Contraction analysis of switched Filippov systems via regularization

We study incremental stability and convergence of switched (bimodal) Filippov systems via contraction analysis. In particular, by using results on regularization of switched dynamical systems, we derive sufficient conditions for convergence of any two trajectories of the Filippov system between each other within some region of interest. We then apply these conditions to the study of different classes of Filippov systems including piecewise smooth (PWS) systems, piecewise affine (PWA) systems and relay feedback systems. We show that contrary to previous approaches, our conditions allow the system to be studied in metrics other than the Euclidean norm. The theoretical results are illustrated by numerical simulations on a set of representative examples that confirm their effectiveness and ease of application.Comment: Preprint submitted to Automatic

Load distribution in small world networks

In this paper we introduce a new model of data packet transport, based on a stochastic approach with the aim of characterizing the load distribution on complex networks. Moreover we analyze the load standard deviation as an index of uniformity of the distribution of packets within the network, to characterize the effects of the network topology. We measure such index on the model proposed by Watts and Strogatz as the redirection probability is increased. We find that the uniformity of the load spread is maximized in the intermediate region, at which the small world effect is observed and both global and local efficiency are high. Moreover we analyze the relationship between load centrality and degree centrality as an approximate measure of the load at the edges. Analogous results are obtained for the load variance computed at the edges as well as at the vertices.Comment: 6 pages, 5 figures. Included in conference proceedings International Conference PhysCon 2005 August 24-26, 2005, Saint Petersburg, RUSSI

NetEvo: A computational framework for the evolution of dynamical complex networks

NetEvo is a computational framework designed to help understand the evolution of dynamical complex networks. It provides flexible tools for the simulation of dynamical processes on networks and methods for the evolution of underlying topological structures. The concept of a supervisor is used to bring together both these aspects in a coherent way. It is the job of the supervisor to rewire the network topology and alter model parameters such that a user specified performance measure is minimised. This performance measure can make use of current topological information and simulated dynamical output from the system. Such an abstraction provides a suitable basis in which to study many outstanding questions related to complex system design and evolution

Bifurcations of piecewise smooth flows:perspectives, methodologies and open problems

In this paper, the theory of bifurcations in piecewise smooth flows is critically surveyed. The focus is on results that hold in arbitrarily (but finitely) many dimensions, highlighting significant areas where a detailed understanding is presently lacking. The clearest results to date concern equilibria undergoing bifurcations at switching boundaries, and limit cycles undergoing grazing and sliding bifurcations. After discussing fundamental concepts, such as topological equivalence of two piecewise smooth systems, discontinuity-induced bifurcations are defined for equilibria and limit cycles. Conditions for equilibria to exist in n-dimensions are given, followed by the conditions under which they generically undergo codimension-one bifurcations. The extent of knowledge of their unfoldings is also summarized. Codimension-one bifurcations of limit cycles and boundary-intersection crossing are described together with techniques for their classification. Codimension-two bifurcations are discussed with suggestions for further study

Impact of right ventricular size on ECG after percutaneous closure of atrial septal defect with Amplatzer Septal Occluder.

To assess ECG changes after percutaneous atrial septal defect (ASD) closure in children with significant left-to-right shunt. Analysis of data of 36 consecutive children with an ASD who had successful percutaneous ASD closure with an Amplatzer Septal Occluder. Assessment comprised echocardiography and ECG the day before and after the procedure and at 1, 6 and 12 months follow-up. The median age (interquartile range) of children was 7.3 (5.3) years. On the day after the procedure the end diastolic diameter of the right ventricle showed already a diminution (34 (12) mm/m2 before intervention vs. 32 (12) mm/m2). ECG changes were first observed at 1 month follow-up (PR interval before intervention 139 (20) ms vs. 132 (20) ms; QRS duration 88 (18) ms vs. 82 (19) ms) and at 6 months follow-up (QRS axis 77 degrees (33) before intervention vs. 72 degrees (53)). With the exception of the QRS duration, ECG intervals and axis were in a normal range in all patients before the procedure. Median QRS duration normalised at 1 year follow-up (83 (8) ms). After transcatheter ASD closure, decrease in right ventricular size began rapidly and was followed by reduction of the QRS duration and PR interval within weeks. Shifting to the left of the QRS axis was observed within 6 months follow-up. This study showed that ECG changes due to right ventricular volume overload can regress and normalise after percutaneous ASD closure in children

Shrinking Point Bifurcations of Resonance Tongues for Piecewise-Smooth, Continuous Maps

Resonance tongues are mode-locking regions of parameter space in which stable periodic solutions occur; they commonly occur, for example, near Neimark-Sacker bifurcations. For piecewise-smooth, continuous maps these tongues typically have a distinctive lens-chain (or sausage) shape in two-parameter bifurcation diagrams. We give a symbolic description of a class of "rotational" periodic solutions that display lens-chain structures for a general $N$-dimensional map. We then unfold the codimension-two, shrinking point bifurcation, where the tongues have zero width. A number of codimension-one bifurcation curves emanate from shrinking points and we determine those that form tongue boundaries.Comment: 27 pages, 6 figure

Valutazioni tecniche ed economiche sull'uso degli inseguitori solari

I processi di antropizzazione connessi allo sviluppo del settore energia hanno determinato delle “impronte” sul nostro pianeta ormai indelebili. Non resta che provare a ridurre i consumi energetici e affidare la produzione dell’energia ad un mix equilibrato di fonti. In questo contesto, con particolare riferimento alla produzione dell’energia elettrica, lo sfruttamento della risorsa solare ha assunto un ruolo di primo ordine. Gran parte delle attività di ricerca e sviluppo del settore si è concentrata sulle tecniche e sulle metodologie innovative di conversione della fonte in energia elettrica. Accanto a queste, a parità di tecnologia di conversione adottata, altre attività di ricerca e sviluppo sono state indirizzate alla ottimizzazione della produzione di energia elettrica mediante “concentrazione” della radiazione solare nel punto di collocazione del dispositivo di conversione ovvero mediante opportuna variazione dell’orientamento del dispositivo rispetto alla direzione della radiazione stessa. Tali attività di ricerca e sviluppo, intraprese dalla comunità scientifica e dal mondo imprenditoriale, certamente favoriranno un migliore sfruttamento della fonte solare e avranno ricadute in tempi diversi. Questo articolo concentra la sua attenzione su gli inseguitori solari, dispositivi di semplice applicazione basati su tecnologie consolidate, la cui diffusa applicazione potrebbe portare, in breve termine, ad un rilevante incremento di producibilità degli impianti fotovoltaici. In particolare, dopo una disamina delle caratteristiche degli inseguitori solari vengono presentati alcuni dati sull’incremento della producibilità degli impianti e alcune considerazioni di ordine tecnico ed economico circa la corretta valutazione della convenienza economica dell’uso di tali dispositivi, che sta alla base dell’effettivo sviluppo del relativo mercato

Simultaneous Border-Collision and Period-Doubling Bifurcations

We unfold the codimension-two simultaneous occurrence of a border-collision bifurcation and a period-doubling bifurcation for a general piecewise-smooth, continuous map. We find that, with sufficient non-degeneracy conditions, a locus of period-doubling bifurcations emanates non-tangentially from a locus of border-collision bifurcations. The corresponding period-doubled solution undergoes a border-collision bifurcation along a curve emanating from the codimension-two point and tangent to the period-doubling locus here. In the case that the map is one-dimensional local dynamics are completely classified; in particular, we give conditions that ensure chaos.Comment: 22 pages; 5 figure

Finding Exogenous Variables in Data with Many More Variables than Observations

Many statistical methods have been proposed to estimate causal models in classical situations with fewer variables than observations (p<n, p: the number of variables and n: the number of observations). However, modern datasets including gene expression data need high-dimensional causal modeling in challenging situations with orders of magnitude more variables than observations (p>>n). In this paper, we propose a method to find exogenous variables in a linear non-Gaussian causal model, which requires much smaller sample sizes than conventional methods and works even when p>>n. The key idea is to identify which variables are exogenous based on non-Gaussianity instead of estimating the entire structure of the model. Exogenous variables work as triggers that activate a causal chain in the model, and their identification leads to more efficient experimental designs and better understanding of the causal mechanism. We present experiments with artificial data and real-world gene expression data to evaluate the method.Comment: A revised version of this was published in Proc. ICANN201