Quantile Process with Applications : Chirp Signal Model

<p>The parameters in the well-known chirp signal model controls the frequency fluctuations of the signals, and consequently, the estimation of the parameters has received considerable attention in the literature of statistical signal processing. In the same spirit with a broader view, this article investigates the quantile estimator of parameters involved in the chirp signal model, which enables us to provide basic features of the entire distribution of the signals. In the course of this study, we establish the limiting behaviour of the associated stochastic process, which we call quantile process. As the applications of this result, we obtain the limiting distributions of various quantile based measures of descriptive statistics, which give us summarized features of the fluctuations of the signals in various senses. Finally, along with extensive simulation study, the practicability of the proposed methodology is shown on a few benchmark real datasets closely related with various chirp signal models.<br></p>

Investigation on optical switching behaviour of regenerated and non-regenerated silk by nanosecond Z-scan technique

The nonlinear optical behaviour of silk, a natural fibre, is investigated in this study. We have considered silk in the cocoon, fibre and film forms of bivoltine and multivoltine breeds. The nonlinear absorption and optical limiting studies were performed using the open aperture Z-scan technique at 1064nm. Interestingly, silk in cocoon and fibre form possess saturable absorption (SA), whereas silk in the film form exhibits reverse saturable absorption (RSA). This shift is attributed to the removal of sericin during the regeneration of silk into a film. Further, silk films exhibit optical limiting behaviour, whose limiting thresholds are in the order of 1012 W/cm2. Functional data analysis (FDA), a statistical approach, is employed to draw correlations amongst physical parameters. FDA offers good insight into the dependencies between silk varieties and their optical parameters. This helps in identifying the sample possessing the best properties.

Quantile Process with Applications : Chirp Signal Model

<p>The parameters in the well-known chirp signal model controls the frequency fluctuations of the signals, and consequently, the estimation of the parameters has received considerable attention in the literature of statistical signal processing. In the same spirit with a broader view, this article investigates the quantile estimator of parameters involved in the chirp signal model, which enables us to provide basic features of the entire distribution of the signals. In the course of this study, we establish the limiting behaviour of the associated stochastic process, which we call quantile process. As the applications of this result, we obtain the limiting distributions of various quantile based measures of descriptive statistics, which give us summarized features of the fluctuations of the signals in various senses. Finally, along with extensive simulation study, the practicability of the proposed methodology is shown on a few benchmark real datasets closely related with various chirp signal models.<br></p>

A Continuous-Time Network Evolution Model Describing 2- and 3-Interactions

A continuous-time network evolution model is considered. The evolution of the network is based on 2- and 3-interactions. 2-interactions are described by edges, and 3-interactions are described by triangles. The evolution of the edges and triangles is governed by a multi-type continuous-time branching process. The limiting behaviour of the network is studied by mathematical methods. We prove that the number of triangles and edges have the same magnitude on the event of non-extinction, and it is eαt, where α is the Malthusian parameter. The probability of the extinction and the degree process of a fixed vertex are also studied. The results are illustrated by simulations.

A Prospective Study of the Quality of Life of Patients with Stress Incontinence before and after a Transobturator Tape (TOT) Procedure—Preliminary Report

Background: Urinary incontinence (UI) is a significant social problem. The latest figures show that it affects as many as 17–60% of the female population, and it is one of the most common chronic diseases. Incontinence substantially decreases the quality of patients’ lives. The transobturator tape (TOT) procedure is the gold standard in surgical treatment due to its high efficacy and low complication rate. Objective: The aim of this study was to assess the quality of life (QoL) of patients with stress incontinence before and after the TOT procedure. Method: The study included 57 patients diagnosed with stress incontinence on the basis of ultrasonography and history. The QoL before and after surgery was measured using the Incontinence Impact Questionnaire (IIQ-7) and the Incontinence Quality of Life (I-QOL) standardised questionnaires. Results: The IIQ-7 scores for each question were higher (indicating poorer quality of life) before surgery than after surgery. The results for almost all domains were statistically significant. The I-QOL results also showed that, in most cases, the quality of patients’ lives improved after the surgery. Statistically significant changes were observed in all three questionnaire domains of avoidance/limiting behaviour, psychosocial impact, and social embarrassment. Conclusion: Surgical treatment of stress incontinence with TOT results in resolution of bothersome symptoms in the majority of patients, leading to improved comfort in life.

On asymptotic joint distributions of cherries and pitchforks for random phylogenetic trees

Tree shape statistics provide valuable quantitative insights into evolutionary mechanisms underpinning phylogenetic trees, a commonly used graph representation of evolutionary relationships among taxonomic units ranging from viruses to species. We study two subtree counting statistics, the number of cherries and the number of pitchforks, for random phylogenetic trees generated by two widely used null tree models: the proportional to distinguishable arrangements (PDA) and the Yule-Harding-Kingman (YHK) models. By developing limit theorems for a version of extended Pólya urn models in which negative entries are permitted for their replacement matrices, we deduce the strong laws of large numbers and the central limit theorems for the joint distributions of these two counting statistics for the PDA and the YHK models. Our results indicate that the limiting behaviour of these two statistics, when appropriately scaled using the number of leaves in the underlying trees, is independent of the initial tree used in the tree generating process.

Sequential Interval Reliability for Discrete-Time Homogeneous Semi-Markov Repairable Systems

In this paper, a new reliability measure, named sequential interval reliability, is introduced for homogeneous semi-Markov repairable systems in discrete time. This measure is the probability that the system is working in a given sequence of non-overlapping time intervals. Many reliability measures are particular cases of this new reliability measure that we propose; this is the case for the interval reliability, the reliability function and the availability function. A recurrent-type formula is established for the calculation in the transient case and an asymptotic result determines its limiting behaviour. The results are illustrated by means of a numerical example which illustrates the possible application of the measure to real systems.

SACF of the Errors of Stationary Time Series Models in the Presence of a Large Additive Outlier

In this paper, the limiting behaviour of the Sample Autocorrelation Function(SACF) of the errors {et} of First-Order Autoregressive (AR(1)), First-Order Moving Average (MA(1)) and First Order Autoregressive First-Order Moving Average (ARMA(1,1)) stationary time series models in the presence of a large Additive Outlier(AO) is discussed. It is found that the errors which are supposed to be uncorrelated due to either white noise process or normally distributed process are not so in the presence of a large additive outlier. The SACF of the errors follows a particular pattern based on the time series model. In the case of AR(1) model, at lag 1, the contaminated errors {et} are correlated, whereas at higher lags, they are uncorrelated. But in the MA(1) and ARMA(1,1) models, the contaminated errors {et} are correlated at all the lags. Furthermore it is observed that the intensity of correlations depends on the parameters of the respective models.