A Phase Space Box-counting based Method for Arrhythmia Prediction from Electrocardiogram Time Series

Arrhythmia is one kind of cardiovascular diseases that give rise to the number of deaths and potentially yields immedicable danger. Arrhythmia is a life threatening condition originating from disorganized propagation of electrical signals in heart resulting in desynchronization among different chambers of the heart. Fundamentally, the synchronization process means that the phase relationship of electrical activities between the chambers remains coherent, maintaining a constant phase difference over time. If desynchronization occurs due to arrhythmia, the coherent phase relationship breaks down resulting in chaotic rhythm affecting the regular pumping mechanism of heart. This phenomenon was explored by using the phase space reconstruction technique which is a standard analysis technique of time series data generated from nonlinear dynamical system. In this project a novel index is presented for predicting the onset of ventricular arrhythmias. Analysis of continuously captured long-term ECG data recordings was conducted up to the onset of arrhythmia by the phase space reconstruction method, obtaining 2-dimensional images, analysed by the box counting method. The method was tested using the ECG data set of three different kinds including normal (NR), Ventricular Tachycardia (VT), Ventricular Fibrillation (VF), extracted from the Physionet ECG database. Statistical measures like mean (μ), standard deviation (σ) and coefficient of variation (σ/μ) for the box-counting in phase space diagrams are derived for a sliding window of 10 beats of ECG signal. From the results of these statistical analyses, a threshold was derived as an upper bound of Coefficient of Variation (CV) for box-counting of ECG phase portraits which is capable of reliably predicting the impeding arrhythmia long before its actual occurrence. As future work of research, it was planned to validate this prediction tool over a wider population of patients affected by different kind of arrhythmia, like atrial fibrillation, bundle and brunch block, and set different thresholds for them, in order to confirm its clinical applicability.

The role of the West African Monsoon in the tropical to mid-latitudes climate

The interaction between atmosphere–land–ocean–biosphere systems plays a prominent role on the atmospheric dynamics and on the convective rainfall distribution over the West Africa monsoon area during the boreal summer. In particular, the initialization of convective systems in the Sub – Sahelian region has been directly linked to soil moisture heterogeneities identified as the major triggering, development and propagation of convective systems. The present study aims at investigating African monsoon large scale convective dynamics and rainfall diurnal cycle through an exploration of the hypothesis behind the mechanisms of a monsoon phenomenon as an emergence of a collective dynamics of many propagating convective systems. Such hypothesis is based on the existence of an internal self – regulation mechanism among the various components. To achieve these results a multiple analysis was performed based on remote sensed rainfall dataset, and global and regional modelling data for a period of 5 seasons: 2004 - 2008. Satellite rainfall data and convective occurrence variability were studied for assessing typical spatio – temporal signatures and characteristics with an emphasis to the diurnal cycle footprint. A global model and regional model simulation datasets, specifically developed for this analysis and based on Regional Atmospheric Modelling System – RAMS, have been analysed. Results from numerical model datasets highlight the evidence of a synchronization between the destabilization of the convective boundary layer and rainfall occurrence due to the solar radiation forcing through the latent heat release. This supports the conclusion that the studied interacting systems are associated with a process of mutual adjustment of rhythms. Furthermore, this rainfall internal coherence was studied in relation to the West African Heat Low pressure system, which has a prominent role in the large scale summer variability over the Mediterranean area since it is acting as one of dynamic link between sub tropical and midlatitudes variability.

Nonverbal emotional regulation in psychotherapy process according to an intersubjective perspective

In recent decades fascinating studies in developmental psychology, especially in infant research (for review see Lavelli, 2007) and recent discoveries in neuroscience (Welsh, et al, 2007; Siegel, 2001; Pally, 2007) have brought great interest to study the mode of sharing subjective experiences (affective states, intentions and attentional focus) in children and adults.It therefore appears today in the clinic is a growing consensus about the fact that the psychological disorder can be read as a deficit in intersubjective processes of affect regulation (see Benecke C. et al 2005; psychodynamic Diagnostic Manual-PDM, 2006) leading many authors to assume the centrality of affect regulation in the construction of the psychotherapeutic process of change (just to name a few Tronick, Greenberg, Stern, Sander, Fonagy, Beebe, Philippot, Rimé etc..). As previously stated, this study has led us to hypothesize that the long process of therapy is to assist with the sessions continue, a growing "emotional attunement" between the communication styles of both patient and therapist. And also to speculate that this synchronization can represent the existence of a significant positive correlation between the increased level of "emotional synchronization" and increased capacity for regulation of emotions by the patient.The research results despite the limitations of small sample showed encouraging results about the verification of the existence of an increasing degree of attunement between therapist and patient long psychotherapy sessions and also showed a good degree of positive correlation between the increase the latter construct and emotional regulation through the implicit mode of expression and nonverbal communication.

Strategie di personalizzazione della terapia di resincronizzazione cardiaca

Solo il 60% dei candidati alla resincronizzazione cardiaca risponde in termini di rimodellamento ventricolare inverso che è il più forte predittore di riduzione della mortalità e delle ospedalizzazioni. Due cause possibili della mancata risposta sono la programmazione del dispositivo e i limiti dell’ approccio transvenoso. Nel corso degli anni di dottorato ho effettuato tre studi per ridurre il numero di non responder. Il primo studio valuta il ritardo interventricolare. Al fine di ottimizzare le risorse e fornire un reale beneficio per il paziente ho ricercato la presenza di predittori di ritardo interventricolare diverso dal simultaneo, impostato nella programmazione di base. L'unico predittore è risultato essere l’ intervallo QRS> 160 ms, quindi ho proposto una flow chart per ottimizzare solo i pazienti che avranno nella programmazione ottimale un intervallo interventricolare non simultaneo. Il secondo lavoro valuta la fissazione attiva del ventricolo sinistro con stent. I dislocamenti, la soglia alta di stimolazione del miocardio e la stimolazione del nervo frenico sono tre problematiche che limitano la stimolazione biventricolare. Abbiamo analizzato più di 200 angiografie per vedere le condizioni anatomiche predisponenti la dislocazione del catetere. Prospetticamente abbiamo deciso di utilizzare uno stent per fissare attivamente il catetere ventricolare sinistro in tutti i pazienti che presentavano le caratteristiche anatomiche favorenti la dislocazione. Non ci sono più state dislocazioni, c’è stata una migliore risposta in termini di rimodellamento ventricolare inverso e non ci sono state modifiche dei parametri elettrici del catetere. Il terzo lavoro ha valutato sicurezza ed efficacia della stimolazione endoventricolare sinistra. Abbiamo impiantato 26 pazienti giudicati non responder alla terapia di resincronizzazione cardiaca. La procedura è risultata sicura, il rischio di complicanze è simile alla stimolazione biventricolare classica, ed efficace nell’arrestare la disfunzione ventricolare sinistra e / o migliorare gli effetti clinici in un follow-up medio.

Cooperative Wireless Systems

This Ph.D. dissertation reports on the work performed at the Wireless Communication Laboratory - University of Bologna and National Research Council - as well as, for six months, at the Fraunhofer Institute for Integrated Circuit (IIS) in Nürnberg. The work of this thesis is in the area of wireless communications, especially with regards to cooperative communications aspects in narrow-band and ultra-wideband systems, cooperative links characterization, network geometry, power allocation techniques,and synchronization between nodes. The underpinning of this work is devoted to developing a general framework for design and analysis of wireless cooperative communication systems, which depends on propagation environment, transmission technique, diversity method, power allocation for various scenarios and relay positions. The optimal power allocation for minimizing the bit error probability at the destination is derived. In addition, a syncronization algorithm for master-slave communications is proposed with the aim of jointly compensate the clock drift and offset of wireless nodes composing the network.

Context-aware wireless networks

This thesis investigates context-aware wireless networks, capable to adapt their behavior to the context and the application, thanks to the ability of combining communication, sensing and localization. Problems of signals demodulation, parameters estimation and localization are addressed exploiting analytical methods, simulations and experimentation, for the derivation of the fundamental limits, the performance characterization of the proposed schemes and the experimental validation. Ultrawide-bandwidth (UWB) signals are in certain cases considered and non-coherent receivers, allowing the exploitation of the multipath channel diversity without adopting complex architectures, investigated. Closed-form expressions for the achievable bit error probability of novel proposed architectures are derived. The problem of time delay estimation (TDE), enabling network localization thanks to ranging measurement, is addressed from a theoretical point of view. New fundamental bounds on TDE are derived in the case the received signal is partially known or unknown at receiver side, as often occurs due to propagation or due to the adoption of low-complexity estimators. Practical estimators, such as energy-based estimators, are revised and their performance compared with the new bounds. The localization issue is addressed with experimentation for the characterization of cooperative networks. Practical algorithms able to improve the accuracy in non-line-of-sight (NLOS) channel conditions are evaluated on measured data. With the purpose of enhancing the localization coverage in NLOS conditions, non-regenerative relaying techniques for localization are introduced and ad hoc position estimators are devised. An example of context-aware network is given with the study of the UWB-RFID system for detecting and locating semi-passive tags. In particular a deep investigation involving low-complexity receivers capable to deal with problems of multi-tag interference, synchronization mismatches and clock drift is presented. Finally, theoretical bounds on the localization accuracy of this and others passive localization networks (e.g., radar) are derived, also accounting for different configurations such as in monostatic and multistatic networks.

On moduli spaces of semistable sheaves on K3 surfaces

Ich untersuche die nicht bereits durch die Arbeit "Singular symplectic moduli spaces" von Kaledin, Lehn und Sorger (Invent. Math. 164 (2006), no. 3) abgedeckten Fälle von Modulräumen halbstabiler Garben auf projektiven K3-Flächen - die Fälle mit Mukai-Vektor (0,c,0) sowie die Modulräume zu nichtgenerischen amplen Divisoren - hinsichtlich der möglichen Konstruktion neuer Beispiele von kompakten irreduziblen symplektischen Mannigfaltigkeiten. Ich stelle einen Zusammenhang zu den bereits untersuchten Modulräumen und Verallgemeinerungen derselben her und erweitere bekannte Ergebnisse auf alle offenen Fälle von Garben vom Rang 0 und viele Fälle von Garben von positivem Rang. Insbesondere kann in diesen Fällen die Existenz neuer Beispiele von kompakten irreduziblen symplektischen Mannigfaltigkeiten, die birational über Komponenten des Modulraums liegen, ausgeschlossen werden.

Use of shared memory in the context of embedded multi-core processors: exploration of the technology and its limits

Modern embedded systems embrace many-core shared-memory designs. Due to constrained power and area budgets, most of them feature software-managed scratchpad memories instead of data caches to increase the data locality. It is therefore programmers’ responsibility to explicitly manage the memory transfers, and this make programming these platform cumbersome. Moreover, complex modern applications must be adequately parallelized before they can the parallel potential of the platform into actual performance. To support this, programming languages were proposed, which work at a high level of abstraction, and rely on a runtime whose cost hinders performance, especially in embedded systems, where resources and power budget are constrained. This dissertation explores the applicability of the shared-memory paradigm on modern many-core systems, focusing on the ease-of-programming. It focuses on OpenMP, the de-facto standard for shared memory programming. In a first part, the cost of algorithms for synchronization and data partitioning are analyzed, and they are adapted to modern embedded many-cores. Then, the original design of an OpenMP runtime library is presented, which supports complex forms of parallelism such as multi-level and irregular parallelism. In the second part of the thesis, the focus is on heterogeneous systems, where hardware accelerators are coupled to (many-)cores to implement key functional kernels with orders-of-magnitude of speedup and energy efficiency compared to the “pure software” version. However, three main issues rise, namely i) platform design complexity, ii) architectural scalability and iii) programmability. To tackle them, a template for a generic hardware processing unit (HWPU) is proposed, which share the memory banks with cores, and the template for a scalable architecture is shown, which integrates them through the shared-memory system. Then, a full software stack and toolchain are developed to support platform design and to let programmers exploiting the accelerators of the platform. The OpenMP frontend is extended to interact with it.

Effetti sulle funzioni autonomiche e sugli stati di veglia e di sonno della manipolazione centrale farmacologica del sistema ipocretinergico nel ratto

Obiettivo della tesi è stato quello di studiare il ruolo svolto dall’ipotalamo laterale (LH) nella regolazione dei processi di integrazione dell’attività autonomica e termoregolatoria con quella degli stati di veglia e sonno. A questo scopo, l’attività dell’LH è stata inibita per 6 ore (Esperimento A) mediante microiniezioni locali dell’agonista GABAA muscimolo nel ratto libero di muoversi, nel quale sono stati monitorati in continuo l’elelttroencefalogramma, l’elettromiogramma nucale, la pressione arteriosa (PA) e la temperatura ipotalamica (Thy) e cutanea. Gli animali sono stati studiati a temperatura ambientale (Ta) di 24°C e 10°C. I risultati hanno mostrato che l’inibizione acuta dell’LH riduce l’attività di veglia e sopprime la comparsa del sonno REM. Ciò avviene attraverso l’induzione di uno stato di sonno NREM caratterizzato da ipersincronizzazione corticale, con scomparsa degli stati transizionali al sonno REM. Quando l’animale è esposto a bassa Ta, tali alterazioni si associano a un ampio calo della Thy, che viene compensato da meccanismi vicarianti solo dopo un paio d’ore dall’iniezione. Sulla base di tali risultati, si è proceduto ad un ulteriore studio (Esperimento B) volto ad indagare il ruolo del neuropeptide ipocretina (prodotto in modo esclusivo a livello dell’LH) nei processi termoregolatori, mediante microiniezioni del medesimo nel bulbo rostrale ventromediale (RVMM), stazione cruciale della rete nervosa preposta all’attivazione dei processi termogenetici. La somministrazione di ipocretina è stata in grado di attivare la termogenesi e di potenziare la comparsa della veglia, con concomitante lieve incremento della PA e della frequenza cardiaca, quando effettuata alle Ta di 24°C o di 10°C, ma non alla Ta di 32°C. In conclusione, i risultati indicano che l’LH svolge un ruolo cruciale nella promozione degli stati di veglia e di sonno REM e, per tramite dell’ipocretina, interviene in modo coplesso a livello del RVMM nella regolazione dei processi di coordinamento dell'attività di veglia con quella termoregolatoria.

Implicazioni teoriche e sperimentali della sincronizzazione assoluta nella teoria della relatività speciale

Sono indagate le implicazioni teoriche e sperimentali derivanti dall'assunzione, nella teoria della relatività speciale, di un criterio di sincronizzazione (detta assoluta) diverso da quello standard. La scelta della sincronizzazione assoluta è giustificata da alcune considerazioni di carattere epistemologico sullo status di fenomeni quali la contrazione delle lunghezze e la dilatazione del tempo. Oltre che a fornire una diversa interpretazione, la sincronizzazione assoluta rappresenta una estensione del campo di applicazione della relatività speciale in quanto può essere attuata anche in sistemi di riferimento accelerati. Questa estensione consente di trattare in maniera unitaria i fenomeni sia in sistemi di riferimento inerziali che accelerati. L'introduzione della sincronizzazione assoluta implica una modifica delle trasformazioni di Lorentz. Una caratteristica di queste nuove trasformazioni (dette inerziali) è che la trasformazione del tempo è indipendente dalle coordinate spaziali. Le trasformazioni inerziali sono ottenute nel caso generale tra due sistemi di riferimento aventi velocità (assolute) u1 e u2 comunque orientate. Viene mostrato che le trasformazioni inerziali possono formare un gruppo pur di prendere in considerazione anche riferimenti non fisicamente realizzabili perché superluminali. È analizzato il moto rigido secondo Born di un corpo esteso considerando la sincronizzazione assoluta. Sulla base delle trasformazioni inerziali si derivano le trasformazioni per i campi elettromagnetici e le equazioni di questi campi (che sostituiscono le equazioni di Maxwell). Si mostra che queste equazioni contengono soluzioni in assenza di cariche che si propagano nello spazio come onde generalmente anisotrope in accordo con quanto previsto dalle trasformazioni inerziali. L'applicazione di questa teoria elettromagnetica a sistemi accelerati mostra l'esistenza di fenomeni mai osservati che, pur non essendo in contraddizione con la relatività standard, ne forzano l'interpretazione. Viene proposto e descritto un esperimento in cui uno di questi fenomeni è misurabile.

Parallel Architectures for Many-Core Systems-On-Chip in Deep Sub-Micron Technology

Despite the several issues faced in the past, the evolutionary trend of silicon has kept its constant pace. Today an ever increasing number of cores is integrated onto the same die. Unfortunately, the extraordinary performance achievable by the many-core paradigm is limited by several factors. Memory bandwidth limitation, combined with inefficient synchronization mechanisms, can severely overcome the potential computation capabilities. Moreover, the huge HW/SW design space requires accurate and flexible tools to perform architectural explorations and validation of design choices. In this thesis we focus on the aforementioned aspects: a flexible and accurate Virtual Platform has been developed, targeting a reference many-core architecture. Such tool has been used to perform architectural explorations, focusing on instruction caching architecture and hybrid HW/SW synchronization mechanism. Beside architectural implications, another issue of embedded systems is considered: energy efficiency. Near Threshold Computing is a key research area in the Ultra-Low-Power domain, as it promises a tenfold improvement in energy efficiency compared to super-threshold operation and it mitigates thermal bottlenecks. The physical implications of modern deep sub-micron technology are severely limiting performance and reliability of modern designs. Reliability becomes a major obstacle when operating in NTC, especially memory operation becomes unreliable and can compromise system correctness. In the present work a novel hybrid memory architecture is devised to overcome reliability issues and at the same time improve energy efficiency by means of aggressive voltage scaling when allowed by workload requirements. Variability is another great drawback of near-threshold operation. The greatly increased sensitivity to threshold voltage variations in today a major concern for electronic devices. We introduce a variation-tolerant extension of the baseline many-core architecture. By means of micro-architectural knobs and a lightweight runtime control unit, the baseline architecture becomes dynamically tolerant to variations.

High gradient magnetic separation (HGMS) of erythrocytes infected with plasmodium falciparum

This thesis was undertaken to explore possible applications of high gradient magnetic separation (HGMS) for the separation of RBCs infected with Plasmodium falciparum, with the dual aim of establishing a novel and superior method for isolating late-stage infected cells, and of obtaining synchronized cell cultures.rnThe presented work presents protocols for HGMS of parasitized RBCs that fulfil these aims. Late-stage parasitized cell can be isolated essentially devoid of contamination with non-infected and ring-stage infected cells. Such an easy method for a highly quantitative and qualitative purification has not yet been reported. Synchronous cultures can be obtained both following depletion of late-stage infected cells, and following isolation of the latter. The quality of synchronization cultures matches that of sorbitol lysis, the current standard method for malaria culture synchronization. An advantage of HGMS is the avoidance of osmotic stress for RBCs. The new methods further have the appeal of high reproducibility, cost-effectiveness, and simple protocol.rnIt should be possible to take the methods beyond Plasmodium infected RBCs. Most magnetic separation techniques in the sector of biomedical research employ columns with a hydrophilic polymer-coated matrix. Our procedure employs an optimized buffer system. Polymer coating becomes unnecessary and uncoated columns are available at a fraction of the cost.

Feeding entrainment of locomotor activity and clock gene expression in Senegalese sole, Solea senegalensis

The present study was conducted to investigate the influence of restricted food access on Solea senegalensis behaviour and daily expression of clock genes in central (diencephalon and optic tectum) and pheripheral (liver) tissues. The Senegalese sole is a marine teleost fish belonging to the Class of Actinopterygii, Order Pleuronectiformes and Family Soleidae. Its geographical distribution in the Mediterranean sea is fairly broad, covering the south and east of the Iberian Peninsula, the North of Africa and Middle East until the coast of Turkey. From a commercial perspective Solea senegalensis has acquired in recent years, a key role in aquacolture industry of the Iberian Peninsula. The Senegalese sole is also acquiring an important relevance in chronobiological studies as the number of published works focused on the sole circadian system has increased in the last few years. The molecular mechanisms underlying sole circadian rhythms has also been explored recently, both in adults and developing sole. Moreover, the consideration of the Pleuronectiformes Order as one of the most evolved teleost groups make the Senegalese sole a species of high interest under a comparative and phylogenetic point of view. All these facts have reinforced the election of Senegalese sole as model species for the present study. The animals were kept under 12L:12D photoperiod conditions and divided into three experimental groups depending on the feeding time: fed at midlight (ML), middark (MD) or random (RND) times. Throughout the experiment, the existence of a daily activity rhythm and it synchronization to the light-dark and feeding cycles was checked. To this end locomotor activity was registred by means of two infrared photocells placed in pvc tube 10 cm below the water surface (upper photocell) and the other one was located 10 cm above the bottom of the tank (bottom photocell). The photocell were connected to a computer so that every time a fish interrupted the infrared light beam, it produced an output signal that was recorded. The number of light beam interruptions was stored every 10 minutes by specialized software for data acquisition.

Controlled reproduction in Anguilla anguilla (L.): advanced studies on broodstock management, spawning techniques and system design for artificial seed production.

The thesis aims to expose the advances achieved in the practices of captive breeding of the European eel (Anguilla anguilla). Aspects investigated concern both approaches livestock (breeding selection, response to hormonal stimulation, reproductive performance, incubation of eggs) and physiological aspects (endocrine plasma profiles of players), as well as engineering aspects. Studies conducted on various populations of wild eel have shown that the main determining factor in the selection of wild females destined to captive breeding must be the Silver Index which may determine the stage of pubertal development. The hormonal induction protocol adopted, with increasing doses of carp pituitary extract, it has proven useful to ovarian development, with a synchronization effect that is positively reflected on egg production. The studies on the effects of photoperiod show how the condition of total darkness can positively influence practices of reproductions in captivity. The effects of photoperiod were also investigated at the physiological level, observing the plasma levels of steroids ( E2, T) and thyroid hormones (T3 and T4) and the expression in the liver of vitellogenin (vtg1 and vtg2) and estradiol membrane receptor (ESR1). From the comparison between spontaneous deposition and insemination techniques through the stripping is inferred as the first ports to a better qualitative and quantitative yield in the production of eggs capable of being fertilized, also the presence of a percentage of oocytes completely transparent can be used to obtain eggs at a good rate of fertility. Finally, the design and implementation of a system for recirculating aquaculture suited to meet the needs of species-specific eel showed how to improve the reproductive results, it would be preferable to adopt low-flow and low density incubation.

Picard-Fuchs equations of dimensionally regulated Feynman integrals

Zusammenfassung In der vorliegenden Arbeit besch¨aftige ich mich mit Differentialgleichungen von Feynman– Integralen. Ein Feynman–Integral h¨angt von einem Dimensionsparameter D ab und kann f¨ur ganzzahlige Dimension als projektives Integral dargestellt werden. Dies ist die sogenannte Feynman–Parameter Darstellung. In Abh¨angigkeit der Dimension kann ein solches Integral divergieren. Als Funktion in D erh¨alt man eine meromorphe Funktion auf ganz C. Ein divergentes Integral kann also durch eine Laurent–Reihe ersetzt werden und dessen Koeffizienten r¨ucken in das Zentrum des Interesses. Diese Vorgehensweise wird als dimensionale Regularisierung bezeichnet. Alle Terme einer solchen Laurent–Reihe eines Feynman–Integrals sind Perioden im Sinne von Kontsevich und Zagier. Ich beschreibe eine neue Methode zur Berechnung von Differentialgleichungen von Feynman– Integralen. ¨ Ublicherweise verwendet man hierzu die sogenannten ”integration by parts” (IBP)– Identit¨aten. Die neue Methode verwendet die Theorie der Picard–Fuchs–Differentialgleichungen. Im Falle projektiver oder quasi–projektiver Variet¨aten basiert die Berechnung einer solchen Differentialgleichung auf der sogenannten Griffiths–Dwork–Reduktion. Zun¨achst beschreibe ich die Methode f¨ur feste, ganzzahlige Dimension. Nach geeigneter Verschiebung der Dimension erh¨alt man direkt eine Periode und somit eine Picard–Fuchs–Differentialgleichung. Diese ist inhomogen, da das Integrationsgebiet einen Rand besitzt und daher nur einen relativen Zykel darstellt. Mit Hilfe von dimensionalen Rekurrenzrelationen, die auf Tarasov zur¨uckgehen, kann in einem zweiten Schritt die L¨osung in der urspr¨unglichen Dimension bestimmt werden. Ich beschreibe außerdem eine Methode, die auf der Griffiths–Dwork–Reduktion basiert, um die Differentialgleichung direkt f¨ur beliebige Dimension zu berechnen. Diese Methode ist allgemein g¨ultig und erspart Dimensionswechsel. Ein Erfolg der Methode h¨angt von der M¨oglichkeit ab, große Systeme von linearen Gleichungen zu l¨osen. Ich gebe Beispiele von Integralen von Graphen mit zwei und drei Schleifen. Tarasov gibt eine Basis von Integralen an, die Graphen mit zwei Schleifen und zwei externen Kanten bestimmen. Ich bestimme Differentialgleichungen der Integrale dieser Basis. Als wichtigstes Beispiel berechne ich die Differentialgleichung des sogenannten Sunrise–Graphen mit zwei Schleifen im allgemeinen Fall beliebiger Massen. Diese ist f¨ur spezielle Werte von D eine inhomogene Picard–Fuchs–Gleichung einer Familie elliptischer Kurven. Der Sunrise–Graph ist besonders interessant, weil eine analytische L¨osung erst mit dieser Methode gefunden werden konnte, und weil dies der einfachste Graph ist, dessen Master–Integrale nicht durch Polylogarithmen gegeben sind. Ich gebe außerdem ein Beispiel eines Graphen mit drei Schleifen. Hier taucht die Picard–Fuchs–Gleichung einer Familie von K3–Fl¨achen auf.