A model for phenotype change in a stochastic framework

some species, an inducible secondary phenotype will develop some time after the environmental change that evokes it. Nishimura (2006) [4] showed how an individual organism should optimize the time it takes to respond to an environmental change ("waiting time''). If the optimal waiting time is considered to act over the population, there are implications for the expected value of the mean fitness in that population. A stochastic predator-prey model is proposed in which the prey have a fixed initial energy budget. Fitness is the product of survival probability and the energy remaining for non-defensive purposes. The model is placed in the stochastic domain by assuming that the waiting time in the population is a normally distributed random variable because of biological variance inherent in mounting the response. It is found that the value of the mean waiting time that maximises fitness depends linearly on the variance of the waiting time

Multiple planar coincidences with N-fold symmetry

Planar coincidence site lattices and modules with N-fold symmetry are well understood in a formulation based on cyclotomic fields, in particular for the class number one case, where they appear as certain principal ideals in the corresponding ring of integers. We extend this approach to multiple coincidences, which apply to triple or multiple junctions. In particular, we give explicit results for spectral, combinatorial and asymptotic properties in terms of Dirichlet series generating functions.Comment: 13 pages, two figures. For previous related work see math.MG/0511147 and math.CO/0301021. Minor changes and references update

Investigating the Potential for Unanticipated Consequences of Teaching the Tentative Nature of Science

If you are reading information supportive of climate science, you may well read that climate science is “settled science.” If you are reading something from a climate science skeptic, you may well read that climate science is “just a theory.” Given that the science education community strongly supports teaching the tentative nature of scientific knowledge, one might think that the skeptic has a legitimate argument. Experts will quickly object that such a deduction is quite wrong, and we agree. Nevertheless, we can’t help but wonder to what extent teaching the tentative nature of scientific knowledge might undermine confidence in science, especially for those who have not grasped important epistemological nuances. Our paper reports the findings from an initial exploration of this possibility

Crucial words for abelian powers

A word is "crucial" with respect to a given set of "prohibited words" (or simply "prohibitions") if it avoids the prohibitions but it cannot be extended to the right by any letter of its alphabet without creating a prohibition. A "minimal crucial word" is a crucial word of the shortest length. A word W contains an "abelian k-th power" if W has a factor of the form X_1X_2...X_k where X_i is a permutation of X_1 for 2<= i <= k. When k=2 or 3, one deals with "abelian squares" and "abelian cubes", respectively. In 2004 (arXiv:math/0205217), Evdokimov and Kitaev showed that a minimal crucial word over an n-letter alphabet A_n = {1,2,..., n} avoiding abelian squares has length 4n-7 for n >= 3. In this paper we show that a minimal crucial word over A_n avoiding abelian cubes has length 9n-13 for n >= 5, and it has length 2, 5, 11, and 20 for n=1, 2, 3, and 4, respectively. Moreover, for n >= 4 and k >= 2, we give a construction of length k^2(n-1)-k-1 of a crucial word over A_n avoiding abelian k-th powers. This construction gives the minimal length for k=2 and k=3. For k >= 4 and n >= 5, we provide a lower bound for the length of crucial words over A_n avoiding abelian k-th powers.Comment: 14 page

A maximum density rule for surfaces of quasicrystals

A rule due to Bravais of wide validity for crystals is that their surfaces correspond to the densest planes of atoms in the bulk of the material. Comparing a theoretical model of i-AlPdMn with experimental results, we find that this correspondence breaks down and that surfaces parallel to the densest planes in the bulk are not the most stable, i.e. they are not so-called bulk terminations. The correspondence can be restored by recognizing that there is a contribution to the surface not just from one geometrical plane but from a layer of stacked atoms, possibly containing more than one plane. We find that not only does the stability of high-symmetry surfaces match the density of the corresponding layer-like bulk terminations but the exact spacings between surface terraces and their degree of pittedness may be determined by a simple analysis of the density of layers predicted by the bulk geometric model.Comment: 8 pages of ps-file, 3 Figs (jpg

Monarch butterflies do not place all of their eggs in one basket: oviposition on nine Midwestern milkweed species

Over the past two decades, the population of monarch butterflies east of the Rocky Mountains has experienced a significant decline in overwintering numbers. Habitat restoration that includes planting milkweeds is essential to boost monarch numbers within the breeding range. Milkweeds are the only host plants for larval monarch butterflies, but female oviposition preference for different milkweed species, especially those with overlapping ranges, is not well documented. We examined the relative inclination to lay eggs on nine milkweed species native to Iowa (no choice), and oviposition preference (choice) among the four most commonly occurring Iowa species (Asclepias incarnata, Asclepias syriaca, Asclepias tuberosa, and Asclepias verticillata). In both experiments, eggs were counted daily for four days. The milkweeds tested were Asclepias exaltata (poke milkweed), Asclepias hirtella (tall green milkweed), A. incarnata (swamp milkweed), Asclepias speciosa (showy milkweed), Asclepias sullivantii (prairie milkweed), A. syriaca (common milkweed), A. tuberosa (butterfly milkweed), A. verticillata (whorled milkweed), and Cynanchum laeve (honeyvine milkweed). When females were given only a single species on which to lay eggs, there were significant differences among milkweed species in the average number of eggs laid; A. incarnata had the highest average egg count. When females were given a choice among A. incarnata, A. syriaca, A. tuberosa, and A. verticillata, there were also differences among milkweed species in the number of eggs laid; again, A. incarnata had the highest average number of eggs laid. Additionally, females laid more total eggs when four plants of different milkweed species were available than when there were four plants of a single milkweed species. Our results show that monarch butterflies will lay eggs on all nine milkweeds, but that there are clear preferences for some milkweed species over others

Different molecular patterns in glioblastoma multiforme subtypes upon recurrence

One of the hallmarks of glioblastoma is its inherent tendency to recur. At this point patients with relapsed GBM show a survival time of only few months. The molecular basis of the recurrence process in GBM is still poorly understood. The aim of the present study was to investigate the genetic profile of relapsed GBM compared to their respective primary tumors. We have included 20 paired GBMs. In all tumor samples, we have analyzed p53 and PTEN status by sequencing analysis, EGFR amplification by semiquantitative PCR and a wide-genome fingerprinting was performed by microsatellite analysis. Among primary GBM, we observed twelve type 2 GBM, four type 1 GBM and four further GBM showing neither p53 mutations nor EGFR amplification (non-type 1–non-type 2 GBM). Upon recurrence, we have detected two molecular patterns of tumor progression: GBM initially showing either type 1 or type 2 profiles conserved them at the time of relapse. In contrast, non-type 1–non-type 2 GBM acquired the typical pattern of type 2 GBM and harbor EGFR amplification without p53 mutation. New PTEN mutations upon relapse were only detected in type 2 GBM. Additional LOH were more frequently identified in relapses of type 2 GBM than in those showing the type 1 signature. Taken together, our results strongly suggest that recurrences of GBM may display two distinct pattern of accumulation of molecular alterations depending on the profile of the original tumor

The Present and Future Role of Insect-Resistant Genetically Modified Maize in IPM

Commercial, genetically-modified (GM) maize was first planted in the United States (USA, 1996) and Canada (1997) but now is grown in 13 countries on a total of over 35 million hectares (\u3e24% of area worldwide). The first GM maize plants produced a Cry protein derived from the soil bacteriumBacillus thuringiensis (Bt), which made them resistant to European corn borer and other lepidopteran maize pests. New GM maize hybrids not only have resistance to lepidopteran pests but some have resistance to coleopteran pests and tolerance to specific herbicides. Growers are attracted to the Btmaize hybrids for their convenience and because of yield protection, reduced need for chemical insecticides, and improved grain quality. Yet, most growers worldwide still rely on traditional integrated pest management (IPM) methods to control maize pests. They must weigh the appeal of buying insect protection “in the bag” against questions regarding economics, environmental safety, and insect resistance management (IRM). Traditional management of maize insects and the opportunities and challenges presented by GM maize are considered as they relate to current and future insect-resistant products. Four countries, two that currently have commercialize Bt maize (USA and Spain) and two that do not (China and Kenya), are highlighted. As with other insect management tactics (e.g., insecticide use or tillage), GM maize should not be considered inherently compatible or incompatible with IPM. Rather, the effect of GM insect-resistance on maize IPM likely depends on how the technology is developed and used