Estimate for the accuracy of the Poisson approximation for the number of empty cells in an equiprobable scheme for group allocation of particles, and applications

2013 ◽  
Vol 282 (1) ◽  
pp. 157-171 ◽  
Author(s):  
V. G. Mikhailov
Keyword(s):  
Poisson Approximation ◽  
Equiprobable Scheme ◽  
Group Allocation

scholarly journals Breakout Group Allocation Schedules and the Social Golfer Problem with Adjacent Group Sizes

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 13
Author(s):  
Alice Miller ◽  
Matthew Barr ◽  
William Kavanagh ◽  
Ivaylo Valkov ◽  
Helen C. Purchase
Keyword(s):  
Design Theory ◽  
Teaching Experience ◽  
Combinatorial Design ◽  
Breakout Group ◽  
Online Resource ◽  
The Social ◽  
Adjacent Group ◽  
Group Allocation ◽  
Novel Variation ◽  
The Ideal

The current pandemic has led schools and universities to turn to online meeting software solutions such as Zoom and Microsoft Teams. The teaching experience can be enhanced via the use of breakout rooms for small group interaction. Over the course of a class (or over several classes), the class will be allocated to breakout groups multiple times over several rounds. It is desirable to mix the groups as much as possible, the ideal being that no two students appear in the same group in more than one round. In this paper, we discuss how the problem of scheduling balanced allocations of students to sequential breakout rooms directly corresponds to a novel variation of a well-known problem in combinatorics (the social golfer problem), which we call the social golfer problem with adjacent group sizes. We explain how solutions to this problem can be obtained using constructions from combinatorial design theory and how they can be used to obtain good, balanced breakout room allocation schedules. We present our solutions for up to 50 students and introduce an online resource that educators can access to immediately generate suitable allocation schedules.

On improvements of the order of approximation in the Poisson limit theorem

1996 ◽  
Vol 33 (01) ◽  
pp. 146-155 ◽  
Author(s):  
K. Borovkov ◽  
D. Pfeifer
Keyword(s):  
Limit Theorem ◽  
Random Variables ◽  
Poisson Approximation ◽  
Order Of Approximation ◽  
Operator Semigroups ◽  
Bernoulli Random Variables ◽  
Usual Rate ◽  
Poisson Limit ◽  
Poisson Measures ◽  
Special Case

In this paper we consider improvements in the rate of approximation for the distribution of sums of independent Bernoulli random variables via convolutions of Poisson measures with signed measures of specific type. As a special case, the distribution of the number of records in an i.i.d. sequence of length n is investigated. For this particular example, it is shown that the usual rate of Poisson approximation of O(1/log n) can be lowered to O(1/n 2). The general case is discussed in terms of operator semigroups.

Comorbidity among alcohol and tobacco dependent patients

2011 ◽  
Vol 26 (S2) ◽  
pp. 132-132
Author(s):  
A. Zoghlami ◽  
D. Blauensteiner ◽  
O. Scheibenbogen ◽  
S. Zadro-Jäger ◽  
M. Musalek
Keyword(s):  
Alcohol Dependence ◽  
Inpatient Treatment ◽  
Preliminary Analysis ◽  
Psychiatric Comorbidity ◽  
Icd 10 ◽  
Withdrawal Therapy ◽  
Clinically Significant ◽  
Drug Use Disorder ◽  
Group Allocation ◽  
Alcohol Dependent

IntroductionPsychiatric concomitant diseases are common with alcohol and tobacco dependent patients. Few studies have compared comorbidities between alcohol dependent smokers and non-smokers.AimsThe aim of this study is to examine the pattern of psychiatric comorbidity among alcohol dependent smokers in an inpatient alcohol therapy unit.Material and methodAfter successfully completing withdrawal therapy, subjects between the ages of 18–65 years who meet the ICD 10 criteria for alcohol dependence and no criteria for other drug use disorder except smoking, and who were participating in an inpatient treatment program for alcohol dependence at Anton Proksch Institut were included.ResultsThis is a preliminary analysis of the survey. In total 81 patients could be examined. 53.1% of the interviewed subjects were female and 46.9% male. The explored samples age ranged from 21–66 years.74.1% of the questioned subjects were smokers, 60% of these patients smoked more than 20 cigarettes per day.Preliminary analysis shows that smoking alcohol dependent patients present a higher comorbidity rate than non-smokers but above all they show a tendency to increased anxiety disorders. Within the population of smokers 48.3% suffer from an anxiety disorder, 48.3% from depression and dysthymia, 12.1% from manic and hypomanic disorder and 5.2% from psychosis. These differences are not clinically significant. This can be explained by the small number of the sample and by the group allocation.ConclusionAlcohol addicted patients exhibit heightened psychiatric comorbidity. Smoking alcohol dependents are more frequently affected and have a disposition to psychiatric disorders.

scholarly journals The lower tail: Poisson approximation revisited

2015 ◽  
Vol 48 (2) ◽  
pp. 219-246 ◽  
Author(s):  
Svante Janson ◽  
Lutz Warnke
Keyword(s):  
Poisson Approximation ◽  
Lower Tail

Poisson approximation for a sum of dependent indicators: an alternative approach

2002 ◽  
Vol 34 (03) ◽  
pp. 609-625 ◽  
Author(s):  
N. Papadatos ◽  
V. Papathanasiou
Keyword(s):  
Total Variation ◽  
Upper Bound ◽  
Random Variables ◽  
Random Variable ◽  
Poisson Approximation ◽  
Total Variation Distance ◽  
Poisson Random Variable ◽  
Birthday Problem ◽  
Alternative Approach ◽  
Variation Distance

The random variablesX1,X2, …,Xnare said to be totally negatively dependent (TND) if and only if the random variablesXiand ∑j≠iXjare negatively quadrant dependent for alli. Our main result provides, for TND 0-1 indicatorsX1,x2, …,Xnwith P[Xi= 1] =pi= 1 - P[Xi= 0], an upper bound for the total variation distance between ∑ni=1Xiand a Poisson random variable with mean λ ≥ ∑ni=1pi. An application to a generalized birthday problem is considered and, moreover, some related results concerning the existence of monotone couplings are discussed.

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