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

Control of a DSTATCOM Coupled with a Flywheel Energy Storage System to Improve the Power Quality of a Wind Power System

Wind power generation is considered the most economic viable alternative within the portfolio of renewable energy resources. Among its main advantages are the large number of potential sites for plant installation and a rapidly evolving technology. However, the lack of controllability over the wind and the type of generation system used cause problems to the electric systems. Among such problems are those produced by wind power short-term fluctuations, e.g., in the power quality and in the dynamics of the system (Slootweg & Kling, 2003; Ackermann, 2005; Suvire & Mercado, 2008; Chen & Spooner, 2001; Mohod & Aware; 2008; Smith et al., 2007). In addition, the reduced cost of power electronic devices as well as the breakthrough of new technologies in the field of electric energy storage makes it possible to incorporate this storage with electronic control into power systems (Brad & McDowall, 2005; Carrasco, 2006; Barton & Infield, 2004; Hebner et al., 2002). These devices allow a dynamic control to be made of both voltage and flows of active and reactive power. Therefore, they offer a great potential in their use to mitigate problems introduced by wind generation. Based on the results obtained by analyzing different selection criteria, a Distribution Static Synchronous Compensator (DSTATCOM) coupled with a Flywheel Energy Storage System (FESS) has been proposed as the most appropriate system for contributing to the smoothing of wind power short-term fluctuations (Suvire & Mercado, 2007).Fil: Suvire, Gaston Orlando. 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