Semisimplicity of the Lyapunov spectrum for irreducible cocycles

Let $G$ be a semisimple Lie group acting on a space $X$, let $\mu$ be a compactly supported measure on $G$, and let $A$ be a strongly irreducible linear cocycle over the action of $G$. We then have a random walk on $X$, and let $T$ be the associated shift map. We show that the cocycle $A$ over the action of $T$ is conjugate to a block conformal cocycle. This statement is used in the recent paper by Eskin-Mirzakhani on the classifications of invariant measures for the SL(2,R) action on moduli space. The ingredients of the proof are essentially contained in the papers of Guivarch and Raugi and also Goldsheid and Margulis.Comment: 27 pages. Final version based on the referee's report. To appear in Israel J. Mat

Collective innovation

Thesis (M.B.A.)--Massachusetts Institute of Technology, Sloan School of Management, 2007.Includes bibliographical references (p. 178-179).The ability to innovate sits at the heart of an organization's ability to succeed in a competitive environment. An organization can innovate by improving existing products, services, or processes or by generating new products, services, or processes. Achieving successful, repeated organizational innovation, however, is a significant challenge. The hurdles to such innovation run the gamut from psychological to structural to procedural. Managers can fall victim to myopia and other human level challenges. Organizational processes, structures, and values can short circuit innovation as well. Given these challenges, we posit that an innovation strategy embracing the concepts of collective intelligence and openness may enable organizations to surmount these hurdles. We refer to this approach as Collective Innovation and define it as a connected, open, and collaborative process that generates, develops, prioritizes, and executes new ideas. To develop our argument, we surveyed literature from a wide array of disciplines including economics, organizational behavior, social psychology, and organizational change.(cont.) We begin this thesis by drawing a connection between the economic theories of Adam Smith and Ronald Coase and research into the changing workplace by Thomas Malone. We then introduce the concepts of collective intelligence and openness, core tenets of Collective Innovation. After introducing Collective Innovation, we examine its place in the history of innovation strategy. Next, we outline and describe the four stages of the Collective Innovation process. Having dealt mainly in theory, we then turn to the application of Collective Innovation and the myriad challenges that managers will face when attempting to implement such a strategy. Keeping in mind these challenges, we outline four ways in which organizations might use Collective Innovation to power the exploration-side of their operations. Finally, we revisit several remaining questions before concluding our analysis.by Alex Slawsby [and] Carlos Rivera.M.B.A

Métodos de Simulación de Armónicos en Sistemas Eléctricos de Potencia

La simulación de armónicos en sistemas de potencia puede realizarse mediante métodos que empleen la dependencia temporal o la dependencia frecuencial de los sistemas eléctricos. Todos los métodos detallados requieren de la solución de las ecuaciones de la red, y es en la forma de estas ecuaciones que los métodos se diferencian. La robustez y rápida convergencia hacen que unos métodos sean más empleados porque pueden entregar resultados más precisos. Los diversos componentes de la red deben ser modelados apropiadamente para que puedan reflejar su comportamiento cuando las variables de estado del sistema tienen a tomar formas altamente distorsionadas y para esto se deben tomar los modelos que se detallan en la literatura. Una vez que se realizan simulaciones de armónicos, se deben comparar los resultados obtenidos con aquellos límites que figuran en normativas específicas de calidad de energía y, en caso de ser excesiva la emisión el paso a seguir es el diseño de estrategias o sistemas de mitigación de armónicos.The harmonic simulation on power systems can be performed using methodologies which are focused on time and frequency domain. The solution of power systems under harmonics require a complete and detailed solution of grid equations, and consequently, different techniques and methodologies are used to solve these equations, which are used based on its application, due to the  act that robustness and convergence speed. On the other hand, not only methodologies are important, but also component models, which it is a mathematical representation of real behavior of electrical devices on power systems. Set in this context, models and techniques are essential to simulate and obtain results, which are measured and compared with international standards on electric power quality, subsequently, impacts and possible techniques for power quality improvement by mitigation of harmonics could be proposed

Switching rates of multi-step reactions

We consider a switching rate of a meta-stable reaction scheme, which includes reactions with arbitrary steps, e.g. $kA\to(k+r)A$. Employing WKB approximation, controlled by a large system size, we evaluate both the exponent and the pre-exponential factor for the rate. The results are illustrated on a number of examples