Recurrence rate in rapidly mixing dynamical systems

For measure preserving dynamical systems on metric spaces we study the time needed by a typical orbit to return back close to its starting point. We prove that when the decay of correlation is super-polynomial the recurrence rates and the pointwise dimensions are equal. This gives a broad class of systems for which the recurrence rate equals the Hausdorff dimension of the invariant measure

The effect of high cholesterol level on recurrence rate of oral ulcer

Introduction: Oral ulcers are one of the most common complaints of the oral mucosa lesion. Ulcer is defined by damage or discontinuity of the epithelium and lamina propria which usually affects the non-keratinized or poorly keratinized surfaces of the oral mucosa. It is a multifactorial condition several predisposing factors have been suggested. Objectives: The aim of this study is to determine the relationship between the increase in cholesterol level and the presence of recurrent oral ulcer. Materials and Methods: A case control study was conducted in oral medicine clinic Kulliyyah of Dentistry International Islamic University Malaysia, Kuantan, Pahang. Convenience sampling was used to select the sample devided into 2 groups patient with recurrent oral ulcer (ROU) (male and female) and control. Patients who fulfilled the criteria were selected. Blood cholesterol and blood pressure of both groups were mesured and recorded. Data analysis was done using independent t-test by, SPSS version 20 for Windows. Results: Cholesterol level was significantly higher in patient with recurrent oral ulcer (6.32 +/- 0.45mmol) compared to control group (4.97 +/- 0.28mmol) (p<0.05). t(46) = 2.75, p = 0.008. It is also found that the control group had statistically significantly lower S.BP (113.77 +/- 2.93 mmHg) compared to the subject group (126.62 +/- 3.61 mmHg), t(46) = 2.75, p = 0.008. Conclusions: This study emphasizes that high cholesterol level is highly associated with ROU

A multicenter prospective study of patients undergoing open ventral hernia repair with intraperitoneal positioning using the monofilament polyester composite ventral patch : interim results of the PANACEA study

This study assessed the recurrence rate and other safety and efficacy parameters following ventral hernia repair with a polyester composite prosthesis (Parietex™ Composite Ventral Patch [PCO-VP])

The Recurrence Rate and Hausdorff Dimension of a Neighbourhood of some Typical Point in the Julia Set of a Rational Map

In this article, we consider hyperbolic rational maps restricted on thier Julia sets and study about the recurrence rate of typical orbits in arbitrarily small neighbourhoods around them and their relationship to the Hausdorff dimension of such small neighbourhoods.Comment: 18 page

Phase synchronization of instrumental music signals

Signal analysis is one of the finest scientific techniques in communication theory. Some quantitative and qualitative measures describe the pattern of a music signal, vary from one to another. Same musical recital, when played by different instrumentalists, generates different types of music patterns. The reason behind various patterns is the psychoacoustic measures - Dynamics, Timber, Tonality and Rhythm, varies in each time. However, the psycho-acoustic study of the music signals does not reveal any idea about the similarity between the signals. For such cases, study of synchronization of long-term nonlinear dynamics may provide effective results. In this context, phase synchronization (PS) is one of the measures to show synchronization between two non-identical signals. In fact, it is very critical to investigate any other kind of synchronization for experimental condition, because those are completely non identical signals. Also, there exists equivalence between the phases and the distances of the diagonal line in Recurrence plot (RP) of the signals, which is quantifiable by the recurrence quantification measure tau-recurrence rate. This paper considers two nonlinear music signals based on same raga played by two eminent sitar instrumentalists as two non-identical sources. The psycho-acoustic study shows how the Dynamics, Timber, Tonality and Rhythm vary for the two music signals. Then, long term analysis in the form of phase space reconstruction is performed, which reveals the chaotic phase spaces for both the signals. From the RP of both the phase spaces, tau-recurrence rate is calculated. Finally by the correlation of normalized tau-recurrence rate of their 3D phase spaces and the PS of the two music signals has been established. The numerical results well support the analysis

Statistical modeling via empirical recurrence rate

A key parameter, most sought after by the modelers of reliability, is the failure rate of a targeted repairable system. Popular modeling techniques based on a point process such as the Power-law process often are handicapped by the requirement of a monotonic failure rate. In this thesis, we show the potential of building a linking bridge between the traditional homogeneous and nonhomogeneous Poisson processes and the classical time series via a sequence of the empirical recurrence rates, calculated at equally spaced intervals of time. The distinctive signature, marking the unique failure pattern of a repairable system, is displayed with an empirical recurrence rate time-plot, referred as the fingerprint or an ERR-plot of a targeted system. A major strength of our approach is that we present an interesting extension of advanced time series analysis techniques into the domain of data exploration of point processes, including but not limited to the events associated with repairable systems or natural phenomena (earthquakes and volcanic eruptions), and make new and innovative use of the well-known ARIMA method possible for modeling the recurrence rate of such events ranging from constant recurrence rate to those show cyclic trends; ARIMA time series modeling techniques are well developed. Therefore, the scope of our study is to investigate the merits of the transformation in terms of the diagnostics on the basic plots and some tests of goodness-of-fit via pseudo and real data

Excision margins in breast conserving surgery

The ideal excision margin in breast conserving surgery is still a matter of debate. The aim is to see if there is any correlation between increasing excision margin distance and local recurrence rate. Patients who had breast conserving surgery at Mater Dei Hospital in 2009 had their notes reviewed retrospectively. Patient demograpichs, including the excision margins were recorded. Local recurrences within a 3 year follow up period were noted. Chi square was used to compare categorical data and a p value of less than 0.05 was considered statistically significant. 91 patients were recruited into the study. 74 patients (81.5%) had negative margins (>1mm), 10 patients (11%) had close margins (<1mm) while 7 patients (7.5%) had positive margins. 5 patients (5.5%) had local recurrence. The highest recurrence rate (14%) was in patients with positive margins, and no statistical signficant difference in recurrence rates was noted with wider excision margins. As long as the margins are negative, increasing excision margins will not result in a better local recurrence rate.peer-reviewe