Abstract:Energy transfer between the interacting waves in a distributed Brillouin sensor can result in a distorted measurement of the local Brillouin gain spectrum, leading to systematic errors. It is demonstrated that this depletion effect can be precisely modelled. This has been validated by experimental tests in an excellent quantitative agreement. Strict guidelines can be enunciated from the model to make the impact of depletion negligible, for any type and any length of fiber. Gonzalez-Herraez, "Brillouin optical time-domain analysis assisted by second-order Raman amplification," Opt. Express 18(18), 18769-18778 (2010). 13. Y. Dong, L. Chen, and X. Bao, "System optimization of a long-range Brillouin-loss-based distributed fiber sensor," Appl. Opt. 49(27), 5020-5025 (2010). 14. M. Niklès, L. Thévenaz, and P. A. Robert, "Simple distributed fiber sensor based on Brillouin gain spectrum analysis," Opt. Lett. 21(10), 758-760 (1996). 15. S. Diaz, S. Mafang-Foaleng, M. Lopez-Amo, and L. Thevenaz, "A high-performance optical time-domain Brillouin distributed fiber sensor," IEEE Sens. J. 8(7), 1268-1272 (2008

We investigate regularized algorithms combining with projection for least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space. We prove convergence results with respect to variants of norms, under a capacity assumption on the hypothesis space and a regularity condition on the target function. As a result, we obtain optimal rates for regularized algorithms with randomized sketches, provided that the sketch dimension is proportional to the effective dimension up to a logarithmic factor. As a byproduct, we obtain similar results for Nyström regularized algorithms. Our results provide optimal, distribution-dependent rates that do not have any saturation effect for sketched/Nyström regularized algorithms, considering both the attainable and non-attainable cases.

CEIs/ARBs therapy might be associated with a reduce risk of CRC development, but whether use of these medications improves the outcomes of CRC remains unknown. Large-scale and more robust studies are needed to further explore this association.

The energy transfer between the two interacting optical waves in a distributed sensor based on stimulated Brillouin scattering can lead to a non-uniform spectral distribution of the pumping power after a long propagation. This results in a spectrally distorted gain that biases the determination of the maximum gain frequency. A quantitative analytical model gives an expression for the tolerable pump power change keeping the maximum bias within a given accuracy.

This article considers recovery of signals that are sparse or approximately sparse in terms of a (possibly) highly overcomplete and coherent tight frame from undersampled data corrupted with additive noise. We show that the properly constrained l 1 -analysis optimization problem, called analysis Dantzig selector, stably recovers a signal which is nearly sparse in terms of a tight frame provided that the measurement matrix satisfies a restricted isometry property adapted to the tight frame. As a special case, we consider the Gaussian noise. Further, under a sparsity scenario, with high probability, the recovery error from noisy data is within a log-like factor of the minimax risk over the class of vectors which are at most s sparse in terms of the tight frame. Similar results for the analysis LASSO are shown.The above two algorithms provide guarantees only for noise that is bounded or bounded with high probability (for example, Gaussian noise). However, when the underlying measurements are corrupted by sparse noise, these algorithms perform suboptimally. We demonstrate robust methods for reconstructing signals that are nearly sparse in terms of a tight frame in the presence of bounded noise combined with sparse noise. The analysis in this paper is based on the restricted isometry property adapted to a tight frame, which is a natural extension to the standard restricted isometry property.

This paper discusses reconstruction of a signal from undersampled data in the situation that the signal is sparse or approximately sparse in terms of a (possibly) highly overcomplete and coherent tight frame via the -analysis optimization problem. Some new sufficient conditions on the -restricted isometry property are given to guarantee stable recovery of signals which are nearly sparse in terms of , from undersampled data with minimal -norm of transform coefficients. One of the main results of this paper shows that if the -restricted isometry constant of the measurement matrix satisfies , then signals which are approximately -sparse in terms of are guaranteed to be stably recovered via the -analysis optimization problem. We point out that with the lemmas and the proof techniques developed in this paper, most of the sufficient conditions on the standard restricted isometry property for stable recovery of nearly sparse signals via standard -minimization, can be similarly extended to the general case of the -restricted isometry property for stable recovery of signals that are nearly sparse in terms of via the -analysis optimization problem, yielding weaker conditions than previously available in the literature.

Our aim of this article is to reconstruct a signal from undersampled data in the situation that the signal is sparse in terms of a tight frame. We present a condition, which is independent of the coherence of the tight frame, to guarantee accurate recovery of signals which are sparse in the tight frame, from undersampled data with minimal l 1 -norm of transform coefficients. This improves the result in [1]. Also, the l q -minimization (0 < q < 1) approaches are introduced. We show that under a suitable condition, there exists a value q 0 ∈ (0, 1] such that for any q ∈ (0, q 0 ), each solution of the l q -minimization is approximately well to the true signal. In particular, when the tight frame is an identity matrix or an orthonormal basis, all results obtained in this paper appeared in [13] and [26].

The nucleation and crystallization kinetics of PbO–BaO–SrO–Nb2O5–B2O3–SiO2‐based glass–ceramics have been investigated. Strontium barium niobate (Sr0.33Ba0.67Nb2O6) with a tetragonal tungsten–bronze structure formed as the major crystalline phase, which nucleates and grows on the surface region of samples. The results of the present study showed an apparent activation energy of 193 kJ/mol for nucleation, which was controlled by the viscous flow of the glass. Quantitative X‐ray analysis and differential thermal analysis showed that the rate‐limiting mechanism of crystallization appeared to be a three‐dimensional interfacial growth, which has an apparent activation energy of 386–430 kJ/mol, a value that is close to the dissociation of Si–O bonds in the glass system.