668 research outputs found
Regression with strongly correlated data
This paper discusses linear regression of strongly correlated data that
arises, for example, in magnetohydrodynamic equilibrium reconstructions. We
have proved that, generically, the covariance matrix of the estimated
regression parameters for fixed sample size goes to zero as the correlations
become unity. That is, in this limit the estimated parameters are known with
perfect accuracy. Simple examples are shown to illustrate this effect and the
nature of the exceptional cases in which the estimate covariance does not go to
zero
Randomness in Competitions
We study the effects of randomness on competitions based on an elementary
random process in which there is a finite probability that a weaker team upsets
a stronger team. We apply this model to sports leagues and sports tournaments,
and compare the theoretical results with empirical data. Our model shows that
single-elimination tournaments are efficient but unfair: the number of games is
proportional to the number of teams N, but the probability that the weakest
team wins decays only algebraically with N. In contrast, leagues, where every
team plays every other team, are fair but inefficient: the top of
teams remain in contention for the championship, while the probability that the
weakest team becomes champion is exponentially small. We also propose a gradual
elimination schedule that consists of a preliminary round and a championship
round. Initially, teams play a small number of preliminary games, and
subsequently, a few teams qualify for the championship round. This algorithm is
fair and efficient: the best team wins with a high probability and the number
of games scales as , whereas traditional leagues require N^3 games to
fairly determine a champion.Comment: 10 pages, 8 figures, reviews arXiv:physics/0512144,
arXiv:physics/0608007, arXiv:cond-mat/0607694, arXiv:physics/061221
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Calcium dynamics during fertilization in C. elegans
BACKGROUND: Of the animals typically used to study fertilization-induced calcium dynamics, none is as accessible to genetics and molecular biology as the model organism Caenorhabditis elegans. Motivated by the experimental possibilities inherent in using such a well-established model organism, we have characterized fertilization-induced calcium dynamics in C. elegans. RESULTS: Owing to the transparency of the nematode, we have been able to study the calcium signal in C. elegans fertilization in vivo by monitoring the fluorescence of calcium indicator dyes that we introduce into the cytosol of oocytes. In C. elegans, fertilization induces a single calcium transient that is initiated soon after oocyte entry into the spermatheca, the compartment that contains sperm. Therefore, it is likely that the calcium transient is initiated by contact with sperm. This calcium elevation spreads throughout the oocyte, and decays monotonically after which the cytosolic calcium concentration returns to that preceding fertilization. Only this single calcium transient is observed. CONCLUSION: Development of a technique to study fertilization induced calcium transients opens several experimental possibilities, e.g., identification of the signaling events intervening sperm binding and calcium elevation, identifying the possible roles of the calcium elevation such as the completion of meiosis, the formation of the eggshell, and the establishing of the embryo's axis of symmetry
Transient Pattern Formation in an Active Matter Contact Poisoning Model
One of the most notable features in repulsive particle based active matter
systems is motility-induced-phase separation (MIPS) where a dense, often
crystalline phase coexists with a low density fluid. In most active matter
studies, the activity is kept constant as a function of time; however, there
are many examples of active systems in which individual particles transition
from living or moving to dead or nonmotile due to lack of fuel, infection, or
poisoning. Here we consider an active matter particle system at densities where
MIPS does not occur. When we add a small number of infected particles that can
effectively poison other particles, rendering them nonmotile, we find a rich
variety of time dependent pattern formation, including MIPS, a wetting phase,
and a fragmented state formed when mobile particles plow through an nonmotile
packing. We map out the patterns as a function of time scaled by the duration
of the epidemic, and show that the pattern formation is robust for a wide range
of poisoning rates and activity levels. We also show that pattern formation
does not occur in a random death model, but requires the promotion of
nucleation by contact poisoning. Our results should be relevant to biological
and active matter systems where there is some form of poisoning, death, or
transition to nonmotility.Comment: 7 pages, 6 figure
How to Choose a Champion
League competition is investigated using random processes and scaling
techniques. In our model, a weak team can upset a strong team with a fixed
probability. Teams play an equal number of head-to-head matches and the team
with the largest number of wins is declared to be the champion. The total
number of games needed for the best team to win the championship with high
certainty, T, grows as the cube of the number of teams, N, i.e., T ~ N^3. This
number can be substantially reduced using preliminary rounds where teams play a
small number of games and subsequently, only the top teams advance to the next
round. When there are k rounds, the total number of games needed for the best
team to emerge as champion, T_k, scales as follows, T_k ~N^(\gamma_k) with
gamma_k=1/[1-(2/3)^(k+1)]. For example, gamma_k=9/5,27/19,81/65 for k=1,2,3.
These results suggest an algorithm for how to infer the best team using a
schedule that is linear in N. We conclude that league format is an ineffective
method of determining the best team, and that sequential elimination from the
bottom up is fair and efficient.Comment: 6 pages, 3 figure
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