University of California, Santa Barbara

About: University of California, Santa Barbara is a education organization based out in Santa Barbara, California, United States. It is known for research contribution in the topics: Population & Galaxy. The organization has 30281 authors who have published 80852 publications receiving 4626827 citations. The organization is also known as: UC Santa Barbara & UCSB.

Kron Reduction of Graphs With Applications to Electrical Networks

Abstract: Consider a weighted undirected graph and its corresponding Laplacian matrix, possibly augmented with additional diagonal elements corresponding to self-loops. The Kron reduction of this graph is again a graph whose Laplacian matrix is obtained by the Schur complement of the original Laplacian matrix with respect to a specified subset of nodes. The Kron reduction process is ubiquitous in classic circuit theory and in related disciplines such as electrical impedance tomography, smart grid monitoring, transient stability assessment, and analysis of power electronics. Kron reduction is also relevant in other physical domains, in computational applications, and in the reduction of Markov chains. Related concepts have also been studied as purely theoretic problems in the literature on linear algebra. In this paper we analyze the Kron reduction process from the viewpoint of algebraic graph theory. Specifically, we provide a comprehensive and detailed graph-theoretic analysis of Kron reduction encompassing topological, algebraic, spectral, resistive, and sensitivity analyses. Throughout our theoretic elaborations we especially emphasize the practical applicability of our results to various problem setups arising in engineering, computation, and linear algebra. Our analysis of Kron reduction leads to novel insights both on the mathematical and the physical side.

Spatial population dynamics: analyzing patterns and processes of population synchrony

Abstract: The search for mechanisms behind spatial population synchrony is currently a major issue in population ecology. Theoretical studies highlight how synchronizing mechanisms such as dispersal, regionally correlated climatic variables and mobile enemies might interact with local dynamics to produce different patterns of spatial covariance. Specialized statistical methods, applied to large-scale survey data, aid in testing the theoretical predictions with empirical estimates. Observational studies and experiments on the demography of local populations are paramount to identify the true ecological mechanisms. The recent achievements illustrate the power of combining theory, observation and/or experimentation and statistical modeling in the ecological research protocol.

Inspired by Distraction Mind Wandering Facilitates Creative Incubation

Abstract: Although anecdotes that creative thoughts often arise when one is engaged in an unrelated train of thought date back thousands of years, empirical research has not yet investigated this potentially critical source of inspiration. We used an incubation paradigm to assess whether performance on validated creativity problems (the Unusual Uses Task, or UUT) can be facilitated by engaging in either a demanding task or an undemanding task that maximizes mind wandering. Compared with engaging in a demanding task, rest, or no break, engaging in an undemanding task during an incubation period led to substantial improvements in performance on previously encountered problems. Critically, the context that improved performance after the incubation period was associated with higher levels of mind wandering but not with a greater number of explicitly directed thoughts about the UUT. These data suggest that engaging in simple external tasks that allow the mind to wander may facilitate creative problem solving.