Redundancy Strategies for a High Splitting Optically Amplified Passive Optical Network

Copyright IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.High splitting, optically amplified, passive optical networks (SuperPONs) are investigated in terms of redundancy provision and protection mechanisms. Options for redundancy, including the important special case of dual homing, are detailed, and it is determined as to which of these options (duplication of the feeder and first distribution section, and N+1 protection of the optical amplifiers in the amplified splitter) would be required to be provided to all attached users to facilitate appropriate availability of the basic telephony service. The distributed amplified splitter dual homing solution is found to outperform the single amplified splitter solution in terms of its survivability. The protection mechanisms necessary to automatically switch to the redundant provision are discussed and it is seen that with the aid of suitable regular precautionary procedures protection switching can generally be provided rapidly (<50 ms). Finally, an availability, and cost versus availability, study confirms the aforementioned redundancy assessment for fiber-to-the-home (FTTH) implementations, but shows fiber-to-the-curb (FTTC) as needing additional redundancyPeer reviewe

Optimal importance sampling for overdamped Langevin dynamics

Calculating averages with respect to multimodal probability distributions is often necessary in applications. Markov chain Monte Carlo (MCMC) methods to this end, which are based on time averages along a realization of a Markov process ergodic with respect to the target probability distribution, are usually plagued by a large variance due to the metastability of the process. In this work, we mathematically analyze an importance sampling approach for MCMC methods that rely on the overdamped Langevin dynamics. Specifically, we study an estimator based on an ergodic average along a realization of an overdamped Langevin process for a modified potential. The estimator we consider incorporates a reweighting term in order to rectify the bias that would otherwise be introduced by this modification of the potential. We obtain an explicit expression in dimension 1 for the biasing potential that minimizes the asymptotic variance of the estimator for a given observable, and propose a general numerical approach for approximating the optimal potential in the multi-dimensional setting. We also investigate an alternative approach where, instead of the asymptotic variance for a given observable, a weighted average of the asymptotic variances corresponding to a class of observables is minimized. Finally, we demonstrate the capabilities of the proposed method by means of numerical experiments

Closed quantum subgroups of locally compact quantum groups

We investigate the fundamental concept of a closed quantum subgroup of a locally compact quantum group. Two definitions - one due to S.Vaes and one due to S.L.Woronowicz - are analyzed and relations between them discussed. Among many reformulations we prove that the former definition can be phrased in terms of quasi-equivalence of representations of quantum groups while the latter can be related to an old definition of Podle\'s from the theory of compact quantum groups. The cases of classical groups, duals of classical groups, compact and discrete quantum groups are singled out and equivalence of the two definitions is proved in the relevant context. A deep relationship with the quantum group generalization of Herz restriction theorem from classical harmonic analysis is also established, in particular, in the course of our analysis we give a new proof of Herz restriction theorem.Comment: 24 pages, v3 adds another reference. The paper will appear in Advances in Mathematic

The Mean Field Ensemble Kalman Filter: Near-Gaussian Setting

The ensemble Kalman filter is widely used in applications because, for high dimensional filtering problems, it has a robustness that is not shared for example by the particle filter; in particular it does not suffer from weight collapse. However, there is no theory which quantifies its accuracy as an approximation of the true filtering distribution, except in the Gaussian setting. To address this issue we provide the first analysis of the accuracy of the ensemble Kalman filter beyond the Gaussian setting. Our analysis is developed for the mean field ensemble Kalman filter. We rewrite the update equations for this filter, and for the true filtering distribution, in terms of maps on probability measures. We introduce a weighted total variation metric to estimate the distance between the two filters and we prove various stability estimates for the maps defining the evolution of the two filters, in this metric. Using these stability estimates we demonstrate that if the true filtering distribution is close to Gaussian in the joint space of state and data, in the weighted total variation metric, then the true-filter is well approximated by the ensemble Kalman filter, in the same metric. Finally, we provide a generalization of these results to the Gaussian projected filter, which can be viewed as a mean field description of the unscented Kalman filter

Monitoring Home-Based Activity of Stroke Patients: A Digital Solution for Visuo-Spatial Neglect Evaluation

The possibility to prescribe home-based rehabilitation activity after stroke strongly increases the amount of exercises to perform, thus helping the maintenance of relearned skills, the completion of the rehabilitation program, the practice of physical and mental concentration. Even more important is the monitoring of the patient activity at home, as it is provided by the Remote Monitoring Validation Engineering System (ReMoVES) platform [1]. The present work refers to the implementation and integration in ReMoVES platform of a digital and web-based version of Albert\u2019s [2] and Line Bisection [3] tests devoted to visuo-spatial neglect evaluation and its remote monitoring. A statistical analysis devoted to validating test-retest reliability is proposed. Concurrent correlation between digital and traditional administration of the tests is presented, in order to evaluate the validity of the remote monitoring of the home-administration through ReMoVES platform

Determination of liposome/water partition coefficients of organic acids and bases by solid-phase microextraction

The extraction of two methylated anilines and three chlorinated phenols by solid-phase microextraction (SPME) fibers coated with polyacrylate was investigated as a function of pH. Only the neutral species of the acids and bases partitioned into the polymer. Extraction kinetics were accelerated for the hydrophobic phenols at pH values around their acidity constant. This is presumably due to a reconstitution of the neutral species in the unstirred aqueous layer adjacent to the polymer surface by the charged species through the fast acid-base equilibrium. Although the charged species is not taken up into the polymer. liposome/water distribution ratios could be measured up to a pH value, where 99% of the compounds were present as charged species. The partition coefficients of the neutral and charged species were extrapolated from the pH profiles of the liposome/water distribution ratios. The resulting values were slightly lower than those measured with equilibrium dialysis. The discrepancies are discussed with respect to differences in the experimental conditions and the possibility of matrix effects during SPME measurements

A Characterization of right coideals of quotient type and its application to classification of Poisson boundaries

Let $G$ be a co-amenable compact quantum group. We show that a right coideal of $G$ is of quotient type if and only if it is the range of a conditional expectation preserving the Haar state and is globally invariant under the left action of the dual discrete quantum group. We apply this result to theory of Poisson boundaries introduced by Izumi for discrete quantum groups and generalize a work of Izumi-Neshveyev-Tuset on $SU_q(N)$ for co-amenable compact quantum groups with the commutative fusion rules. More precisely, we prove that the Poisson integral is an isomorphism between the Poisson boundary and the right coideal of quotient type by maximal quantum subgroup of Kac type. In particular, the Poisson boundary and the quantum flag manifold are isomorphic for any q-deformed classical compact Lie group.Comment: 28 pages, Remark 4.9 adde

Classification of minimal actions of a compact Kac algebra with amenable dual

We show the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II$_1$. This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type intertwining argument.Comment: 68 pages, Introduction rewritten; minor correction