Finite element approximation for the fractional eigenvalue problem

The purpose of this work is to study a finite element method for finding solutions to the eigenvalue problem for the fractional Laplacian. We prove that the discrete eigenvalue problem converges to the continuous one and we show the order of such convergence. Finally, we perform some numerical experiments and compare our results with previous work by other authors.Comment: 20 pages, 6 figure

Inferring broken detailed balance in the absence of observable currents

Identifying dissipation is essential for understanding the physical mechanisms underlying nonequilibrium processes. {In living systems, for example, the dissipation is directly related to the hydrolysis of fuel molecules such as adenosine triphosphate (ATP)}. Nevertheless, detecting broken time-reversal symmetry, which is the hallmark of dissipative processes, remains a challenge in the absence of observable directed motion, flows, or fluxes. Furthermore, quantifying the entropy production in a complex system requires detailed information about its dynamics and internal degrees of freedom. Here we introduce a novel approach to detect time irreversibility and estimate the entropy production from time-series measurements, even in the absence of observable currents. We apply our technique to two different physical systems, namely, a partially hidden network and a molecular motor. Our method does not require complete information about the system dynamics and thus provides a new tool for studying nonequilibrium phenomena.Comment: 14 pages, 6 figure

Physical qubits from charged particles: IR divergences in quantum information

We consider soft photons effects (IR structure of QED) on the construction of physical qubits. Soft-photons appear when we build charged qubits from the asymptotic states of QED. This construction is necessary in order to include the effect of soft photons on entanglement measures. The nonexistence of free charged particles (due to the long range of QED interactions) lead us to question the sense of the very concept of free charged qubit. In this letter, using the "dressing" formalism, we build physical charged qubits from dressed fields which have the correct asymptotic behavior, are gauge invariant, their propagators have a particle pole structure and are free from infrared divergences. Finally, we discuss the impact of the soft corrections on the entanglement measures.Comment: 4 pages, 2 figures, RevTeX. Version 2: Some references update

A semantic-based probabilistic approach for real-time video event recognition

This is the author’s version of a work that was accepted for publication in Journal Computer Vision and Image Understanding. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal Computer Vision and Image Understanding, 116, 9 (2012) DOI: 10.1016/j.cviu.2012.04.005This paper presents an approach for real-time video event recognition that combines the accuracy and descriptive capabilities of, respectively, probabilistic and semantic approaches. Based on a state-of-art knowledge representation, we define a methodology for building recognition strategies from event descriptions that consider the uncertainty of the low-level analysis. Then, we efficiently organize such strategies for performing the recognition according to the temporal characteristics of events. In particular, we use Bayesian Networks and probabilistically-extended Petri Nets for recognizing, respectively, simple and complex events. For demonstrating the proposed approach, a framework has been implemented for recognizing human-object interactions in the video monitoring domain. The experimental results show that our approach improves the event recognition performance as compared to the widely used deterministic approach.This work has been partially supported by the Spanish Administration agency CDTI (CENIT-VISION 2007- 1007), by the Spanish Government (TEC2011-25995 EventVideo), by the Consejería de Educación of the Comunidad de Madrid and by The European Social Fund