scholarly journals Standard deviation of recurrence times for piecewise linear transformations

2017 ◽  
Vol 10 (01) ◽  
pp. 1750009
Author(s):  
Mimoon Ismael ◽  
Rodney Nillsen ◽  
Graham Williams

This paper is concerned with dynamical systems of the form [Formula: see text], where [Formula: see text] is a bounded interval and [Formula: see text] comes from a class of measure-preserving, piecewise linear transformations on [Formula: see text]. If [Formula: see text] is a Borel set and [Formula: see text], the Poincaré recurrence time of [Formula: see text] relative to [Formula: see text] is defined to be the minimum of [Formula: see text], if the minimum exists, and [Formula: see text] otherwise. The mean of the recurrence time is finite and is given by Kac’s recurrence formula. In general, the standard deviation of the recurrence times need not be finite but, for the systems considered here, a bound for the standard deviation is derived.

1975 ◽  
Vol 12 (03) ◽  
pp. 647-652 ◽  
Author(s):  
G. G. S. Pegram

Expressions for the mean and variance of the recurrence time of non-overlapping draft-patterns of draft from a Moran Reservoir Model (discrete-state and discrete-time Markov chain) are derived using Feller's Renewal argument. In addition an expression for the mean recurrence time for self-overlapping patterns of draft is derived using run-theory.


1976 ◽  
Vol 13 (03) ◽  
pp. 604-607 ◽  
Author(s):  
Raymond J. Huntington

Given an unlimited sequence of Bernoulli trials, let E be the recurrent event that k or more successes occur within m consecutive trials in the sequence. Let μk, m denote the mean recurrence time for E. Previous work finds expressions for μk, m for limited values of k and m. The present paper derives a closed expression for μk, m for all k, m. Tables for μk, m are also presented.


1975 ◽  
Vol 12 (3) ◽  
pp. 647-652 ◽  
Author(s):  
G. G. S. Pegram

Expressions for the mean and variance of the recurrence time of non-overlapping draft-patterns of draft from a Moran Reservoir Model (discrete-state and discrete-time Markov chain) are derived using Feller's Renewal argument. In addition an expression for the mean recurrence time for self-overlapping patterns of draft is derived using run-theory.


1976 ◽  
Vol 13 (3) ◽  
pp. 604-607 ◽  
Author(s):  
Raymond J. Huntington

Given an unlimited sequence of Bernoulli trials, let E be the recurrent event that k or more successes occur within m consecutive trials in the sequence. Let μk, m denote the mean recurrence time for E. Previous work finds expressions for μk, m for limited values of k and m. The present paper derives a closed expression for μk, m for all k, m. Tables for μk, m are also presented.


1969 ◽  
Vol 14 (9) ◽  
pp. 470-471
Author(s):  
M. DAVID MERRILL
Keyword(s):  

1972 ◽  
Vol 28 (03) ◽  
pp. 447-456 ◽  
Author(s):  
E. A Murphy ◽  
M. E Francis ◽  
J. F Mustard

SummaryThe characteristics of experimental error in measurement of platelet radioactivity have been explored by blind replicate determinations on specimens taken on several days on each of three Walker hounds.Analysis suggests that it is not unreasonable to suppose that error for each sample is normally distributed ; and while there is evidence that the variance is heterogeneous, no systematic relationship has been discovered between the mean and the standard deviation of the determinations on individual samples. Thus, since it would be impracticable for investigators to do replicate determinations as a routine, no improvement over simple unweighted least squares estimation on untransformed data suggests itself.


2020 ◽  
Vol 1 (2) ◽  
pp. 56-66
Author(s):  
Irma Linda

Background: Early marriages are at high risk of marital failure, poor family quality, young pregnancies at risk of maternal death, and the risk of being mentally ill to foster marriage and be responsible parents. Objective: To determine the effect of reproductive health education on peer groups (peers) on the knowledge and perceptions of adolescents about marriage age maturity. Method: This research uses the Quasi experimental method with One group pre and post test design, conducted from May to September 2018. The statistical analysis used in this study is a paired T test with a confidence level of 95% (α = 0, 05). Results: There is an average difference in the mean value of adolescent knowledge between the first and second measurements is 0.50 with a standard deviation of 1.922. The mean difference in mean scores of adolescent perceptions between the first and second measurements was 4.42 with a standard deviation of 9.611. Conclusion: There is a significant difference between adolescent knowledge on the pretest and posttest measurements with a value of P = 0.002, and there is a significant difference between adolescent perceptions on the pretest and posttest measurements with a value of p = 0.001. Increasing the number of facilities and facilities related to reproductive health education by peer groups (peers) in adolescents is carried out on an ongoing basis at school, in collaboration with local health workers as prevention of risky pregnancy.


1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.


1988 ◽  
Vol 60 (1) ◽  
pp. 1-29 ◽  
Author(s):  
E. D. Young ◽  
J. M. Robert ◽  
W. P. Shofner

1. The responses of neurons in the ventral cochlear nucleus (VCN) of decerebrate cats are described with regard to their regularity of discharge and latency. Regularity is measured by estimating the mean and standard deviation of interspike intervals as a function of time during responses to short tone bursts (25 ms). This method extends the usual interspike-interval analysis based on interval histograms by allowing the study of temporal changes in regularity during transient responses. The coefficient of variation (CV), equal to the ratio of standard deviation to mean interspike interval, is used as a measure of irregularity. Latency is measured as the mean and standard deviation of the latency of the first spike in response to short tone bursts, with 1.6-ms rise times. 2. The regularity and latency properties of the usual PST histogram response types are shown. Five major PST response type classes are used: chopper, primary-like, onset, onset-C, and unusual. The presence of a prepotential in a unit's action potentials is also noted; a prepotential implies that the unit is recorded from a bushy cell. 3. Units with chopper PST histograms give the most regular discharge. Three varieties of choppers are found. Chop-S units (regular choppers) have CVs less than 0.35 that are approximately constant during the response; chop-S units show no adaptation of instantaneous rate, as measured by the inverse of the mean interspike interval. Chop-T units have CVs greater than 0.35, show an increase in irregularity during the response and show substantial rate adaptation. Chop-U units have CVs greater than 0.35, show a decrease in irregularity during the response, and show a variety of rate adaptation behaviors, including negative adaptation (an increase in rate during a short-tone response). Irregular choppers (chop-T and chop-U units) rarely have CVs greater than 0.5. Choppers have the longest latencies of VCN units; all three groups have mean latencies at least 1 ms longer than the shortest auditory nerve (AN) fiber mean latencies. 4. Chopper units are recorded from stellate cells in VCN (35, 42). Our results for chopper units suggest a model for stellate cells in which a regularly firing action potential generator is driven by the summation of the AN inputs to the cell, where the summation is low-pass filtered by the membrane capacitance of the cell.(ABSTRACT TRUNCATED AT 400 WORDS)


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