Two mean values which characterize the Poisson process

1973 ◽  
Vol 10 (3) ◽  
pp. 678-681 ◽  
Author(s):  
Erhan Çinlar ◽  
Peter Jagers
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Recurrence Time ◽  
Mean Values ◽  
The Mean ◽  
Forward Recurrence Time ◽  
Backward Recurrence Time ◽  
Interval Distribution

The Poisson process enjoys two special properties: the mean forward recurrence time at time t does not depend on t, and the mean backward recurrence time at time t is the “mean” of the interval distribution truncated at t. Poisson process is the only renewal process with these properties.

Two mean values which characterize the Poisson process

1973 ◽  
Vol 10 (03) ◽  
pp. 678-681 ◽  
Author(s):  
Erhan Çinlar ◽  
Peter Jagers
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Recurrence Time ◽  
Mean Values ◽  
The Mean ◽  
Forward Recurrence Time ◽  
Backward Recurrence Time ◽  
Interval Distribution

The Poisson process enjoys two special properties: the mean forward recurrence time at time t does not depend on t, and the mean backward recurrence time at time t is the “mean” of the interval distribution truncated at t. Poisson process is the only renewal process with these properties.

A characterization of the Poisson process using forward recurrence times

1975 ◽  
Vol 78 (3) ◽  
pp. 513-516 ◽  
Author(s):  
Valerie Isham ◽  
D. N. Shanbhag ◽  
M. Westcott
Keyword(s):  
Distribution Function ◽  
Poisson Process ◽  
Real Line ◽  
Renewal Process ◽  
Recurrence Time ◽  
Recurrence Times ◽  
Arithmetic Distribution ◽  
Image Position ◽  
Forward Recurrence Time

Consider a renewal process on the nonnegative real line with non-arithmetic distribution function F(x). Denote by V(x; t) the distribution function of the forward recurrence time from t, t ≤ 0. If t is chosen at random with distribution function Ф(t), the corresponding unconditional forward recurrence time has distribution function

Some renewal process models for single neuron discharge

1971 ◽  
Vol 8 (4) ◽  
pp. 802-808 ◽  
Author(s):  
Howard G. Hochman ◽  
Stephen E. Fienberg
Keyword(s):  
Single Neuron ◽  
Interspike Interval ◽  
Poisson Processes ◽  
Process Models ◽  
Recurrence Time ◽  
The Laplace Transform ◽  
Mean And Variance ◽  
The Mean ◽  
Interspike Interval Distribution ◽  
Interval Distribution

Leslie (1969) obtained the Laplace transform for the recurrence time of clusters of Poisson processes, which can be thought of as yielding the interspike interval distribution for a neuron that receives Poisson excitatory inputs subject to decay. Here, several extensions of this model are derived, each including Poisson inhibitory inputs. Expressions for the mean and variance are derived for each model, and the results for the different models are compared.

Critical growth of a semi-linear process

2004 ◽  
Vol 41 (2) ◽  
pp. 355-367
Author(s):  
Ilya Molchanov ◽  
Vadim Shcherbakov ◽  
Sergei Zuyev
Keyword(s):  
Renewal Process ◽  
Survival Probability ◽  
Linear Process ◽  
Recurrence Time ◽  
Soil Drying ◽  
Time Process ◽  
Positive Probability ◽  
Drying Process ◽  
Dry Patch ◽  
Backward Recurrence Time

This paper is motivated by the modelling of leaching of bacteria through soil. A semi-linear process Xt− may be used to describe the soil-drying process between rain showers. This is a backward recurrence time process that corresponds to the renewal process of instances of rain. If a bacterium moves according to another process h, then the fact that h(t) stays above Xt− means that the bacterium never hits a dry patch of soil and so survives. We describe a critical behaviour of h that separates the cases when survival is possible with a positive probability from the cases when this probability vanishes. An explicit formula for the survival probability is obtained in case h is linear and rain showers follow a Poisson process.

Some renewal process models for single neuron discharge

1971 ◽  
Vol 8 (04) ◽  
pp. 802-808
Author(s):  
Howard G. Hochman ◽  
Stephen E. Fienberg
Keyword(s):  
Single Neuron ◽  
Interspike Interval ◽  
Poisson Processes ◽  
Process Models ◽  
Recurrence Time ◽  
The Laplace Transform ◽  
Mean And Variance ◽  
The Mean ◽  
Interspike Interval Distribution ◽  
Interval Distribution

Leslie (1969) obtained the Laplace transform for the recurrence time of clusters of Poisson processes, which can be thought of as yielding the interspike interval distribution for a neuron that receives Poisson excitatory inputs subject to decay. Here, several extensions of this model are derived, each including Poisson inhibitory inputs. Expressions for the mean and variance are derived for each model, and the results for the different models are compared.

Critical growth of a semi-linear process

2004 ◽  
Vol 41 (02) ◽  
pp. 355-367
Author(s):  
Ilya Molchanov ◽  
Vadim Shcherbakov ◽  
Sergei Zuyev
Keyword(s):  
Renewal Process ◽  
Survival Probability ◽  
Linear Process ◽  
Recurrence Time ◽  
Soil Drying ◽  
Time Process ◽  
Positive Probability ◽  
Drying Process ◽  
Dry Patch ◽  
Backward Recurrence Time

This paper is motivated by the modelling of leaching of bacteria through soil. A semi-linear process X t − may be used to describe the soil-drying process between rain showers. This is a backward recurrence time process that corresponds to the renewal process of instances of rain. If a bacterium moves according to another process h, then the fact that h(t) stays above X t − means that the bacterium never hits a dry patch of soil and so survives. We describe a critical behaviour of h that separates the cases when survival is possible with a positive probability from the cases when this probability vanishes. An explicit formula for the survival probability is obtained in case h is linear and rain showers follow a Poisson process.

Articulatory Behavior Pre and Post Full-Mouth Tooth Extraction and Alveoloplasty

1980 ◽  
Vol 23 (3) ◽  
pp. 630-645 ◽  
Author(s):  
Gerald Zimmermann ◽  
J.A. Scott Kelso ◽  
Larry Lander
Keyword(s):  
Control Subject ◽  
High Speed ◽  
Tooth Extraction ◽  
Kinematic Parameters ◽  
Experimental Conditions ◽  
Mean Values ◽  
Articulatory Movements ◽  
The Mean ◽  
Experimental Subjects ◽  
Normal Speech

High speed cinefluorography was used to track articulatory movements preceding and following full-mouth tooth extraction and alveoloplasty in two subjects. Films also were made of a control subject on two separate days. The purpose of the study was to determine the effects of dramatically altering the structural dimensions of the oral cavity on the kinematic parameters of speech. The results showed that the experimental subjects performed differently pre and postoperatively though the changes were in different directions for the two subjects. Differences in both means and variabilities of kinematic parameters were larger between days for the experimental (operated) subjects than for the control subject. The results for the Control subject also showed significant differences in the mean values of kinematic variables between days though these day-to-day differences could not account for the effects found pre- and postoperatively. The results of the kinematic analysis, particularly the finding that transition time was most stable over the experimental conditions for the operated subjects, are used to speculate about the coordination of normal speech.

Comparative Study of Intranasal, Subcutaneous and Intravenous Administration of Desamino-D-Arginine Vasopressin (DDAVP)

1986 ◽  
Vol 55 (01) ◽  
pp. 108-111 ◽  
Author(s):  
M Köhler ◽  
P Hellstern ◽  
C Miyashita ◽  
G von Blohn ◽  
E Wenzel
Keyword(s):  
Factor Viii ◽  
Von Willebrand Factor ◽  
Factor Xii ◽  
Additional Advantage ◽  
Mean Values ◽  
Routes Of Administration ◽  
The Mean ◽  
Von Willebrand ◽  
Willebrand Factor ◽  
Factor Antigen

SummaryThis study was performed to evaluate the influence of different routes of administration on the efficacy of DDAVP treatment. Ten healthy volunteers received DDAVP intranasally (i.n.), subcutaneously (s.c.) and intravenously (i.v.) in a randomized cross-over trial. Factor XII and high molecular weight (HMW)-kininogen levels increased only slightly after DDAVP administration. The mean increase of factor VIII: C was 3.1 (i. v.), 2.3 (s. c.), and 1.3 (i.n.) - fold over baseline. Ristocetin cofactor (von Willebrand factor antigen) increased 3.1 (2.5), 2.0 (2.3) and 1.2 (1.2) - fold over baseline mean values after i.v., s.c. and i.n. DDAVP, respectively. The half-disappearance time of factor VIII and von Willebrand factor (vWF) after DDAVP ranged from five (factor VIII: C) to eight hours (vWF). The mean increase of fibrinolytic activity was more pronounced after i.v. DDAVP. The antidiuretic effect was moderate with no apparent differences between the routes of application. This study provides further evidence that both i.v. and s.c. DDAVP administration result in an appropriate and reliable stimulation of haemostasis. An additional advantage of s. c. administration is its suitability for home treatment.

Comparative Study of effectiveness of mobilization with movement (MWM) and End range mobilization (ERM) techniques in frozen shoulder

2018 ◽  
Vol 4 (4) ◽  
pp. 519-522
Author(s):  
Jeyakumar S ◽  
Jagatheesan Alagesan ◽  
T.S. Muthukumar
Keyword(s):  
Range Of Motion ◽  
Frozen Shoulder ◽  
Type I ◽  
Mean Values ◽  
Functional Activities ◽  
Group A ◽  
The Mean ◽  
Group B

Background: Frozen shoulder is disorder of the connective tissue that limits the normal Range of motion of the shoulder in diabetes, frozen shoulder is thought to be caused by changes to the collagen in the shoulder joint as a result of long term Hypoglycemia. Mobilization is a therapeutic movement of the joint. The goal is to restore normal joint motion and rhythm. The use of mobilization with movement for peripheral joints was developed by mulligan. This technique combines a sustained application of manual technique “gliding” force to the joint with concurrent physiologic motion of joint, either actively or passively. This study aims to find out the effects of mobilization with movement and end range mobilization in frozen shoulder in Type I diabetics. Materials and Methods: 30 subjects both male and female, suffering with shoulder pain and clinically diagnosed with frozen shoulder was recruited for the study and divided into two groups with 15 patients each based on convenient sampling method. Group A patients received mobilization with movement and Group B patients received end range mobilization for three weeks. The outcome measurements were SPADI, Functional hand to back scale, abduction range of motion using goniometer and VAS. Results: The mean values of all parameters showed significant differences in group A as compared to group B in terms of decreased pain, increased abduction range and other outcome measures. Conclusion: Based on the results it has been concluded that treating the type 1 diabetic patient with frozen shoulder, mobilization with movement exercise shows better results than end range mobilization in reducing pain and increase functional activities and mobility in frozen shoulder.

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