Gaussian perturbations of circle maps: A spectral approach

In this work, we examine spectral properties of Markov transition operators corresponding to Gaussian perturbations of discrete time dynamical systems on the circle. We develop a method for calculating asymptotic expressions for eigenvalues (in the zero noise limit) and show that changes to the number or period of stable orbits for the deterministic system correspond to changes in the number of limiting modulus 1 eigenvalues of the transition operator for the perturbed process. We call this phenomenon a $\lambda$-bifurcation. Asymptotic expressions for the corresponding eigenfunctions and eigenmeasures are also derived and are related to Hermite functions.Comment: Published in at http://dx.doi.org/10.1214/08-AAP573 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Traveling waves of selective sweeps

The goal of cancer genome sequencing projects is to determine the genetic alterations that cause common cancers. Many malignancies arise during the clonal expansion of a benign tumor which motivates the study of recurrent selective sweeps in an exponentially growing population. To better understand this process, Beerenwinkel et al. [PLoS Comput. Biol. 3 (2007) 2239--2246] consider a Wright--Fisher model in which cells from an exponentially growing population accumulate advantageous mutations. Simulations show a traveling wave in which the time of the first $k$-fold mutant, $T_k$, is approximately linear in $k$ and heuristics are used to obtain formulas for $ET_k$. Here, we consider the analogous problem for the Moran model and prove that as the mutation rate $\mu\to0$, $T_k\sim c_k\log(1/\mu)$, where the $c_k$ can be computed explicitly. In addition, we derive a limiting result on a log scale for the size of $X_k(t)={}$the number of cells with $k$ mutations at time $t$.Comment: Published in at http://dx.doi.org/10.1214/10-AAP721 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Evolution in predator-prey systems

We study the adaptive dynamics of predator-prey systems modeled by a dynamical system in which the traits of predators and prey are allowed to evolve by small mutations. When only the prey are allowed to evolve, and the size of the mutational change tends to 0, the system does not exhibit long term prey coexistence and the trait of the resident prey type converges to the solution of an ODE. When only the predators are allowed to evolve, coexistence of predators occurs. In this case, depending on the parameters being varied, we see (i) the number of coexisting predators remains tight and the differences in traits from a reference species converge in distribution to a limit, or (ii) the number of coexisting predators tends to infinity, and we calculate the asymptotic rate at which the traits of the least and most "fit" predators in the population increase. This last result is obtained by comparison with a branching random walk killed to the left of a linear boundary and a finite branching-selection particle system.Comment: Major revisions to the introduction and definitions of the evolutionary processes considered, minor revisions to the proofs of Propositions 1.1 and 1.

SARDSRN: A NEURAL NETWORK SHIFT-REDUCE PARSER

Simple Recurrent Networks (SRNs) have been widely used in natural language tasks. SARDSRN extends the SRN by explicitly representing the input sequence in a SARDNET self-organizing map. The distributed SRN component leads to good generalization and robust cognitive properties, whereas the SARDNET map provides exact representations of the sentence constituents. This combination allows SARDSRN to learn to parse sentences with more complicated structure than can the SRN alone, and suggests that the approach could scale up to realistic natural language

State Government support for WA farmers experiencing adverse seasons in 1998 to 2001: A comment

In response to a series of adverse weather events, in parts of the cereal crop belt from 1998 to 2001, the State and the Commonwealth Governments implemented support measures for farmers in the cereal belt of Western Australia. A critique of the State Government Adverse Seasonal Conditions in the Agricultural Sector (ASCAS) support packages is presented. The schemes are expensive, could adversely affect the normal adjustment process, have subjective boundaries, deliver grants to some multi millionaires, attract a small element of clearly ineligible claimants, and in 2001 the second ASCAS package was provided prior to excellent late winter and spring rains.adverse weather, drought relief policy, Crop Production/Industries, Environmental Economics and Policy,

The impacts of Meta Data Management on Social Dynamics: A Research Case Study

Meta data management practices often overlook the role social dynamics play in harnessing the value of an organisation’s unique business language and the behaviours it creates. Using evidence from literature, interviews and cognitive ethnography, this research case sets out to explain the impacts of meta data management on social dynamics. The emerging themes (that is, newness, continual adaption, engagement tension, production tension, inefficiency and unreliability) represent salient factors by which organisations can be constrained in exploiting the worth of their meta data. This research emphasises the critical importance of organisations having a deeper understanding of the purpose and meaning of information. This understanding is a strength for creating value and for exploiting the worth arising in networks and in the social dynamics created within those networks. This strength contributes to organisations’ economic growth and is interdependent with their ability to manage complex phenomenon in a growing interconnected society

Patient Compliance-Gaining: A Look At Care Facility vs. Home Health

The patient compliance-gaining strategies employed by health care providers in the care facility and home health environments were investigated. Each participant completed a two-page, open-ended survey. A content analysis, and more specifically a thematic analysis of the research, allowed for similarities and differences between the two settings to be compared to current literature. Results indicated that participants used similar strategies to those suggested by researchers in the field. The results showed that strategies applied by health care providers in this particular study are effective for gaining patient compliance