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

Gender Separation Increases Somatic Growth in Females but Does Not Affect Lifespan in Nothobranchius furzeri

According to life history theory, physiological and ecological traits and parameters influence an individual's life history and thus, ultimately, its lifespan. Mating and reproduction are costly activities, and in a variety of model organisms, a negative correlation of longevity and reproductive effort has been demonstrated. We are employing the annual killifish Nothobranchius furzeri as a vertebrate model for ageing. N. furzeri is the vertebrate displaying the shortest known lifespan in captivity with particular strains living only three to four months under optimal laboratory conditions. The animals show explosive growth, early sexual maturation and age-dependent physiological and behavioural decline. Here, we have used N. furzeri to investigate a potential reproduction-longevity trade-off in both sexes by means of gender separation. Though female reproductive effort and offspring investment were significantly reduced after separation, as investigated by analysis of clutch size, eggs in the ovaries and ovary mass, the energetic surplus was not reallocated towards somatic maintenance. In fact, a significant extension of lifespan could not be observed in either sex. This is despite the fact that separated females, but not males, grew significantly larger and heavier than the respective controls. Therefore, it remains elusive whether lifespan of an annual species evolved in periodically vanishing habitats can be prolonged on the cost of reproduction at all

Viral Networks: Connecting Digital Humanities and Medical History

This volume of original essays explores the power of network thinking and analysis for humanities research. Contributing authors are all scholars whose research focuses on a medical history topic—from the Black Death in fourteenth-century Provence to psychiatric hospitals in twentieth-century Alabama. The chapters take readers through a variety of situations in which scholars must determine if network analysis is right for their research; and, if the answer is yes, what the possibilities are for implementation. Along the way, readers will find practical tips on identifying an appropriate network to analyze, finding the best way to apply network analysis, and choosing the right tools for data visualization. All the chapters in this volume grew out of the 2018 Viral Networks workshop, hosted by the History of Medicine Division of the National Library of Medicine (NIH), funded by the Office of Digital Humanities of the National Endowment for the Humanities, and organized by Virginia Tech

Demography and Life Histories of Sympatric Patas Monkeys, Erythrocebus patas, and Vervets, Cercopithecus aethiops, in Laikipia, Kenya

Mortality patterns are thought to be strong selective forces on life history traits, with high adult mortality and low immature mortality favoring early and rapid reproduction. Patas monkeys (Erythrocebus patas) have the highest potential rates of population increase for their body size of any haplorhine primate because they reproduce both earlier and more often. We report here 10 yr of comparative demographic data on a population of patas monkeys and a sympatric population of vervet monkeys (Cercopithecus aethiops), a closely related species differing in aspects of social system, ecology, and life history. The data reveal that 1) adult female patas monkeys have significantly higher mortality than adult female vervets; 2) infant mortality in patas monkeys is relatively low compared to the norm for mammals because it is not significantly different from that of adult female patas monkeys; and 3) infant mortality is significantly higher than adult female mortality in vervets. For both species, much of the mortality could be attributed to predation. An epidemic illness was also a major contributor to the mortality of adult female patas monkeys whereas chronic exposure to pathogens in a cold and damp microenvironment may have contributed to the mortality of infant vervets. Both populations experienced large fluctuations during the study period. Our results support the prediction from demographic models of life history evolution that high adult mortality relative to immature mortality selects for early maturation

Correlated Equilibria in Continuous Games: Characterization and Computation

We present several new characterizations of correlated equilibria in games with continuous utility functions. These have the advantage of being more computationally and analytically tractable than the standard definition in terms of departure functions. We use these characterizations to construct effective algorithms for approximating a single correlated equilibrium or the entire set of correlated equilibria of a game with polynomial utility functions.Comment: Games and Economic Behavior, In Press, Accepted Manuscript, Available online 16 April 201