16,401 research outputs found
Having the Second Leg At Home - Advantage in the UEFA Champions League Knockout Phase?
In soccer knockout ties which are played in a two-legged format the team having the return match at home is usually seen as advantaged. For checking this common belief, we analyzed matches of the UEFA Champions League knockout phase since 1995. It is shown that the observed differences in frequencies of winning between teams first playing away and those which are first playing at home can be completely explained by their performances on the group stage and - more importantly - by the teams' general strength
Persistence in fluctuating environments
Understanding under what conditions interacting populations, whether they be
plants, animals, or viral particles, coexist is a question of theoretical and
practical importance in population biology. Both biotic interactions and
environmental fluctuations are key factors that can facilitate or disrupt
coexistence. To better understand this interplay between these deterministic
and stochastic forces, we develop a mathematical theory extending the nonlinear
theory of permanence for deterministic systems to stochastic difference and
differential equations. Our condition for coexistence requires that there is a
fixed set of weights associated with the interacting populations and this
weighted combination of populations' invasion rates is positive for any
(ergodic) stationary distribution associated with a subcollection of
populations. Here, an invasion rate corresponds to an average per-capita growth
rate along a stationary distribution. When this condition holds and there is
sufficient noise in the system, we show that the populations approach a unique
positive stationary distribution. Moreover, we show that our coexistence
criterion is robust to small perturbations of the model functions. Using this
theory, we illustrate that (i) environmental noise enhances or inhibits
coexistence in communities with rock-paper-scissor dynamics depending on
correlations between interspecific demographic rates, (ii) stochastic variation
in mortality rates has no effect on the coexistence criteria for discrete-time
Lotka-Volterra communities, and (iii) random forcing can promote genetic
diversity in the presence of exploitative interactions.Comment: 25 page
Correlating Cell Behavior with Tissue Topology in Embryonic Epithelia
Measurements on embryonic epithelial tissues in a diverse range of organisms
have shown that the statistics of cell neighbor numbers are universal in
tissues where cell proliferation is the primary cell activity. Highly
simplified non-spatial models of proliferation are claimed to accurately
reproduce these statistics. Using a systematic critical analysis, we show that
non-spatial models are not capable of robustly describing the universal
statistics observed in proliferating epithelia, indicating strong spatial
correlations between cells. Furthermore we show that spatial simulations using
the Subcellular Element Model are able to robustly reproduce the universal
histogram. In addition these simulations are able to unify ostensibly divergent
experimental data in the literature. We also analyze cell neighbor statistics
in early stages of chick embryo development in which cell behaviors other than
proliferation are important. We find from experimental observation that cell
neighbor statistics in the primitive streak region, where cell motility and
ingression are also important, show a much broader distribution. A non-spatial
Markov process model provides excellent agreement with this broader histogram
indicating that cells in the primitive streak may have significantly weaker
spatial correlations. These findings show that cell neighbor statistics provide
a potentially useful signature of collective cell behavior.Comment: PLoS one 201
Coping with dating errors in causality estimation
We consider the problem of estimating causal influences between observed processes from time series possibly corrupted by errors in the time variable (dating errors) which are typical in palaeoclimatology, planetary science and astrophysics. "Causality ratio" based on the Wiener-Granger causality is proposed and studied for a paradigmatic class of model systems to reveal conditions under which it correctly indicates directionality of unidirectional coupling. It is argued that in the case of a priori known directionality, the causality ratio allows a characterization of dating errors and observational noise. Finally, we apply the developed approach to palaeoclimatic data and quantify the influence of solar activity on tropical Atlantic climate dynamics over the last two millennia. A stronger solar influence in the first millennium A.D. is inferred. The results also suggest a dating error of about 20 years in the solar proxy time series over the same period
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