Differential invariants of second-order ordinary differential equations

The notion of a differential invariant for systems of second-order differential equations on a manifold M with respect to the group of vertical automorphisms of the projection is de?ned and the Chern connection attached to a SODE allows one to determine a basis for second-order differential invariants of a SODE.

Computational Schemes for Optimizing Domains of Attraction in Dynamical Systems

In this paper, several computational schemes are presented for the optimal tuning of the global behavior of nonlinear dynamical sys- tems. Specifically, the maximization of the size of domains of attraction associated with invariants in parametrized dynamical sys- tems is addressed. Cell Mapping (CM) tech- niques are used to estimate the size of the domains, and such size is then maximized via different optimization tools. First, a ge- netic algorithm is tested whose performance shows to be good for determining global maxima at the expense of high computa- tional cost. Secondly, an iterative scheme based on a Stochastic Approximation proce- dure (the Kiefer-Wolfowitz algorithm) is eval- uated showing acceptable performance at low cost. Finally, several schemes combining neu- ral network based estimations and optimiza- tion procedures are addressed with promising results. The performance of the methods is illus- trated with two applications: first on the well-known van der Pol equation with stan- dard parametrization, and second the tuning of a controller for saturated systems.

Classification of discrete systems on a square lattice

We consider the classification up to a Möbius transformation of real linearizable and integrable partial difference equations with dispersion defined on a square lattice by the multiscale reduction around their harmonic solution. We show that the A1, A2, and A3 linearizability and integrability conditions constrain the number of parameters in the equation, but these conditions are insufficient for a complete characterization of the subclass of multilinear equations on a square lattice.

Improving automatic detection of obstructive sleep apnea through nonlinear analysis of sustained speech

We present a novel approach for the detection of severe obstructive sleep apnea (OSA) based on patients' voices introducing nonlinear measures to describe sustained speech dynamics. Nonlinear features were combined with state-of-the-art speech recognition systems using statistical modeling techniques (Gaussian mixture models, GMMs) over cepstral parameterization (MFCC) for both continuous and sustained speech. Tests were performed on a database including speech records from both severe OSA and control speakers. A 10 % relative reduction in classification error was obtained for sustained speech when combining MFCC-GMM and nonlinear features, and 33 % when fusing nonlinear features with both sustained and continuous MFCC-GMM. Accuracy reached 88.5 % allowing the system to be used in OSA early detection. Tests showed that nonlinear features and MFCCs are lightly correlated on sustained speech, but uncorrelated on continuous speech. Results also suggest the existence of nonlinear effects in OSA patients' voices, which should be found in continuous speech.

Nonlinear normal modes in mechanical systems: concept and computation with numerical continuation

The purpose of this Project is, first and foremost, to disclose the topic of nonlinear vibrations and oscillations in mechanical systems and, namely, nonlinear normal modes NNMs to a greater audience of researchers and technicians. To do so, first of all, the dynamical behavior and properties of nonlinear mechanical systems is outlined from the analysis of a pair of exemplary models with the harmonic balanced method. The conclusions drawn are contrasted with the Linear Vibration Theory. Then, it is argued how the nonlinear normal modes could, in spite of their limitations, predict the frequency response of a mechanical system. After discussing those introductory concepts, I present a Matlab package called 'NNMcont' developed by a group of researchers from the University of Liege. This package allows the analysis of nonlinear normal modes of vibration in a range of mechanical systems as extensions of the linear modes. This package relies on numerical methods and a 'continuation algorithm' for the computation of the nonlinear normal modes of a conservative mechanical system. In order to prove its functionality, a two degrees of freedom mechanical system with elastic nonlinearities is analized. This model comprises a mass suspended on a foundation by means of a spring-viscous damper mechanism -analogous to a very simplified model of most suspended structures and machines- that has attached a mass damper as a passive vibration control system. The results of the computation are displayed on frequency energy plots showing the NNMs branches along with modal curves and time-series plots for each normal mode. Finally, a critical analysis of the results obtained is carried out with an eye on devising what they can tell the researcher about the dynamical properties of the system.

Impacts of projected maximum temperature extremes for C21 by an ensemble of regional climate models on cereal cropping systems in the Iberian Peninsula

Crops growing in the Iberian Peninsula may be subjected to damagingly high temperatures during the sensitive development periods of flowering and grain filling. Such episodes are considered important hazards and farmers may take insurance to offset their impact. Increases in value and frequency of maximum temperature have been observed in the Iberian Peninsula during the 20th century, and studies on climate change indicate the possibility of further increase by the end of the 21st century. Here, impacts of current and future high temperatures on cereal cropping systems of the Iberian Peninsula are evaluated, focusing on vulnerable development periods of winter and summer crops. Climate change scenarios obtained from an ensemble of ten Regional Climate Models (multimodel ensemble) combined with crop simulation models were used for this purpose and related uncertainty was estimated. Results reveal that higher extremes of maximum temperature represent a threat to summer-grown but not to winter-grown crops in the Iberian Peninsula. The study highlights the different vulnerability of crops in the two growing seasons and the need to account for changes in extreme temperatures in developing adaptations in cereal cropping systems. Finally, this work contributes to clarifying the causes of high-uncertainty impact projections from previous studies.

Non-linear gain - look-up table based approach for modeling a family of DC to DC converters based on transient response analysis

The purpose of this work is to propose a structure for simulating power systems using behavioral models of nonlinear DC to DC converters implemented through a look-up table of gains. This structure is specially designed for converters whose output impedance depends on the load current level, e.g. quasi-resonant converters. The proposed model is a generic one whose parameters can be obtained by direct measuring the transient response at different operating points. It also includes optional functionalities for modeling converters with current limitation and current sharing in paralleling characteristics. The pusposed structured also allows including aditional characteristics of the DC to DC converter as the efficency as a function of the input voltage and the output current or overvoltage and undervoltage protections. In addition, this proposed model is valid for overdamped and underdamped situations.

The internal structure of hydrogen-air difussion flames

The Internal Structure of Hydrogen-Air Diffusion Flames. Tho purpose of this paper is to study finite rate chemistry effects in diffusion controlled hydrogenair flames undor conditions appearing in some cases in a supersonic combustor. Since for large reaction rates the flame is close to chemical equilibrium, the reaction takes place in a very thin region, so thata "singular perturbation "treatment" of the problem seems appropriate. It has been shown previously that, within the inner or reaction zone, convection effects may be neglocted, the temperature is constant across the flame, and tho mass fraction distributions are given by ordinary differential equations, whore tho only independent variable involved is tho coordinate normal to the flame surface. Tho solution of the outer problom, which is a pure mixing problem with the additional condition that fuol and oxidizer do not coexist in any zone, provides t h e following information: tho flame position, rates of fuel consumption, temperature, concentrators of species, fluid velocity outside of tho flame, and the boundary conditions required to solve the "inner problem." The main contribution of this paper consists in the introduction of a fairly complicated chemical kinetic scheme representing hydrogen-oxygen reaction. The nonlinear equations expressing the conservation of chemical species are approximately integrated by means of an integral method. It has boen found that, in the case considered of a near-equilibrium diffusion flame, tho role played by the dissociation-recombination reactions is purely marginal, and that somo of the second order "shuffling" reactions are close to equilibrium. The method shown here may be applied to compute the distanco from the injector corresponding to a given separation from equilibrium, say ten to twenty percent. For the casos whore this length is a small fraction of the combustion zone length, the equilibrium treatment describes properly tho flame behavior.

Early dysfunction of functional connectivity in healthy elderly with subjective memory complaints

It is still an open question whether subjective memory complaints (SMC) can actually be considered to be clinically relevant predictors for the development of an objective memory impairment and even dementia. There is growing evidence that suggests that SMC are associated with an increased risk of dementia and with the presence of biological correlates of early Alzheimer's disease. In this paper, in order to shed some light on this issue, we try to discern whether subjects with SMC showed a different profile of functional connectivity compared with subjects with mild cognitive impairment (MCI) and healthy elderly subjects. In the present study, we compare the degree of synchronization of brain signals recorded with magnetoencephalography between three groups of subjects (56 in total): 19 with MCI, 12 with SMC and 25 healthy controls during a memory task. Synchronization likelihood, an index based on the theory of nonlinear dynamical systems, was used to measure functional connectivity. Briefly, results show that subjects with SMC have a very similar pattern of connectivity to control group, but on average, they present a lower synchronization value. These results could indicate that SMC are representing an initial stage with a hypo-synchronization (in comparison with the control group) where the brain system is still not compensating for the failing memory networks, but behaving as controls when compared with the MCI subjects.

Influence of delay time on regularity estimation for voice pathology detection

The employment of nonlinear analysis techniques for automatic voice pathology detection systems has gained popularity due to the ability of such techniques for dealing with the underlying nonlinear phenomena. On this respect, characterization using nonlinear analysis typically employs the classical Correlation Dimension and the largest Lyapunov Exponent, as well as some regularity quantifiers computing the system predictability. Mostly, regularity features highly depend on a correct choosing of some parameters. One of those, the delay time �, is usually fixed to be 1. Nonetheless, it has been stated that a unity � can not avoid linear correlation of the time series and hence, may not correctly capture system nonlinearities. Therefore, present work studies the influence of the � parameter on the estimation of regularity features. Three � estimations are considered: the baseline value 1; a � based on the Average Automutual Information criterion; and � chosen from the embedding window. Testing results obtained for pathological voice suggest that an improved accuracy might be obtained by using a � value different from 1, as it accounts for the underlying nonlinearities of the voice signal.

Systems in Engineering Education: account of an experience

Systems Engineering (SE in the following) has not received much attention as a subject matter in engineering curricula. There are several dozens of universities around the world offering programs (most of them at the graduate level) on systems science and engineering. However, SE is, per se, rarely found among the courses offered by engineering schools. This observation does not strictly mean that systems concepts be left apart. For example, it is usual to find specialized courses for systems of some particular classes (e.g., courses on software systems engineering for computing curricula) or for particular phases of the system life cycle (e.g., courses on systems analysis). Even so, these kinds of courses tend to over-emphasize the importance of specific methodologies and, in consequence, to deviate the attention from the realm of systernness

Large-Scale smart grids as system of systems

Smart Grids are advanced power networks that introduce intelligent management, control, and operation systems to address the new challenges generated by the growing energy demand and the appearance of renewal energies. In the literature, Smart Grids are presented as an exemplar SoS: systems composed of large heterogeneous and independent systems that leverage emergent behavior from their interaction. Smart Grids are currently scaling up the electricity service to millions of customers. These Smart Grids are known as Large-Scale Smart Grids. From the experience in several projects about Large-Scale Smart Grids, this paper defines Large-Scale Smart Grids as a SoS that integrate a set of SoS and conceptualizes the properties of this SoS. In addition, the paper defines the architectural framework for deploying the software architectures of Large-Scale Smart Grid SoS.

First order mem-circuits: modeling, nonlinear oscillations and bifurcations

This paper presents a theoretical framework intended to accommodate circuit devices described by characteristics involving more than two fundamental variables. This framework is motivated by the recent appearance of a variety of so-called mem-devices in circuit theory, and makes it possible to model the coexistence of memory effects of different nature in a single device. With a compact formalism, this setting accounts for classical devices and also for circuit elements which do not admit a two-variable description. Fully nonlinear characteristics are allowed for all devices, driving the analysis beyond the framework of Chua and Di Ventra We classify these fully nonlinear circuit elements in terms of the variables involved in their constitutive relations and the notions of the differential- and the state-order of a device. We extend the notion of a topologically degenerate configuration to this broader context, and characterize the differential-algebraic index of nodal models of such circuits. Additionally, we explore certain dynamical features of mem-circuits involving manifolds of non-isolated equilibria. Related bifurcation phenomena are explored for a family of nonlinear oscillators based on mem-devices.

Towards an abstract domain for resource analysis of logic programs using sized types

We present a novel general resource analysis for logic programs based on sized types.Sized types are representations that incorporate structural (shape) information and allow expressing both lower and upper bounds on the size of a set of terms and their subterms at any position and depth. They also allow relating the sizes of terms and subterms occurring at different argument positions in logic predicates. Using these sized types, the resource analysis can infer both lower and upper bounds on the resources used by all the procedures in a program as functions on input term (and subterm) sizes, overcoming limitations of existing analyses and enhancing their precision. Our new resource analysis has been developed within the abstract interpretation framework, as an extension of the sized types abstract domain, and has been integrated into the Ciao preprocessor, CiaoPP. The abstract domain operations are integrated with the setting up and solving of recurrence equations for both, inferring size and resource usage functions. We show that the analysis is an improvement over the previous resource analysis present in CiaoPP and compares well in power to state of the art systems.

Resource usage analysis of logic programs via abstract interpretation using sized types

We present a novel general resource analysis for logic programs based on sized types. Sized types are representations that incorporate structural (shape) information and allow expressing both lower and upper bounds on the size of a set of terms and their subterms at any position and depth. They also allow relating the sizes of terms and subterms occurring at different argument positions in logic predicates. Using these sized types, the resource analysis can infer both lower and upper bounds on the resources used by all the procedures in a program as functions on input term (and subterm) sizes, overcoming limitations of existing resource analyses and enhancing their precision. Our new resource analysis has been developed within the abstract interpretation framework, as an extension of the sized types abstract domain, and has been integrated into the Ciao preprocessor, CiaoPP. The abstract domain operations are integrated with the setting up and solving of recurrence equations for inferring both size and resource usage functions. We show that the analysis is an improvement over the previous resource analysis present in CiaoPP and compares well in power to state of the art systems.