Abstract The traditional methods of analysing heart rate variability based on means and variance are unable to detect subtle but potentially important changes in interbeat heart rate behaviour. This research was designed to evaluate the clinical applicability and prognostic significance of new dynamical methods of analysing heart rate behaviour derived from nonlinear mathematics. The study covered four different patient populations, their controls and one general population of elderly people. The first patient group consisted of 38 patients with coronary artery disease without previous myocardial infarction, the second of 40 coronary artery disease patients with a prior Q-wave myocardial infarction, and the third of 45 patients with a history of ventricular tachyarrhythmia. The fourth group comprised 10 patients with a previous myocardial infarction who had experienced ventricular fibrillation during electrocardiographic recordings. The fifth group comprised a random sample of 347 community-living elderly people invited for a follow-up of 10 years after electrocardiographic recordings. Heart rate variability was analysed by traditional time and frequency domain methods. The new dynamical measures derived from nonlinear dynamics were: 1) approximate entropy, which reflects the complexity of the data, 2) detrended fluctuation analysis, which describes the presence or absence of fractal correlation properties of time series data, and 3) power-law relationship analysis, which demonstrates the distribution of spectral characteristics of RR intervals, but does not reflect the magnitude of spectral power in different spectral bands. Approximate entropy was higher in postinfarction patients (1.17 ± 0.22), but lower in coronary artery disease patients without myocardial infarction (0.93 ± 0.17) than in healthy controls (1.03 ± 014, p < 0.01, p < 0.05 respectively). It did not differ between patients with and without ventricular arrhythmia. The short term fractal-like scaling exponent of the detrended fluctuation analysis was higher in coronary artery disease patients without myocardial infarction (1.34 ± 0.15, p < 0.001), but not in postinfarction patients without arrhythmia (1.06 ± 0.13) compared with healthy controls (1.09 ± 0.13). The short term exponent was markedly reduced in patients with life-threatening arrhythmia (0.85 ± 0.25 ventricular tachycardia patients, 0.68 ± 0.18 ventricular fibrillation patients, p < 0.001 for both). The long term power-law slope of the power-law scaling analysis was lower in the ventricular fibrillation group than in postinfarction controls without arrhythmia risk (-1.63 ± 0.24 vs. -1.33 ± 0.23, p < 0.01) and predicted mortality in a general elderly population with an adjusted relative risk of 1.74 (95% CI 1.42–2.13). The present observations demonstrate that dynamic analysis of heart rate behaviour gives new insight into analysis of heart rate dynamics in various cardiovascular disorders. The breakdown of the normal fractal-like organising principle of heart rate variability is associated with an increased risk of mortality and vulnerability to life-threatening arrhythmias.

This thesis presents the results of a study of the effect of variations of systemic parameters on the structural response of single degree of freedom systems subjected to Incremental Dynamic Analysis. The systemic parameters are mass, stiffness, damping, yield strength and geometric stiffness. Each of these parameters was varied one at a time while the other values were kept constant. For each variation of parameters a set of single-record IDA curves was obtained. Five to six ground motions were used for this study to generate the single-record IDA curves. These ground motions were scaled prior to their application on the structure. The scaling factor was based on the spectral acceleration at the fundamental frequency of the structure at 5% of critical damping. The scale factor is affected if the system parameters are changed. An important issue for this study was whether to persist with scaling corresponding to the median value from the range of the values of the parameter or to update the scaling according to the system. Based on some tests using both methods, the median scaling approach was found to be more suitable. The IDA curves for variation of parameters were then investigated to identify any trends that may help in qualitatively predicting the response of a system relative to another system. The response was measured by the peak displacement and the maximum base shear of the system. A clear trend was identified when the damping or the yield strength was varied. However, no definite trend was observed when the material stiffness or the geometric stiffness of the system was varied. / Master of Science

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Vehicle classification data especially trucks has an important role in both pavement maintenance and highway planning strategy. An advanced microelectromechanical system (MEMS) accelerometer for vehicle classification based on axle count and spacing was designed, tested, and applied to the pavement. Vehicle-pavement interaction was collected by the vibration sensor while vehicle axle count and spacing were calibrated later. Collected vibration data also used to analyze the pavement surface condition and compared with simulation using dynamic loading analysis. Laboratory tests using MMLS3 device to verify the accuracy of MEMS accelerometer and reaction under different surface condition were tested. An algorithm for calculating axle spacing and axle count was developed. Acceleration of different pavement surface condition were analyzed and compared with simulation results, the influence of surface condition to the pavement acceleration was concluded. / Master of Science

Η παρούσα εργασία μελετά αναλυτικά – αριθμητικά υπό συνθήκες επίπεδης παραμόρφωσης τη δυναμική απόκριση οδοστρώματος επί εδάφους δύο στρώσεων σε κινούμενα με σταθερή ταχύτητα φορτία. Η ανώτερη στρώση αποτελείται από ασφαλτικό σκυρόδεμα, η μεσαία στρώση από ποροελαστκό υλικό χωρίς νερό στους πόρους και το κατώτερο στρώμα με ποροελαστικό πλήρως κορεσμένο υλικό. Το όλο σύστημα υποστηρίζεται από απαραμόρφωτο βραχώδες υλικό. Στο σύστημα οδοστρώματος – εδάφους χρησιμοποιήθηκε η θεωρία του Biot με την τροποποίηση των Mei and Foda για το μεσαίο και το κατώτερο στρώμα και η θεωρία ιξωδοελαστικότητας των Sousa and Monismith για το ασφαλτικό σκυρόδεμα. Το φορτίο καθώς και η απόκριση προσομοιώνονται με σειρές Fourier. Έτσι οι εξισώσεις για κάθε στρώση καταλήγουν σε συνήθεις διαφορικές που επιλύονται αναλυτικά. Για τις συνοριακές συνθήκες του προβλήματος ισχύει η ισορροπία των ενεργών τάσεων και πιέσεων και η συνέχεια των μετακινήσεων και έτσι δημιουργείται ένα σύστημα 14 εξισώσεων με 14 αγνώστους. Η λύση του συστήματος δίνει τα διαγράμματα των τάσεων, των παραμορφώσεων και της πίεσης του νερού των πόρων σε οποιοδήποτε σημείο του εδαφικού όγκου, κάθε χρονική στιγμή. Τα αποτελέσματα παρουσιάζονται γραφικά και συγκρίνονται για διάφορες τιμές των παραμέτρων με αντίστοιχα άλλων εργασιών. Η παρούσα μέθοδος περιγράφει επαρκώς τόσοτην απόκριση ενός μέσου τριών στρώσεων που υπόκεινται σε κινούμενη φόρτιση, όσο και την εξάρτηση των παραμέτρων αυτών μεταξύ τους. / -

The purpose of this project is to create a theoretical dynamic analysis model to assess the dynamic response of light, wood-framed structures before and after fire conditions. This information is useful for predicting the damage to structural integrity due to a fire. The mass and stiffness matrices used for the dynamic model are derived from a standard residential building created for an existing project at WPI funded through the DHS/FEMA/USFA Assistance to Firefighters Grant program. The damping matrix is derived via the Rayleigh Damping Method using the mass and stiffness matrices obtained through SAP. Then, theoretical impact forces are applied to the developed dynamic model, and the acceleration response is estimated using Matlab. Both acceleration time history and frequency responses are used as the evaluation method. Finally, the dynamic model is integrated with a fire simulation model to investigate the impact of fire conditions on dynamic responses of residential buildings. The results show that frequencies can shift due to the structural degradation due to fire.

The application of composite action ushered a new era in the use of double-layer spaceframes as efficient floor systems in addition to their competitiveness as roof coveringstructural systems. Earlier research on space frames demonstrated large improvementsin their static behaviour caused by the introduction of composite action. Theseimprovements included an increase in ductility to avoid progressive collapse, a largeincrease in load-carrying capacity and a considerable reduction in materialconsumption.In this work, the effect of introducing composite action in changing the dynamiccharacteristics of space frames, in particular the natural frequencies and damping ratioswas presented. The study was expanded to determine the effect of composite action inchanging the response to dynamic excitations. The measured responses included thelateral displacements and changes in the internal member force distribution undershaking table vibrations.Three aluminium space frame models of the square on square (SOS) configuration weremanufactured. The first model was non-composite, while composite action was appliedto the other two models with a top aluminium deck and a timber deck, respectively.Two common cases of support conditions were used in connecting the models to theloading frame, which was the platform of the shaking table.Initial displacement method (snap test) was used to determine the frequency of vibrationand the damping ratio of test models in the vertical and horizontal directions usinglogarithmic decrement method. All models were then exposed to shaking tablevibrations to determine the changes in dynamic responses between different models.These tests were repeated for the three models after the successive removal of panelsfrom one direction to identify the changes to their characteristics and behaviour withdifferent aspect ratios.The second part of the study was carried out numerically by using the finite elementpackage ABAQUS. It started by selecting a valid finite element model from nineproposed models using experimental test results on physical structures. A parametricstudy was conducted using the validated finite element model to expand the study toinclude two common space frame configurations; the square on large square (SOLS)and square on diagonal (SOD), and two other cases of support configurations, namely,fully edge-supported and supports at corners and middle edges of models.Based on the work done in this study, it can be concluded that composite actionchanged the dynamic characteristics of space frames, which was clear in the increase oftheir vibration frequencies in all directions as a result of the increase in stiffness.Furthermore, the increase in stiffness resulted in a general reduction in the dampingratio of space frames covered with aluminium deck, while the high friction with topjoints and the nature of timber as a good energy absorbent material resulted in a variableeffect on the damping ratio associated with the increase in aspect ratio.The effect of composite action was clear in reducing the lateral displacement ofcomposite models by more than 50% compared to the non-composite case. Moreover,composite action resulted in changing the distribution of internal forces in diagonal andlower chord members such that forces became more concentrated at corners and edgesparallel to the direction of vibrations in both cases of corner and edge-supportedmodels.

Despite the immense progress made by molecular biology in cataloging andcharacterizing molecular elements of life and the success in genome sequencing, therehave not been comparable advances in the functional study of complex phenotypes.This is because isolated study of one molecule, or one gene, at a time is not enough byitself to characterize the complex interactions in organism and to explain the functionsthat arise out of these interactions. Mathematical modeling of biological systems isone way to meet the challenge.My research formulates the modeling of gene regulation as a control problem andapplies systems and control theory to the identification, analysis, and optimal controlof genetic regulatory networks. The major contribution of my work includes biologicallyconstrained estimation, dynamical analysis, and optimal control of genetic networks.In addition, parameter estimation of nonlinear models of biological networksis also studied, as a parameter estimation problem of a general nonlinear dynamicalsystem. Results demonstrate the superior predictive power of biologically constrainedstate-space models, and that genetic networks can have differential dynamic propertieswhen subjected to different environmental perturbations. Application of optimalcontrol demonstrates feasibility of regulating gene expression levels. In the difficultproblem of parameter estimation, generalized EM algorithm is deployed, and a set of explicit formula based on extended Kalman filter is derived. Application of themethod to synthetic and real world data shows promising results.

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