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

Recent Results for Supercritical Controlled Branching Processes with Control Random Functions

2000 Mathematics Subject Classification: 60J80, 60F05

Implementation of the EM Algorithm for Maximum Likelihood Estimation of a Random Effects Model for One Longitudinal Ordinal Outcome

2010 Mathematics Subject Classification: 62J99.

Raman gain and random distributed feedback generation in nitrogen doped silica core fiber

Recently, the concept of a random distributed feedback (DFB) lasing in optical fibers has been demonstrated [1], A number of different random DFB fiber lasers has been demonstrated so far including tunable, multiwalength, cascaded generation, generation in different spectral bands etc [2-7]. All systems are based on standard low-loss germanium doped silica core fibres having relatively low Rayleigh scattering coefficient. Thus, the typical length of random DFB fiber lasers is in the range from several kilometres to tens of kilometres to accumulate enough random feedback. Here we demonstrate for the first time to our knowledge the random DFB fiber laser based on a nitrogen doped silica core (N-doped) fiber. The fiber has several times higher Rayleigh scattering coefficient compared to standard telecommunication fibres. Thus, the generation is achieved in 500 meters long fiber only. © 2013 IEEE.

NLSE-based modelling of a random distributed feedback fiber laser

Random distributed feedback (DFB) fiber lasers have attracted a great attention since first demonstration [1]. Despite big advance in practical laser systems, random DFB fiber laser spectral properties are far away to be understood or even numerically modelled. Up to date, only generation power could be calculated and optimized numerically [1,2] or analytically [3] within the power balance model. However, spectral and statistical properties of random DFB fiber laser can not be found in this way. Here we present first numerical modelling of the random DFB fiber laser, including its spectral and statistical properties, using NLSE-based model. © 2013 IEEE.

Spectral width optimization in random DFB fiber laser

Lasers with random distributed feedback (DFB) owing to Rayleigh scattering in optical fibers [1] have attracted a great interest: a number of papers demonstrating new laser schemes and applications have been proposed [2-7] recently. Moreover, the generation output power and, more generally, generation power distribution could be described both analytically and numerically within simple balance models [8-9]. However, spectral properties of random DFB fiber lasers are not studied except some attempt made in [10]. Generation spectrum of random DFB fiber laser is quite broad (more than 1 nm), and physical mechanisms of its formation and broadening are still unclear. There is no any practical solution up to date to minimize the generation spectrum width. Here we experimentally show the way to minimize the generation spectral width. © 2013 IEEE.