A normal form analysis in a finite neighborhood of a hopf bifurcation: on the center manifold dimension

The problem of determining the bounds of applicability of perturbation expansions in terms both of the system parameters and the state-space variable amplitude is a key point in the perturbation analysis of nonlinear systems. In the present paper an analysis in a finite neighborhood of a Hopf bifurcation is presented in order to analyze the conditions under which a Normal Form zero-divisors-based approach fails to describe the local dynamics and, therefore, a small divisor approach is required. The condition of “smallness” referred to the divisors is analyzed from both a qualitative and a quantitative point of view. Finally, a simple but effective analytical and numerical example is introduced to illustrate the theoretical issues along with an interpretation within a codimension-two framework

TF-IDF vs Word Embeddings for Morbidity Identification in Clinical Notes: An Initial Study

Today, we are seeing an ever-increasing number of clinical notes that contain clinical results, images, and textual descriptions of patient's health state. All these data can be analyzed and employed to cater novel services that can help people and domain experts with their common healthcare tasks. However, many technologies such as Deep Learning and tools like Word Embeddings have started to be investigated only recently, and many challenges remain open when it comes to healthcare domain applications. To address these challenges, we propose the use of Deep Learning and Word Embeddings for identifying sixteen morbidity types within textual descriptions of clinical records. For this purpose, we have used a Deep Learning model based on Bidirectional Long-Short Term Memory (LSTM) layers which can exploit state-of-the-art vector representations of data such as Word Embeddings. We have employed pre-trained Word Embeddings namely GloVe and Word2Vec, and our own Word Embeddings trained on the target domain. Furthermore, we have compared the performances of the deep learning approaches against the traditional tf-idf using Support Vector Machine and Multilayer perceptron (our baselines). From the obtained results it seems that the latter outperforms the combination of Deep Learning approaches using any word embeddings. Our preliminary results indicate that there are specific features that make the dataset biased in favour of traditional machine learning approaches.Comment: 12 pages, 2 figures, 2 tables, SmartPhil 2020-First Workshop on Smart Personal Health Interfaces, Associated to ACM IUI 202

Atherosclerosis, dyslipidemia, and inflammation: the significant role of polyunsaturated fatty acids

Phospholipids play an essential role in cell membrane structure and function. The length and number of double bonds of fatty acids in membrane phospholipids are main determinants of fluidity, transport systems, activity of membrane-bound enzymes, and susceptibility to lipid peroxidation. The fatty acid profile of serum lipids, especially the phospholipids, reflects the fatty acid composition of cell membranes. Moreover, long-chain n-3 polyunsatured fatty acids decrease very-low-density lipoprotein assembly and secretion reducing triacylglycerol production. N-6 and n-3 polyunsatured fatty acids are the precursors of signalling molecules, termed “eicosanoids,” which play an important role in the regulation of inflammation. Eicosanoids derived from n-6 polyunsatured fatty acids have proinflammatory actions, while eicosanoids derived from n-3 polyunsatured fatty acids have antiinflammatory ones. Previous studies showed that inflammation contributes to both the onset and progression of atherosclerosis: actually, atherosclerosis is predominantly a chronic low-grade inflammatory disease of the vessel wall. Several studies suggested the relationship between long-chain n-3 polyunsaturated fatty acids and inflammation, showing that fatty acids may decrease endothelial activation and affect eicosanoid metabolis

Whipping-based criterion for the identification of slamming events

In this paper, a new criterion for the identification of slamming events is formulated. This criterion is based on the analysis of the high-frequency response, expressed in terms of the amidships VBM, which occurs after the slams. For this reason, it is named ‘whipping’ criterion underlining that is based on the analysis of global effects than on the kinematic description of the impact dynamics that was provided by Ochi criterion. Both the new ‘whipping’ criterion and the Ochi criterion are presented and compared also with respect to their practical application to the experimental data collected in the seakeeping tests with an elastic segmented model

Limit-cycle stability reversal via singular perturbation and wing-flap flutter

A three-degree-of-freedom aeroelastic typical section with a trailing-edge control surface is theoretically modelled, including nonlinear springs for both the nonlinear description of the torsional stiffness and of the hinge elastic moment. Furthermore, augmented states for linear unsteady aerodynamic of 2-D incompressible potential flow, have been considered in the model. First, the system response is determined by numerically integrating the governing equations using a standard Runge-Kutta algorithm in conjunction with a 'shooting method'. The numerical analysis has revealed the presence of stable and unstable limit cycles, along with stability reversal in the neighborhood of a Hopf bifurcation. Consequently, the equations of motion are analysed by a singular perturbation technique based on the normal-form method. This method, originally introduced by strictly applying a resonance condition, is herein extended by applying a near-resonance condition in order to improve the semi-analytical description of the stability reversal behavior. Therefore, amplitudes and frequencies of limit cycles depending on the flow speed V are obtained from the normal-form equations, and the terms which are essentially responsible for the nonlinear system behavior are identified. (C) 2004 Elsevier Ltd. All rights reserved

A nonlinear analysis of stability and gust response of aeroelastic systems

In this paper, the mechanism of limit-cycle excitation is investigated for an aeroelastic system with structural nonlinearities. The analysis is performed on a simplified acroelastic model retaining only two structural modes (first bending and first torsional modes) and with a simplified description of both unsteady loads due to wing oscillation and external gust excitation. Two cases are considered, without and with gust excitation. In the first case, normal form analysis is employed to give an approximation of the basin of attraction of stable limit cycles in the space of initial conditions. In the second case, a critical gust intensity for a given gust gradient leading again to undamped oscillations is identified. (c) 2007 Elsevier Ltd. All rights reserved

POD analysis for free response of linear and nonlinear marginally stable aeroelastic dynamical systems

The aim of this work is to study the relationship between Proper Orthogonal Modes (POMs) and Values (POVs) - as obtained by the free response analysis of linear and nonlinear aeroelastic (namely, marginally stable) systems - and the intrinsic invariants of such systems like modes (linear case) or manifolds (nonlinear case). The present investigation is first conducted for linear systems, by extending the results obtained in previous works, and then for nonlinear systems in the neighborhood of and beyond a Hopf bifurcation, where interesting features like limit cycle oscillations and chaotic response appear. The key point of the present theoretical analysis consists of avoiding the use of complex state-space variables to identify the subspaces where the distinguishing system dynamics - each associated to a couple of complex conjugated eigenvalues - live. Thus, a relation between the invariants obtained by the asymptotic expansion provided by Multiple Time Scale (MTS) method and POMs has been established. The typical section and the panel flutter problems do not only provide significant numerical test-cases for validation, but also suggest some insight about an alternate way of performing the Karhunen-Loeve decomposition by combining POD analysis with Galerkin representation of the solution. (C) 2012 Elsevier Ltd. All rights reserved

Slave-modes analysis beyond a bifurcating dynamical system

Objective: Analysis of the interaction between master and slave modes of a nonlinear system experiencing an Hopf bifurcation Main focus on: Centre Manifold within Hopf bifurcation (HBCM assumption) Activation mechanism of the linearly damped / slave modes Investigation technique: Numerical integration of the equations Normal form analysis Proper Orthogonal Decomposition Two cases: Dynamical system of two coupled nonlinear oscillators Aeroelastic system (panel flutter problem