The exit problem for diffusions with time-periodic drift and stochastic resonance

Physical notions of stochastic resonance for potential diffusions in periodically changing double-well potentials such as the spectral power amplification have proved to be defective. They are not robust for the passage to their effective dynamics: continuous-time finite-state Markov chains describing the rough features of transitions between different domains of attraction of metastable points. In the framework of one-dimensional diffusions moving in periodically changing double-well potentials we design a new notion of stochastic resonance which refines Freidlin's concept of quasi-periodic motion. It is based on exact exponential rates for the transition probabilities between the domains of attraction which are robust with respect to the reduced Markov chains. The quality of periodic tuning is measured by the probability for transition during fixed time windows depending on a time scale parameter. Maximizing it in this parameter produces the stochastic resonance points.Comment: Published at http://dx.doi.org/10.1214/105051604000000530 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Toplogical derivative for nonlinear magnetostatic problem

The topological derivative represents the sensitivity of a domain-dependent functional with respect to a local perturbation of the domain and is a valuable tool in topology optimization. Motivated by an application from electrical engineering, we derive the topological derivative for an optimization problem which is constrained by the quasilinear equation of two-dimensional magnetostatics. Here, the main ingredient is to establish a sufficiently fast decay of the variation of the direct state at scale 1 as $|x|\rightarrow \infty$. In order to apply the method in a bi-directional topology optimization algorithm, we derive both the sensitivity for introducing air inside ferromagnetic material and the sensitivity for introducing material inside an air region. We explicitly compute the arising polarization matrices and introduce a way to efficiently evaluate the obtained formulas. Finally, we employ the derived formulas in a level-set based topology optimization algorithm and apply it to the design optimization of an electric motor.Comment: 54 pages, 9 figure

Magnetic Monopoles in (Noncommutative) Quantum Mechanics

We utilize the close relation between the complex space $\textbf{C}^2$ and the real space $\textbf{R}^3$ to reformulate quantum mechanics in a manner which allows to, either or both, describe magnetic monopoles and quantize the underlying space, obtaining (noncommutative) quantum mechanics (with magnetic monopoles).Comment: 8 page

Magnetic monopoles and symmetries in noncommutative space

In this paper, we review the progress in the analysis of magnetic monopoles as generalized states in quantum mechanics. We show that the considered model contains rich algebraic structure that generates symmetries which have been utilized in different physical contexts. Even though are we focused on quantum mechanics in noncommutative space $\textbf{R}_\lambda^3$, the results can be reconstructed in ordinary quantum mechanics in $\textbf{R}^3$ as well.Comment: 7 page

Bank Networks from Text: Interrelations, Centrality and Determinants

In the wake of the still ongoing global financial crisis, bank interdependencies have come into focus in trying to assess linkages among banks and systemic risk. To date, such analysis has largely been based on numerical data. By contrast, this study attempts to gain further insight into bank interconnections by tapping into financial discourse. We present a text-to-network process, which has its basis in co-occurrences of bank names and can be analyzed quantitatively and visualized. To quantify bank importance, we propose an information centrality measure to rank and assess trends of bank centrality in discussion. For qualitative assessment of bank networks, we put forward a visual, interactive interface for better illustrating network structures. We illustrate the text-based approach on European Large and Complex Banking Groups (LCBGs) during the ongoing financial crisis by quantifying bank interrelations and centrality from discussion in 3M news articles, spanning 2007Q1 to 2014Q3.Comment: Quantitative Finance, forthcoming in 201

These confabulations are guaranteed to improve your marriage! Toward a teleological theory of confabulation

Confabulation is typically understood to be dysfunctional. But this understanding neglects the phenomenon’s potential benefits. In fact, we think that the benefits of non-clinical confabulation provide a better foundation for a general account of confabulation. In this paper, we start from these benefits to develop a social teleological account of confabulation. Central to our account is the idea that confabulation manifests a kind of willful ignorance. By understanding confabulation in this way, we can provide principled explanations for the difference between clinical and non-clinical cases of confabulation and the extent to which confabulation is rational