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

Sexual HIV Risk Among Male Parolees and Their Female Partners: The Relate Project

Background: The massively disproportionate impact of America’s prison boom on communities of color has raised questions about how incarceration may affect health disparities, including disparities in HIV. Primary partners are an important source of influence on sexual health. In this paper, we investigate sexual HIV risk among male-female couples following a man’s release from prison. Methods: We draw upon data from the Relate Project, a novel cross-sectional survey of recently released men and their female partners in Oakland and San Francisco, California (N=344). Inferential analyses use the actor-partner model to explore actor and partner effects on sexual HIV risk outcomes. Results: Dyadic analyses of sexual HIV risk among male parolees and their female partners paint a complex portrait of couples affected by incarceration and of partners’ influences on each other. Findings indicate that demographic factors such as education level and employment status, individual psycho-social factors such as perception of risk, and relationship factors such as commitment and power affect sexual HIV risk outcomes. Conclusion: The Relate Project provides a novel dataset for the dyadic analysis of sexual risk among male parolees and their female partners, and results highlight the importance of focusing on the couple as a unit when assessing HIV risk and protective behaviors. Results also indicate potentially fruitful avenues for population-specific interventions that may help to reduce sexual health disparities among couples affected by incarceration

The Adventure of Relevance: Speculative Reconstructions in Contemporary Social Science

At a time when the institutional and intellectual futures of the social sciences are under threat, there has been growing concern among researchers and policy makers around the question of how to foster and enhance the relevance of their knowledge-practices. This thesis problematises such demands by elaborating a concept of ‘relevance’ that renders it not the product of a subjective act of interpretation, but an event that is part and parcel of the immanent processes by which the facts that compose situations come (in)to matter. By expanding on the work of William Connolly, Gilles Deleuze, John Dewey, Donna Haraway, William James, Michel Serres, Isabelle Stengers and Alfred North Whitehead, among others, I follow the implications of the concept of relevance through a speculative exploration of modes of knowledge-making in contemporary social science. As I show, such an exploration requires a transformation of the ethos with which social scientific inquiries are identified. If the former could be characterised as an ‘ethics of estrangement’ whereby to inquire is to estrange oneself from an apparent reality in order to gain access to a realm of social causes and reasons, an ethos oriented by the concept of relevance must reject that bifurcation of reality and cultivate, instead, a deep empiricism that is both singularly attentive to the coming into matter of the facts that compose a situation, and inventive of propositions that may contribute to the possible transformation of those situations that demand inquiry. It is this latter ethos, one which I call an ‘adventure’, that my thesis develops

Intraspecific variability modulates interspecific variability in animal organismal stoichiometry.

Interspecific differences in organismal stoichiometry (OS) have been documented in a wide range of animal taxa and are of significant interest for understanding evolutionary patterns in OS. In contrast, intraspecific variation in animal OS has generally been treated as analytical noise or random variation, even though available data suggest intraspecific variability in OS is widespread. Here, we assess how intraspecific variation in OS affects inferences about interspecific OS differences using two co-occurring Neotropical fishes: Poecilia reticulata and Rivulus hartii. A wide range of OS has been observed within both species and has been attributed to environmental differences among stream systems. We assess the contributions of species identity, stream system, and the interactions between stream and species to variability in N:P, C:P, and C:N. Because predation pressure can impact the foraging ecology and life-history traits of fishes, we compare predictors of OS between communities that include predators, and communities where predators are absent. We find that species identity is the strongest predictor of N:P, while stream or the interaction of stream and species contribute more to the overall variation in C:P and C:N. Interspecific differences in N:P, C:P, and C:N are therefore not consistent among streams. The relative contribution of stream or species to OS qualitatively changes between the two predation communities, but these differences do not have appreciable effects in interspecific patterns. We conclude that although species identity is a significant predictor of OS, intraspecific OS is sometimes sufficient to overwhelm or obfuscate interspecific differences in OS

On the sums of two cubes

We solve the equation $f(x,y)^3 + g(x,y)^3 = x^3 + y^3$ for homogeneous $f, g \in \mathbb C(x,y)$, completing an investigation begun by Vi\`ete in 1591. The usual addition law for elliptic curves and composition give rise to two binary operations on the set of solutions. We show that a particular subset of the set of solutions is ring-isomorphic to $\mathbb Z[e^{2 \pi i / 3}]$.Comment: Revised version, to appear in the International Journal of Number Theor

Metabolic rate evolves rapidly and in parallel with the pace of life history

Metabolic rates and life history strategies are both thought to set the "pace of life", but whether they evolve in tandem is not well understood. Here, using a common garden experiment that compares replicate paired populations, we show that Trinidadian guppy (Poecilia reticulata) populations that evolved a fast-paced life history in high-predation environments have consistently higher metabolic rates than guppies that evolved a slow-paced life history in low-predation environments. Furthermore, by transplanting guppies from high- to low-predation environments, we show that metabolic rate evolves in parallel with the pace of life history, at a rapid rate, and in the same direction as found for naturally occurring populations. Together, these multiple lines of inference provide evidence for a tight evolutionary coupling between metabolism and the pace of life history

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

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

On the Generation of Positivstellensatz Witnesses in Degenerate Cases

One can reduce the problem of proving that a polynomial is nonnegative, or more generally of proving that a system of polynomial inequalities has no solutions, to finding polynomials that are sums of squares of polynomials and satisfy some linear equality (Positivstellensatz). This produces a witness for the desired property, from which it is reasonably easy to obtain a formal proof of the property suitable for a proof assistant such as Coq. The problem of finding a witness reduces to a feasibility problem in semidefinite programming, for which there exist numerical solvers. Unfortunately, this problem is in general not strictly feasible, meaning the solution can be a convex set with empty interior, in which case the numerical optimization method fails. Previously published methods thus assumed strict feasibility; we propose a workaround for this difficulty. We implemented our method and illustrate its use with examples, including extractions of proofs to Coq.Comment: To appear in ITP 201

Manipulation of feeding regime alters sexual dimorphism for lifespan and reduces sexual conflict in Drosophila melanogaster

Sexual dimorphism for lifespan (SDL) is widespread, but poorly understood. A leading hypothesis, which we test here, is that strong SDL can reduce sexual conflict, by allowing each sex to maximise its sex-specific fitness. We used replicated experimental evolution lines of the fruit fly, Drosophila melanogaster, which had been maintained for over 360 generations on either unpredictable ‘Random’ or predictable ‘Regular’ feeding regimes. This evolutionary manipulation of feeding regime led to robust, enhanced SDL in Random over control, Regular lines. Enhanced SDL was associated with a significant increase in the fitness of focal males, tested with wild type females. This was due to sex-specific changes to male life history, manifested as increased early reproductive output and reduced survival. In contrast, focal female fitness, tested with wild type males, did not differ across regimes. Hence increased SDL was associated with a reduction in sexual conflict, which increased male fitness and maintained fitness in females. Differences in SDL were not associated with developmental time or developmental survival. Overall, the results showed that the expression of enhanced SDL, resulting from experimental evolution of feeding regimes, was associated with male-specific changes in life history, leading to increased fitness and reduced sexual conflict