An Investigation into Mechanisms of Loss of Safe Basins in a 2 D.O.F. Nonlinear Oscillator

In this work we consider the transient stability of coupled motions of a 2 D.O.F. nonlinear oscillator that can represent, for example, the motions of a sea vessel under the action of trains of regular lateral waves. Instability is studied as the escape of the system from a safe potential well. The set of initial conditions in phase space that lead to acceptable motions constitutes its safe basin. We investigate the evolution of these safe basins under variation of parameters such as frequency and amplitude of waves, and an internal tuning parameter. Complex nonlinear phenomena are known to play an important role in determining the loss of safe basins as, say, wave amplitude is increased. We therefore investigate those processes, and attempt to classify them in terms of their speed relative to changes in parameter values. "Mechanism basins" are produced depicting regions of parameter space in which rapid or slow losses of safe basin are observed. We propose that a comprehensive understanding of mechanisms of loss of safe basins can be a valuable tool in assessing stability properties of these systems, and we give a conceptual view of how such information could be used.

Experimental Vibration Characteristics of a Beam with Nonlinear Support Using Receptance Coupling Analysis

This paper applies the Multi-Harmonic Nonlinear Receptance Coupling Approach (MUHANORCA) (Ferreira 1998) to evaluate the frequency response characteristics of a beam which is clamped at one end and supported at the other end by a nonlinear cubic stiffness joint. In order to apply the substructure coupling technique, the problem was characterised by coupling a clamped linear beam with a nonlinear cubic stiffness joint. The experimental results were obtained by a sinusoidal excitation with a special force control algorithm where the level of the fundamental force is kept constant and the level of the harmonics is kept zero for all the frequencies measured.

Application of the center manifold theory to the study of slewing flexible Non-ideal structures with nonlinear curvature: a case study

In this paper is Analyzed the local dynamical behavior of a slewing flexible structure considering nonlinear curvature. The dynamics of the original (nonlinear) governing equations of motion are reduced to the center manifold in the neighborhood of an equilibrium solution with the purpose of locally study the stability of the system. In this critical point, a Hopf bifurcation occurs. In this region, one can find values for the control parameter (structural damping coefficient) where the system is unstable and values where the system stability is assured (periodic motion). This local analysis of the system reduced to the center manifold assures the stable / unstable behavior of the original system around a known solution.

Efficient Optimization Algorithms for Nonlinear Data Analysis

Identification of low-dimensional structures and main sources of variation from multivariate data are fundamental tasks in data analysis. Many methods aimed at these tasks involve solution of an optimization problem. Thus, the objective of this thesis is to develop computationally efficient and theoretically justified methods for solving such problems. Most of the thesis is based on a statistical model, where ridges of the density estimated from the data are considered as relevant features. Finding ridges, that are generalized maxima, necessitates development of advanced optimization methods. An efficient and convergent trust region Newton method for projecting a point onto a ridge of the underlying density is developed for this purpose. The method is utilized in a differential equation-based approach for tracing ridges and computing projection coordinates along them. The density estimation is done nonparametrically by using Gaussian kernels. This allows application of ridge-based methods with only mild assumptions on the underlying structure of the data. The statistical model and the ridge finding methods are adapted to two different applications. The first one is extraction of curvilinear structures from noisy data mixed with background clutter. The second one is a novel nonlinear generalization of principal component analysis (PCA) and its extension to time series data. The methods have a wide range of potential applications, where most of the earlier approaches are inadequate. Examples include identification of faults from seismic data and identification of filaments from cosmological data. Applicability of the nonlinear PCA to climate analysis and reconstruction of periodic patterns from noisy time series data are also demonstrated. Other contributions of the thesis include development of an efficient semidefinite optimization method for embedding graphs into the Euclidean space. The method produces structure-preserving embeddings that maximize interpoint distances. It is primarily developed for dimensionality reduction, but has also potential applications in graph theory and various areas of physics, chemistry and engineering. Asymptotic behaviour of ridges and maxima of Gaussian kernel densities is also investigated when the kernel bandwidth approaches infinity. The results are applied to the nonlinear PCA and to finding significant maxima of such densities, which is a typical problem in visual object tracking.

Effect of dietary fat saturation on lipid metabolism, arachidonic acid turnover and peritoneal macrophage oxidative stress in mice

We investigated the effects of a saturated fat diet on lipid metabolism and arachidonic acid (AA) turnover in mouse resident peritoneal macrophages. The pro-oxidative effect of this diet was also studied. Female C57BL/6 mice were weaned at 21 days of age and assigned to either the experimental diet containing coconut oil (COCO diet), or the control diet containing soybean oil as fat source (10 mice per group). The fat content of each diet was 15% (w/w). Mice were fed for 6 weeks and then sacrificed. The concentration of total lipids, triglycerides, (LDL + VLDL)-cholesterol, thiobarbituric acid-reactive substances (TBARS) and reduced glutathione were increased in the plasma of mice fed the COCO diet, without changes in phospholipid or total cholesterol concentrations compared to control. The concentrations of total cholesterol, free and esterified cholesterol, triglycerides, and TBARS were increased in the macrophages of COCO-fed mice, while the content of total phospholipids did not change. The phospholipid composition showed an increase of phosphatidylcholine and a decrease of phosphatidylethanolamine. The [³H]-AA distribution in the phospholipid classes showed an increase in phosphatidylcholine and phosphatidylethanolamine. Incorporation of [³H]-cholesterol into the macrophages of COCO-fed mice and into the cholesterol ester fraction was increased. The COCO diet did not affect [³H]-AA uptake but induced an increase in [³H]-AA release. The COCO diet also enhanced AA mobilization induced by lipopolysaccharide. These results indicate that the COCO diet, high in saturated fatty acids, alters the lipid metabolism and AA turnover of peritoneal macrophages in female mice and also produces a significant degree of oxidative stress.

Initialization of Continuous Nonlinear Models Using Extended Kalman Filter

The two main objectives of Bayesian inference are to estimate parameters and states. In this thesis, we are interested in how this can be done in the framework of state-space models when there is a complete or partial lack of knowledge of the initial state of a continuous nonlinear dynamical system. In literature, similar problems have been referred to as diffuse initialization problems. This is achieved first by extending the previously developed diffuse initialization Kalman filtering techniques for discrete systems to continuous systems. The second objective is to estimate parameters using MCMC methods with a likelihood function obtained from the diffuse filtering. These methods are tried on the data collected from the 1995 Ebola outbreak in Kikwit, DRC in order to estimate the parameters of the system.

Modulation of peritoneal macrophage activity by the saturation state of the fatty acid moiety of phosphatidylcholine

To determine the effects of saturated and unsaturated fatty acids in phosphatidylcholine (PC) on macrophage activity, peritoneal lavage cells were cultured in the presence of phosphatidylcholine rich in saturated or unsaturated fatty acids (sat PC and unsat PC, respectively), both used at concentrations of 32 and 64 µM. The treatment of peritoneal macrophages with 64 µM unsat PC increased the production of hydrogen peroxide by 48.3% compared to control (148.3 ± 16.3 vs 100.0 ± 1.8%, N = 15), and both doses of unsat PC increased adhesion capacity by nearly 50%. Moreover, 64 µM unsat PC decreased neutral red uptake by lysosomes by 32.5% compared to the untreated group (67.5 ± 6.8 vs 100.0 ± 5.5%, N = 15), while both 32 and 64 µM unsat PC decreased the production of lipopolysaccharide-elicited nitric oxide by 30.4% (13.5 ± 2.6 vs 19.4 ± 2.5 µM) and 46.4% (10.4 ± 3.1 vs 19.4 ± 2.5 µM), respectively. Unsat PC did not affect anion production in non-stimulated cells or phagocytosis of unopsonized zymosan particles. A different result pattern was obtained for macrophages treated with sat PC. Phorbol 12-miristate 13-acetate-elicited superoxide production and neutral red uptake were decreased by nearly 25% by 32 and 64 µM sat PC, respectively. Sat PC did not affect nitric oxide or hydrogen peroxide production, adhesion capacity or zymosan phagocytosis. Thus, PC modifies macrophage activity, but this effect depends on cell activation state, fatty acid saturation and esterification to PC molecule and PC concentration. Taken together, these results indicate that the fatty acid moiety of PC modulates macrophage activity and, consequently, is likely to affect immune system regulation in vivo.

Linear and nonlinear analysis of heart rate variability in healthy subjects and after acute myocardial infarction in patients

The objectives of this study were to evaluate and compare the use of linear and nonlinear methods for analysis of heart rate variability (HRV) in healthy subjects and in patients after acute myocardial infarction (AMI). Heart rate (HR) was recorded for 15 min in the supine position in 10 patients with AMI taking β-blockers (aged 57 ± 9 years) and in 11 healthy subjects (aged 53 ± 4 years). HRV was analyzed in the time domain (RMSSD and RMSM), the frequency domain using low- and high-frequency bands in normalized units (nu; LFnu and HFnu) and the LF/HF ratio and approximate entropy (ApEn) were determined. There was a correlation (P < 0.05) of RMSSD, RMSM, LFnu, HFnu, and the LF/HF ratio index with the ApEn of the AMI group on the 2nd (r = 0.87, 0.65, 0.72, 0.72, and 0.64) and 7th day (r = 0.88, 0.70, 0.69, 0.69, and 0.87) and of the healthy group (r = 0.63, 0.71, 0.63, 0.63, and 0.74), respectively. The median HRV indexes of the AMI group on the 2nd and 7th day differed from the healthy group (P < 0.05): RMSSD = 10.37, 19.95, 24.81; RMSM = 23.47, 31.96, 43.79; LFnu = 0.79, 0.79, 0.62; HFnu = 0.20, 0.20, 0.37; LF/HF ratio = 3.87, 3.94, 1.65; ApEn = 1.01, 1.24, 1.31, respectively. There was agreement between the methods, suggesting that these have the same power to evaluate autonomic modulation of HR in both AMI patients and healthy subjects. AMI contributed to a reduction in cardiac signal irregularity, higher sympathetic modulation and lower vagal modulation.

Nonlinear Monetary Policy Rules: Some New Evidence for the U.S.

This paper derives optimal monetary policy rules in setups where certainty equivalence does not hold because either central bank preferences are not quadratic, and/or the aggregate supply relation is nonlinear. Analytical results show that these features lead to sign and size asymmetries, and nonlinearities in the policy rule. Reduced-form estimates indicate that US monetary policy can be characterized by a nonlinear policy rule after 1983, but not before 1979. This finding is consistent with the view that the Fed's inflation preferences during the Volcker-Greenspan regime differ considerably from the ones during the Burns-Miller regime.

Estimating Nonlinear DSGE Models by the Simulated Method of Moments

This paper studies the application of the simulated method of moments (SMM) for the estimation of nonlinear dynamic stochastic general equilibrium (DSGE) models. Monte Carlo analysis is employed to examine the small-sample properties of SMM in specifications with different curvature. Results show that SMM is computationally efficient and delivers accurate estimates, even when the simulated series are relatively short. However, asymptotic standard errors tend to overstate the actual variability of the estimates and, consequently, statistical inference is conservative. A simple strategy to incorporate priors in a method of moments context is proposed. An empirical application to the macroeconomic effects of rare events indicates that negatively skewed productivity shocks induce agents to accumulate additional capital and can endogenously generate asymmetric business cycles.

Essays on numerically efficient inference in nonlinear and non-Gaussian state space models, and commodity market analysis.

The first two articles build procedures to simulate vector of univariate states and estimate parameters in nonlinear and non Gaussian state space models. We propose state space speci fications that offer more flexibility in modeling dynamic relationship with latent variables. Our procedures are extension of the HESSIAN method of McCausland[2012]. Thus, they use approximation of the posterior density of the vector of states that allow to : simulate directly from the state vector posterior distribution, to simulate the states vector in one bloc and jointly with the vector of parameters, and to not allow data augmentation. These properties allow to build posterior simulators with very high relative numerical efficiency. Generic, they open a new path in nonlinear and non Gaussian state space analysis with limited contribution of the modeler. The third article is an essay in commodity market analysis. Private firms coexist with farmers' cooperatives in commodity markets in subsaharan african countries. The private firms have the biggest market share while some theoretical models predict they disappearance once confronted to farmers cooperatives. Elsewhere, some empirical studies and observations link cooperative incidence in a region with interpersonal trust, and thus to farmers trust toward cooperatives. We propose a model that sustain these empirical facts. A model where the cooperative reputation is a leading factor determining the market equilibrium of a price competition between a cooperative and a private firm

La saturation de la mémoire auditive à court terme, une étude en électrophysiologie

La présente étude vise à approfondir les connaissances relatives aux mécanismes neuronaux qui sous-tendent la maintenance de sons variant en hauteur dans la mémoire auditive à court terme (MACT), plus précisément lors de sa saturation. À cet effet, la technique des potentiels reliés aux évènements (PRE) en électrophysiologie a été utilisée. La sélection des participants s’est déroulée par l’entremise de deux expériences comportementales : l’une était une tâche de discrimination et l’autre, une tâche qui évaluait l’habileté générale des participants à réussir une tâche similaire à celle de l’expérience principale en électroencéphalographie (EEG). Les résultats comportementaux de notre tâche en EEG ont montré que la performance diminuait de façon significative plus la charge en mémoire augmentait (séquences de 2, 4, 6 et 8 sons) et que l’estimation de la capacité de la MACT mesurée par K augmentait entre 2 et 4 sons pour atteindre un plafond à 4 sons (effet plafond). Le K maximum étant de 2.84 sons, l’empan mnésique (EM) auditif semble être près de 3 sons. Les résultats électrophysiologiques ont montré que la composante électrophysiologique reliée à la maintenance de sons en MACT, la Sustained Anterior Negativity (SAN), était modulée par le nombre de sons à maintenir : son amplitude augmentait de 2 à 4 sons et ce, jusqu’à l’atteinte d’un plafond à 4 sons. Ces résultats suggèrent que la maintenance de sons additionnels dans la MACT n’est plus possible après sa saturation. Nous soutenons donc que la SAN est un index électrophysiologique de l’activité neuronale associée à la maintenance d’items auditifs dans la MACT et que son amplitude est un bon indicateur de la capacité individuelle de la MACT, estimée par K. Des résultats post-hoc ont démontré que les musiciens et les non-musiciens tendent à avoir des différences au niveau de la SAN, sans pour autant modifier l’effet de charge en mémoire. Une analyse qualitative et quantitative de l’utilisation des stratégies mnésiques ont permis de clarifier leur implication et leur nature au sein d’une tâche cognitive de mémoire, plus précisément en audition. Pour conclure, l’ensemble de ces résultats suggère également que la SAN est reliée à la maintenance de sons dans la MACT et ainsi, un bon indicateur de sa capacité.

STUDIES ON THE STRESS FLUCTUATIONS IN SHEARED STOKESIAN SUSPENSIONS USING CHAOS THEORY AND NONLINEAR DYNAMICS

The thesis report results obtained from a detailed analysis of the fluctuations of the rheological parameters viz. shear and normal stresses, simulated by means of the Stokesian Dynamics method, of a macroscopically homogeneous sheared suspension of neutrally buoyant non-Brownian suspension of identical spheres in the Couette gap between two parallel walls in the limit of vanishingly small Reynolds numbers using the tools of non-linear dynamics and chaos theory for a range of particle concentration and Couette gaps. The thesis used the tools of nonlinear dynamics and chaos theory viz. average mutual information, space-time separation plots, visual recurrence analysis, principal component analysis, false nearest-neighbor technique, correlation integrals, computation of Lyapunov exponents for a range of area fraction of particles and for different Couette gaps. The thesis observed that one stress component can be predicted using another stress component at the same area fraction. This implies a type of synchronization of one stress component with another stress component. This finding suggests us to further analysis of the synchronization of stress components with another stress component at the same or different area fraction of particles. The different model equations of stress components for different area fraction of particles hints at the possible existence a general formula for stress fluctuations with area fraction of particle as a parameter