Optimization results for a generalized coupon collector problem

Anceaume, Emmanuelle; Busnel, Yann; Schulte-Geers, Ernst; Séricola, Bruno

doi:10.1017/jpr.2016.27

Cited by 8 publications

(11 citation statements)

References 12 publications

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“…. Given the type configuration in generation g − 1, the parental relations are now generated in a two-step manner: First, assign the random weights W (g− 1) to the individuals in generation g − 1, then follow the rule…”

Section: A Paintbox Representation Incorporating Selectionmentioning

confidence: 99%

“…To see that the l.h.s. almost surely implies the r.h.s., consider the first pick that falls into the area Γ (g−1) and assume that it lands in a horizontal stripe belonging to a wildtype individual in generation g − 1. Then this must be also the first one of the picks that lands in [0, 1 − s N ] × [0, 1], and no one of the preceding picks could have landed in a horizontal stripe belonging to a beneficial individual in generation g − 1.…”

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confidence: 99%

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Haldane’s formula in Cannings models: the case of moderately weak selection

Boenkost¹,

Casanova²,

Pokalyuk³

et al. 2021

Electron. J. Probab.

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We introduce a Cannings model with directional selection via a paintbox construction and establish a strong duality with the line counting process of a new Cannings ancestral selection graph in discrete time. This duality also yields a formula for the fixation probability of the beneficial type. Haldane's formula states that for a single selectively advantageous individual in a population of haploid individuals of size N the probability of fixation is asymptotically (as N → ∞) equal to the selective advantage of haploids sN divided by half of the offspring variance. For a class of offspring distributions within Kingman attraction we prove this asymptotics for sequences sN obeying N −1 sN N −1/2 , which is a regime of "moderately weak selection". It turns out that for sN N −2/3 the Cannings ancestral selection graph is so close to the ancestral selection graph of a Moran model that a suitable coupling argument allows to play the problem back asymptotically to the fixation probability in the Moran model, which can be computed explicitly.

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Section: A Paintbox Representation Incorporating Selectionmentioning

confidence: 99%

mentioning

confidence: 99%

Haldane’s formula in Cannings models: the case of moderately weak selection

Boenkost¹,

Casanova²,

Pokalyuk³

et al. 2021

Electron. J. Probab.

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“…Remark 6.8. A very recent and similar study in [39] proves inequalities (6.2) and ( 6.3) of theorem 6.3 through a different procedure. Our contribution offers a more elegant argument, based on use of fundamental formulae (3.2) and (3.3) in different contexts.…”

Section: Relationship Between the Risk Distribution And The Speed Of Parasitizationmentioning

confidence: 85%

The coupon collector urn model with unequal probabilities in ecology and evolution

Zoroa

Lesigne

Fernández-Sáez

et al. 2017

J. R. Soc. Interface.

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The sequential sampling of populations with unequal probabilities and with replacement in a closed population is a recurrent problem in ecology and evolution. Examples range from biodiversity sampling, epidemiology to the estimation of signal repertoire in animal communication. Many of these questions can be reformulated as urn problems, often as special cases of the coupon collector problem, most simply expressed as the number of coupons that must be collected to have a complete set. We aimed to apply the coupon collector model in a comprehensive manner to one example-hosts (balls) being searched (draws) and parasitized (ball colour change) by parasitic waspsto evaluate the influence of differences in sampling probabilities between items on collection speed. Based on the model of a complete multinomial process over time, we define the distribution, distribution function, expectation and variance of the number of hosts parasitized after a given time, as well as the inverse problem, estimating the sampling effort. We develop the relationship between the risk distribution on the set of hosts and the speed of parasitization and propose a more elegant proof of the weak stochastic dominance among speeds of parasitization, using the concept of Schur convexity and the 'Robin Hood transfer' numerical operation. Numerical examples are provided and a conjecture about strong dominance-an ordering characteristic of random variables-is proposed. The speed at which new items are discovered is a function of the entire shape of the sampling probability distribution. The sole comparison of values of variances is not sufficient to compare speeds associated with different distributions, as generally assumed in ecological studies.

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“…. , p n ), we will use the notation T c,n (p) instead of T c,n , meaning by the way that the dimension of vector p is n. We have from [2] that the expectation of T c,n (p) is given for every n ≥ 1 and c = 1, . .…”

Section: A Principles Of the Solutionmentioning

confidence: 99%

“…It has been observed (Theorem 3 in [2]) that for vectors p = (p j,s ) j∈J k and with p 0 = 1 − P J k and 0…”

Section: A Principles Of the Solutionmentioning

confidence: 99%

Identifying Global Icebergs in Distributed Streams

Anceaume

Busnel

Rivetti

et al. 2015

2015 IEEE 34th Symposium on Reliable Distributed Systems (SRDS)

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International audience—We consider the problem of identifying global iceberg attacks in massive and physically distributed streams. A global iceberg is a distributed denial of service attack, where some elements globally recur many times across the distributed streams, but locally, they do not appear as a deny of service. A natural solution to defend against global iceberg attacks is to rely on multiple routers that locally scan their network traffic, and regularly provide monitoring information to a server in charge of collecting and aggregating all the monitored information. Any relevant solution to this problem must minimise the communication between the routers and the coordinator, and the space required by each node to analyse its stream. We propose a distributed algorithm that tracks global icebergs on the fly with guaranteed error bounds, limited memory and processing requirements. We present a thorough analysis of our algorithm performance. In particular we derive a tight upper bound on the number of bits communicated between the multiple routers and the coordinator in presence of an oblivious adversary. Finally, we present the main results of the experiments we have run on a cluster of single-board computers. Those experiments confirm the efficiency and accuracy of our algorithm to track global icebergs hidden in very large input data streams exhibiting different shapes

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Optimization results for a generalized coupon collector problem

Cited by 8 publications

References 12 publications

Haldane’s formula in Cannings models: the case of moderately weak selection

Haldane’s formula in Cannings models: the case of moderately weak selection

The coupon collector urn model with unequal probabilities in ecology and evolution

Identifying Global Icebergs in Distributed Streams

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