Efficient parametric inference for stochastic biological systems with measured variability

Stochastic systems in biology often exhibit substantial variability within and between cells. This variability, as well as having dramatic functional consequences, provides information about the underlying details of the system's behaviour. It is often desirable to infer properties of the parameters governing such systems given experimental observations of the mean and variance of observed quantities. In some circumstances, analytic forms for the likelihood of these observations allow very efficient inference: we present these forms and demonstrate their usage. When likelihood functions are unavailable or difficult to calculate, we show that an implementation of approximate Bayesian computation (ABC) is a powerful tool for parametric inference in these systems. However, the calculations required to apply ABC to these systems can also be computationally expensive, relying on repeated stochastic simulations. We propose an ABC approach that cheaply eliminates unimportant regions of parameter space, by addressing computationally simple mean behaviour before explicitly simulating the more computationally demanding variance behaviour. We show that this approach leads to a substantial increase in speed when applied to synthetic and experimental datasets.Comment: 11 pages, 4 fig

Endless love: On the termination of a playground number game

A simple and popular childhood game, `LOVES' or the `Love Calculator', involves an iterated rule applied to a string of digits and gives rise to surprisingly rich behaviour. Traditionally, players' names are used to set the initial conditions for an instance of the game: its behaviour for an exhaustive set of pairings of popular UK childrens' names, and for more general initial conditions, is examined. Convergence to a fixed outcome (the desired result) is not guaranteed, even for some plausible first name pairings. No pairs of top-50 common first names exhibit non-convergence, suggesting that it is rare in the playground; however, including surnames makes non-convergence more likely due to higher letter counts (for example, `Reese Witherspoon LOVES Calvin Harris'). Different game keywords (including from different languages) are also considered. An estimate for non-convergence propensity is derived: if the sum $m$ of digits in a string of length $w$ obeys $m > 18/(3/2)^{w-4}$, convergence is less likely. Pairs of top UK names with pairs of `O's and several `L's (for example, Chloe and Joseph, or Brooke and Scarlett) often attain high scores. When considering individual names playing with a range of partners, those with no `LOVES' letters score lowest, and names with intermediate (not simply the highest) letter counts often perform best, with Connor and Evie averaging the highest scores when played with other UK top names.Comment: 12 pages, 9 figure

SSME main injector 4000 Hertz phenomenon

Several Space Shuttle Main Engines (SSME) have experienced very high acceleration responses measured in the main injector of the powerhead during static firings. Data from previous hot fire SSME tests relating to the 4000 hertz phenomenon were reviewed to provide a better understanding of the nature of this structural response. The objective was to technically understand the way this phenomenon works, recommend a fix and test the fix

One Last Chance: The Economic Case for a New Approach to Fisheries Management in New England

Documents the decline of the New England fishing industry as a result of mismanagement, presents examples of successful and sustainable fisheries, and examines the viability of proposed community-based, fishermen-run cooperatives as a solution

Boolean algebras and Lubell functions

Let $2^{[n]}$ denote the power set of $[n]:=\{1,2,..., n\}$. A collection \B\subset 2^{[n]} forms a $d$-dimensional {\em Boolean algebra} if there exist pairwise disjoint sets $X_0, X_1,..., X_d \subseteq [n]$, all non-empty with perhaps the exception of $X_0$, so that \B={X_0\cup \bigcup_{i\in I} X_i\colon I\subseteq [d]}. Let $b(n,d)$ be the maximum cardinality of a family \F\subset 2^X that does not contain a $d$-dimensional Boolean algebra. Gunderson, R\"odl, and Sidorenko proved that $b(n,d) \leq c_d n^{-1/2^d} \cdot 2^n$ where $c_d= 10^d 2^{-2^{1-d}}d^{d-2^{-d}}$. In this paper, we use the Lubell function as a new measurement for large families instead of cardinality. The Lubell value of a family of sets \F with \F\subseteq \tsupn is defined by h_n(\F):=\sum_{F\in \F}1/{{n\choose |F|}}. We prove the following Tur\'an type theorem. If \F\subseteq 2^{[n]} contains no $d$-dimensional Boolean algebra, then h_n(\F)\leq 2(n+1)^{1-2^{1-d}} for sufficiently large $n$. This results implies $b(n,d) \leq C n^{-1/2^d} \cdot 2^n$, where $C$ is an absolute constant independent of $n$ and $d$. As a consequence, we improve several Ramsey-type bounds on Boolean algebras. We also prove a canonical Ramsey theorem for Boolean algebras.Comment: 10 page

The high-energy gamma-ray light curve of PSR B1259 -63

The high-energy gamma-ray light curve of the binary system PSR B1259 -63, is computed using the approach that successfully predicted the spectrum at periastron. The simultaneous INTEGRAL and H.E.S.S. spectra taken 16 days after periastron currently permit both a model with dominant radiative losses, high pulsar wind Lorentz factor and modest efficiency as well as one with dominant adiabatic losses, a slower wind and higher efficiency. In this paper we shown how the long-term light curve may help to lift this degeneracy.Comment: 4 pages, to appear in proceedings of: Astrophysical Sources of High Energy Particles and Radiation, Torun (2005

Stratospheric column NO2 measurements from three Antarctic sites

The significance of stratospheric odd-nitrogen compounds in Antarctic ozone depletion studies has prompted an increase in Antarctic activities. Although several species are being studied, work has concentrated on the acquisition of NO2 data. Ground-based measurements of stratospheric column NO2 have been made at Arrival Heights, Antarctica, since spring 1982, with some gaps in the data base. Additional data has been acquired since February 1986 at Pole Station and Halley Bay, thus providing a chain of stations across the continent. The technique used is that of absorption spectroscopy in several wavelength regions, although here only those measurements are reported in the 430 to 450 nm region where strongly structured absorption been determined experimentally. However, theory features due to NO2 are identified in scattered sunlight in the zenith sky. Operation of a moon-tracking system at Arrival Heights has provided some additional data during the polar night. Previous analyses have shown that the NO2 column observed from the ground is strongly influenced by the season, and by the location of the site with respect to that of the polar vortex. The column amount correlates strongly with stratospheric temperature at about 70 mbar. The present data set further illustrates these features, and demonstrates both the strengths and qualifications apparent in the technique