We demonstrate a computational network model that integrates 18 in vitro, high-throughput screening assays measuring estrogen receptor (ER) binding, dimerization, chromatin binding, transcriptional activation, and ER-dependent cell proliferation. The network model uses activity patterns across the in vitro assays to predict whether a chemical is an ER agonist or antagonist, or is otherwise influencing the assays through a manner dependent on the physics and chemistry of the technology platform ("assay interference"). The method is applied to a library of 1812 commercial and environmental chemicals, including 45 ER positive and negative reference chemicals. Among the reference chemicals, the network model correctly identified the agonists and antagonists with the exception of very weak compounds whose activity was outside the concentration range tested. The model agonist score also correlated with the expected potency class of the active reference chemicals. Of the 1812 chemicals evaluated, 111 (6.1%) were predicted to be strongly ER active in agonist or antagonist mode. This dataset and model were also used to begin a systematic investigation of assay interference. The most prominent cause of false-positive activity (activity in an assay that is likely not due to interaction of the chemical with ER) is cytotoxicity. The model provides the ability to prioritize a large set of important environmental chemicals with human exposure potential for additional in vivo endocrine testing. Finally, this model is generalizable to any molecular pathway for which there are multiple upstream and downstream assays available.

We prove that those non-uniformly hyperbolic maps and flows (with singularities) that enjoy the K-property are also Bernoulli. In particular, many billiard systems, including those systems of hard balls and stadia that have the K-property, and hyperbolic billiards, such as the Lorentz gas in any dimension, are Bernoulli. We obtain the Bernoulli property for both the billiard flows and the associated maps on the boundary of the phase space.

In the Beverton Holt difference equation of population biology with intrinsic growth parameter above its critical value, any initial non-zero population will approach an asymptotically stable fixed point, the carrying capacity of the environment. When this carrying capacity is allowed to vary periodically it is known that there is a globally asymptotically stable periodic solution and the average of the state variable along this solution is strictly less than the average of the carrying capacities, i.e. the varying environment has a deleterious effect on the state average. In this work we consider the case of a randomly varying environment and show that there is a unique invariant density to which all other density distributions on the state variable converge. Further, for every initial non-zero state variable and almost all random sequences of carrying capacities, the averages of the state variable along an orbit and the carrying capacities exist and the former is strictly less than the latter.

In this paper, we investigate the long-term behaviour of solutions of the periodic Sigmoid Beverton-Holt equationwhere the a n and δ n are p-periodic positive sequences. Under certain conditions, there are shown to exist an asymptotically stable p-periodic state and a p-periodic Allee state with the property that populations smaller than the Allee state are driven to extinction while populations greater than the Allee state approach the stable state, thus accounting for the long-term behaviour of all initial states. This appears to be the first study of the equation with variable δ. The results are discussed with possible interpretations in Population Dynamics with emphasis on fish populations and smooth cordgrass.