Hybrid constraint programming and metaheuristic methods for large scale optimization problems

This work presents hybrid Constraint Programming (CP) and metaheuristic methods for the solution of Large Scale Optimization Problems; it aims at integrating concepts and mechanisms from the metaheuristic methods to a CP-based tree search environment in order to exploit the advantages of both approaches. The modeling and solution of large scale combinatorial optimization problem is a topic which has arisen the interest of many researcherers in the Operations Research field; combinatorial optimization problems are widely spread in everyday life and the need of solving difficult problems is more and more urgent. Metaheuristic techniques have been developed in the last decades to effectively handle the approximate solution of combinatorial optimization problems; we will examine metaheuristics in detail, focusing on the common aspects of different techniques. Each metaheuristic approach possesses its own peculiarities in designing and guiding the solution process; our work aims at recognizing components which can be extracted from metaheuristic methods and re-used in different contexts. In particular we focus on the possibility of porting metaheuristic elements to constraint programming based environments, as constraint programming is able to deal with feasibility issues of optimization problems in a very effective manner. Moreover, CP offers a general paradigm which allows to easily model any type of problem and solve it with a problem-independent framework, differently from local search and metaheuristic methods which are highly problem specific. In this work we describe the implementation of the Local Branching framework, originally developed for Mixed Integer Programming, in a CP-based environment. Constraint programming specific features are used to ease the search process, still mantaining an absolute generality of the approach. We also propose a search strategy called Sliced Neighborhood Search, SNS, that iteratively explores slices of large neighborhoods of an incumbent solution by performing CP-based tree search and encloses concepts from metaheuristic techniques. SNS can be used as a stand alone search strategy, but it can alternatively be embedded in existing strategies as intensification and diversification mechanism. In particular we show its integration within the CP-based local branching. We provide an extensive experimental evaluation of the proposed approaches on instances of the Asymmetric Traveling Salesman Problem and of the Asymmetric Traveling Salesman Problem with Time Windows. The proposed approaches achieve good results on practical size problem, thus demonstrating the benefit of integrating metaheuristic concepts in CP-based frameworks.

Campi elettromagnetici pulsanti nella terapia dell'artrosi del cane

The aim of this study is to evaluate the effects of the pulsed electromagnetic fields (PEMFS) on pain relief and functional capacity of dogs with osteoarthritis by which a single centre study prospective clinical trial. PEMFs are non ionized, athermic and time varying electromagnetic fields that has been successfully used for the treatment of osteoarthritis in human thanks to their chondroprotective, antinflammatory and analgesic property. 20 dogs were treated with PEMFs , 3 times per week for a total of 20 sessions.We found beneficial effects on pain relief and lameness in the absence of adverse effect. The decrease of pain impacted positively on the health-dogs related quality of life and the grade of satisfaction of their owner was very high. The benefits were obvious at half therapy and lasted for a medium long time. This is the first published report concerning PEMFs treatment on canine osteoarthtitis. The result of this study proves that PEMFs is a non –invasive remedy, lacking in adverse effect , easy to employ and useful for controlling pain and inflammation associated with osteoarthritis.

Evoluzione Morfotettonica delle Aree Alpine "Sempione" e "Brennero" attraverso Studi Termocronologici di bassa temperatura

E’ mostrata l’analisi e la modellazione di dati termocronologici di bassa temperatura da due regioni Alpine: il Sempione ed il Brennero. Le faglie distensive presenti bordano settori crostali profondi appartenenti al dominio penninico: il duomo metamorfico Lepontino al Sempione e la finestra dei Tauri al Brennero. I dati utilizzati sono FT e (U-Th)/He su apatite. Per il Sempione i dati provengono dalla bibliografia; per il Brennero si è provveduto ad un nuovo campionamento, sia in superficie che in sotterraneo. Gli attuali lavori per la galleria di base del Brennero (BBT), hanno consentito, per la prima volta, di raccogliere dati di FT e (U-Th)/He in apatite in sottosuolo per la finestra dei Tauri occidentale. Le analisi sono state effettuate tramite un codice a elementi finiti, Pecube, risolvente l’equazione di diffusione del calore per una topografia evolvente nel tempo. Il codice è stato modificato per tener conto dei dati sotterranei. L’inversione dei dati è stata effettuata usando il Neighbourhood Algorithm (NA), per ottenere il più plausibile scenario di evoluzione morfotettonico. I risultati ottenuti per il Sempione mostrano: ipotetica evoluzione dello stile tettonico della faglia del Sempione da rolling hinge a low angle detachment a 6.5 Ma e la cessazione dell’attività a 3 Ma; costruzione del rilievo fino a 5.5 Ma, smantellamento da 5.5 Ma ad oggi, in coincidenza dei cambiamenti climatici Messiniani e relativi all’inizio delle maggiori glaciazioni; incremento dell’esumazione da 0–0.6 mm/anno a 0.6–1.2 mm/anno a 2.4 Ma nell’emisfero settentrionale. I risultati al Brennero mostrano: maggiore attività tettonica della faglia del Brennero (1.3 mm/anno), maggiore attività esumativa (1–2 mm/anno) prima dei 10 Ma; crollo dell’attività della faglia del Brennero fra 10 Ma e oggi (0.1 mm/anno) e dell’attività esumativa nello stesso periodo (0.1–0.3 mm/anno); nessun aumento del tasso esumativo o variazioni topografiche negli ultimi 5 Ma.

Methods for the estimation of the cortical activity and connectivity during cognitive tasks in humans

The research activity characterizing the present thesis was mainly centered on the design, development and validation of methodologies for the estimation of stationary and time-varying connectivity between different regions of the human brain during specific complex cognitive tasks. Such activity involved two main aspects: i) the development of a stable, consistent and reproducible procedure for functional connectivity estimation with a high impact on neuroscience field and ii) its application to real data from healthy volunteers eliciting specific cognitive processes (attention and memory). In particular the methodological issues addressed in the present thesis consisted in finding out an approach to be applied in neuroscience field able to: i) include all the cerebral sources in connectivity estimation process; ii) to accurately describe the temporal evolution of connectivity networks; iii) to assess the significance of connectivity patterns; iv) to consistently describe relevant properties of brain networks. The advancement provided in this thesis allowed finding out quantifiable descriptors of cognitive processes during a high resolution EEG experiment involving subjects performing complex cognitive tasks.

Nonlinear Control of Magnetically Actuated Spacecraft

The topic of this thesis is the feedback stabilization of the attitude of magnetically actuated spacecraft. The use of magnetic coils is an attractive solution for the generation of control torques on small satellites flying inclined low Earth orbits, since magnetic control systems are characterized by reduced weight and cost, higher reliability, and require less power with respect to other kinds of actuators. At the same time, the possibility of smooth modulation of control torques reduces coupling of the attitude control system with flexible modes, thus preserving pointing precision with respect to the case when pulse-modulated thrusters are used. The principle based on the interaction between the Earth's magnetic field and the magnetic field generated by the set of coils introduces an inherent nonlinearity, because control torques can be delivered only in a plane that is orthogonal to the direction of the geomagnetic field vector. In other words, the system is underactuated, because the rotational degrees of freedom of the spacecraft, modeled as a rigid body, exceed the number of independent control actions. The solution of the control issue for underactuated spacecraft is also interesting in the case of actuator failure, e.g. after the loss of a reaction-wheel in a three-axes stabilized spacecraft with no redundancy. The application of well known control strategies is no longer possible in this case for both regulation and tracking, so that new methods have been suggested for tackling this particular problem. The main contribution of this thesis is to propose continuous time-varying controllers that globally stabilize the attitude of a spacecraft, when magneto-torquers alone are used and when a momentum-wheel supports magnetic control in order to overcome the inherent underactuation. A kinematic maneuver planning scheme, stability analyses, and detailed simulation results are also provided, with new theoretical developments and particular attention toward application considerations.

Nonlinear Observers for Sensorless Control of Permanent Magnet Synchronous Motors

In this thesis, the industrial application of control a Permanent Magnet Synchronous Motor in a sensorless configuration has been faced, and in particular the task of estimating the unknown “parameters” necessary for the application of standard motor control algorithms. In literature several techniques have been proposed to cope with this task, among them the technique based on model-based nonlinear observer has been followed. The hypothesis of neglecting the mechanical dynamics from the motor model has been applied due to practical and physical considerations, therefore only the electromagnetic dynamics has been used for the observers design. First observer proposed is based on stator currents and Stator Flux dynamics described in a generic rotating reference frame. Stator flux dynamics are known apart their initial conditions which are estimated, with speed that is also unknown, through the use of the Adaptive Theory. The second observer proposed is based on stator currents and Rotor Flux dynamics described in a self-aligning reference frame. Rotor flux dynamics are described in the stationary reference frame exploiting polar coordinates instead of classical Cartesian coordinates, by means the estimation of amplitude and speed of the rotor flux. The stability proof is derived in a Singular Perturbation Framework, which allows for the use the current estimation errors as a measure of rotor flux estimation errors. The stability properties has been derived using a specific theory for systems with time scale separation, which guarantees a semi-global practical stability. For the two observer ideal simulations and real simulations have been performed to prove the effectiveness of the observers proposed, real simulations on which the effects of the Inverter nonlinearities have been introduced, showing the already known problems of the model-based observers for low speed applications.

Gold and the Stock Market: 3 Essays on Gold Investments

This thesis gives an overview of the history of gold per se, of gold as an investment good and offers some institutional details about gold and other precious metal markets. The goal of this study is to investigate the role of gold as a store of value and hedge against negative market movements in turbulent times. I investigate gold’s ability to act as a safe haven during periods of financial stress by employing instrumental variable techniques that allow for time varying conditional covariance. I find broad evidence supporting the view that gold acts as an anchor of stability during market downturns. During periods of high uncertainty and low stock market returns, gold tends to have higher than average excess returns. The effectiveness of gold as a safe haven is enhanced during periods of extreme crises: the largest peaks are observed during the global financial crises of 2007-2009 and, in particular, during the Lehman default (October 2008). A further goal of this thesis is to investigate whether gold provides protection from tail risk. I address the issue of asymmetric precious metal behavior conditioned to stock market performance and provide empirical evidence about the contribution of gold to a portfolio’s systematic skewness and kurtosis. I find that gold has positive coskewness with the market portfolio when the market is skewed to the left. Moreover, gold shows low cokurtosis with the market returns during volatile periods. I therefore show that gold is a desirable investment good to risk averse investors, since it tends to decrease the probability of experiencing extreme bad outcomes, and the magnitude of losses in case such events occur. Gold thus bears very important and under-researched characteristics as an asset class per se, which this thesis contributed to address and unveil.

Studio di caratteri correlati a stress idrico in una collezione di cultivar di frumento duro (Triticum durum Desf.)

L’agricoltura si trova ad affrontare una diminuzione della disponibilità d’acqua ed una crescente domanda della produzione di cereali per scopi alimentari. Sono perciò necessarie strategie di coltivazione innovative per migliorare la produttività e nuovi genotipi migliorati nell'efficienza dell’uso delle risorse in condizioni di siccità. Questi rappresentano gli obietti principali del progetto “DROPS” (Drought tolerant yielding Plants) all’interno del quale ha avuto luogo il mio progetto di Dottorato. La mia attività di ricerca è stata svolta come segue: 1. Caratterizzazione molecolare di un panel di188 accessioni di frumento duro con marcatori SSR e DaRT; 2. Esperimenti in serra su 100 accessioni del panel per valutare la Water-Use Efficiency (WUE) in sei repliche secondo un Alpha Lattice design; 3. Prove sul campo, effettuate secondo un Alpha Lattice design, in due stagioni di crescita: a. 2010/11, valutazione di 100 accessioni presso l’Azienda sperimentale dell'Università di Cadriano (BO); b. 2011/12, valutazione del panel completo in 3 ambienti, con due diversi regimi irrigui In entrambi gli anni, abbiamo valutato caratteri agronomici correlati con il ciclo di sviluppo, la resa di granella e sue componenti, nonché diversi fattori ambientali e del suolo. Per quanto riguarda WUE, abbiamo trovato differenze altamente significative tra accessioni; inoltre, cinque accessioni hanno mostrato elevati valori di WUE e cinque accessioni valori molto bassi di WUE in tutte e sei le repliche. Gli esperimenti di campo nelle stagioni 2011 e 2012 hanno evidenziato differenze altamente significative tra le accessioni del panel per la maggior parte dei caratteri analizzati, confermando inoltre che il panel di fiorisce entro una settimana. L'esperimento del secondo anno ci ha permesso osservare un significativa interazione Genotipo X Ambiente. Questi risultati saranno integrati con ulteriori analisi QTL, per identificare regioni cromosomiche coinvolte nel controllo genetico dei caratteri di interesse e verificare la stabilità dei QTL in diversi ambienti.

Einzelmolekülspektroskopie an einer homologen Reihe von Rylendiimiden und an einem bichromophoren Modellsystem für elektronischen Energietransfer

In dieser Arbeit wurden Untersuchungen zur Fluoreszenzdynamik und zum Mechanismus des Photobleichens einzelner Farbstoffmoleküle einer homologen Reihe von Rylentetracarbonsäurediimiden durchgeführt. Mit der Erweiterung des elektronischen π-Systems verringert sich die HOMO/LUMO-Energiedifferenz, so dass strahlungslose Relaxationsprozesse gemäß des Energielückengesetzes zunehmen. Die konfokale Einzelmolekülspektroskopie in Kombination mit zeitkorrelierter Einzelphotonenzählung ermöglicht es, Fluktuationen der inneren Konversionsrate zu detektieren. Der limitierende Faktor jedes Einzelmolekülexperiments ist die Photostabilität der Moleküle. Für die homologe Reihe konnten mindestens zwei Photobleichmechanismen identifiziert werden. Wenn Singulett-Sauerstoff durch Selbstsensibilisierung erzeugt werden kann, ist unter Luft die Photooxidation der wahrscheinlichste Mechanismus. Unter Ausschluss von Luftsauerstoff spielt die Bildung langlebiger Dunkelzustände eine entscheidende Rolle, die bevorzugt über höher angeregte Triplett- und Singulett-Zustände abläuft. Es wird angenommen, dass es sich hierbei um einen reversiblen Ionisierungsprozess handelt, bei dem das Radikal-Kation der Rylendiimide gebildet wird. Es konnte gezeigt werden, dass durch eine geeignete Wahl der Anregungsbedingungen die Dunkelzustandspopulierung verhindert und zugleich die Photostabilität der Fluorophore deutlich erhöht wird. Durch die Verknüpfung der beiden niedrigsten Homologen erhält man ein Donor-Akzeptor-Modellsystem, bei dem die Anregungsenergie mit hoher Effizienz vom Donor- auf den Akzeptor-Chromophor übertragen wird. In der Fluoreszenz einzelner Bichromophore wurden bei selektiver Anregung des Donors kollektive Auszeiten beobachtet, die durch effiziente Singulett-Triplett-Annihilation verursacht werden.

Secondary Microseisms Characterization and Green’s Function Extraction at the Larderello-Travale Geothermal Field (Italy)

Over the past ten years, the cross-correlation of long-time series of ambient seismic noise (ASN) has been widely adopted to extract the surface-wave part of the Green’s Functions (GF). This stochastic procedure relies on the assumption that ASN wave-field is diffuse and stationary. At frequencies <1Hz, the ASN is mainly composed by surface-waves, whose origin is attributed to the sea-wave climate. Consequently, marked directional properties may be observed, which call for accurate investigation about location and temporal evolution of the ASN-sources before attempting any GF retrieval. Within this general context, this thesis is aimed at a thorough investigation about feasibility and robustness of the noise-based methods toward the imaging of complex geological structures at the local (∼10-50km) scale. The study focused on the analysis of an extended (11 months) seismological data set collected at the Larderello-Travale geothermal field (Italy), an area for which the underground geological structures are well-constrained thanks to decades of geothermal exploration. Focusing on the secondary microseism band (SM;f>0.1Hz), I first investigate the spectral features and the kinematic properties of the noise wavefield using beamforming analysis, highlighting a marked variability with time and frequency. For the 0.1-0.3Hz frequency band and during Spring- Summer-time, the SMs waves propagate with high apparent velocities and from well-defined directions, likely associated with ocean-storms in the south- ern hemisphere. Conversely, at frequencies >0.3Hz the distribution of back- azimuths is more scattered, thus indicating that this frequency-band is the most appropriate for the application of stochastic techniques. For this latter frequency interval, I tested two correlation-based methods, acting in the time (NCF) and frequency (modified-SPAC) domains, respectively yielding esti- mates of the group- and phase-velocity dispersions. Velocity data provided by the two methods are markedly discordant; comparison with independent geological and geophysical constraints suggests that NCF results are more robust and reliable.

Essays in Macroecometrics: methodological aspects and empirical applications

In the first chapter, I develop a panel no-cointegration test which extends Pesaran, Shin and Smith (2001)'s bounds test to the panel framework by considering the individual regressions in a Seemingly Unrelated Regression (SUR) system. This allows to take into account unobserved common factors that contemporaneously affect all the units of the panel and provides, at the same time, unit-specific test statistics. Moreover, the approach is particularly suited when the number of individuals of the panel is small relatively to the number of time series observations. I develop the algorithm to implement the test and I use Monte Carlo simulation to analyze the properties of the test. The small sample properties of the test are remarkable, compared to its single equation counterpart. I illustrate the use of the test through a test of Purchasing Power Parity in a panel of EU15 countries. In the second chapter of my PhD thesis, I verify the Expectation Hypothesis of the Term Structure in the repurchasing agreements (repo) market with a new testing approach. I consider an "inexact" formulation of the EHTS, which models a time-varying component in the risk premia and I treat the interest rates as a non-stationary cointegrated system. The effect of the heteroskedasticity is controlled by means of testing procedures (bootstrap and heteroskedasticity correction) which are robust to variance and covariance shifts over time. I fi#nd that the long-run implications of EHTS are verified. A rolling window analysis clarifies that the EHTS is only rejected in periods of turbulence of #financial markets. The third chapter introduces the Stata command "bootrank" which implements the bootstrap likelihood ratio rank test algorithm developed by Cavaliere et al. (2012). The command is illustrated through an empirical application on the term structure of interest rates in the US.

Implementazione su fpga di un pre-distorsore digitale a banda larga per sistemi a microonde di backhaul

The development of next generation microwave technology for backhauling systems is driven by an increasing capacity demand. In order to provide higher data rates and throughputs over a point-to-point link, a cost-effective performance improvement is enabled by an enhanced energy-efficiency of the transmit power amplification stage, whereas a combination of spectrally efficient modulation formats and wider bandwidths is supported by amplifiers that fulfil strict constraints in terms of linearity. An optimal trade-off between these conflicting requirements can be achieved by resorting to flexible digital signal processing techniques at baseband. In such a scenario, the adaptive digital pre-distortion is a well-known linearization method, that comes up to be a potentially widely-used solution since it can be easily integrated into base stations. Its operation can effectively compensate for the inter-modulation distortion introduced by the power amplifier, keeping up with the frequency-dependent time-varying behaviour of the relative nonlinear characteristic. In particular, the impact of the memory effects become more relevant and their equalisation become more challenging as the input discrete signal feature a wider bandwidth and a faster envelope to pre-distort. This thesis project involves the research, design and simulation a pre-distorter implementation at RTL based on a novel polyphase architecture, which makes it capable of operating over very wideband signals at a sampling rate that complies with the actual available clock speed of current digital devices. The motivation behind this structure is to carry out a feasible pre-distortion for the multi-band spectrally efficient complex signals carrying multiple channels that are going to be transmitted in near future high capacity and reliability microwave backhaul links.

Konfokalmikroskopie an stabilen und metastabilen kolloidalen Hartkugel-Fluiden : interne Struktur, Kristallnukleation und Kristallwachstum

Die vorliegende Forschungsarbeit behandelt konfokalmikroskopische Untersuchungen zur Strukturbildung in kolloidalen Suspensionen, die als experimentelles Modellsystem für harte Kugeln verwendet werden. Die lokale und globale Struktur wurde im stabilen und metastabilen Fluid bestimmt. Bereits unterhalb des Gefriervolumenbruchs wurden nah-geordnete Cluster vorgefunden, die mit zunehmendem Volumenbruch häufiger und größer werden. Das Kristallwachstum aus der metastabilen kolloidalen Schmelze konnte quantitativ analysiert werden und es zeigt sich eine Übereinstimmung mehrerer Kenngrößen mit Literaturdaten nahe dem Schmelzvolumenbruch. Die Untersuchung demonstrierte die Realisierbarkeit der quantitativen Analyse der Kristallisationskinetik mittels konfokaler Mikroskopie. Es zeigte sich ein mehrstufiges Nukleationsszenario bei dem zuerst nah-geordnete Cluster gebildet werden, die im weiteren Verlauf zu kristall-artigen Clustern transformieren. Die Beobachtungen belegen den Mechanismus der Precursornukleation in Hartkugelsystemen. Die heterogene Nukleation wurde an glatten und an hexagonal strukturierten Substraten untersucht. Anhand der Kristallisationskinetik und der direkten Messung der Benetzungswinkel konnte ein Übergang des Benetzungsverhaltens unter Variation des Substratgitterabstands nachgewiesen werden: An glatten und an kommensurabel strukturierten Substraten zeigten sich eine vollständige Bedeckung des Substrats mit der kristallinen Phase und ein sofortiges unidirektionales Wachstum. Bei inkommensurabel strukturierten Substraten wurde eine unvollständige Bedeckung des strukturierten Substrats mit der kristallinen Phase sowie ein verzögertes isotropes Wachstum bei fortwährender Kristallnukleation beobachtet.

Life history, ecology and the biogeography of strong genetic breaks among 15 species of PaciWc rockWsh, Sebastes

Strong genetic change over short spatial scales is surprising among marine species with high dispersal potential. Concordant breaks among several species signals a role for geographic barriers to dispersal. Along the coast of California, such breaks have not been seen across the biogeographic barrier of Point Conception, but other potential geographic boundaries have been surveyed less often.;We tested for strong-population structure in 11 species of Sebastes sampled across two regions containing potential dispersal barriers, and conducted a meta-analysis including four additional species. We show two strong breaks north of Monterey Bay, spanning an oceanographic gradient and an upwelling jet. Moderate genetic structure is just as common in the north as it is in the south, across the biogeographic break at Point Conception. Gene Xow is generally higher among deep-water species, but these conclusions are confounded by phylogeny. Species in the subgenus Sebastosomus have higher structure than those in the subgenus;Pteropodus, despite having larvae with longer pelagic phases. DiVerences in settlement behavior in the face of ocean currents might help explain these diVerences. Across similar species across the same coastal environment, we document a wide variety of patterns in gene Xow, suggesting that interaction of individual species traits such as settlement behavior with environmental factors such as;oceanography can strongly impact population structure

Long-term clinical outcomes of biodegradable polymer biolimus-eluting stents versus durable polymer sirolimus-eluting stents in patients with coronary artery disease (LEADERS): 4 year follow-up of a randomised non-inferiority trial

Background The effectiveness of durable polymer drug-eluting stents comes at the expense of delayed arterial healing and subsequent late adverse events such as stent thrombosis (ST). We report the 4 year follow-up of an assessment of biodegradable polymer-based drug-eluting stents, which aim to improve safety by avoiding the persistent inflammatory stimulus of durable polymers. Methods We did a multicentre, assessor-masked, non-inferiority trial. Between Nov 27, 2006, and May 18, 2007, patients aged 18 years or older with coronary artery disease were randomly allocated with a computer-generated sequence to receive either biodegradable polymer biolimus-eluting stents (BES) or durable polymer sirolimus-eluting stents (SES; 1:1 ratio). The primary endpoint was a composite of cardiac death, myocardial infarction, or clinically-indicated target vessel revascularisation (TVR); patients were followed-up for 4 years. Analysis was by intention to treat. This trial is registered with ClinicalTrials.gov, number NCT00389220. Findings 1707 patients with 2472 lesions were randomly allocated to receive either biodegradable polymer BES (857 patients, 1257 lesions) or durable polymer SES (850 patients, 1215 lesions). At 4 years, biodegradable polymer BES were non-inferior to durable polymer SES for the primary endpoint: 160 (18·7%) patients versus 192 (22·6%) patients (rate ratios [RR] 0·81, 95% CI 0·66–1·00, p for non-inferiority <0·0001, p for superiority=0·050). The RR of definite ST was 0·62 (0·35–1·08, p=0·09), which was largely attributable to a lower risk of very late definite ST between years 1 and 4 in the BES group than in the SES group (RR 0·20, 95% CI 0·06–0·67, p=0·004). Conversely, the RR of definite ST during the first year was 0·99 (0·51–1·95; p=0·98) and the test for interaction between RR of definite ST and time was positive (pinteraction=0·017). We recorded an interaction with time for events associated with ST but not for other events. For primary endpoint events associated with ST, the RR was 0·86 (0·41–1·80) during the first year and 0·17 (0·04–0·78) during subsequent years (pinteraction=0·049). Interpretation Biodegradable polymer BES are non-inferior to durable polymer SES and, by reducing the risk of cardiac events associated with very late ST, might improve long-term clinical outcomes for up to 4 years compared with durable polymer SES. Funding Biosensors Europe SA, Switzerland.