Lower bounds for polynomials using geometric programming

We make use of a result of Hurwitz and Reznick, and a consequence of this result due to Fidalgo and Kovacec, to determine a new sufficient condition for a polynomial $f\in\mathbb{R}[X_1,...,X_n]$ of even degree to be a sum of squares. This result generalizes a result of Lasserre and a result of Fidalgo and Kovacec, and it also generalizes the improvements of these results given in [6]. We apply this result to obtain a new lower bound $f_{gp}$ for $f$, and we explain how $f_{gp}$ can be computed using geometric programming. The lower bound $f_{gp}$ is generally not as good as the lower bound $f_{sos}$ introduced by Lasserre and Parrilo and Sturmfels, which is computed using semidefinite programming, but a run time comparison shows that, in practice, the computation of $f_{gp}$ is much faster. The computation is simplest when the highest degree term of $f$ has the form $\sum_{i=1}^n a_iX_i^{2d}$, $a_i>0$, $i=1,...,n$. The lower bounds for $f$ established in [6] are obtained by evaluating the objective function of the geometric program at the appropriate feasible points

Distinguishing separable and entangled states

We show how to design families of operational criteria that distinguish entangled from separable quantum states. The simplest of these tests corresponds to the well-known Peres-Horodecki positive partial transpose (PPT) criterion, and the more complicated tests are strictly stronger. The new criteria are tractable due to powerful computational and theoretical methods for the class of convex optimization problems known as semidefinite programs. We successfully applied the results to many low-dimensional states from the literature where the PPT test fails. As a byproduct of the criteria, we provide an explicit construction of the corresponding entanglement witnesses.Comment: 4 pages, Latex2e. Expanded discussion of numerical procedures. Accepted for publication in Physical Review Letter

Sex-Specific Differences in Shoaling Affect Parasite Transmission in Guppies

Background: Individuals have to trade-off the costs and benefits of group membership during shoaling behaviour. Shoaling can increase the risk of parasite transmission, but this cost has rarely been quantified experimentally. Guppies (Poecilia reticulata) are a model system for behavioural studies, and they are commonly infected by gyrodactylid parasites, notorious fish pathogens that are directly transmitted between guppy hosts. Methodology/Principal Findings:Parasite transmission in single sex shoals of male and female guppies were observed using an experimental infection of Gyrodactylus turnbulli. Parasite transmission was affected by sex-specific differences in host behaviour, and significantly more parasites were transmitted when fish had more frequent and more prolonged contact with each other. Females shoaled significantly more than males and had a four times higher risk to contract an infection. Conclusions/Significance: Intersexual differences in host behaviours such as shoaling are driven by differences in natural and sexual selection experienced by both sexes. Here we show that the potential benefits of an increased shoaling tendency are traded off against increased risks of contracting an infectious parasite in a group-living species

Sex-specific local life-history adaptation in surface- and cave-dwelling Atlantic mollies (Poecilia mexicana)

Cavefishes have long been used as model organisms showcasing adaptive diversification, but does adaptation to caves also facilitate the evolution of reproductive isolation from surface ancestors? We raised offspring of wild-caught surface- and cave-dwelling ecotypes of the neotropical fish Poecilia mexicana to sexual maturity in a 12-month common garden experiment. Fish were raised under one of two food regimes (high vs. low), and this was crossed with differences in lighting conditions (permanent darkness vs. 12:12 h light:dark cycle) in a 2 × 2 factorial design, allowing us to elucidate potential patterns of local adaptation in life histories. Our results reveal a pattern of sex-specific local life-history adaptation: Surface molly females had the highest fitness in the treatment best resembling their habitat of origin (high food and a light:dark cycle), and suffered from almost complete reproductive failure in darkness, while cave molly females were not similarly affected in any treatment. Males of both ecotypes, on the other hand, showed only weak evidence for local adaptation. Nonetheless, local life-history adaptation in females likely contributes to ecological diversification in this system and other cave animals, further supporting the role of local adaptation due to strong divergent selection as a major force in ecological speciation

Empiricism and the Principle of Conditions in the Evolution of the Police Power: A Model for Definitional Scrutiny

This article explores the development and consequences of the application of the principle of conditions in and to the evolution of the police power

Negative phenotypic and genetic associations between copulation duration and longevity in male seed beetles

Reproduction can be costly and is predicted to trade-off against other characters. However, while these trade-offs are well documented for females, there has been less focus on aspects of male reproduction. Furthermore, those studies that have looked at males typically only investigate phenotypic associations, with the underlying genetics often ignored. Here, we report on phenotypic and genetic trade-offs in male reproductive effort in the seed beetle, Callosobruchus maculatus. We find that the duration of a male's first copulation is negatively associated with subsequent male survival, phenotypically and genetically. Our results are consistent with life-history theory and suggest that like females, males trade-off reproductive effort against longevity

Reading, Trauma and Literary Caregiving 1914-1918: Helen Mary Gaskell and the War Library

This article is about the relationship between reading, trauma and responsive literary caregiving in Britain during the First World War. Its analysis of two little-known documents describing the history of the War Library, begun by Helen Mary Gaskell in 1914, exposes a gap in the scholarship of war-time reading; generates a new narrative of "how," "when," and "why" books went to war; and foregrounds gender in its analysis of the historiography. The Library of Congress's T. W. Koch discovered Gaskell's ground-breaking work in 1917 and reported its successes to the American Library Association. The British Times also covered Gaskell's library, yet researchers working on reading during the war have routinely neglected her distinct model and method, skewing the research base on war-time reading and its association with trauma and caregiving. In the article's second half, a literary case study of a popular war novel demonstrates the extent of the "bitter cry for books." The success of Gaskell's intervention is examined alongside H. G. Wells's representation of textual healing. Reading is shown to offer sick, traumatized and recovering combatants emotional and psychological caregiving in ways that she could not always have predicted and that are not visible in the literary/historical record