Top-hat random fiber Bragg grating

We examined the possibility of using noise or pseudo-random variations of the refractive index in the design of fiber Bragg gratings (FBGs). We demonstrated theoretically and experimentally that top-hat FBGs may be designed and fabricated using this approach. The reflectivity of the fabricated top-hat FBG matches quite well with that of the designed one. © 2015 Optical Society of America.

Ultra-long fibre-based random lasers

The emerging science and applications of ultra-long random fibre lasers will be overviewed. The lasers with cavity length up to several hundred km exploit random distributed feedback provided by Rayleigh scattering amplified through Raman effect. © 2014 OSA.

Robust Parametric Estimation of Branching Processes with a Random Number of Ancestors

2000 Mathematics Subject Classification: 60J80.

Quasi-Likelihood Estimation for Ornstein-Uhlenbeck Diffusion Observed at Random Time Points

2000 Mathematics Subject Classification: 60J60, 62M99.

Unrepeatered DP-QPSK transmission over 352.8 km SMF using random DFB fiber laser amplification

Unrepeatered 100 Gbit/s per channel wave-divisionmultiplexed dual-polarization-QPSK transmission with random distributed feedback fiber laser-based Raman amplification using fiber Bragg grating is demonstrated. Transmission of 1.4 Tb/s (14 × 100 Gbit/s) was possible in 352.8 km link and 2.2 Tb/s (22 × 100 Gbit/s) was achieved in 327.6 km without employing remote optically pumped amplifier or speciality fibers.

Large Distinct Part Sizes in a Random Integer Partition

A partition of a positive integer n is a way of writing it as the sum of positive integers without regard to order; the summands are called parts. The number of partitions of n, usually denoted by p(n), is determined asymptotically by the famous partition formula of Hardy and Ramanujan [5]. We shall introduce the uniform probability measure P on the set of all partitions of n assuming that the probability 1/p(n) is assigned to each n-partition. The symbols E and V ar will be further used to denote the expectation and variance with respect to the measure P . Thus, each conceivable numerical characteristic of the parts in a partition can be regarded as a random variable.

Limit Theorems for Branching Processes with Random Migration Components

The classical Bienaymé-Galton-Watson (BGW) branching process can be interpreted as mathematical model of population dynamics when the members of an isolated population reproduce themselves independently of each other according to a stochastic law.

Branching Processes in Autoregressive Random Environment

2000 Mathematics Subject Classification: 60J80, 60K05.

Estimation of Fraction of Distinguished Elements in Population Based on Partially Realized Random Sample

2000 Mathematics Subject Classi cation: 62D05.

The Number of Parts of Given Multiplicity in a Random Integer Partition

2000 Mathematics Subject Classification: 05A16, 05A17.

Limit Theorems for Maxima of Heavy-Tailed Terms with Random Dependent Weights

2000 Mathematics Subject Classification: Primary 60F17, 60G52, 60G70 secondary 60E07, 62E20.

Analysing Conjoint Analysis Data by a Random Coefficient Regression Model

2000 Mathematics Subject Classification: 62J12, 62K15, 91B42, 62H99.

Parameterized Link Functions in Generalized Linear Random Effect Models: a Case Study on Breast Cancer Treatment

In non-linear random effects some attention has been very recently devoted to the analysis ofsuitable transformation of the response variables separately (Taylor 1996) or not (Oberg and Davidian 2000) from the transformations of the covariates and, as far as we know, no investigation has been carried out on the choice of link function in such models. In our study we consider the use of a random effect model when a parameterized family of links (Aranda-Ordaz 1981, Prentice 1996, Pregibon 1980, Stukel 1988 and Czado 1997) is introduced. We point out the advantages and the drawbacks associated with the choice of this data-driven kind of modeling. Difficulties in the interpretation of regression parameters, and therefore in understanding the influence of covariates, as well as problems related to loss of efficiency of estimates and overfitting, are discussed. A case study on radiotherapy usage in breast cancer treatment is discussed.

Optimisation of random DFB Raman laser amplifier

We numerically optimise 2nd-order random DFB Raman laser amplifiers for transmission for the first time. Optical signal to noise ratio, nonlinear phase shift, signal power variation and the impact of the reflectivity of FBG are investigated in the links from 10 - 120 km.

Parametric Estimation in Branching Processes with an Increasing Random Number of Ancestors

2000 Mathematics Subject Classification: 60J80, 62M05