Achieving an understanding of the nature of monogenetic volcanic fields depends on identification of the spatial and temporal patterns of volcanism in these fields, and their relationships to structures mapped in the shallow crust and inferred in the deep crust and mantle through interpretation of geochemical, radiometric and geophysical data. We investigate the spatial and temporal distributions of volcanism in the Abu Monogenetic Volcano Group, Southwest Japan. E-W elongated volcano distribution, which is identified by a nonparametric kernel method, is found to be consistent with the spatial extent of P-wave velocity anomalies in the lower crust and upper mantle, supporting the idea that the spatial density map of volcanic vents reflects the geometry of a mantle diapir. Estimated basalt supply to the lower crust is constant. This observation and the spatial distribution of volcanic vents suggest stability of magma productivity and essentially constant two-dimensional size of the source mantle diapir. We mapped conduits, dike segments, and sills in the San Rafael sub-volcanic field, Utah, where the shallowest part of a Pliocene magmatic system is exceptionally well exposed. The distribution of conduits matches the major features of dike distribution, including development of clusters and distribution of outliers. The comparison of San Rafael conduit distribution and the distributions of volcanoes in several recently active volcanic fields supports the use of statistical models, such as nonparametric kernel methods, in probabilistic hazard assessment for distributed volcanism. We developed a new recurrence rate calculation method that uses a Monte Carlo procedure to better reflect and understand the impact of uncertainties of radiometric age determinations on uncertainty of recurrence rate estimates for volcanic activity in the Abu, Yucca Mountain Region, and Izu-Tobu volcanic fields. Results suggest that the recurrence rates of volcanic fields can change by more than one order of magnitude on time scales of several hundred thousand to several million years. This suggests that magma generation rate beneath volcanic fields may change over these time scales. Also, recurrence rate varies more than one order of magnitude between these volcanic fields, consistent with the idea that distributed volcanism may be influenced by both the rate of magma generation and the potential for dike interaction during ascent.

Η στεφανιαία νόσος αποτελεί ένα από τα πιο συχνά αίτια νοσηρότητας και θνητότητας στο γενικό πληθυσμό. Ένα μεγάλο ποσοστό από τους ασθενείς με στεφανιαία νόσο οδηγείται σε αγγειοπλαστική στεφανιαίων αρτηριών (PTCA) με ή χωρίς εμφύτευση stent, όταν η στένωση στο αγγείο είναι ≥ 70-75%. Παρά την πρόοδο στον τομέα της αγγειοπλαστικής, με τη χρήση των drug-eluting stents και την ελάττωση της επαναστένωσης σε ποσοστό <5-10%, το υψηλό ποσοστό (20-25%) επαναστένωσης παραμένει η Αχίλλειος πτέρνα στα συμβατικά, μεταλλικά(bare)stents. Η χρήση των drug-eluting stents περιορίζεται σε περιπτώσεις με επαναστένωση, σε σακχαροδιαβητικούς και σε υψηλού κινδύνου βλάβες για επαναστένωση. Τα μεγάλα ποσοστά όψιμης επαναστένωσης(≥ 9-10%) και το υψηλό κόστος τους, κάνουν ακόμα πιο επιτακτική την ανάγκη εντατικοποίησης της έρευνας προς την κατεύθυνση εντοπισμού παραγόντων σχετιζόμενων με την επαναστένωση. Σκοπός της εργασίας μας ήταν να διερευνήσει τον πιθανό ρόλο πολυμορφισμών γονιδίων στην υποτροπή ισχαιμίας μετά από αγγειοπλαστική στεφανιαίων αρτηριών και εμφύτευση μεταλλικών stents. Συγκεκριμένα, εξετάσθηκε αναλυτικά ο γενετικός πολυμορφισμός των γονιδίων α2Β-αδρενεργικού υποδοχέα και της CETP(πρωτεΐνη μεταφοράς εστέρων χοληστερόλης). Η υπόθεση στηρίχτηκε στο γεγονός ότι σε μια σημαντική μελέτη 912 αρρένων Φινλανδών μέσης ηλικίας, αποδείχτηκε ότι ο D/D γονότυπος σε σχέση με τον I/D γονότυπο και τον I/I γονότυπο, εμφανίζει 2,5 φορές μεγαλύτερο κίνδυνο για οξέα στεφανιαία επεισόδια, συμπεριλαμβανομένου του εμφράγματος μυοκαρδίου. Η εκσεσημασμένη αγγειοσύσπαση, τόσο στην περιφέρεια, όσο και στις στεφανιαίες αρτηρίες μέσω του πολυμορφισμού του γονιδίου α2Β που θεωρείται πιθανό αίτιο για τα οξέα στεφανιαία επεισόδια, μαζί με το σημαντικό ρόλο του α2Β αδρενεργικού υποδοχέα στην υπερπλασία και μετανάστευση των λείων μυϊκών κυττάρων, πιθανόν να έχει μεγάλη συμβολή στη διεργασία της υποτροπής ισχαιμίας. Μελετήσαμε προοπτικά 96 Έλληνες που υπέστησαν επιτυχή PTCA και εμφύτευση stents, εκ των οποίων 81 ήταν άνδρες και 15 γυναίκες(μέση ηλικία ± σταθερά απόκλιση=57,7± 10,1 ετών, με όρια 37-76 ετών) που προσήλθαν με συμπτωματική στεφανιαία νόσο. Όλοι οι παραπάνω ασθενείς συμμετείχαν στη μελέτη μεταξύ των ετών 2001 και 2003 και παρακολουθήθηκαν κλινικά για 6-8 μήνες μετά από μια επιτυχή τεχνική διάνοιξης του αποφραγμένου αγγείου. Αμέσως μετά την PTCA και για ένα(1) μήνα οι ασθενείς έλαβαν ασπιρίνη(100-325mg/day) και κλοπιδογρέλη 75mg/day. Η εκτίμηση της υποτροπής ισχαιμίας βασίστηκε σε στατικό και δυναμικό σπινθηρoγράφημα θαλλίου στους 3 και 6-8 μήνες μετά την PTCA. Αιμοδυναμικά, σε όσους υπέστησαν νέα στεφανιογραφία μέχρι και τους 6-8 μήνες, η επαναστένωση ορίσθηκε ως ≥ 50% στένωση του αυλού του αγγείου στο σημείο όπου έγινε η αγγειοπλαστική. Εκτός από την ομάδα των ασθενών και μια ομάδα υγιών μαρτύρων 83 ατόμων, συμμετείχε στη μελέτη για σύγκριση της συχνότητας του γονότυπου. Το τελικό καταληκτικό σημείο για την παραπάνω μελέτη, ήταν η συχνότητα της υποτροπής ισχαιμίας στους 8 μήνες κλινικής παρακολούθησης. Υποτροπή ισχαιμίας και της επαναστένωσης ≥ 50% σε όσους υπεβλήθησαν σε νέα στεφανιογραφία, συνέβη σε 15 από τους 96 ασθενείς. Ας σημειωθεί ότι οι περισσότεροι ασθενείς (70/96) είχαν το φυσιολογικό γονότυπο με το αλληλόμορφο I, λιγότεροι ασθενείς (23/96) είχαν το Insertion/Deletion και μόλις 3/96 είχαν το Deletion/ Deletion γονότυπο. Από το γονοτυπικό group, υποτροπή ισχαιμίας παρουσιάσθηκε σε 11/70 για τον I/I, 3/23 για τον I/D γονότυπο και 1/3 για τον D/D γονότυπο. Δε βρέθηκε συσχέτιση μεταξύ πολυμορφισμού γονιδίου και υποτροπής ισχαιμίας στους ασθενείς μετά από αγγειοπλαστική στεφανιαίων αρτηριών. Προηγούμενες μελέτες έχουν ερευνήσει τη συσχέτιση των πολυμορφισμών των γονιδίων της ACE, του AT1 υποδοχέα της αγγειοτενσίνης II και της CETP με την επαναστένωση μετά από αγγειοπλαστική. Εντούτοις, καμιά μελέτη δεν πραγματοποιήθηκε που να συγκρίνει τον α2Β-AR πολυμορφισμό και την υποτροπή ισχαιμίας μετά από αγγειοπλαστική στεφανιαίων αρτηριών. Όπως αρχικά αναφέρθηκε, ο γονότυπος α2Β ευνοεί τη μετανάστευση των αγγειακών SMCs, επηρεάζει τη λειτουργία του Α.Ν.Σ. και συσχετίζει το α2Β-AR αλληλόμορφο D deletion με οξέα στεφανιαία επεισόδια. Όλα τα παραπάνω στοιχεία μπορεί να δικαιολογούν το ρόλο του α2Β-AR πολυμορφισμού στην υποτροπή ισχαιμίας και πιθανόν την επαναστένωση μετά από αγγειοπλαστική στεφανιαίων αρτηριών. Βέβαια, η αρνητική συσχέτιση των πολυμορφισμών του α2Β-AR και της CETP ΤaqIB με την υποτροπή ισχαιμίας μετά από αγγειοπλαστική, μπορεί να θεωρηθεί προκαταρκτική, δεδομένου ότι συμμετείχε σχετικά μικρός αριθμός ασθενών συγκριτικά με μεγάλες πληθυσμιακές μελέτες και επειδή ο D/D γονότυπος δεν είναι ιδιαίτερα συχνός(για τη μελέτη των α2Β-AR). Όσον αφορά τη μελέτη με τη CETP, διερευνήσαμε τον πολυμορφισμό ΤaqIB που είναι μια σιωπηρή μετάλλαξη βάσης στο 277 νουκλεοτίδιο της CETP(η οποία μπορεί να αναγνωρισθεί με την περιοριστική ενδονουκλεάση ΤaqI), με την πιθανότητα υποτροπής ισχαιμίας μετά από αγγειοπλαστική στεφανιαίων αρτηριών. Οι όροι Β1 και Β2 αντίστοιχα χρησιμοποιήθηκαν για να δηλώσουν την ύπαρξη ή μη της περιοριστικής περιοχής (site) της ΤaqIB. Το Β2 αλληλόμορφο σχετίζεται με αυξημένα επίπεδα HDL και ελαττωμένα επίπεδα CETP, τόσο σε υγιείς όσο και σε άτομα με στεφανιαία νόσο(μοιάζει με ήπιας μορφής ανεπάρκεια CETP). Αντίθετα το Β1 αλληλόμορφο σχετίζεται με ελαττωμένα επίπεδα HDL και με αυξημένα επίπεδα και δραστηριότητα CETP. Επειδή η ΤaqIB σχετίζεται με χαμηλά επίπεδα HDL και αυξημένο κίνδυνο για CHD(επηρεάζοντας το μεταβολισμό των λιποπρωτεϊνών), μπορεί να συμμετέχει στην παθοφυσιολογία της υποτροπής ισχαιμίας μετά από αγγειοπλαστική. Μελετήσαμε 204 ασθενείς από το έτος 2001 έως και το 2003 με την προοπτική να διερευνηθεί η συσχέτιση ΤaqIB στον Ελλαδικό πληθυσμό με την πιθανότητα υποτροπής ισχαιμίας μετά από αγγειοπλαστική σε άτομα που φέρουν τον παραπάνω γονότυπο. Η συχνότητα της ΤaqIB(54%) ήταν παρόμοια με τη συχνότητα του πολυμορφισμού σε μια ομάδα 35 υγιών μαρτύρων. Το αποτέλεσμα από αυτή τη μελέτη δεν αποδεικνύει ότι ο ΤaqIB πολυμορφισμός στο γονίδιο της CETP είναι σημαντικός προγνωστικός παράγων για εκτίμηση του κινδύνου υποτροπής ισχαιμίας μετά από αγγειοπλαστική στεφανιαίων αρτηριών. Συμπερασματικά, η υποτροπή ισχαιμίας μετά από αγγειοπλαστική στεφανιαίων αρτηριών οφείλεται σε έναν πολύπλοκο μηχανισμό και σε ένα πολυπαραγοντικό φαινόμενο. Μπορεί οι πολυμορφισμοί του α2Β και της CETP, να μην αναδείχθηκαν ως ανεξάρτητοι παράγοντες υποτροπής ισχαιμίας μετά από αγγειοπλαστική στεφανιαίων αρτηριών, αλλά σε συνδυασμό με άλλους πολυμορφισμούς γονιδίων και υπό την επίδραση συγκεκριμένων περιβαλλοντικών παραγόντων, είναι πολύ πιθανόν να συμμετέχουν στην παραπάνω διεργασία της υποτροπής ισχαιμίας και κατ’επέκταση της επαναστένωσης μετά από PTCA. / Coronary heart disease is one of the most common causes of morbidity and mortality in the population. A great percent of the patients with coronary heart disease may undergo percutaneous coronary angioplasty (PTCA) with or without the implantation of stents, mainly when the stenosis of the vessel is ≥ 70-75%. Despite the progress made with the introduction of drug-eluting stents and the reduction of the restenosis rate up to 5%-10%, the Achillean heel of the angioplasty using bare metal stents, is the restenosis rate which is 20%-25% of all cases. The use of drug-eluting stents is limited in cases with restenosis, in patients with diabetes mellitus and in high-risk for restenosis lesions. The great percent of late restenosis(≥ 9-10%) and the high price of drug-eluting stents, make more urgent the necessity for more intense research on the identification of the exact factors involved in the pathophysiology of restenosis. The primary objective of our study is to define the role of gene polymorphisms in the recurrence of ischaemia after PTCA and the implantation of the stents. Virtually, we scrutinely examined the role of the genetic polymorhisms of α2Badrenergic receptor and the CETP(Cholesteryl Ester Transfer Protein)-TaqIB polymorphism. Our assumption was based on the conclusion drawn by a study conducted in Finnish patients, which showed that D/D genotype confers 2,5 increase in the risk for acute coronary events(including acute myocardial infarction). The intense vasoconstriction properties of the α2Badrenergic polymorphism both on the coronary arteries and the periphery is considered to be the primary cause of the acute coronary events. The aforementioned statement with the significant role of α2B adrenergic receptor α2B-AR on the hyperplasia and mainly the migration of smooth muscle cells, probably correlates well with the pathophysiology of the recurrence of ischaemia after PTCA. We conducted a genetic association/prospective follow-up study in 96 Greek coronary artery disease patients undergoing coronary angioplasty and stent implantation. 81 patients were men and 15 women(mean age ± standard deviation=57,7± 10,1 years, ranges 37-76 years old) who presented with symptomatic CAD. All patients were enrolled in the study between 2001 and 2003 and were followed-up clinically for 6-8 months after an initially successful procedure. Post-angioplasty and for one (1) month following the procedure, all the patients received aspirin(100-325mg/day) and clopidogrel(75mg/day). Assessment of recurrence of ischaemia was based on positive thallium stress testing(at least moderate defect to the distribution of the culprit lesion of the vessel which was revascularised). Hemodynamically, restenosis was defined as ≥50% narrowing of the vessel at the point where angioplasty was performed. In addition to the patient group, a control group of totally 83 asymptomatic individuals were included in the study for comparison of the frequency of the genotype. The final end-point of the current study was the incidence of restenosis at 8 months of clinical follow-up. Recurrence of ischaemia (including restenosis rate ≥50% to the patients who underwent coronary angiography) occurred in 15 of the 96 patients. In note, the majotiy of patients (70/96) had the Insertion/Insertion genotype, fewer patients (23/96) had the Insertion/Deletion genotype and only 3/96 had the Deletion /Deletion genotype. With regard to to the genotype groups , restenosis was found in 11/70 for I/I, 3/23 for I/D and 1/3 for the D/D genotype. No association between gene polymorphisms and recurrence of ischaemia was detected to the patients who underwent coronary angioplasty. Previous studies have investigated the association between gene polymorhisms of angiotensin-converting enzyme(ACE), the AT1 receptor for angiotensin II and cholesteryl ester transfer protein (CETP) with restenosis in patients after coronary angioplasty. However, no study has been performed to involve the α2B-AR polymorphism with recurrence of ischaemia after percutaneous angioplasty of coronary vessels. As it was initially mentioned, α2B genotype promotes the migration of vascular SMCs, influences the function of autonomic nervous system and the α2B-AR deletion variant is associated with acute coronary events. All these data might correlate the role of α2B-AR polymorphism with the recurrence of ischaemia and probably with the restenosis after an angioplasty of coronary vessels. Nevertheless, the negative findings of our study might be considered preliminary, taking into account the small number of patients that were studied and the rarity of the Deletion/Deletion(D/D) genotype. As far as the CETP study, we investigated the TaqIB polymorphism, which is a silent base change affecting the 277th nucleotide and can be identified by the restriction endonuclease TaqI, with the chance of recurrence of ischaemia after PTCA. The terms B1 and B2 are used to denote the presence and absence, respectively, of the TaqI restriction site. The B2 allele has been associated with increased HDL levels and decreased CETP levels and activity in both patients with CHD and healthy subjects(resembling a mild form of CETP deficiency). On the other hand, the B1 allele has been associated with decreased HDL levels and increased CETP levels and activity. Due to the fact that TaqIB is associated with decreased HDL levels and increased risk for CHD, affecting the lipoprotein metabolism might be involved in the pathophysiology of reccurence of ischaemia after PTCA. We studied 204 patients between 2001 and 2003 with the primary objective to investigate the frequency of TaqIB and possible association with reccurence of ischaemia after PTCA in the patients who have this genotype. The frequency of TaqIB was 54% similar to the frequency of the polymorphism in a group of 35 healthy controls. The results from this study does not indicate that the TaqIB polymorphism at the CETP gene locus is a significant predictor for assessing the risk of reccurence of ischaemia after PTCA. As a conclusion, reccurence of ischaemia after PTCA is due to a complicated mechanism and to a multifactoral phenomenon. Virtually, we didn’t find any correlation of α2ΒAR polymorphism and CETP TaqIB with reccurence of ischaemia, especially as causitive factors, but based on their role in the pathophysiology, under certain circumstances, especially with the cooperation of other genes, these polymorphisms can not be definitely excluded in the reccurence of ischaemia and the restenosis after PTCA.

After reviewing some properties of the two dimensional hyperbolic toral automorphism called Arnold's discrete cat map, including its generalizations with matrices having positive unit determinant, this thesis contains a definition of a novel cat map where the elements of the matrix are found in the sequence of Pell numbers. This mapping is therefore denoted as Pell's cat map. The main result of this thesis is a theorem determining the upper bound for the minimal period of Pell's cat map. From numerical results four conjectures regarding properties of Pell's cat map are also stated. A brief exposition of some applications of Arnold's discrete cat map is found in the last part of the thesis.

Neural tube defects (NTD) result from the failure of the neural tube to close properly very early in gestation. A child born with an NTD may experience an early death or life-long disability. In the 1990s, the critical role of folic acid in the prevention of NTDs was confirmed and as a strategy to increase blood folate concentrations of women of childbearing age, folic acid fortification programs were mandated in Canada and the US. However, this change impacted the entire population not just women of childbearing age and not everyone may benefit from the increased folate intake. The objective of this research was to investigate the impact of higher intakes of folates on the mortality rates of children with acute lymphoblastic leukemia (ALL) and the risk of colorectal cancer (CRC) in adult populations. To address the impact in children with ALL, a comparison of the mortality rates between the pre- and post-fortification time periods in Ontario was performed using data from the Pediatric Oncology Group of Ontario. A second comparison between the mortality rates in these children in non-folic acid fortifying countries and the US was also completed. These analyses suggest that folic acid fortification is not negatively impacting mortality. With respect to CRC, one systematic review and two meta-analyses were conducted investigating folate intake and the risk of CRC or adenoma recurrence. The first analysis, in observational studies, compared high versus low folate intake and the risk of CRC. The second examined folate intake within the various polymorphisms of the methylene tetrahydrofolate reductase enzyme. The final study examined the impact of supplementation of 1 milligram or more per day of folic acid and the risk of colorectal adenoma recurrence in those adults with a history of colorectal adenomas. The findings from the completed observational studies suggest that there is an associated risk reduction in colorectal cancer from the intake of higher levels of folates. The investigations into the impact of the folic acid fortification program suggest that the program is not associated with having a negative impact on mortality of children with ALL or on the risk of colorectal cancer.

Neural tube defects (NTD) result from the failure of the neural tube to close properly very early in gestation. A child born with an NTD may experience an early death or life-long disability. In the 1990s, the critical role of folic acid in the prevention of NTDs was confirmed and as a strategy to increase blood folate concentrations of women of childbearing age, folic acid fortification programs were mandated in Canada and the US. However, this change impacted the entire population not just women of childbearing age and not everyone may benefit from the increased folate intake. The objective of this research was to investigate the impact of higher intakes of folates on the mortality rates of children with acute lymphoblastic leukemia (ALL) and the risk of colorectal cancer (CRC) in adult populations. To address the impact in children with ALL, a comparison of the mortality rates between the pre- and post-fortification time periods in Ontario was performed using data from the Pediatric Oncology Group of Ontario. A second comparison between the mortality rates in these children in non-folic acid fortifying countries and the US was also completed. These analyses suggest that folic acid fortification is not negatively impacting mortality. With respect to CRC, one systematic review and two meta-analyses were conducted investigating folate intake and the risk of CRC or adenoma recurrence. The first analysis, in observational studies, compared high versus low folate intake and the risk of CRC. The second examined folate intake within the various polymorphisms of the methylene tetrahydrofolate reductase enzyme. The final study examined the impact of supplementation of 1 milligram or more per day of folic acid and the risk of colorectal adenoma recurrence in those adults with a history of colorectal adenomas. The findings from the completed observational studies suggest that there is an associated risk reduction in colorectal cancer from the intake of higher levels of folates. The investigations into the impact of the folic acid fortification program suggest that the program is not associated with having a negative impact on mortality of children with ALL or on the risk of colorectal cancer.

La papillomatose respiratoire récurrente (PRR) juvénile est causée par les génotypes 6 et 11 du virus du papillome humain (VPH). Cette maladie est caractérisée par des verrues récurrentes généralement au larynx. La forme sévère peut avoir un impact dévastateur sur la santé et la qualité de vie de l’enfant atteint et de sa famille en raison des conséquences des multiples chirurgies nécessaires et du risque d'obstruction des voies respiratoires. Objectif: Examiner les facteurs de risque associés aux manifestations sévères de la PRR. Méthode: Étude rétrospective des 31 cas diagnostiqués entre janvier 1995 et décembre 2008. Les données démographiques, cliniques, génétiques et virologiques ont été évaluées. Des régressions logistiques furent effectuées afin d'évaluer le rôle des variables indépendantes sur la sévérité de la maladie. Résultats: Nos données suggèrent que les facteurs de risque de sévérité de la PRR seraient associés au genre féminin (Rapport de cotes (RC)=2.60, intervalles de confiance (IC) 95% : 0.44-15.44), au fait d’être premier-né (RC=3.51, IC 95% : 0.17-72.32), à un statut économique faible (RC=5.31, IC 95% : 0.17-164.19), à un jeune âge (RC=0.83, IC 95% : 0.68-1.01), à une charge virale élevée (RC=3.81, IC 95% : 0.23-63.16) et aux condylomes chez la mère pendant la grossesse (RC=12.05, IC 95% : 0.97-149.85). Conclusion: La sévérité de la PRR serait le résultat d'une combinaison de déterminants qui favoriseraient la croissance cellulaire particulièrement chez les jeunes enfants. Des mesures préventives et thérapeutiques visant à restreindre la contamination et la réplication du virus pourraient réduire le fardeau de la maladie. / Juvenile Recurrent Respiratory Papillomatosis is caused by Human Papillomavirus genotypes 6 or 11. It is characterised by recurring warts most commonly in the larynx. The severe form of the disease has a devastating impact on health and life quality of the child and its family because of the consequences of multiple surgical procedures and the constant risk of airway obstruction. Objectives: To study the risk factors associated with severe forms of RRP. Method: We conducted a retrospective case series of the 31 patients diagnosed between January 1995 and December 2008. We analyzed demographic and clinical variables, as well as viral and host factors. Logistic regressions were performed to evaluate the impact of each of independent variables on the disease severity. Results: Our data suggest that risk factors for severe forms of RRP in children could be associated with female gender (OR=2.60, 95% CI: 0.44-15.44), being first-born (OR=3.51 95% CI: 0.17-72.32), lower socio-economic status (OR=5.31, 95% CI: 0.17-164.19), younger age (OR=0.83, 95% CI: 0.68-1.01), high viral load (OR=3.81, 95% CI: 0.230-63.16) and history of condylomas of the mother during pregnancy, (OR=12.05, 95% CI: 0.97-149.85). Conclusion: The severity of the RRP would be the result of a combination of factors which would favor the cellular growth particularly in the young children. Therapeutics and preventive measures to restrict the contamination and the replication of the virus could reduce considerably the burden of this disease.

When statistical assumptions do not hold and coherent structures are present in spatially extended systems such as fluid flows, flame fronts and field theories, a dynamical description of turbulent phenomena becomes necessary. In the dynamical systems approach, theory of turbulence for a given system, with given boundary conditions, is given by (a) the geometry of its infinite-dimensional state space and (b) the associated measure, that is, the likelihood that asymptotic dynamics visits a given state space region. In this thesis this vision is pursued in the context of Kuramoto-Sivashinsky system, one of the simplest physically interesting spatially extended nonlinear systems. With periodic boundary conditions, continuous translational symmetry endows state space with additional structure that often dictates the type of observed solutions. At the same time, the notion of recurrence becomes relative: asymptotic dynamics visits the neighborhood of any equivalent, translated point, infinitely often. Identification of points related by the symmetry group action, termed symmetry reduction, although conceptually simple as the group action is linear, is hard to implement in practice, yet it leads to dramatic simplification of dynamics. Here we propose a scheme, based on the method of moving frames of Cartan, to efficiently project solutions of high-dimensional truncations of partial differential equations computed in the original space to a reduced state space. The procedure simplifies the visualization of high-dimensional flows and provides new insight into the role the unstable manifolds of equilibria and traveling waves play in organizing Kuramoto-Sivashinsky flow. This in turn elucidates the mechanism that creates unstable modulated traveling waves (periodic orbits in reduced space) that provide a skeleton of the dynamics. The compact description of dynamics thus achieved sets the stage for reduction of the dynamics to mappings between a set of Poincare sections.

Diss. (sammanfattning) Linköping : Linköpings universitet, 2007. / Härtill 5 uppsatser.

Made available in DSpace on 2014-06-11T19:26:56Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-02-27Bitstream added on 2014-06-13T20:16:04Z : No. of bitstreams: 1 nunes_jb_me_sjrp.pdf: 1005590 bytes, checksum: 7da54a97a1f2ab452a315062071f2c4e (MD5) / Este trabalho trata do estudo da localização dos zeros dos polinômios gerados por uma determinada relação de recorrência de três termos. O objetivo principal é estudar limitantes, em termos dos coeficientes da relação de recorrência, para as regiões onde os zeros estão localizados. Os zeros são explorados atravé do problema de autovalor associado a uma matriz de Hessenberg. As aplicações são consideradas para polinômios de Szego fSng, alguns polinômios para- ortogonais ½Sn(z) + S¤n (z) 1 + Sn(0) ¾ e ½Sn(z) ¡ S¤n (z) 1 ¡ Sn+1(0) ¾, especialmente quando os coeficientes de reflexão são reais. Um outro caso especial considerado são os zeros do polinômio Pn(z) = n Xm=0 bmzm, onde os coeficientes bm; para m = 0; 1; : : : ; n, são complexos e diferentes de zeros. / In this work we studied the localization the zeros of polynomials generated by a certain three term recurrence relation. The main objective is to study bounds, in terms of the coe±cients of the recurrence relation, for the regions where the zeros are located. The zeros are explored through an eigenvalue representation associated with a Hessenberg matrix. Applications are considered to Szeg}o polynomials fSng, some para-orthogonal polyno- mials ½Sn(z) + S¤n (z) 1 + Sn(0) ¾and ½Sn(z) ¡ S¤n (z) 1 ¡ Sn+1(0) ¾, especially when the re°ection coe±cients are real. As another special case, the zeros of the polynomial Pn(z) = n Xm=0 bmzm, where the non-zero complex coe±cients bm for m = 0; 1; : : : ; n, were considered.

Introduction: When planning Class II malocclusion treatment it is importat to consider the magnitude of the anteroposterior discrepancy, the treatment time, the amount of patient compliance needed and also the long-term stability of the results obtained. The aim of this study was to evaluate the Class II malocclusion nonextraction treatment stability, according to the initial anteroposterior discrepancy severity. Methods: Two groups of patients were selected according to the initial malocclusion severity. The Half-cusp Class II Group comprised 30 patients (16 boys, 14 girls) with an initial mean age of 13.15 years (S.D. 3.62) and the Complete Class II Group comprised 30 patients (15 boys, 15 girls) with an initial mean age of 11.99 years (S.D. 1.26). Lateral cephalograms, panoramic radiographs and dental casts were obtained at pretreatment (T1), posttreatment (T2), and at a minimum period of 2 years posttreatment (T3). Intragroup comparisons of changes in variables during the posttreatment period (T3T2) were made with paired t tests. The initial cephalometric characteristics and malocclusion severity, changes during the treatment period and during the posttreatment period were compared between groups using t tests. A multiple linear regression analysis was used to evaluate the influence of pretreatment characteristics and amount of treatment changes in the amount of posttreatment relapse. Results were regarded as significant at p<0.05. Results: During the posttreatment period (T2-T3) there were no significant differences between groups. The occlusal analysis demonstrated a small but significant relapse of molar relationship for both groups. The initial amount of overjet, the severity of canine and molar relationships and the amount of anteroposterior changes during treatment were significantly correlated to the amount of posttreatment molar relationship relapse. When subgroups of patients with matching treatment time were compared, there was significantly greater relapse in molar relationship in the Complete Class II Group. Conclusions: The initial Class II malocclusion anteroposterior discrepancy severity demonstrated a significant influence on the amount of posttreatment relapse. When treated without extractions, complete Class II malocclusion presented greater relapse than a less severe Class II molar relationship. / Introdução: Durante o planejamento do tratamento da má oclusão de Classe II é importante considerar a magnitude da discrepância ântero-posterior, o tempo de tratamento, a necessidade de cooperação do paciente, assim como a estabilidade em longo prazo dos resultados obtidos. O objetivo do presente estudo foi avaliar a estabilidade do tratamento sem extrações da má oclusão de Classe II, de acordo com a severidade da discrepância ântero-posterior inicial. Métodos: Dois grupos de pacientes foram selecionados de acordo com a severidade inicial da má oclusão. O Grupo Meia Classe II compreendeu 30 pacientes (16 meninos, 14 meninas) com idade média inicial de 13,15 anos (D.P. 3,62) e o Grupo Classe II Completa compreendeu 30 pacientes (15 meninos, 15 meninas) com idade inicial média de 11,99 anos (D.P. 1,26). Radiografias em norma lateral, radiografias panorâmicas e modelos de estudo foram obtidos pré-tratamento (T1), pós-tratamento (T2), e após um período mínimo de 2 anos pós-tratamento (T3). As comparações intragrupos das alterações das variáveis durante o período de pós-tratamento (T3-T2) foram realizadas por testes t pareados. As características cefalométricas e severidade da má oclusão inicial, alterações durante os períodos de tratamento e pós-tratamento foram comparadas entre os grupos por testes t. Uma análise de regressão linear múltipla foi conduzida para avaliar a influência das características pré-tratamento e da quantidade de alterações com o tratamento sobre a recidiva pós-tratamento. Os resultados foram considerados significantes para p<0,05. Resultados: Durante o período de pós-tratamento (T2-T3) não foram encontradas diferenças significantes entre os grupos. A avaliação oclusal demonstrou discreta mas significante recidiva da relação molar em ambos os grupos. A severidade inicial da sobressaliência, das relações canino e molar e a quantidade de alteração anteroposterior com o tratamento foram significantemente correlacionadas à recidiva da relação molar. Quando subgrupos de pacientes com tempos de tratamento compatíveis foram comparados, foi encontrada recidiva significantemente maior da relação molar no Grupo Classe II Completa. Conclusões: A severidade da discrepância ânteroposterior inicial da má oclusão de Classe II demonstrou influenciar significantemente a quantidade de recidiva pós-tratamento. Quando tratada sem extrações, a má oclusão de Classe II completa apresentou maior recidiva que uma relação molar Classe II menos severa.