Optimal adult growth of Daphnia in a seasonal environment

1. The cladoceran Daphnia serves as an example of an iteroparous organism, with overlapping generations, that is capable of substantial adult growth. The life history of Daphnia was modelled as the consequence of a series of decisions about allocation of energetic resources to growth and reproduction. 2. We used numerical methods to find resource allocation patterns that maximized fitness of Daphnia in a temporally variable environment. Temporal variation was modelled as alternating active and dormant seasons; length of the active season was uniformly distributed. Fitness was measured by the geometric mean of resting eggs produced at the end of the active season. We examined effects of mean and range of the active season on the optimal life history; we also examined effects of increasing (invertebrate predation), constant (non-selective) and decreasing (fish) size-specific survival rates. For comparison, we found resource allocation patterns that maximized fitness in a constant environment, where fitness was measured by the intrinsic rate of increase r. 3. Life histories optimized for seasonal environments generally showed earlier maturity and greater adult growth than those optimized for constant environments. Adult growth occurred with non-selective predation, and even with fish predation, conditions under which it does not occur in the optimal life histories for constant environments. 4. Greatest size at maturity and adult growth occurred in life histories optimized to invertebrate predation in seasonal environments. Smallest size at maturity and least adult growth occurred in life histories optimized to fish predation. 5. In the optimal life histories, size at maturity generally increased with mean length of the active season. Adult growth reached a maximum for mean seasons of length equal to about one-half to one life span of Daphnia. 6. Increasing the variation in season length decreased adult growth in the optimal life history, but had little effect on size at maturity. 7. We expect that life histories are adapted to the long-term average of season length and its variation. If the animals can detect the type of predator, selection could favour phenotypic variation in resource allocation

The Sine Transform of Isotropic Measures

Sharp isoperimetric inequalities for the sine transform of even isotropic measures are established. The corresponding reverse inequalities are obtained in an asymptotically optimal form. These new inequalities have direct applications to strong volume estimates for convex bodies from data about their sections or projections

Two-component plasma in a gravitational field

In this paper we study a model for the sedimentation equilibrium of a charged colloidal suspension: the two-dimensional two-component plasma in a gravitational field which is exactly solvable at a special value of the reduced inverse temperature Gamma=2. The density profiles are computed. The heavy particles accumulate at the bottom of the cointainer. If the container is high enough, an excess of light counterions form a cloud floating at some altitude.Comment: 17 pages, 3 Encapsulated Postscript figures, LaTeX with the graphicx packag

The Cube Recurrence

We construct a combinatorial model that is described by the cube recurrence, a nonlinear recurrence relation introduced by Propp, which generates families of Laurent polynomials indexed by points in $\mathbb{Z}^3$. In the process, we prove several conjectures of Propp and of Fomin and Zelevinsky, and we obtain a combinatorial interpretation for the terms of Gale-Robinson sequences. We also indicate how the model might be used to obtain some interesting results about perfect matchings of certain bipartite planar graphs

New age-metallicity diagnostic diagram for the Washington photometric system

The age calibration of the Washington deltaT1 index is mainly used to estimate ages of star clusters older than 1 Gyr, no age-metallicity degeneracy effect is considered. We have profusely exploited synthetic T1 versus C-T1 colour magnitude diagrams aiming at exploring the intrinsic behaviour of the deltaT1 index. The analysis shows that deltaT1 varies with age and metal content as well. In general, the dependence on age weakens for ages greater than ~ 6 Gyr, and results even less sensitive to age as the metallicity decreases. For ages younger than ~ 5 Gyr deltaT1 shows a strong correlation with both age and metallicity. The deltaC index -defined as deltaT1 for the C passband- is also a combined measurement of age and metallicity. We introduce a new age-metallicity diagnostic diagram, deltaT1 versus deltaC - deltaT1, which has shown the ability of unambiguously providing age and metallicity estimates, simultaneously. The new procedure allows to derive ages from 1 up to 13 Gyr and metallicities [Fe/H] from -2.0 up to +0.5 dex, and is independent of the cluster reddening and distance modulus. It does solve the constraints found in the deltaT1 index and surpasses the performance of the standard giant branch metallicity method. All these features make the diagnostic diagram a powerful tool for estimating accurate ages as well as metallicities.Comment: 14 pages, 7 figures, accepted for publication in MNRA

Bounding the size of a vertex-stabiliser in a finite vertex-transitive graph

In this paper we discuss a method for bounding the size of the stabiliser of a vertex in a $G$-vertex-transitive graph $\Gamma$. In the main result the group $G$ is quasiprimitive or biquasiprimitive on the vertices of $\Gamma$, and we obtain a genuine reduction to the case where $G$ is a nonabelian simple group. Using normal quotient techniques developed by the first author, the main theorem applies to general $G$-vertex-transitive graphs which are $G$-locally primitive (respectively, $G$-locally quasiprimitive), that is, the stabiliser $G_\alpha$ of a vertex $\alpha$ acts primitively (respectively quasiprimitively) on the set of vertices adjacent to $\alpha$. We discuss how our results may be used to investigate conjectures by Richard Weiss (in 1978) and the first author (in 1998) that the order of $G_\alpha$ is bounded above by some function depending only on the valency of $\Gamma$, when $\Gamma$ is $G$-locally primitive or $G$-locally quasiprimitive, respectively

trackr: A Framework for Enhancing Discoverability and Reproducibility of Data Visualizations and Other Artifacts in R

Research is an incremental, iterative process, with new results relying and building upon previous ones. Scientists need to find, retrieve, understand, and verify results in order to confidently extend them, even when the results are their own. We present the trackr framework for organizing, automatically annotating, discovering, and retrieving results. We identify sources of automatically extractable metadata for computational results, and we define an extensible system for organizing, annotating, and searching for results based on these and other metadata. We present an open-source implementation of these concepts for plots, computational artifacts, and woven dynamic reports generated in the R statistical computing language