotic stress for RBCs. The new methods further have the appeal of high reproducibility, cost-effectiveness, and simple protocol.rnIt should be possible to take the methods beyond Plasmodium infected RBCs. Most magnetic separation techniques in the sector of biomedical research employ columns with a hydrophilic polymer-coated matrix. Our procedure employs an optimized buffer system. Polymer coating becomes unnecessary and uncoated columns are available at a fraction of the cost.

Regularization methods for the solution of a nonlinear least-squares problem in tomography

In this work we study a polyenergetic and multimaterial model for the breast image reconstruction in Digital Tomosynthesis, taking into consideration the variety of the materials forming the object and the polyenergetic nature of the X-rays beam. The modelling of the problem leads to the resolution of a high-dimensional nonlinear least-squares problem that, due to its nature of inverse ill-posed problem, needs some kind of regularization. We test two main classes of methods: the Levenberg-Marquardt method (together with the Conjugate Gradient method for the computation of the descent direction) and two limited-memory BFGS-like methods (L-BFGS). We perform some experiments for different values of the regularization parameter (constant or varying at each iteration), tolerances and stop conditions. Finally, we analyse the performance of the several methods comparing relative errors, iterations number, times and the qualities of the reconstructed images.

Geophysical Analysis of Seasonal Montandon Gravel Ridge Water Table Fluctuation and Moisture Gradient Variation due to Storm Events

The purpose of this research project is to continue exploring the Montandon Long-Term Hydrologic Research Site(LTHR) by using multiple geophysical methods to obtain more accurate and precise information regarding subsurface hydrologic properties of a local gravel ridge,which are important to both the health of surrounding ecosystems and local agriculture. Through using non-invasive geophysical methods such as seismic refraction, Direct Current resistivity and ground penetrating radar (GPR) instead of invasive methods such as boreholedrilling which displace sediment and may alter water flow, data collection is less likely to bias the data itself. In addition to imaging the gravel ridge subsurface, another important researchpurpose is to observe how both water table elevation and the moisture gradient (moisture content of the unsaturated zone) change over a seasonal time period and directly after storm events. The combination of three types of data collection allows the strengths of each method combine together and provide a relatively strongly supported conclusions compared to previous research. Precipitation and geophysical data suggest that an overall increase in precipitation during the summer months causes a sharp decrease in subsurface resistivity within the unsaturated zone. GPR velocity data indicate significant immediate increase in moisture content within the shallow vadose zone (< 1m), suggesting that rain water was infiltrating into the shallow subsurface. Furthermore, the combination of resistivity and GPR results suggest that the decreased resistivity within the shallow layers is due to increased ion content within groundwater. This is unexpected as rainwater is assumed to have a DC resistivity value of 3.33*105 ohm-m. These results may suggest that ions within the sediment must beincorporated into the infiltrating water.

Squared Extrapolation Methods (SQUAREM): A New Class of Simple and Efficient Numerical Schemes for Accelerating the Convergence of the EM Algorithm

We derive a new class of iterative schemes for accelerating the convergence of the EM algorithm, by exploiting the connection between fixed point iterations and extrapolation methods. First, we present a general formulation of one-step iterative schemes, which are obtained by cycling with the extrapolation methods. We, then square the one-step schemes to obtain the new class of methods, which we call SQUAREM. Squaring a one-step iterative scheme is simply applying it twice within each cycle of the extrapolation method. Here we focus on the first order or rank-one extrapolation methods for two reasons, (1) simplicity, and (2) computational efficiency. In particular, we study two first order extrapolation methods, the reduced rank extrapolation (RRE1) and minimal polynomial extrapolation (MPE1). The convergence of the new schemes, both one-step and squared, is non-monotonic with respect to the residual norm. The first order one-step and SQUAREM schemes are linearly convergent, like the EM algorithm but they have a faster rate of convergence. We demonstrate, through five different examples, the effectiveness of the first order SQUAREM schemes, SqRRE1 and SqMPE1, in accelerating the EM algorithm. The SQUAREM schemes are also shown to be vastly superior to their one-step counterparts, RRE1 and MPE1, in terms of computational efficiency. The proposed extrapolation schemes can fail due to the numerical problems of stagnation and near breakdown. We have developed a new hybrid iterative scheme that combines the RRE1 and MPE1 schemes in such a manner that it overcomes both stagnation and near breakdown. The squared first order hybrid scheme, SqHyb1, emerges as the iterative scheme of choice based on our numerical experiments. It combines the fast convergence of the SqMPE1, while avoiding near breakdowns, with the stability of SqRRE1, while avoiding stagnations. The SQUAREM methods can be incorporated very easily into an existing EM algorithm. They only require the basic EM step for their implementation and do not require any other auxiliary quantities such as the complete data log likelihood, and its gradient or hessian. They are an attractive option in problems with a very large number of parameters, and in problems where the statistical model is complex, the EM algorithm is slow and each EM step is computationally demanding.

Clinical outcomes of patients with low-flow, low-gradient, severe aortic stenosis and either preserved or reduced ejection fraction undergoing transcatheter aortic valve implantation

AIMS Our aim was to evaluate the invasive haemodynamic indices of high-risk symptomatic patients presenting with 'paradoxical' low-flow, low-gradient, severe aortic stenosis (AS) (PLF-LG) and low-flow, low-gradient severe AS (LEF-LG) and to compare clinical outcomes following transcatheter aortic valve implantation (TAVI) among these challenging AS subgroups. METHODS AND RESULTS Of 534 symptomatic patients undergoing TAVI, 385 had a full pre-procedural right and left heart catheterization. A total of 208 patients had high-gradient severe AS [HGAS; mean gradient (MG) ≥40 mmHg], 85 had PLF-LG [MG ≤ 40 mmHg, indexed aortic valve area [iAVA] ≤0.6 cm(2) m(-2), stroke volume index ≤35 mL/m(2), ejection fraction (EF) ≥50%], and 61 had LEF-LG (MG ≤ 40 mmHg, iAVA ≤0.6 cm(2) m(-2), EF ≤40%). Compared with HGAS, PLF-LG and LEF-LG had higher systemic vascular resistances (HGAS: 1912 ± 654 vs. PLF-LG 2006 ± 586 vs. LEF-LG 2216 ± 765 dyne s m(-5), P = 0.007) but lower valvulo-arterial impedances (HGAS: 7.8 ± 2.7 vs. PLF-LG 6.9 ± 1.9 vs. LEF-LG 7.7 ± 2.5 mmHg mL(-1) m(-2), P = 0.027). At 30 days, no differences in cardiac death (6.5 vs. 4.9 vs. 6.6%, P = 0.90) or death (8.4 vs. 6.1 vs. 6.6%, P = 0.88) were observed among HGAS, PLF-LG, and LEF-LG groups, respectively. At 1 year, New York Heart Association functional improvement occurred in most surviving patients (HGAS: 69.2% vs. PLF-LG 71.7% vs. LEF-LG 89.3%, P = 0.09) and no significant differences in overall mortality were observed (17.6 vs. 20.5 vs. 24.5%, P = 0.67). Compared with HGAS, LEF-LG had a higher 1 year cardiac mortality (adjusted hazard ratio 2.45, 95% confidence interval 1.04-5.75, P = 0.04). CONCLUSION TAVI in PLF-LG or LEF-LG patients is associated with overall mortality rates comparable with HGAS patients and all groups profit symptomatically to a similar extent.

Identification of the Causative Bacteria in Musculoskeletal Infections Using 16s rDNA - Denaturing Gradient Gel Electrophoresis Analysis

Musculoskeletal infections are infections of the bone and surrounding tissues. They are currently diagnosed based on culture analysis, which is the gold standard for pathogen identification. However, these clinical laboratory methods are frequently inadequate for the identification of the causative agents, because a large percentage (25-50%) of confirmed musculoskeletal infections are false negatives in which no pathogen is identified in culture. My data supports these results. The goal of this project was to use PCR amplification of a portion of the 16S rRNA gene to test an alternative approach for the identification of these pathogens and to assess the diversity of the bacteria involved. The advantages of this alternative method are that it should increase sample sensitivity and the speed of detection. In addition, bacteria that are non-culturable or in low abundance can be detected using this molecular technique. However, a complication of this approach is that the majority of musculoskeletal infections are polymicrobial, which prohibits direct identification from the infected tissue by DNA sequencing of the initial 16S rDNA amplification products. One way to solve this problem is to use denaturing gradient gel electrophoresis (DGGE) to separate the PCR products before DNA sequencing. Denaturing gradient gel electrophoresis (DGGE) separates DNA molecules based on their melting point, which is determined by their DNA sequence. This analytical technique allows a mixture of PCR products of the same length that electrophoreses through agarose gels as one band, to be separated into different bands and then used for DNA sequence analysis. In this way, the DGGE allows for the identification of individual bacterial species in polymicrobial-infected tissue, which is critical for improving clinical outcomes. By combining the 16S rDNA amplification and the DGGE techniques together, an alternative approach for identification has been used. The 16S rRNA gene PCR-DGGE method includes several critical steps: DNA extraction from tissue biopsies, amplification of the bacterial DNA, PCR product separation by DGGE, amplification of the gel-extracted DNA, and DNA sequencing and analysis. Each step of the method was optimized to increase its sensitivity and for rapid detection of the bacteria present in human tissue samples. The limit of detection for the DNA extraction from tissue was at least 20 Staphylococcus aureus cells and the limit of detection for PCR was at least 0.05 pg of template DNA. The conditions for DGGE electrophoreses were optimized by using a double gradient of acrylamide (6 – 10%) and denaturant (30-70%), which increased the separation between distinct PCR products. The use of GelRed (Biotium) improved the DNA visualization in the DGGE gel. To recover the DNA from the DGGE gels the gel slices were excised, shredded in a bead beater, and the DNA was allowed to diffuse into sterile water overnight. The use of primers containing specific linkers allowed the entire amplified PCR product to be sequenced and then analyzed. The optimized 16S rRNA gene PCR-DGGE method was used to analyze 50 tissue biopsy samples chosen randomly from our collection. The results were compared to those of the Memorial Hermann Hospital Clinical Microbiology Laboratory for the same samples. The molecular method was congruent for 10 of the 17 (59%) culture negative tissue samples. In 7 of the 17 (41%) culture negative the molecular method identified a bacterium. The molecular method was congruent with the culture identification for 7 of the 33 (21%) positive cultured tissue samples. However, in 8 of the 33 (24%) the molecular method identified more organisms. In 13 of the 15 (87%) polymicrobial cultured tissue samples the molecular method identified at least one organism that was also identified by culture techniques. Overall, the DGGE analysis of 16S rDNA is an effective method to identify bacteria not identified by culture analysis.

Pulmonary veins to left atrium cycle length gradient predicts procedural and clinical outcomes of persistent atrial fibrillation ablation.

BACKGROUND Rapid pulmonary vein (PV) activity has been shown to maintain paroxysmal atrial fibrillation (AF). We evaluated in persistent AF the cycle length (CL) gradient between PVs and the left atrium (LA) in an attempt to identify the subset of patients where PVs play an important role. METHODS AND RESULTS Ninety-seven consecutive patients undergoing first ablation for persistent AF were studied. For each PV, the CL of the fastest activation was assessed over 1 minute (PVfast) using Lasso recordings. The PV to LA CL gradient was quantified by the ratio of PVfast to LA appendage (LAA) AF CL. Stepwise ablation terminated AF in 73 patients (75%). In the AF termination group, the PVfast CL was much shorter than the LAA CL resulting in lower PVfast/LAA ratios compared with the nontermination group (71±10% versus 92±7%; P<0.001). Within the termination group, PVfast/LAA ratios were notably lower if AF terminated after PV isolation or limited adjunctive substrate ablation compared with patients who required moderate or extensive ablation (63±6% versus 75±8%; P<0.001). PVfast/LAA ratio <69% predicted AF termination after PV isolation or limited substrate ablation with 74% positive predictive value and 95% negative predictive value. After a mean follow-up of 29±17 months, freedom from arrhythmia recurrence off-antiarrhythmic drugs was achieved in most patients with PVfast/LAA ratios <69% as opposed to the remaining population (80% versus 43%; P<0.001). CONCLUSIONS The PV to LA CL gradient may identify the subset of patients in whom persistent AF is likely to terminate after PV isolation or limited substrate ablation and better long-term outcomes are achieved.

Impact of mitral regurgitation on clinical outcomes of patients with low-ejection fraction, low-gradient severe aortic stenosis undergoing transcatheter aortic valve implantation.

BACKGROUND Up to 1 in 6 patients undergoing transcatheter aortic valve implantation (TAVI) present with low-ejection fraction, low-gradient (LEF-LG) severe aortic stenosis and concomitant relevant mitral regurgitation (MR) is present in 30% to 55% of these patients. The effect of MR on clinical outcomes of LEF-LG patients undergoing TAVI is unknown. METHODS AND RESULTS Of 606 consecutive patients undergoing TAVI, 113 (18.7%) patients with LEF-LG severe aortic stenosis (mean gradient ≤40 mm Hg, aortic valve area <1.0 cm(2), left ventricular ejection fraction <50%) were analyzed. LEF-LG patients were dichotomized into ≤mild MR (n=52) and ≥moderate MR (n=61). Primary end point was all-cause mortality at 1 year. No differences in mortality were observed at 30 days (P=0.76). At 1 year, LEF-LG patients with ≥moderate MR had an adjusted 3-fold higher rate of all-cause mortality (11.5% versus 38.1%; adjusted hazard ratio, 3.27 [95% confidence interval, 1.31-8.15]; P=0.011), as compared with LEF-LG patients with ≤mild MR. Mortality was mainly driven by cardiac death (adjusted hazard ratio, 4.62; P=0.005). As compared with LEF-LG patients with ≥moderate MR assigned to medical therapy, LEF-LG patients with ≥moderate MR undergoing TAVI had significantly lower all-cause mortality (hazard ratio, 0.38; 95% confidence interval, 0.019-0.75) at 1 year. CONCLUSIONS Moderate or severe MR is a strong independent predictor of late mortality in LEF-LG patients undergoing TAVI. However, LEF-LG patients assigned to medical therapy have a dismal prognosis independent of MR severity suggesting that TAVI should not be withheld from symptomatic patients with LEF-LG severe aortic stenosis even in the presence of moderate or severe MR.

Improved methods for measuring forest landscape structure: LiDAR complements field-based habitat assessment

Conservation and monitoring of forest biodiversity requires reliable information about forest structure and composition at multiple spatial scales. However, detailed data about forest habitat characteristics across large areas are often incomplete due to difficulties associated with field sampling methods. To overcome this limitation we employed a nationally available light detection and ranging (LiDAR) remote sensing dataset to develop variables describing forest landscape structure across a large environmental gradient in Switzerland. Using a model species indicative of structurally rich mountain forests (hazel grouse Bonasa bonasia), we tested the potential of such variables to predict species occurrence and evaluated the additional benefit of LiDAR data when used in combination with traditional, sample plot-based field variables. We calibrated boosted regression trees (BRT) models for both variable sets separately and in combination, and compared the models’ accuracies. While both field-based and LiDAR models performed well, combining the two data sources improved the accuracy of the species’ habitat model. The variables retained from the two datasets held different types of information: field variables mostly quantified food resources and cover in the field and shrub layer, LiDAR variables characterized heterogeneity of vegetation structure which correlated with field variables describing the understory and ground vegetation. When combined with data on forest vegetation composition from field surveys, LiDAR provides valuable complementary information for encompassing species niches more comprehensively. Thus, LiDAR bridges the gap between precise, locally restricted field-data and coarse digital land cover information by reliably identifying habitat structure and quality across large areas.

Extratropical fronts in the lower troposphere-global perspectives obtained from two automated methods

In this study two commonly used automated methods to detect atmospheric fronts in the lower troposphere are compared in various synoptic situations. The first method is a thermal approach, relying on the gradient of equivalent potential temperature (TH), while the second method is based on temporal changes in the 10 m wind (WND). For a comprehensive objective comparison of the outputs of these methods of frontal identification, both schemes are firstly applied to an idealised strong baroclinic wave simulation in the absence of topography. Then, two case-studies (one in the Northern Hemisphere (NH) and one in the Southern Hemisphere (SH)) were conducted to contrast fronts detected by the methods. Finally, we obtain global winter and summer frontal occurrence climatologies (derived from ERA-Interim for 1979–2012) and compare the structure of these. TH is able to identify cold and warm fronts in strong baroclinic cases that are in good agreement with manual analyses. WND is particularly suited for the detection of strongly elongated, meridionally oriented moving fronts, but has very limited ability to identify zonally oriented warm fronts. We note that the areas of the main TH frontal activity are shifted equatorwards compared to the WND patterns and are located upstream of regions of main WND front activity. The number of WND fronts in the NH shows more interseasonal variations than TH fronts, decreasing by more than 50% from winter to summer. In the SH there is a weaker seasonal variation of the number of observed WND fronts, however TH front activity reduces from summer (DJF) to winter (JJA). The main motivation is to give an overview of the performance of these methods, such that researchers can choose the appropriate one for their particular interest.