Community detection in networks via nonlinear modularity eigenvectors

Revealing a community structure in a network or dataset is a central problem arising in many scientific areas. The modularity function $Q$ is an established measure quantifying the quality of a community, being identified as a set of nodes having high modularity. In our terminology, a set of nodes with positive modularity is called a \textit{module} and a set that maximizes $Q$ is thus called \textit{leading module}. Finding a leading module in a network is an important task, however the dimension of real-world problems makes the maximization of $Q$ unfeasible. This poses the need of approximation techniques which are typically based on a linear relaxation of $Q$, induced by the spectrum of the modularity matrix $M$. In this work we propose a nonlinear relaxation which is instead based on the spectrum of a nonlinear modularity operator $\mathcal M$. We show that extremal eigenvalues of $\mathcal M$ provide an exact relaxation of the modularity measure $Q$, however at the price of being more challenging to be computed than those of $M$. Thus we extend the work made on nonlinear Laplacians, by proposing a computational scheme, named \textit{generalized RatioDCA}, to address such extremal eigenvalues. We show monotonic ascent and convergence of the method. We finally apply the new method to several synthetic and real-world data sets, showing both effectiveness of the model and performance of the method

Beyond the arithmetic mean : extensions of spectral clustering and semi-supervised learning for signed and multilayer graphs via matrix power means

In this thesis we present extensions of spectral clustering and semi-supervised learning to signed and multilayer graphs. These extensions are based on a one-parameter family of matrix functions called Matrix Power Means. In the scalar case, this family has the arithmetic, geometric and harmonic means as particular cases. We study the effectivity of this family of matrix functions through suitable versions of the stochastic block model to signed and multilayer graphs. We provide provable properties in expectation and further identify regimes where the state of the art fails whereas our approach provably performs well. Some of the settings that we analyze are as follows: first, the case where each layer presents a reliable approximation to the overall clustering; second, the case when one single layer has information about the clusters whereas the remaining layers are potentially just noise; third, the case when each layer has only partial information but all together show global information about the underlying clustering structure. We present extensive numerical verifications of all our results and provide matrix-free numerical schemes. With these numerical schemes we are able to show that our proposed approach based on matrix power means is scalable to large sparse signed and multilayer graphs. Finally, we evaluate our methods in real world datasets. For instance, we show that our approach consistently identifies clustering structure in a real signed network where previous approaches failed. This further verifies that our methods are competitive to the state of the art.In dieser Arbeit stellen wir Erweiterungen von spektralem Clustering und teilüberwachtem Lernen auf signierte und mehrschichtige Graphen vor. Diese Erweiterungen basieren auf einer einparametrischen Familie von Matrixfunktionen, die Potenzmittel genannt werden. Im skalaren Fall hat diese Familie die arithmetischen, geometrischen und harmonischen Mittel als Spezialfälle. Wir untersuchen die Effektivität dieser Familie von Matrixfunktionen durch Versionen des stochastischen Blockmodells, die für signierte und mehrschichtige Graphen geeignet sind. Wir stellen beweisbare Eigenschaften vor und identifizieren darüber hinaus Situationen in denen neueste, gegenwärtig verwendete Methoden versagen, während unser Ansatz nachweislich gut abschneidet. Wir untersuchen unter anderem folgende Situationen: erstens den Fall, dass jede Schicht eine zuverlässige Approximation an die Gesamtclusterung darstellt; zweitens den Fall, dass eine einzelne Schicht Informationen über die Cluster hat, während die übrigen Schichten möglicherweise nur Rauschen sind; drittens den Fall, dass jede Schicht nur partielle Informationen hat, aber alle zusammen globale Informationen über die zugrunde liegende Clusterstruktur liefern. Wir präsentieren umfangreiche numerische Verifizierungen aller unserer Ergebnisse und stellen matrixfreie numerische Verfahren zur Verfügung. Mit diesen numerischen Methoden sind wir in der Lage zu zeigen, dass unser vorgeschlagener Ansatz, der auf Potenzmitteln basiert, auf große, dünnbesetzte signierte und mehrschichtige Graphen skalierbar ist. Schließlich evaluieren wir unsere Methoden an realen Datensätzen. Zum Beispiel zeigen wir, dass unser Ansatz konsistent Clustering-Strukturen in einem realen signierten Netzwerk identifiziert, wo frühere Ansätze versagten. Dies ist ein weiterer Nachweis, dass unsere Methoden konkurrenzfähig zu den aktuell verwendeten Methoden sind

Influencia del compromiso organizacional en la relación entre conflictos interpersonales y el síndrome de quemarse por el trabajo (burnout) en profesionales de servicios (salud y educación)

El objetivo de esta investigación es analizar la influencia de los conflictos interpersonales en el trabajo y del compromiso organizacional sobre el síndrome de quemarse por el trabajo (burnout), una respuesta psicológica al estrés laboral crónico que aparece en los profesionales del sector servicio que trabajan hacia personas. La muestra del estudio estuvo compuesta por 389 mexicanos de los sectores salud y educación. Los resultados obtenidos indicaron que los conflictos interpersonales tienen un efecto directo positivo y significativo sobre el síndrome de quemarse por el trabajo (Hipótesis 1), mientras que el efecto del compromiso organizacional resultó negativo y significativo (Hipótesis 2). Los resultados alcanzados mediante el análisis de regresión múltiple jerárquica permiten afirmar que la interacción entre ambas variables (conflictos interpersonales y compromiso organizacional) establece diferencias significativas en los niveles del síndrome de quemarse por el trabajo (Hipótesis 3). Se concluye que al potenciar el compromiso organizacional se contribuye a disminuir el síndrome de quemarse por el trabajo, aunque ante la presencia de conflictos interpersonales el personal con alto compromiso organizacional (normativo y afectivo) es más sensible al desarrollo del síndrome. Por tanto, se debe intervenir conjuntamente sobre la organización y los empleados

Modelling and Control Design of Pitch-Controlled Variable Speed Wind Turbines

This chapter provides an overall perspective of modern wind power systems, including a discussion of major wind turbine concepts and technologies. More specifically, of the various wind turbine designs, pitch-controlled variable speed wind turbines controlled by means of power electronic converters have been considered. Among them, direct-in-line wind turbines with full-scale power converter and using direct-driven permanent magnet synchronous generators have increasingly drawn more interests to wind turbine manufactures due to its advantages over the other variable-speed wind turbines. Based on this issue, major operating characteristics of these devices are thoroughly analyzed and a three-phase grid-connected wind turbine system, incorporating a maximum power point tracker for dynamic active power generation is presented. Moreover, a simplified state-space averaged mathematical model of the wind turbine system is provided. An efficient power conditioning system of the selected wind turbine design and a new three-level control scheme by using concepts of instantaneous power in the synchronous-rotating d-q reference frame in order to simultaneously and independently control active and reactive power flow in the distribution network level are proposed. Dynamic system simulation studies in the MATLAB/Simulink environment is used in order to demonstrate the effectiveness of the proposed multi-level control approaches in d-q coordinates and the full detailed models presented. The fast response of power electronic devices and the enhanced performance of the proposed control techniques allow taking full advantage of the wind turbine generator.Fil: Molina, Marcelo Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Ingeniería. Instituto de Energía Eléctrica; ArgentinaFil: Mercado, Pedro Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Ingeniería. Instituto de Energía Eléctrica; Argentin