scholarly journals Expected Number of Distinct Part Sizes in a Random Integer Composition

2000 ◽  
Vol 9 (6) ◽  
pp. 519-527 ◽  
Author(s):  
P. HITCZENKO ◽  
G. STENGLE
Keyword(s):  
Expected Number ◽  
Distinct Part ◽  
Random Integer

An asymptotics, as n → ∞, for the expected number of distinct part sizes in a random composition of an integer n is obtained.

scholarly journals The effect of change in population size on DNA polymorphism.

Genetics ◽  
1989 ◽  
Vol 123 (3) ◽  
pp. 597-601 ◽  
Author(s):  
F Tajima
Keyword(s):  
Population Size ◽  
Dna Sequences ◽  
Dna Polymorphism ◽  
Population Bottleneck ◽  
Expected Number ◽  
Original Population ◽  
Current Population ◽  
Segregating Sites

Abstract The expected number of segregating sites and the expectation of the average number of nucleotide differences among DNA sequences randomly sampled from a population, which is not in equilibrium, have been developed. The results obtained indicate that, in the case where the population size has changed drastically, the number of segregating sites is influenced by the size of the current population more strongly than is the average number of nucleotide differences, while the average number of nucleotide differences is affected by the size of the original population more severely than is the number of segregating sites. The results also indicate that the average number of nucleotide differences is affected by a population bottleneck more strongly than is the number of segregating sites.

Intercepting a Stealthy Network

2021 ◽  
Vol 17 (2) ◽  
pp. 1-39
Author(s):  
Mai Ben Adar Bessos ◽  
Amir Herzberg
Keyword(s):  
Mobile Devices ◽  
Short Range ◽  
Low Energy ◽  
Expected Number ◽  
Relay Communication

We investigate an understudied threat: networks of stealthy routers (S-Routers) , relaying messages to a hidden destination . The S-Routers relay communication along a path of multiple short-range, low-energy hops, to avoid remote localization by triangulation. Mobile devices called Interceptors can detect communication by an S-Router, but only when the Interceptor is next to the transmitting S-Router. We examine algorithms for a set of mobile Interceptors to find the destination of the communication relayed by the S-Routers. The algorithms are compared according to the number of communicating rounds before the destination is found, i.e., rounds in which data is transmitted from the source to the destination . We evaluate the algorithms analytically and using simulations, including against a parametric, optimized strategy for the S-Routers. Our main result is an Interceptors algorithm that bounds the expected number of communicating rounds by a term quasilinear in the number of S-Routers. For the case where S-Routers transmit at every round (“continuously”), we present an algorithm that improves this bound.

scholarly journals Average Number of Nucleotide Differences in a Sample From a Single Subpopulation: A Test for Population Subdivision

Genetics ◽  
1987 ◽  
Vol 117 (1) ◽  
pp. 149-153
Author(s):  
Curtis Strobeck
Keyword(s):  
Monte Carlo Simulation ◽  
Population Structure ◽  
Random Mating ◽  
Population Subdivision ◽  
Expected Number ◽  
Migration Rates ◽  
Mating Population ◽  
Unbiased Estimates ◽  
Increasing Function ◽  
Stepping Stone Model

ABSTRACT Unbiased estimates of θ = 4Nµ in a random mating population can be based on either the number of alleles or the average number of nucleotide differences in a sample. However, if there is population structure and the sample is drawn from a single subpopulation, these two estimates of θ behave differently. The expected number of alleles in a sample is an increasing function of the migration rates, whereas the expected average number of nucleotide differences is shown to be independent of the migration rates and equal to 4N  Tµ for a general model of population structure which includes both the island model and the circular stepping-stone model. This contrast in the behavior of these two estimates of θ is used as the basis of a test for population subdivision. Using a Monte-Carlo simulation developed so that independent samples from a single subpopulation could be obtained quickly, this test is shown to be a useful method to determine if there is population subdivision.

scholarly journals A Search for a General Phenomenon of Adaptive Mutability

Genetics ◽  
1996 ◽  
Vol 143 (2) ◽  
pp. 645-659 ◽  
Author(s):  
Timothy Galitski ◽  
John R Roth
Keyword(s):  
Rank Correlation ◽  
Selective Medium ◽  
Chromosomal Gene ◽  
Galactosidase Activity ◽  
Bacteriophage Mu ◽  
Reversion Rate ◽  
General Phenomenon ◽  
Expected Number ◽  
Leaky Mutants ◽  
Residual Growth

Abstract The most prominent systems for the study of adaptive mutability depend on the specialized activities of genetic elements like bacteriophage Mu and the F plasmid. Searching for general adaptive mutability, we have investigated the behavior of Salmonella typhimurium strains with chromosomal lacZ mutations. We have studied 30 revertible nonsense, missense, frameshift, and insertion alleles. One-third of the mutants produced ≥10 late revertant colonies (appearing three to seven days after plating on selective medium). For the prolific mutants, the number of late revertants showed rank correlation with the residual β-galactosidase activity; for the same mutants, revertant number showed no correlation with the nonselective reversion rate (from fluctuation tests). Leaky mutants, which grew slowly on selective medium, produced late revertants whereas tight nongrowing mutants generally did not produce late revertants. However, the number of late revertants was not proportional to residual growth. Using total residual growth and the nonselective reversion rate, the expected number of late revertants was calculated. For several leaky mutants, the observed revertant number exceeded the expected number. We suggest that excess late revertants from these mutants arise from general adaptive mutability available to any chromosomal gene.

scholarly journals Different approaches to quantify years of life lost from COVID-19

2021 ◽  
Author(s):  
Tamás Ferenci
Keyword(s):  
Years Of Life Lost ◽  
Expected Number ◽  
Long Term Conditions ◽  
Developed Country ◽  
Individual Patient Level ◽  
Level Data ◽  
Parametric Survival Model ◽  
Epidemiologic Risk ◽  
Parametric Survival

AbstractThe burden of an epidemic is often characterized by death counts, but this can be misleading as it fails to acknowledge the age of the deceased patients. Years of life lost is therefore widely used as a more relevant metric, however, such calculations in the context of COVID-19 are all biased upwards: patients dying from COVID-19 are typically multimorbid, having far worse life expectation than the general population. These questions are quantitatively investigated using a unique Hungarian dataset that contains individual patient level data on comorbidities for all COVID-19 deaths in the country. To account for the comorbidities of the patients, a parametric survival model using 11 important long-term conditions was used to estimate a more realistic years of life lost. As of 12 May, 2021, Hungary reported a total of 27,837 deaths from COVID-19 in patients above 50 years of age. The usual calculation indicates 10.5 years of life lost for each death, which decreases to 9.2 years per death after adjusting for 11 comorbidities. The expected number of years lost implied by the life table, reflecting the mortality of a developed country just before the pandemic is 11.1 years. The years of life lost due to COVID-19 in Hungary is therefore 12% or 1.3 years per death lower when accounting for the comorbidities and is below its expected value, but how this should be interpreted is still a matter of debate. Further research is warranted on how to optimally integrate this information into epidemiologic risk assessments during a pandemic.

Distribution of the number of alleles in multigene families

1992 ◽  
Vol 29 (04) ◽  
pp. 759-769
Author(s):  
R. C. Griffiths
Keyword(s):  
Stochastic Model ◽  
Gene Conversion ◽  
Lower Bounds ◽  
Multigene Families ◽  
Expected Number ◽  
Allele Type ◽  
The Mean

The distribution of the number of alleles in samples from r chromosomes is studied. The stochastic model used includes gene conversion within chromosomes and mutation at loci on the chromosomes. A method is described for simulating the distribution of alleles and an algorithm given for computing lower bounds for the mean number of alleles. A formula is derived for the expected number of samples from r chromosomes which contain the allele type of a locus chosen at random.

scholarly journals Derivation of the mean highest reversal floor and expected number of stops in lift systems

1979 ◽  
Vol 3 (4) ◽  
pp. 275-279 ◽  
Author(s):  
N.A. Alexandris ◽  
G.C. Barney ◽  
C.J. Harris
Keyword(s):  
Expected Number ◽  
The Mean

n-point, win-by-k games

1989 ◽  
Vol 26 (4) ◽  
pp. 807-814 ◽  
Author(s):  
Kyle Siegrist
Keyword(s):  
Exit Time ◽  
Bernoulli Trials ◽  
Expected Number ◽  
First Exit Time ◽  
World Series ◽  
Time Space ◽  
Gambler’S Ruin ◽  
Gambler's Ruin Problem ◽  
Positive Integers ◽  
Made In

Consider a sequence of Bernoulli trials between players A and B in which player A wins each trial with probability p∈ [0, 1]. For positive integers n and k with k ≦ n, an (n, k) contest is one in which the first player to win at least n trials and to be ahead of his opponent by at least k trials wins the contest. The (n, 1) contest is the Banach match problem and the (n, n) contest is the gambler's ruin problem. Many real contests (such as the World Series in baseball and the tennis game) have an (n, 1) or an (n, 2) format. The (n, k) contest is formulated in terms of the first-exit time of the graph of a random walk from a certain region of the state-time space. Explicit results are obtained for the probability that player A wins an (n, k) contest and the expected number of trials in an (n, k) contest. Comparisons of (n, k) contests are made in terms of the probability that the stronger player wins and the expected number of trials.

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