Interval Oscillation for Second Order Nonlinear Differential Equations with a Damping Term

2000 Mathematics Subject Classification: 34C10, 34C15.

Oscillation Criteria of Second-Order Quasi-Linear Neutral Delay Difference Equations

2000 Mathematics Subject Classification: 39A10.

Extended reach of 116 Gb/s DP-QPSK transmission using random DFB fiber laser based Raman amplification and bidirectional second-order pumping

We propose a novel random DFB fiber laser based Raman amplification using bidirectional second-order pumping. This extends the reach of 116 Gb/s DP-QPSK WDM transmission up to 7915 km, compared with other Raman amplification techniques.

Transmission performance improvement using random DFB laser based Raman amplification and bidirectional second-order pumping

We demonstrate that a distributed Raman amplification scheme based on random distributed feedback (DFB) fiber laser enables bidirectional second-order Raman pumping without increasing relative intensity noise (RIN) of the signal. This extends the reach of 10 × 116 Gb/s DP-QPSK WDM transmission up to 7915 km, compared with conventional Raman amplification schemes. Moreover, this scheme gives the longest maximum transmission distance among all the Raman amplification schemes presented in this paper, whilst maintaining relatively uniform and symmetric signal power distribution, and is also adjustable in order to be highly compatible with different nonlinearity compensation techniques, including mid-link optical phase conjugation (OPC) and nonlinear Fourier transform (NFT).

Effect of second order signal-noise interactions in nonlinearity compensated optical transmission systems

In this Letter, we theoretically and numerically analyze the performance of coherent optical transmission systems that deploy inline or transceiver based nonlinearity compensation techniques. For systems where signal-signal nonlinear interactions are fully compensated, we find that beyond the performance peak the signal-to-noise ratio degradation has a slope of 3 dBSNR/dBPower suggesting a quartic rather than quadratic dependence on signal power. This is directly related to the fact that signals in a given span will interact not only with linear amplified spontaneous emission noise, but also with the nonlinear four-wave mixing products generated from signal-noise interaction in previous (hitherto) uncompensated spans. The performance of optical systems employing different nonlinearity compensation schemes were numerically simulated and compared against analytical predictions, showing a good agreement within a 0.4 dB margin of error.

RIN mitigation in second-order pumped Raman fibre laser based amplification

We experimentally investigate three Raman fibre laser based amplification techniques with second-order bidirectional pumping. Relatively intensity noise (RIN) being transferred to the signal can be significantly suppressed by reducing first-order reflection near the input end. © 2015 OSA.

Brillouin optical time-domain analysis assisted by second-order Raman amplification

We propose and experimentally demonstrate a new method to extend the range of Brillouin optical time domain analysis (BOTDA) systems. It exploits the virtual transparency created by second-order Raman pumping in optical fibers. The idea is theoretically analyzed and experimentally demonstrated in a 50 km fiber. By working close to transparency, we also show that the measurement length of the BOTDA can be increased up to 100 km with 2 meter resolution. We envisage extensions of this technique to measurement lengths well beyond this value, as long as the issue of relative intensity noise (RIN) of the primary Raman pump can be avoided. © 2010 Optical Society of America.

A Prescription for the Future of Religious Studies: Second-Order Tradition and the Spirit of Modern Science

An examination of the efficacy of religious studies scholarship through a Kuhnian lens.

Second-Order Risk Constraints

This paper discusses how numerically imprecise information can be modelled and how a risk evaluation process can be elaborated by integrating procedures for numerically imprecise probabilities and utilities. More recently, representations and methods for stating and analysing probabilities and values (utilities) with belief distributions over them (second order representations) have been suggested. In this paper, we are discussing some shortcomings in the use of the principle of maximising the expected utility and of utility theory in general, and offer remedies by the introduction of supplementary decision rules based on a concept of risk constraints taking advantage of second-order distributions.

Anomaly Detection in Noisy Images

Finding rare events in multidimensional data is an important detection problem that has applications in many fields, such as risk estimation in insurance industry, finance, flood prediction, medical diagnosis, quality assurance, security, or safety in transportation. The occurrence of such anomalies is so infrequent that there is usually not enough training data to learn an accurate statistical model of the anomaly class. In some cases, such events may have never been observed, so the only information that is available is a set of normal samples and an assumed pairwise similarity function. Such metric may only be known up to a certain number of unspecified parameters, which would either need to be learned from training data, or fixed by a domain expert. Sometimes, the anomalous condition may be formulated algebraically, such as a measure exceeding a predefined threshold, but nuisance variables may complicate the estimation of such a measure. Change detection methods used in time series analysis are not easily extendable to the multidimensional case, where discontinuities are not localized to a single point. On the other hand, in higher dimensions, data exhibits more complex interdependencies, and there is redundancy that could be exploited to adaptively model the normal data. In the first part of this dissertation, we review the theoretical framework for anomaly detection in images and previous anomaly detection work done in the context of crack detection and detection of anomalous components in railway tracks. In the second part, we propose new anomaly detection algorithms. The fact that curvilinear discontinuities in images are sparse with respect to the frame of shearlets, allows us to pose this anomaly detection problem as basis pursuit optimization. Therefore, we pose the problem of detecting curvilinear anomalies in noisy textured images as a blind source separation problem under sparsity constraints, and propose an iterative shrinkage algorithm to solve it. Taking advantage of the parallel nature of this algorithm, we describe how this method can be accelerated using graphical processing units (GPU). Then, we propose a new method for finding defective components on railway tracks using cameras mounted on a train. We describe how to extract features and use a combination of classifiers to solve this problem. Then, we scale anomaly detection to bigger datasets with complex interdependencies. We show that the anomaly detection problem naturally fits in the multitask learning framework. The first task consists of learning a compact representation of the good samples, while the second task consists of learning the anomaly detector. Using deep convolutional neural networks, we show that it is possible to train a deep model with a limited number of anomalous examples. In sequential detection problems, the presence of time-variant nuisance parameters affect the detection performance. In the last part of this dissertation, we present a method for adaptively estimating the threshold of sequential detectors using Extreme Value Theory on a Bayesian framework. Finally, conclusions on the results obtained are provided, followed by a discussion of possible future work.

Second-order cyclostationarity-based detection and classification of LTE SC-FDMA signals for cognitive radio

Cognitive radio (CR) was developed for utilizing the spectrum bands efficiently. Spectrum sensing and awareness represent main tasks of a CR, providing the possibility of exploiting the unused bands. In this thesis, we investigate the detection and classification of Long Term Evolution (LTE) single carrier-frequency division multiple access (SC-FDMA) signals, which are used in uplink LTE, with applications to cognitive radio. We explore the second-order cyclostationarity of the LTE SC-FDMA signals, and apply results obtained for the cyclic autocorrelation function to signal detection and classification (in other words, to spectrum sensing and awareness). The proposed detection and classification algorithms provide a very good performance under various channel conditions, with a short observation time and at low signal-to-noise ratios, with reduced complexity. The validity of the proposed algorithms is verified using signals generated and acquired by laboratory instrumentation, and the experimental results show a good match with computer simulation results.

A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems

We develop the a-posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite element methods for a class of second-order quasilinear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh-dependent) energy norm. The bounds are explicit in the local mesh size and the local degree of the approximating polynomial. The performance of the proposed estimators within an automatic hp-adaptive refinement procedure is studied through numerical experiments.