Wavelet estimation in diffusions with periodicity

Wir betrachten einen zeitlich inhomogenen Diffusionsprozess, der durch eine stochastische Differentialgleichung gegeben wird, deren Driftterm ein deterministisches T-periodisches Signal beinhaltet, dessen Periodizität bekannt ist. Dieses Signal sei in einem Besovraum enthalten. Wir schätzen es mit Hilfe eines nichtparametrischen Waveletschätzers. Unser Schätzer ist von einem Wavelet-Dichteschätzer mit Thresholding inspiriert, der 1996 in einem klassischen iid-Modell von Donoho, Johnstone, Kerkyacharian und Picard konstruiert wurde. Unter gewissen Ergodizitätsvoraussetzungen an den Prozess können wir nichtparametrische Konvergenzraten angegeben, die bis auf einen logarithmischen Term den Raten im klassischen iid-Fall entsprechen. Diese Raten werden mit Hilfe von Orakel-Ungleichungen gezeigt, die auf Ergebnissen über Markovketten in diskreter Zeit von Clémencon, 2001, beruhen. Außerdem betrachten wir einen technisch einfacheren Spezialfall und zeigen einige Computersimulationen dieses Schätzers.

Extracting evolutionary information from the spectral decomposition of early-type galaxies.

Holding the major share of stellar mass in galaxies and being also old and passively evolving, early-type galaxies (ETGs) are the primary probes in investigating these various evolution scenarios, as well as being useful means to provide insights on cosmological parameters. In this thesis work I focused specifically on ETGs and on their capability in constraining galaxy formation and evolution; in particular, the principal aims were to derive some of the ETGs evolutionary parameters, such as age, metallicity and star formation history (SFH) and to study their age-redshift and mass-age relations. In order to infer galaxy physical parameters, I used the public code STARLIGHT: this program provides a best fit to the observed spectrum from a combination of many theoretical models defined in user-made libraries. the comparison between the output and input light-weighted ages shows a good agreement starting from SNRs of ∼ 10, with a bias of ∼ 2.2% and a dispersion 3%. Furthermore, also metallicities and SFHs are well reproduced. In the second part of the thesis I performed an analysis on real data, starting from Sloan Digital Sky Survey (SDSS) spectra. I found that galaxies get older with cosmic time and with increasing mass (for a fixed redshift bin); absolute light-weighted ages, instead, result independent from the fitting parameters or the synthetic models used. Metallicities, instead, are very similar from each other and clearly consistent with the ones derived from the Lick indices. The predicted SFH indicates the presence of a double burst of star formation. Velocity dispersions and extinctiona are also well constrained, following the expected behaviours. As a further step, I also fitted single SDSS spectra (with SNR∼ 20), to verify that stacked spectra gave the same results without introducing any bias: this is an important check, if one wants to apply the method at higher z, where stacked spectra are necessary to increase the SNR. Our upcoming aim is to adopt this approach also on galaxy spectra obtained from higher redshift Surveys, such as BOSS (z ∼ 0.5), zCOSMOS (z 1), K20 (z ∼ 1), GMASS (z ∼ 1.5) and, eventually, Euclid (z 2). Indeed, I am currently carrying on a preliminary study to estabilish the applicability of the method to lower resolution, as well as higher redshift (z 2) spectra, just like the Euclid ones.

Wavetrack, implementazione ottimizzata di un algoritmo di pitch tracking basato su wavelet

WaveTrack é un'implementazione ottimizzata di un algoritmo di pitch tracking basato su wavelet, nello specifico viene usata la trasformata Fast Lifting Wavelet Transform con la wavelet di Haar. La libreria è stata scritta nel linguaggio C e tra le sue peculiarità può vantare tempi di latenza molto bassi, un'ottima accuratezza e una buona flessibilità d'uso grazie ad alcuni parametri configurabili.

Trasformate wavelet

La presente tesi vuole dare una descrizione delle Trasformate Wavelet indirizzata alla codifica dell’immagine in formato JPEG2000. Dopo aver quindi descritto le prime fasi della codifica di un’immagine, procederemo allo studio dei difetti derivanti dall’analisi tramite la Trasformata Discreta del Coseno (utilizzata nel formato predecessore JPEG). Dopo aver quindi descritto l’analisi multirisoluzione e le caratteristiche che la differenziano da quest’ultima, analizzeremo la Trasformata Wavelet dandone solo pochi accenni teorici e cercando di dedurla, in una maniera più indirizzata all’applicazione. Concluderemo la tesi descrivendo la codifica dei coefficienti calcolati, e portando esempi delle innumerevoli applicazioni dell’analisi multirisoluzione nei diversi campi scientifici e di trasmissione dei segnali.

Analyse zur Auswirkung der irreversiblen Wavelet-Kompression (JPEG2000) auf CT-Bildverarbeitungs- und Darstellungsalgorithmen

Der technische Fortschritt konfrontiert die medizinische Bildgebung wie keine andere Sparte der Medizin mit einem rasanten Anstieg zu speichernder Daten. Anschaffung, Wartung und Ausbau der nötigen Infrastruktur entwickeln sich zunehmend zu einem ökonomischen Faktor. Ein Verfahren, welches diesem Trend etwas entgegensetzten könnte ist die irreversible Bilddatenkompression. Sie ist seit über 10 Jahren Gegenstand vieler Studien, deren Ergebnisse sich wiederum in Empfehlungen zum Einsatz irreversibler Kompression mehrerer nationaler und internationaler Organisation, wie CAR, DRG, RCR und ESR wiederspiegeln. Tenor dieser Empfehlungen ist, dass der Einsatz von moderater irreversibler Bilddatenkompression sicher und sinnvoll ist. Teil dieser Empfehlungen sind auch Angaben über das Maß an Kompression, ausgedrückt in Kompressionsraten, welche je nach Untersuchung und anatomischer Region als sicher anwendbar gelten und keinen diagnostisch relevanten Verlust der komprimierten Bilder erzeugen.rnVerschiedene Kompressionsalgorithmen wurden vorgeschlagen. Letztendlich haben sich vor allem die beiden weit verbreiteten Algorithmen JPEG und JPEG2000 bewährt. Letzterer erfährt in letzter Zeit zunehmen Anwendung, aufgrund seiner einfacheren Handhabung und seiner umfangreichen Zusatzfunktionen.rnAufgrund rechtlich-ethischer Bedenken hat die irreversible Kompression keine breite praktische Anwendung finden können. Dafür verantwortlich ist unter anderem auch die Unklarheit, wie sich irreversible Kompression auf Nach- und Weiterverarbeitung (sog. Postprocessing) medizinischer Bilder, wie Segmentierung, Volumetrie oder 3D-Darstellung, auswirkt. Bisherige Studien zu diesem Thema umfassen vier verschiedene Postprocessing-Algorithmen. Die untersuchten Algorithmen zeigten sich bei verlustbehafteter Kompression im Bereich der erwähnten, publizierten Kompressionsraten weitgehend unbeeinflusst. Lediglich die computergestützte Messung von Stenosegraden in der digitalen Koronarangiographie kollidiert mit den in Großbritannien geltenden Empfehlungen. Die Verwendung unterschiedlicher Kompressionsalgorithmen schränkt die allgemeinernAussagekraft dieser Studienergebnisse außerdem ein.rnZur Erweiterung der Studienlage wurden vier weitere Nach- und Weiterverarbeitungsalgorithmen auf ihre Kompressionstoleranz untersucht. Dabei wurden die Kompressionsraten von 8:1, 10:1 und 15:1 verwendet, welche um die empfohlenen Kompressionsraten von CAR, DRG, RCR und ESR liegen und so ein praxisnahes Setting bieten. Als Kompressionsalgorithmus wurde JPEG2000 verwendet, aufgrund seiner zunehmenden Nutzung in Studien sowie seiner bereits erwähnten Vorzüge in Sachen Handhabung und Zusatzfunktionen. Die vier Algorithmen umfassten das 3D-Volume rendering von CT-Angiographien der Becken-Bein-Gefäße, die Computer-assistierte Detektion von Lungenrundherden, die automatisierte Volumetrie von Leberrundherden und die funktionelle Bestimmung der Ejektionsfraktion in computertomographischen Aufnahmen des Herzens.rnAlle vier Algorithmen zeigten keinen Einfluss durch irreversibler Bilddatenkompression in denrngewählten Kompressionsraten (8:1, 10:1 und 15:1). Zusammen mit der bestehenden Literatur deuten die Ergebnisse an, dass moderate irreversible Kompression im Rahmen aktueller Empfehlungen keinen Einfluss auf Nach- und Weiterverarbeitung medizinischer Bilder hat. Eine explizitere Vorhersage zu einem bestimmten, noch nicht untersuchten Algorithmus ist jedoch aufgrund der unterschiedlichen Funktionsweisen und Programmierungen nicht sicher möglich.rnSofern ein Postprocessing Algorithmus auf komprimiertes Bildmaterial angewendet werden soll, muss dieser zunächst auf seine Kompressionstoleranz getestet werden. Dabei muss der Test eine rechtlich-ethische Grundlage für den Einsatz des Algorithmus bei komprimiertem Bildmaterial schaffen. Es sind vor allem zwei Optionen denkbar, die Testung institutsintern, eventuell unter Zuhilfenahme von vorgefertigten Bibliotheken, oder die Testung durch den Hersteller des Algorithmus.

Trasformata di Fourier e trasformata Wavelet

Questo elaborato si concentra sullo studio della trasformata di Fourier e della trasformata Wavelet. Nella prima parte della tesi si analizzano gli aspetti fondamentali della trasformata di Fourier. Si definisce poi la trasformata di Fourier su gruppi abeliani finiti, richiamando opportunamente la struttura di tali gruppi. Si mostra che calcolare la trasformata di Fourier nel quoziente richiede un minor numero di operazioni rispetto a calcolarla direttamente nel gruppo di partenza. L'ultima parte dell'elaborato si occupa dello studio delle Wavelet, dette ondine. Viene presentato quindi il sistema di Haar che permette di definire una funzione come serie di funzioni di Haar in alternativa alla serie di Fourier. Si propone poi un vero e proprio metodo per la costruzione delle ondine e si osserva che tale costruzione è strettamente legata all'analisi multirisoluzione. Un ruolo cruciale viene svolto dall'identità di scala, un'identità algebrica che permette di definire certi coefficienti che determinano completamente le ondine. Interviene poi la trasformata di Fourier che riduce la ricerca dei coefficienti sopra citati, alla ricerca di certe funzioni opportune che determinano esplicitamente le Wavelet. Non tutte le scelte di queste funzioni sono accettabili. Ci sono vari approcci, qui viene presentato l'approccio di Ingrid Daubechies. Le Wavelet costituiscono basi per lo spazio di funzioni a quadrato sommabile e sono particolarmente interessanti per la decomposizione dei segnali. Sono quindi in relazione con l'analisi armonica e sono adottate in un gran numero di applicazioni. Spesso sostituiscono la trasformata di Fourier convenzionale.

Curve Decomposition for Large Deflection Analysis of Fixed-Guided Beams With Application to Statically Balanced Compliant Mechanisms

Statically balanced compliant mechanisms require no holding force throughout their range of motion while maintaining the advantages of compliant mechanisms. In this paper, a postbuckled fixed-guided beam is proposed to provide the negative stiffness to balance the positive stiffness of a compliant mechanism. To that end, a curve decomposition modeling method is presented to simplify the large deflection analysis. The modeling method facilitates parametric design insight and elucidates key points on the force-deflection curve. Experimental results validate the analysis. Furthermore, static balancing with fixed-guided beams is demonstrated for a rectilinear proof-of-concept prototype.

No adverse effect of genetically modified antifungal wheat on decomposition dynamics and the soil fauna community - a field study

The cultivation of genetically modified (GM) plants has raised several environmental concerns. One of these concerns regards non-target soil fauna organisms, which play an important role in the decomposition of organic matter and hence are largely exposed to GM plant residues. Soil fauna may be directly affected by transgene products or indirectly by pleiotropic effects such as a modified plant metabolism. Thus, ecosystem services and functioning might be affected negatively. In a litterbag experiment in the field we analysed the decomposition process and the soil fauna community involved. Therefore, we used four experimental GM wheat varieties, two with a race-specific antifungal resistance against powdery mildew (Pm3b) and two with an unspecific antifungal resistance based on the expression of chitinase and glucanase. We compared them with two non-GM isolines and six conventional cereal varieties. To elucidate the mechanisms that cause differences in plant decomposition, structural plant components (i.e. C:N ratio, lignin, cellulose, hemicellulose) were examined and soil properties, temperature and precipitation were monitored. The most frequent taxa extracted from decaying plant material were mites (Cryptostigmata, Gamasina and Uropodina), springtails (Isotomidae), annelids (Enchytraeidae) and Diptera (Cecidomyiidae larvae). Despite a single significant transgenic/month interaction for Cecidomyiidae larvae, which is probably random, we detected no impact of the GM wheat on the soil fauna community. However, soil fauna differences among conventional cereal varieties were more pronounced than between GM and non-GM wheat. While leaf residue decomposition in GM and non-GM wheat was similar, differences among conventional cereals were evident. Furthermore, sampling date and location were found to greatly influence soil fauna community and decomposition processes. The results give no indication of ecologically relevant adverse effects of antifungal GM wheat on the composition and the activity of the soil fauna community.

A multi-level decomposition of variance in somatic symptom reporting in families with adolescent children

OBJECTIVES: This paper examines four different levels of possible variation in symptom reporting: occasion, day, person and family. DESIGN: In order to rule out effects of retrospection, concurrent symptom reporting was assessed prospectively using a computer-assisted self-report method. METHODS: A decomposition of variance in symptom reporting was conducted using diary data from families with adolescent children. We used palmtop computers to assess concurrent somatic complaints from parents and children six times a day for seven consecutive days. In two separate studies, 314 and 254 participants from 96 and 77 families, respectively, participated. A generalized multilevel linear models approach was used to analyze the data. Symptom reports were modelled using a logistic response function, and random effects were allowed at the family, person and day level, with extra-binomial variation allowed for on the occasion level. RESULTS: Substantial variability was observed at the person, day and occasion level but not at the family level. CONCLUSIONS: To explain symptom reporting in normally healthy individuals, situational as well as person characteristics should be taken into account. Family characteristics, however, would not help to clarify symptom reporting in all family members.

From EEG dependency multichannel matching pursuit to sparse topographic EEG decomposition

In this work, we present a multichannel EEG decomposition model based on an adaptive topographic time-frequency approximation technique. It is an extension of the Matching Pursuit algorithm and called dependency multichannel matching pursuit (DMMP). It takes the physiologically explainable and statistically observable topographic dependencies between the channels into account, namely the spatial smoothness of neighboring electrodes that is implied by the electric leadfield. DMMP decomposes a multichannel signal as a weighted sum of atoms from a given dictionary where the single channels are represented from exactly the same subset of a complete dictionary. The decomposition is illustrated on topographical EEG data during different physiological conditions using a complete Gabor dictionary. Further the extension of the single-channel time-frequency distribution to a multichannel time-frequency distribution is given. This can be used for the visualization of the decomposition structure of multichannel EEG. A clustering procedure applied to the topographies, the vectors of the corresponding contribution of an atom to the signal in each channel produced by DMMP, leads to an extremely sparse topographic decomposition of the EEG.

How does spatial extent of fMRI datasets affect independent component analysis decomposition?

Spatial independent component analysis (sICA) of functional magnetic resonance imaging (fMRI) time series can generate meaningful activation maps and associated descriptive signals, which are useful to evaluate datasets of the entire brain or selected portions of it. Besides computational implications, variations in the input dataset combined with the multivariate nature of ICA may lead to different spatial or temporal readouts of brain activation phenomena. By reducing and increasing a volume of interest (VOI), we applied sICA to different datasets from real activation experiments with multislice acquisition and single or multiple sensory-motor task-induced blood oxygenation level-dependent (BOLD) signal sources with different spatial and temporal structure. Using receiver operating characteristics (ROC) methodology for accuracy evaluation and multiple regression analysis as benchmark, we compared sICA decompositions of reduced and increased VOI fMRI time-series containing auditory, motor and hemifield visual activation occurring separately or simultaneously in time. Both approaches yielded valid results; however, the results of the increased VOI approach were spatially more accurate compared to the results of the decreased VOI approach. This is consistent with the capability of sICA to take advantage of extended samples of statistical observations and suggests that sICA is more powerful with extended rather than reduced VOI datasets to delineate brain activity.