1,309 research outputs found
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
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 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 for , and we
explain how can be computed using geometric programming. The lower
bound is generally not as good as the lower bound 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 is much faster. The computation is simplest when the highest degree
term of has the form , , . The
lower bounds for established in [6] are obtained by evaluating the
objective function of the geometric program at the appropriate feasible points
On the sums of two cubes
We solve the equation for homogeneous , 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 .Comment: Revised version, to appear in the International Journal of Number
Theor
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
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
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