Rigidity of abnormal extrema in the problem of non-linear programming with mixed constraints

We study abnormal extremum in the problem of non-linear pro- gramming with mixed constraints. Abnormal extremum occurs when in necessary optimality conditions the Lagrange multiplier, which cor- responds to the objective function, vanishes. We demonstrate that in this case abnormal second-order su±cient optimality conditions guar- antee rigidity of the corresponding extremal point, which means iso- latedness of this point in the set determined by the constraints

Graduate School: Course Decriptions, 1972-73

Official publication of Cornell University V.64 1972/7

Neurogeometry of reaching

The purpose of the thesis is to develop a model for the functional behaviour of neurons in the primary motor cortex (M1) responsible for arm reaching movements. From Georgopoulos neurophysiological data, we provide a first bundle structure compatible with the hypercolumnar organization and with the position-direction selectivity of motor cortical cells. We then extend this model to encode the direction of arm movement which varies in time, as experimentally measured by Hatsopoulos by introducing the notion of movement fragments. We provide a sub-Riemannian model which describes the time-dependent directional selectivity of cells though integral curves of the geometric structure we set up. The sub-Riemannian distance we define allows to implement a grouping algorithm able to detect a set of hand motor trajectories. These paths, identified by using a kernel defined in terms of kinematic variables, are compatible with the motor primitives obtained from neurophysiological results by spectral analysis applied directly on cortical variables. In a second part of the work, we propose geodesics in this space as an alternative model of models for arm movement trajectories. We define a special class of curves, called admissible, on which to study the geodesics problem: we provide a connectivity property in terms of admissible paths and the existence of normal length minimizers. Admissible geodesics are used as a model of reaching paths, finding a first validation through Flash and Hogan minimizing trajectories

On the Use of Continuous Wavelet Transforms to Analyse Accelerometer Data Collected by the NAT Device to Characterise Parkinson's Disease

Parkinson’s disease (PD) is treated using drugs with powerful side-effects, and has similar symptoms to a range of other diseases. It is therefore important to diagnose PD accurately, and then to monitor its progression, to avoid mis-prescribing and under- and over-prescription of these drugs. Although diagnosis by experts in PD is fairly accurate, there is certainly room for improvement, and most initial diagnoses are carried out by non-expert medical staff with a much lower degree of accuracy. It is therefore desirable that automatic methods of diagnosis and monitoring be developed, and this Thesis examines the use of wavelets like those used in the Continuous Wavelet Transform (CWT), using wavelets extracted from the data itself, to try and detect features in the data pertaining to PD patients and controls. We believe that we have successfully automatically detected distinct features, with the proviso that this has been done with very little data, opening up the possibility of tracking the development of the disease as different characteristics alter in importance, or of distinguishing subtypes of PD (analyses of the genome have determined that such subtypes exist). However, the CWTs generated by wavelets corresponding to individual features, do not suffice as a basis for diagnosis, as the features may only be intermittently present. In combination, either with other wavelets of the same type, or other methods entirely, diagnosis remains a possibility. We used Neural Acquisition Tracker (NAT) devices to obtain tri-axial accelerometer data as input to these methods, and will analyse the effect of finite bandwidth on their performance. We believe the following list sums up the main novelty of our techniques: Libraries of motion shapes: at least within the field of the analysis of the motion of PD subjects; Representing motion shapes: by equivalence classes of piecewise polynomial wavelet triplets, which are invariant under rotations and reflections; Distance functions: working out the form of a distance based on the L_2 distance between individual functions, but which works on the equivalence classes mentioned above; hierarchical k-medoids: an approximation to k-medoids, using the clustering of cluster centres, which runs faster than k-medoids

Artificial Intelligence and Cognitive Computing

Artificial intelligence (AI) is a subject garnering increasing attention in both academia and the industry today. The understanding is that AI-enhanced methods and techniques create a variety of opportunities related to improving basic and advanced business functions, including production processes, logistics, financial management and others. As this collection demonstrates, AI-enhanced tools and methods tend to offer more precise results in the fields of engineering, financial accounting, tourism, air-pollution management and many more. The objective of this collection is to bring these topics together to offer the reader a useful primer on how AI-enhanced tools and applications can be of use in today’s world. In the context of the frequently fearful, skeptical and emotion-laden debates on AI and its value added, this volume promotes a positive perspective on AI and its impact on society. AI is a part of a broader ecosystem of sophisticated tools, techniques and technologies, and therefore, it is not immune to developments in that ecosystem. It is thus imperative that inter- and multidisciplinary research on AI and its ecosystem is encouraged. This collection contributes to that

Numerical modelling of the growth and remodelling phenomena in biological tissues

Living biological tissues are complex structures that have the capacity of evolving in response to external loads and environmental stimuli. The adequate modelling of soft biological tissue behaviour is a key issue in successfully reproducing biomechanical problems through computational analysis. This study presents a general constitutive formulation capable of representing the behaviour of these tissues through finite element simulation. It is based on phenomenological models that, used in combination with the generalized mixing theory, can numerically reproduce a wide range of material behaviours. First, the passive behaviour of tissues is characterized by means of hyperelastic and finite-strain damage models. A new generalized damage model is proposed, providing a flexible and versatile formulation that can reproduce a wide range of tissue behaviour. It can be particularized to any hyperelastic model and requires identifying only two material parameters. Then, the use of these constitutive models with generalized mixing theory in a finite-strain framework is described and tools to account for the anisotropic behaviour of tissues are put forth. The active behaviour of tissues is characterized through constitutive models capable of reproducing the growth and remodelling phenomena. These are built on the hyperelastic and damage formulations described above and, thus, represent the active extension of the passive tissue behaviour. A growth model considering biological availability is used and extended to include directional growth. In addition, a novel constitutive model for homeostatic-driven turnover remodelling is presented and discussed. This model captures the stiffness recovery that occurs in healing tissues, understood as a recovery or reversal of damage in the tissue, which is driven by both mechanical and biochemical stimuli. Finally, the issue of correctly identifying the material parameters for computational modelling is addressed. An inverse method using optimization techniques is developed to facilitate the identification of these parameters.Els teixits biològics vius són estructures complexes que tenen la capacitat d'evolucionar en resposta a càrregues externes i estímuls ambientals. El modelat adequat del comportament del teixit biològic tou és un tema clau per poder reproduir amb èxit problemes biomecànics mitjançant anàlisi computacional. Aquest estudi presenta una formulació constitutiva general capaç de representar el comportament d'aquests teixits mitjançant la simulació amb elements finits. Es basa en models fenomenològics que, usats en combinació amb la teoria de mescles generalitzada, permeten reproduir numèricament un ampli ventall de comportaments materials. Primer, el comportament passiu dels teixits es caracteritza amb models hiperelàstics i de dany en grans deformacions. Es proposa un model generalitzat de dany que proporciona una formulació versàtil i flexible per poder reproduir una extensa gamma de conductes de teixits. Pot ser particularitzat amb qualsevol model hiperelàstic i requereix identificar tan sols dos paràmetres materials. Llavors, es descriu l'ús d'aquests models constitutius en conjunt amb la teoria generalitzada de mescles, desenvolupada en el marc de grans deformacions, i es presenten eines que permeten incorporar les propietats anisòtropes dels teixits. El comportament actiu dels teixits es caracteritza mitjançant models constitutius capaços de reproduir els fenòmens de creixement i remodelació. Aquests es construeixen sobre les formulacions d'hiperelasticitat i dany descrites anteriorment i, per tant, suposen l'extensió activa del comportament passiu del teixit. Es fa servir un model de creixement que té en compte la disponibilitat biològica de l'organisme, que després s'amplia per incloure dany direccional en el model. També es presenta i analitza un nou model constitutiu per al remodelat per renovació tendint a l’homeòstasi (homeostatic-driven turnover remodelling). Aquest model captura la recuperació de rigidesa que s'observa en teixits que es guareixen. Aquí, el remodelat s'entén com la recuperació o inversió del dany en el teixit i és motivat tant per estímuls mecànics com bioquímics. Finalment, s'aborda el tema de la identificació correcta dels paràmetres materials per al modelat computacional. Es desenvolupa un mètode invers que fa ús de tècniques d'optimització per facilitar la identificació d'aquests paràmetre