Path formulation for Z(2) circle plus Z(2)-equivariant bifurcation problems

M. Manoel and I. Stewart 0101) classify Z(2) circle plus Z(2)-equivariant bifurcation problems up to codimension 3 and 1 modal parameter, using the classical techniques of singularity theory of Golubistky and Schaeffer [8]. In this paper we classify these same problems using an alternative form: the path formulation (Theorem 6.1). One of the advantages of this method is that the calculates to obtain the normal forms are easier. Furthermore, in our classification we observe the presence of only one modal parameter in the generic core. It differs from the classical classification where the core has 2 modal parameters. We finish this work comparing our classification to the one obtained in [10].

Sobre o teorema de fibração de Milnor

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Rotações no espaço tridimensional por meio de produtos quaterniônicos

Pós-graduação em Matemática Universitária - IGCE

Decompositions of powers of quadratic forms

We analyze the Waring decompositions of the powers of any quadratic form over the field of complex numbers. Our main objective is to provide detailed information about their rank and border rank. These forms are of significant importance because of the classical decomposition expressing the space of polynomials of a fixed degree as a direct sum of the spaces of harmonic polynomials multiplied by a power of the quadratic form. Using the fact that the spaces of harmonic polynomials are irreducible representations of the special orthogonal group over the field of complex numbers, we show that the apolar ideal of the s-th power of a non-degenerate quadratic form in n variables is generated by the set of harmonic polynomials of degree s+1. We also generalize and improve upon some of the results about real decompositions, provided by B. Reznick in his notes from 1992, focusing on possibly minimal decompositions and providing new ones, both real and complex. We investigate the rank of the second power of a non-degenerate quadratic form in n variables, which is equal to (n^2+n+2)/2 in most cases. We also study the border rank of any power of an arbitrary ternary non-degenerate quadratic form, which we determine explicitly using techniques of apolarity and a specific subscheme contained in its apolar ideal. Based on results about smoothability, we prove that the smoothable rank of the s-th power of such form corresponds exactly to its border rank and to the rank of its middle catalecticant matrix, which is equal to (s+1)(s+2)/2.

Employment of Real-Time/FPGA Architectures for Test and Control of Automotive Engines

Nowadays the production of increasingly complex and electrified vehicles requires the implementation of new control and monitoring systems. This reason, together with the tendency of moving rapidly from the test bench to the vehicle, leads to a landscape that requires the development of embedded hardware and software to face the application effectively and efficiently. The development of application-based software on real-time/FPGA hardware could be a good answer for these challenges: FPGA grants parallel low-level and high-speed calculation/timing, while the Real-Time processor can handle high-level calculation layers, logging and communication functions with determinism. Thanks to the software flexibility and small dimensions, these architectures can find a perfect collocation as engine RCP (Rapid Control Prototyping) units and as smart data logger/analyser, both for test bench and on vehicle application. Efforts have been done for building a base architecture with common functionalities capable of easily hosting application-specific control code. Several case studies originating in this scenario will be shown; dedicated solutions for protype applications have been developed exploiting a real-time/FPGA architecture as ECU (Engine Control Unit) and custom RCP functionalities, such as water injection and testing hydraulic brake control.

Real-time hand tracking for rehabilitation and character animation

Hand and finger tracking has a major importance in healthcare, for rehabilitation of hand function required due to a neurological disorder, and in virtual environment applications, like characters animation for on-line games or movies. Current solutions consist mostly of motion tracking gloves with embedded resistive bend sensors that most often suffer from signal drift, sensor saturation, sensor displacement and complex calibration procedures. More advanced solutions provide better tracking stability, but at the expense of a higher cost. The proposed solution aims to provide the required precision, stability and feasibility through the combination of eleven inertial measurements units (IMUs). Each unit captures the spatial orientation of the attached body. To fully capture the hand movement, each finger encompasses two units (at the proximal and distal phalanges), plus one unit at the back of the hand. The proposed glove was validated in two distinct steps: a) evaluation of the sensors’ accuracy and stability over time; b) evaluation of the bending trajectories during usual finger flexion tasks based on the intra-class correlation coefficient (ICC). Results revealed that the glove was sensitive mainly to magnetic field distortions and sensors tuning. The inclusion of a hard and soft iron correction algorithm and accelerometer and gyro drift and temperature compensation methods provided increased stability and precision. Finger trajectories evaluation yielded high ICC values with an overall reliability within application’s satisfying limits. The developed low cost system provides a straightforward calibration and usability, qualifying the device for hand and finger tracking in healthcare and animation industries.

Discretization of complex-order algorithms for control applications

In this article we describe several methods for the discretization of the differintegral operator sa, where α = u + jv is a complex value. The concept of the conjugated-order differintegral is also introduced, which enables the use of complex-order differintegrals while still producing real-valued time responses and transfer functions. The performance of the resulting approximations is analysed in both the time and frequency domains. Several results are presented that demonstrate its utility in control system design.

Calibration of CES functions for real-world multisectoral modeling

We show how to calibrate CES production and utility functions when indirect taxation affecting inputs and consumption is present. These calibrated functions can then be used in computable general equilibrium models. Taxation modifies the standard calibration procedures since any taxed good has two associated prices and a choice of reference value units has to be made. We also provide an example of computer code to solve the calibration of CES utilities under two alternate normalizations. To our knowledge, this paper fills a methodological gap in the CGE literature.

Modulation of the Endocannabinoids N-Arachidonoylethanolamine (AEA) and 2-Arachidonoylglycerol (2-AG) on Executive Functions in Humans.

Animal studies point to an implication of the endocannabinoid system on executive functions. In humans, several studies have suggested an association between acute or chronic use of exogenous cannabinoids (Δ9-tetrahydrocannabinol) and executive impairments. However, to date, no published reports establish the relationship between endocannabinoids, as biomarkers of the cannabinoid neurotransmission system, and executive functioning in humans. The aim of the present study was to explore the association between circulating levels of plasma endocannabinoids N-arachidonoylethanolamine (AEA) and 2-Arachidonoylglycerol (2-AG) and executive functions (decision making, response inhibition and cognitive flexibility) in healthy subjects. One hundred and fifty seven subjects were included and assessed with the Wisconsin Card Sorting Test; Stroop Color and Word Test; and Iowa Gambling Task. All participants were female, aged between 18 and 60 years and spoke Spanish as their first language. Results showed a negative correlation between 2-AG and cognitive flexibility performance (r = -.37; p<.05). A positive correlation was found between AEA concentrations and both cognitive flexibility (r = .59; p<.05) and decision making performance (r = .23; P<.05). There was no significant correlation between either 2-AG (r = -.17) or AEA (r = -.08) concentrations and inhibition response. These results show, in humans, a relevant modulation of the endocannabinoid system on prefrontal-dependent cognitive functioning. The present study might have significant implications for the underlying executive alterations described in some psychiatric disorders currently associated with endocannabinoids deregulation (namely drug abuse/dependence, depression, obesity and eating disorders). Understanding the neurobiology of their dysexecutive profile might certainly contribute to the development of new treatments and pharmacological approaches.

Visual functions in the healthy and schizophrenic brain : from stimulus control to illusory perceptions using electrical neuroimaging

ABSTRACT (FRENCH)Ce travail de thèse basé sur le système visuel chez les sujets sains et chez les patients schizophrènes, s'articule autour de trois articles scientifiques publiés ou en cours de publication. Ces articles traitent des sujets suivants : le premier article présente une nouvelle méthode de traitement des composantes physiques des stimuli (luminance et fréquence spatiale). Le second article montre, à l'aide d'analyses de données EEG, un déficit de la voie magnocellulaire dans le traitement visuel des illusions chez les patients schizophrènes. Ceci est démontré par l'absence de modulation de la composante PI chez les patients schizophrènes contrairement aux sujets sains. Cette absence est induite par des stimuli de type illusion Kanizsa de différentes excentricités. Finalement, le troisième article, également à l'aide de méthodes de neuroimagerie électrique (EEG), montre que le traitement des contours illusoires se trouve dans le complexe latéro-occipital (LOC), à l'aide d'illusion « misaligned gratings ». De plus il révèle que les activités démontrées précédemment dans les aires visuelles primaires sont dues à des inférences « top- down ».Afin de permettre la compréhension de ces trois articles, l'introduction de ce manuscrit présente les concepts essentiels. De plus des méthodes d'analyses de temps-fréquence sont présentées. L'introduction est divisée en quatre parties : la première présente le système visuel depuis les cellules retino-corticales aux deux voix du traitement de l'information en passant par les régions composant le système visuel. La deuxième partie présente la schizophrénie par son diagnostic, ces déficits de bas niveau de traitement des stimuli visuel et ces déficits cognitifs. La troisième partie présente le traitement des contours illusoires et les trois modèles utilisés dans le dernier article. Finalement, les méthodes de traitement des données EEG seront explicitées, y compris les méthodes de temps-fréquences.Les résultats des trois articles sont présentés dans le chapitre éponyme (du même nom). De plus ce chapitre comprendra les résultats obtenus à l'aide des méthodes de temps-fréquenceFinalement, la discussion sera orientée selon trois axes : les méthodes de temps-fréquence ainsi qu'une proposition de traitement de ces données par une méthode statistique indépendante de la référence. La discussion du premier article en montrera la qualité du traitement de ces stimuli. La discussion des deux articles neurophysiologiques, proposera de nouvelles d'expériences afin d'affiner les résultats actuels sur les déficits des schizophrènes. Ceci pourrait permettre d'établir un marqueur biologique fiable de la schizophrénie.ABSTRACT (ENGLISH)This thesis focuses on the visual system in healthy subjects and schizophrenic patients. To address this research, advanced methods of analysis of electroencephalographic (EEG) data were used and developed. This manuscript is comprised of three scientific articles. The first article showed a novel method to control the physical features of visual stimuli (luminance and spatial frequencies). The second article showed, using electrical neuroimaging of EEG, a deficit in spatial processing associated with the dorsal pathway in chronic schizophrenic patients. This deficit was elicited by an absent modulation of the PI component in terms of response strength and topography as well as source estimations. This deficit was orthogonal to the preserved ability to process Kanizsa-type illusory contours. Finally, the third article resolved ongoing debates concerning the neural mechanism mediating illusory contour sensitivity by using electrical neuroimaging to show that the first differentiation of illusory contour presence vs. absence is localized within the lateral occipital complex. This effect was subsequent to modulations due to the orientation of misaligned grating stimuli. Collectively, these results support a model where effects in V1/V2 are mediated by "top-down" modulation from the LOC.To understand these three articles, the Introduction of this thesis presents the major concepts used in these articles. Additionally, a section is devoted to time-frequency analysis methods not presented in the articles themselves. The introduction is divided in four parts. The first part presents three aspects of the visual system: cellular, regional, and its functional interactions. The second part presents an overview of schizophrenia and its sensoiy-cognitive deficits. The third part presents an overview of illusory contour processing and the three models examined in the third article. Finally, advanced analysis methods for EEG are presented, including time- frequency methodology.The Introduction is followed by a synopsis of the main results in the articles as well as those obtained from the time-frequency analyses.Finally, the Discussion chapter is divided along three axes. The first axis discusses the time frequency analysis and proposes a novel statistical approach that is independent of the reference. The second axis contextualizes the first article and discusses the quality of the stimulus control and direction for further improvements. Finally, both neurophysiologic articles are contextualized by proposing future experiments and hypotheses that may serve to improve our understanding of schizophrenia on the one hand and visual functions more generally.

Mammalian target of rapamycin complex 1 orchestrates invariant NKT cell differentiation and effector function.

Invariant NKT (iNKT) cells play critical roles in bridging innate and adaptive immunity. The Raptor containing mTOR complex 1 (mTORC1) has been well documented to control peripheral CD4 or CD8 T cell effector or memory differentiation. However, the role of mTORC1 in iNKT cell development and function remains largely unknown. By using mice with T cell-restricted deletion of Raptor, we show that mTORC1 is selectively required for iNKT but not for conventional T cell development. Indeed, Raptor-deficient iNKT cells are mostly blocked at thymic stage 1-2, resulting in a dramatic decrease of terminal differentiation into stage 3 and severe reduction of peripheral iNKT cells. Moreover, residual iNKT cells in Raptor knockout mice are impaired in their rapid cytokine production upon αGalcer challenge. Bone marrow chimera studies demonstrate that mTORC1 controls iNKT differentiation in a cell-intrinsic manner. Collectively, our data provide the genetic evidence that iNKT cell development and effector functions are under the control of mTORC1 signaling.

Quasiconformal mappings and inequalities involving special functions

This PhD thesis in Mathematics belongs to the field of Geometric Function Theory. The thesis consists of four original papers. The topic studied deals with quasiconformal mappings and their distortion theory in Euclidean n-dimensional spaces. This theory has its roots in the pioneering papers of F. W. Gehring and J. Väisälä published in the early 1960’s and it has been studied by many mathematicians thereafter. In the first paper we refine the known bounds for the so-called Mori constant and also estimate the distortion in the hyperbolic metric. The second paper deals with radial functions which are simple examples of quasiconformal mappings. These radial functions lead us to the study of the so-called p-angular distance which has been studied recently e.g. by L. Maligranda and S. Dragomir. In the third paper we study a class of functions of a real variable studied by P. Lindqvist in an influential paper. This leads one to study parametrized analogues of classical trigonometric and hyperbolic functions which for the parameter value p = 2 coincide with the classical functions. Gaussian hypergeometric functions have an important role in the study of these special functions. Several new inequalities and identities involving p-analogues of these functions are also given. In the fourth paper we study the generalized complete elliptic integrals, modular functions and some related functions. We find the upper and lower bounds of these functions, and those bounds are given in a simple form. This theory has a long history which goes back two centuries and includes names such as A. M. Legendre, C. Jacobi, C. F. Gauss. Modular functions also occur in the study of quasiconformal mappings. Conformal invariants, such as the modulus of a curve family, are often applied in quasiconformal mapping theory. The invariants can be sometimes expressed in terms of special conformal mappings. This fact explains why special functions often occur in this theory.

Large-eddy simulation of wind flows over complex terrains for wind energy applications

Wind energy has obtained outstanding expectations due to risks of global warming and nuclear energy production plant accidents. Nowadays, wind farms are often constructed in areas of complex terrain. A potential wind farm location must have the site thoroughly surveyed and the wind climatology analyzed before installing any hardware. Therefore, modeling of Atmospheric Boundary Layer (ABL) flows over complex terrains containing, e.g. hills, forest, and lakes is of great interest in wind energy applications, as it can help in locating and optimizing the wind farms. Numerical modeling of wind flows using Computational Fluid Dynamics (CFD) has become a popular technique during the last few decades. Due to the inherent flow variability and large-scale unsteadiness typical in ABL flows in general and especially over complex terrains, the flow can be difficult to be predicted accurately enough by using the Reynolds-Averaged Navier-Stokes equations (RANS). Large- Eddy Simulation (LES) resolves the largest and thus most important turbulent eddies and models only the small-scale motions which are more universal than the large eddies and thus easier to model. Therefore, LES is expected to be more suitable for this kind of simulations although it is computationally more expensive than the RANS approach. With the fast development of computers and open-source CFD software during the recent years, the application of LES toward atmospheric flow is becoming increasingly common nowadays. The aim of the work is to simulate atmospheric flows over realistic and complex terrains by means of LES. Evaluation of potential in-land wind park locations will be the main application for these simulations. Development of the LES methodology to simulate the atmospheric flows over realistic terrains is reported in the thesis. The work also aims at validating the LES methodology at a real scale. In the thesis, LES are carried out for flow problems ranging from basic channel flows to real atmospheric flows over one of the most recent real-life complex terrain problems, the Bolund hill. All the simulations reported in the thesis are carried out using a new OpenFOAM® -based LES solver. The solver uses the 4th order time-accurate Runge-Kutta scheme and a fractional step method. Moreover, development of the LES methodology includes special attention to two boundary conditions: the upstream (inflow) and wall boundary conditions. The upstream boundary condition is generated by using the so-called recycling technique, in which the instantaneous flow properties are sampled on aplane downstream of the inlet and mapped back to the inlet at each time step. This technique develops the upstream boundary-layer flow together with the inflow turbulence without using any precursor simulation and thus within a single computational domain. The roughness of the terrain surface is modeled by implementing a new wall function into OpenFOAM® during the thesis work. Both, the recycling method and the newly implemented wall function, are validated for the channel flows at relatively high Reynolds number before applying them to the atmospheric flow applications. After validating the LES model over simple flows, the simulations are carried out for atmospheric boundary-layer flows over two types of hills: first, two-dimensional wind-tunnel hill profiles and second, the Bolund hill located in Roskilde Fjord, Denmark. For the twodimensional wind-tunnel hills, the study focuses on the overall flow behavior as a function of the hill slope. Moreover, the simulations are repeated using another wall function suitable for smooth surfaces, which already existed in OpenFOAM® , in order to study the sensitivity of the flow to the surface roughness in ABL flows. The simulated results obtained using the two wall functions are compared against the wind-tunnel measurements. It is shown that LES using the implemented wall function produces overall satisfactory results on the turbulent flow over the two-dimensional hills. The prediction of the flow separation and reattachment-length for the steeper hill is closer to the measurements than the other numerical studies reported in the past for the same hill geometry. The field measurement campaign performed over the Bolund hill provides the most recent field-experiment dataset for the mean flow and the turbulence properties. A number of research groups have simulated the wind flows over the Bolund hill. Due to the challenging features of the hill such as the almost vertical hill slope, it is considered as an ideal experimental test case for validating micro-scale CFD models for wind energy applications. In this work, the simulated results obtained for two wind directions are compared against the field measurements. It is shown that the present LES can reproduce the complex turbulent wind flow structures over a complicated terrain such as the Bolund hill. Especially, the present LES results show the best prediction of the turbulent kinetic energy with an average error of 24.1%, which is a 43% smaller than any other model results reported in the past for the Bolund case. Finally, the validated LES methodology is demonstrated to simulate the wind flow over the existing Muukko wind farm located in South-Eastern Finland. The simulation is carried out only for one wind direction and the results on the instantaneous and time-averaged wind speeds are briefly reported. The demonstration case is followed by discussions on the practical aspects of LES for the wind resource assessment over a realistic inland wind farm.

Individual differences in risk-taking and associated characteristics : a test of specificity in executive functions /

Multiple measures have been devised by clinicians and theorists from many different backgrounds for the purpose of assessing the influence of the frontal lobes on behaviour. Some utilize self-report measures to investigate behavioural characteristics such as risktaking, sensation seeking, impulsivity, and sensitivity to reward and punishment in an attempt to understand complex human decision making. Others rely more on neuroimaging and electrophysiological investigation involving experimental tasks thought to demonstrate executive functions in action, while other researchers prefer to study clinical populations with selective damage. Neuropsychological models of frontal lobe functioning have led to a greater appreciation of the dissociations among various aspects of prefrontal cortex function. This thesis involves (1) an examination of various psychometric and experimental indices of executive functions for coherence as one would predict on the basis of highly developed neurophysiological models of prefrontal function, particularly those aspects of executive function that involve predominantly cognitive abilities versus processes characterized by affect regulation; and (2) investigation of the relations between risk-taking, attentional abilties and their associated characteristics using a neurophysiological model of prefrontal functions addressed in (1). Late adolescence is a stage in which the prefrontal cortices undergo intensive structural and functional maturational changes; this period also involves increases in levels of risky and sensation driven behaviours, as well as a hypersensitivity to reward and a reduction in inhibition. Consequently, late adolescence spears to represent an ideal developmental period in which to examine these decision-making behaviours due to the maximum variability of behavioural characteristics of interest. Participants were 45 male undergraduate 18- to 19-year olds, who completed a battery of measures that included self-report, experimental and behavioural measures designed to assess particular aspects of prefrontal and executive functioning. As predicted, factor analysis supported the grouping of executive process by type (either primarily cognitive or affective), conforming to the orbitofrontal versus dorsolateral typology; risk-taking and associated characteristics were associated more with the orbitofrontal than the dorsolateral factor, whereas attentional and planning abilities tended to correlate more strongly with the dorsolateral factor. Results are discussed in light of future assessment, investigation and understanding of complex human decision-making and executive functions. Implications, applications and suggestions for future research are also proposed.

Annual CREMRU-JCI survey of corporate real estate practices in Europe and North America: 1993-2002

The annual survey of corporate real estate practices has been conducted by CREMRU since 1993 and in collaboration with Johnsons Controls Inc. since 1997. This year the survey forms the first stage of a broader research project: International Survey of Corporate Real Estate Practices: longitudinal study 1993-2002, being undertaken for the Innovative Construction Research Centre at the University of Reading, funded by the Engineering and Physical Sciences Research Council. The survey has been endorsed by CoreNet, the leading professional association concerned with corporate real estate, which opened it to a wider audience. This summary of the ten annual surveys focuses on the incidence of corporate real estate management (CREM) policies, functions and activities, as well as the assessment of knowledge or skills relevant to the CREM function in the future. Both are of vital interest to educational institutions concerned with this field, as well as the personnel and training functions within organisations concerned with better management of their property.