TCTAP C-194 Treated or Don't Treat the White-ball Lesion Over LAD and How to Treat it

A sampling procedure involving an urn with red and white balls in it is studied. Initially, the urn contains n balls, r of them being white. At each step, a white ball is removed, and one more ball is selected at random, painted red (if it was white before) and put back into the urn. R. F. Green proposed this scheme in 1980 as a stochastic model of cannibalistic behavior in a biological population, with red balls interpreted as cannibals. Of primary interest is the distribution of Xnr, the terminal number of red balls. A study of R. F. Green and C. A. Robertson led them to conjecture that, for r = 1 and n →∞, Xnr is asymptotically normal with mean ≈ n exp(–1) and variance ≈ n(3 exp(–2) –exp(–1)). In this paper we prove that the conjecture — its natural extension, in fact — is true. Namely, for r/n bounded away from 1, Xnr is shown to be asymptotically normal with mean ≈ n exp(ρ – 1) and variance ≈ n exp[2(ρ – 1)] (ρ 2 – 3ρ + 3 – exp(l – ρ)); ρ = r/n.

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Generalized Coupon Collection: The Superlinear Case

Journal of Applied Probability ◽

10.1017/s0021900200007713 ◽

2011 ◽

Vol 48 (01) ◽

pp. 189-199 ◽

Cited By ~ 2

Author(s):

R. T. Smythe

Keyword(s):

Random Number ◽

White Ball ◽

Martingale Representation ◽

Poisson Limit ◽

Coupon Collection ◽

Upper Boundary

We consider a generalized form of the coupon collection problem in which a random number,S, of balls is drawn at each stage from an urn initially containingnwhite balls (coupons). Each white ball drawn is colored red and returned to the urn; red balls drawn are simply returned to the urn. The question considered is then: how many white balls (uncollected coupons) remain in the urn after thekndraws? Our analysis is asymptotic asn→ ∞. We concentrate on the case whenkndraws are made, wherekn/n→ ∞ (the superlinear case), although we sketch known results for other ranges ofkn. A Gaussian limit is obtained via a martingale representation for the lower superlinear range, and a Poisson limit is derived for the upper boundary of this range via the Chen-Stein approximation.

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Buffalo’s Black and White Ball

First of the Year: 2009 ◽

10.4324/9780203791868-32 ◽

2017 ◽

pp. 122-123

Author(s):

Talty Stephan

Keyword(s):

White Ball ◽

Black And White

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“Another” white ball appearance on the ligated varix ruptured by suction during endoscopic variceal ligation

Gastrointestinal Endoscopy ◽

10.1016/s0016-5107(99)70327-5 ◽

1999 ◽

Vol 49 (6) ◽

pp. 819 ◽

Cited By ~ 2

Author(s):

Mitsunobu Matsushita ◽

Kiyoshi Hajiro ◽

Hiroshi Takakuwa ◽

Akiyoshi Nishio

Keyword(s):

Endoscopic Variceal Ligation ◽

White Ball

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An urn model for cannibal behavior

Journal of Applied Probability ◽

10.2307/3214275 ◽

1987 ◽

Vol 24 (2) ◽

pp. 522-526 ◽

Cited By ~ 7

Author(s):

B. Pittel

Keyword(s):

Stochastic Model ◽

Natural Extension ◽

Sampling Procedure ◽

White Ball ◽

Urn Model ◽

Primary Interest ◽

Asymptotically Normal ◽

Biological Population

A sampling procedure involving an urn with red and white balls in it is studied. Initially, the urn contains n balls, r of them being white. At each step, a white ball is removed, and one more ball is selected at random, painted red (if it was white before) and put back into the urn. R. F. Green proposed this scheme in 1980 as a stochastic model of cannibalistic behavior in a biological population, with red balls interpreted as cannibals. Of primary interest is the distribution of Xnr, the terminal number of red balls. A study of R. F. Green and C. A. Robertson led them to conjecture that, for r = 1 and n →∞, Xnr is asymptotically normal with mean ≈ n exp(–1) and variance ≈ n(3 exp(–2) –exp(–1)). In this paper we prove that the conjecture — its natural extension, in fact — is true. Namely, for r/n bounded away from 1, Xnr is shown to be asymptotically normal with mean ≈ n exp(ρ – 1) and variance ≈ n exp[2(ρ – 1)] (ρ2– 3ρ + 3 – exp(l – ρ)); ρ = r/n.

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Pink Cricket Balls May Be Visually Challenging at Sunset

i-Perception ◽

10.1177/2041669516687049 ◽

2017 ◽

Vol 8 (1) ◽

pp. 204166951668704 ◽

Cited By ~ 1

Author(s):

Joshua M. Adie ◽

Derek H. Arnold

Keyword(s):

White Ball ◽

Traditional Form ◽

Hard Ball

Cricket is one of the world’s most popular sports, followed by hundreds of millions of people. It can be dangerous, played with a hard ball flying at great velocities, and accidents have occasionally been fatal. Traditionally, cricket has been played during the day, using a dark red ball. Since the late 1970s, a shorter form of one-day cricket has been played both during the day and at night under floodlights. To overcome visibility issues, one-day cricket uses a white ball, and players wear coloured clothing. There is now a desire to play a traditional form of cricket during the day and at night, using a ‘pink’ ball while players wear white clothing. Concerns regarding visibility, and player and umpire safety, have been raised in this context. Here, we report that these concerns have a sound basis.

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Qigongas a Traditional Vegetative Biofeedback Therapy: Long-Term Conditioning of Physiological Mind-Body Effects

BioMed Research International ◽

10.1155/2015/531789 ◽

2015 ◽

Vol 2015 ◽

pp. 1-6 ◽

Cited By ~ 21

Author(s):

Luís Carlos Matos ◽

Cláudia Maria Sousa ◽

Mário Gonçalves ◽

Joaquim Gabriel ◽

Jorge Machado ◽

...

Keyword(s):

Heart Rate ◽

Vegetative State ◽

White Ball ◽

Biofeedback Therapy ◽

Therapeutic Measure ◽

Functional Changes ◽

Functional Patterns ◽

The Individual ◽

Vegetative Patterns

A contemporary understanding of Chinese Medicine (CM) regards CM diagnosis as a functional vegetative state that may be treated by vegetative reflex therapies such as acupuncture. Within this context, traditional mind-body exercises such asQigongcan be understood as an attempt to enhance physiological proprioception, by combining a special state of “awareness” with posture, movement, and breath control. We have formerly trained young auditing flutists in “White Ball”Qigongto minimize anxiety-induced cold hands and lower anxiety-induced heart rate. Functional changes occurred 2–5 min after training and were observed over the whole training program, allowing the children to control their symptoms. In our current work, we report that warm fingers and calm hearts could be induced by the children even withoutQigongexercises. Thus, these positive changes once induced and “conditioned” vegetatively were stable after weeks of training. This may show the mechanism by whichQigongacts as a therapeutic measure in disease: positive vegetative pathways may be activated instead of dysfunctional functional patterns. The positive vegetative patterns then may be available in critical stressful situations.Qigongexercise programs may therefore be understood as an ancient vegetative biofeedback exercise inducing positive vegetative functions which are added to the individual reactive repertoire.

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