Inverse four-wave mixing and self-parametric amplification in optical fibre

An important group of nonlinear processes in optical fibre involve the mixing of four waves due to the intensity dependence of the refractive index. It is customary to distinguish between nonlinear effects that require external/pumping waves (cross-phase modulation and parametric processes such as four-wave mixing) and those arising from self-action of the propagating optical field (self-phase modulation and modulation instability). Here, we present a new nonlinear self-action effect—self-parametric amplification—which manifests itself as optical spectrum narrowing in normal dispersion fibre, leading to very stable propagation with a distinctive spectral distribution. The narrowing results from inverse four-wave mixing, resembling an effective parametric amplification of the central part of the spectrum by energy transfer from the spectral tails. Self-parametric amplification and the observed stable nonlinear spectral propagation with a random temporal waveform can find applications in optical communications and high-power fibre lasers with nonlinear intracavity dynamics.

Impact of reduced complexity inverse Volterra series transfer function-based nonlinear equalizer in coherent OFDM systems for next-generation core networks

A modern electronic nonlinearity equalizer (NLE) based on inverse Volterra series transfer function (IVSTF) with reduced complexity is applied on coherent optical orthogonal frequency-division multiplexing (CO-OFDM) signals for next-generation long- and ultra-long-haul applications. The OFDM inter-subcarrier crosstalk effects are explored thoroughly using the IVSTF-NLE and compared with the case of linear equalization (LE) for transmission distances of up to 7000 km. © 2013 IEEE.

Inverse Problems Involving Generalized Axial-Symmetric Helmholtz Equation

MSC 2010: 35J05, 33C10, 45D05

The Direct and Inverse Spectral Problems for some Banded Matrices

2000 Mathematics Subject Classification: 15A29.

Bayesian and Frequentist Two-Sample Predictions of the Inverse Weibull Model Based on Generalized Order Statistics

2000 Mathematics Subject Classification: 62E16,62F15, 62H12, 62M20.

Uniqueness and counterexamples in some inverse source problems

Uniqueness of a solution is investigated for some inverse source problems arising in linear parabolic equations. We prove new uniqueness results formulated in Theorems 3.1 and 3.2. We also show optimality of the conditions under which uniqueness holds by explicitly constructing counterexamples, that is by constructing more than one solution in the case when the conditions for uniqueness are violated.

Modified nonlinear inverse synthesis for optical links with distributed Raman amplification

We propose a modification of the nonlinear digital signal processing technique based on the nonlinear inverse synthesis for the systems with distributed Raman amplification. The proposed path-average approach offers 3 dB performance gain, regardless of the signal power profile.

Demonstration of nonlinear inverse synthesis transmission over transoceanic distances

Nonlinear Fourier transform (NFT) and eigenvalue communication with the use of nonlinear signal spectrum (both discrete and continuous), have been recently discussed as promising transmission methods to combat fiber nonlinearity impairments. In this paper, for the first time, we demonstrate the generation, detection and transmission performance over transoceanic distances of 10 Gbaud and nonlinear inverse synthesis (NIS) based signal (4 Gb/s line rate), in which the transmitted information is encoded directly onto the continuous part of the signal nonlinear spectrum. By applying effective digital signal processing techniques, a reach of 7344 km was achieved with a bit-error-rate (BER) (2.1×10-2) below the 20% FEC threshold. This represents an improvement by a factor of ~12 in data capacity x distance product compared with other previously demonstrated NFT-based systems, showing a significant advance in the active research area of NFT-based communication systems.

A new inverse DEA method for merging banks

This study suggests a novel application of Inverse Data Envelopment Analysis (InvDEA) in strategic decision making about mergers and acquisitions in banking. The conventional DEA assesses the efficiency of banks based on the information gathered about the quantities of inputs used to realize the observed level of outputs produced. The decision maker of a banking unit willing to merge/acquire another banking unit needs to decide about the inputs and/or outputs level if an efficiency target for the new banking unit is set. In this paper, a new InvDEA-based approach is developed to suggest the required level of the inputs and outputs for the merged bank to reach a predetermined efficiency target. This study illustrates the novelty of the proposed approach through the case of a bank considering merging with or acquiring one of its competitors to synergize and realize higher level of efficiency. A real data set of 42 banking units in Gulf Corporation Council countries is used to show the practicality of the proposed approach.

Inverse space-dependent force problems for the wave equation

The determination of the displacement and the space-dependent force acting on a vibrating structure from measured final or time-average displacement observation is thoroughly investigated. Several aspects related to the existence and uniqueness of a solution of the linear but ill-posed inverse force problems are highlighted. After that, in order to capture the solution a variational formulation is proposed and the gradient of the least-squares functional that is minimized is rigorously and explicitly derived. Numerical results obtained using the Landweber method and the conjugate gradient method are presented and discussed illustrating the convergence of the iterative procedures for exact input data. Furthermore, for noisy data the semi-convergence phenomenon appears, as expected, and stability is restored by stopping the iterations according to the discrepancy principle criterion once the residual becomes close to the amount of noise. The present investigation will be significant to researchers concerned with wave propagation and control of vibrating structures.

First experimental demonstration of nonlinear inverse synthesis transmission over transoceanic distances

We demonstrate for the first time, the transmission performance of 10Gbaud nonlinear inverse synthesis based signal over transoceanic distances, showing a significant improvement in data capacity x distance product (x12) compared with other NFT-based systems.

Serum α-tocopherol has a nonlinear inverse association with periodontitis among US adults

Previous experimental models suggest that vitamin E may ameliorate periodontitis. However, epidemiologic studies show inconsistent evidence in supporting this plausible association. We aimed to investigate the association between serum α-tocopherol (αT) and γ-tocopherol (γT) and periodontitis in a large cross-sectional US population. This study included 4708 participants in the 1999–2001 NHANES. Serum tocopherols were measured by HPLC and values were adjusted by total cholesterol (TC). Periodontal status was assessed by mean clinical attachment loss (CAL) and probing pocket depth (PPD). Total periodontitis (TPD) was defined as the sum of mild, moderate, and severe periodontitis. All measurements were performed by NHANES. Means ± SDs of serum αT:TC ratio from low to high quartiles were 4.0 ± 0.4, 4.8 ± 0.2, 5.7 ± 0.4, and 9.1 ± 2.7 μmol/mmol. In multivariate regression models, αT:TC quartiles were inversely associated with mean CAL (P-trend = 0.06), mean PPD (P-trend < 0.001), and TPD (P-trend < 0.001) overall. Adjusted mean differences (95% CIs) between the first and fourth quartile of αT:TC were 0.12 mm (0.03, 0.20; P-difference = 0.005) for mean CAL and 0.12 mm (0.06, 0.17; P < 0.001) for mean PPD, whereas corresponding OR for TPD was 1.65 (95% CI: 1.26, 2.16; P-difference = 0.001). In a dose-response analysis, a clear inverse association between αT:TC and mean CAL, mean PPD, and TPD was observed among participants with relatively low αT:TC. No differences were seen in participants with higher αT:TC ratios. Participants with γT:TC ratio in the interquartile range showed a significantly lower mean PPD than those in the highest quartile. A nonlinear inverse association was observed between serum αT and severity of periodontitis, which was restricted to adults with normal but relatively low αT status. These findings warrant further confirmation in longitudinal or intervention settings.

The existence of an inverse limit of inverse system of measure spaces - a purely measurable case

The existence of an inverse limit of an inverse system of (probability) measure spaces has been investigated since the very beginning of the birth of the modern probability theory. Results from Kolmogorov [10], Bochner [2], Choksi [5], Metivier [14], Bourbaki [3] among others have paved the way of the deep understanding of the problem under consideration. All the above results, however, call for some topological concepts, or at least ones which are closely related topological ones. In this paper we investigate purely measurable inverse systems of (probability) measure spaces, and give a sucient condition for the existence of a unique inverse limit. An example for the considered purely measurable inverse systems of (probability) measure spaces is also given.

Color-based surface reflectance separation for scene illumination estimation and rendering

Given the importance of color processing in computer vision and computer graphics, estimating and rendering illumination spectral reflectance of image scenes is important to advance the capability of a large class of applications such as scene reconstruction, rendering, surface segmentation, object recognition, and reflectance estimation. Consequently, this dissertation proposes effective methods for reflection components separation and rendering in single scene images. Based on the dichromatic reflectance model, a novel decomposition technique, named the Mean-Shift Decomposition (MSD) method, is introduced to separate the specular from diffuse reflectance components. This technique provides a direct access to surface shape information through diffuse shading pixel isolation. More importantly, this process does not require any local color segmentation process, which differs from the traditional methods that operate by aggregating color information along each image plane. ^ Exploiting the merits of the MSD method, a scene illumination rendering technique is designed to estimate the relative contributing specular reflectance attributes of a scene image. The image feature subset targeted provides a direct access to the surface illumination information, while a newly introduced efficient rendering method reshapes the dynamic range distribution of the specular reflectance components over each image color channel. This image enhancement technique renders the scene illumination reflection effectively without altering the scene’s surface diffuse attributes contributing to realistic rendering effects. ^ As an ancillary contribution, an effective color constancy algorithm based on the dichromatic reflectance model was also developed. This algorithm selects image highlights in order to extract the prominent surface reflectance that reproduces the exact illumination chromaticity. This evaluation is presented using a novel voting scheme technique based on histogram analysis. ^ In each of the three main contributions, empirical evaluations were performed on synthetic and real-world image scenes taken from three different color image datasets. The experimental results show over 90% accuracy in illumination estimation contributing to near real world illumination rendering effects. ^