FPTAS for optimizing polynomials over the mixed-integer points of polytopes in fixed dimension

We show the existence of a fully polynomial-time approximation scheme (FPTAS) for the problem of maximizing a non-negative polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. Moreover, using a weaker notion of approximation, we show the existence of a fully polynomial-time approximation scheme for the problem of maximizing or minimizing an arbitrary polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed.Comment: 16 pages, 4 figures; to appear in Mathematical Programmin

On the Computational Complexity and Geometry of the First-Order Theory of the Reals, Part I

PLEASE NOTE: The original Technical Report TR00853 is missing. A copy can be found at http://www.sciencedirect.com/science/article/pii/S0747717110800033This paper published in the "Journal of Symbolic Computation" 13 (1992) 255-35

The Complexity of Drawing Graphs on Few Lines and Few Planes

It is well known that any graph admits a crossing-free straight-line drawing in $\mathbb{R}^3$ and that any planar graph admits the same even in $\mathbb{R}^2$. For a graph $G$ and $d \in \{2,3\}$, let $\rho^1_d(G)$ denote the minimum number of lines in $\mathbb{R}^d$ that together can cover all edges of a drawing of $G$. For $d=2$, $G$ must be planar. We investigate the complexity of computing these parameters and obtain the following hardness and algorithmic results. - For $d\in\{2,3\}$, we prove that deciding whether $\rho^1_d(G)\le k$ for a given graph $G$ and integer $k$ is ${\exists\mathbb{R}}$-complete. - Since $\mathrm{NP}\subseteq{\exists\mathbb{R}}$, deciding $\rho^1_d(G)\le k$ is NP-hard for $d\in\{2,3\}$. On the positive side, we show that the problem is fixed-parameter tractable with respect to $k$. - Since ${\exists\mathbb{R}}\subseteq\mathrm{PSPACE}$, both $\rho^1_2(G)$ and $\rho^1_3(G)$ are computable in polynomial space. On the negative side, we show that drawings that are optimal with respect to $\rho^1_2$ or $\rho^1_3$ sometimes require irrational coordinates. - Let $\rho^2_3(G)$ be the minimum number of planes in $\mathbb{R}^3$ needed to cover a straight-line drawing of a graph $G$. We prove that deciding whether $\rho^2_3(G)\le k$ is NP-hard for any fixed $k \ge 2$. Hence, the problem is not fixed-parameter tractable with respect to $k$ unless $\mathrm{P}=\mathrm{NP}$

Ubiquitous microplastics in the upper gastrointestinal tracts of Florida coastal seabirds

Plastic pollution is increasingly recognized as a global problem. In particular, plastic pieces \u3c5 mm in size (‘microplastics’) are of interest due to their prevalence and association with harmful, persistent organic pollutants (POPs). Very little is known about the prevalence of microplastics in coastal birds. Yet, these water-associated birds are at a high risk of ingesting microplastics that accumulate near the water’s surface. This study describes the microplastics found in the proventriculus and ventriculus of four species of coastal birds regarding quantity, size, type (fiber or fragment), and color (light, mid, or dark). A total of 643 microplastic particles were identified, with 43 of the 44 study specimens containing microplastics (97.7% frequency). The ‘fiber’ type and the ‘mid’ color were the most common microplastics. There were no significant differences between species for particle sizes, but Brown Pelicans contained significantly more particles than the other three species. These results highlight the prevalence of plastic pollution in medium-sized seabirds, but more work is needed to determine microplastic patterns between taxa and foraging environments

The Most Temperature-Adapted Corals Have an Achilles\u27 Heel

The corals of the Persian/Arabian Gulf are better adapted to temperature fluctuations than elsewhere in the Indo-Pacific. The Gulf is an extreme marine environment displaying the highest known summer water temperatures for any reef area. The small and shallow sea can be considered a good analogue to future conditions for the rest of the world’s oceans under global warming. The fact that corals can persist in such a demanding environment indicates that they have been able to acclimatize and selectively adapt to elevated temperature. The implication being that colonies elsewhere may be able to follow suit. This in turn provides hope that corals may, given sufficient time, similarly adapt to survive even in an impoverished form, under conditions of acidification-driven lowering of CaCO3 saturation state, a further consequence of raised atmospheric CO2. This paper demonstrates, however, that the uniquely adapted corals of the Gulf may, within the next three centuries, be threatened by a chronic habitat shortage brought about by the dissolution of the lithified seabed on which they rely for colonisation. This will occur due to modifications in the chemical composition of the Gulf waters due to climate change

Parts of Quantum States

It is shown that generic N-party pure quantum states (with equidimensional subsystems) are uniquely determined by their reduced states of just over half the parties; in other words, all the information in almost all N-party pure states is in the set of reduced states of just over half the parties. For N even, the reduced states in fewer than N/2 parties are shown to be an insufficient description of almost all states (similar results hold when N is odd). It is noted that Real Algebraic Geometry is a natural framework for any analysis of parts of quantum states: two simple polynomials, a quadratic and a cubic, contain all of their structure. Algorithmic techniques are described which can provide conditions for sets of reduced states to belong to pure or mixed states.Comment: 10 pages, 1 figur

Semidefinite Representation of the kk-Ellipse

The $k$-ellipse is the plane algebraic curve consisting of all points whose sum of distances from $k$ given points is a fixed number. The polynomial equation defining the $k$-ellipse has degree $2^k$ if $k$ is odd and degree $2^k{-}\binom{k}{k/2}$ if $k$ is even. We express this polynomial equation as the determinant of a symmetric matrix of linear polynomials. Our representation extends to weighted $k$-ellipses and $k$-ellipsoids in arbitrary dimensions, and it leads to new geometric applications of semidefinite programming.Comment: 16 pages, 5 figure

How to assess the effectiveness of nasal influenza vaccines? Role and measurement of sIgA in mucosal secretions

Secretory IgAs (sIgA) constitute the principal isotype of antibodies present in nasal and mucosal secretions. They are secreted by plasma cells adjacent to the mucosal epithelial cells, the site where infection occurs, and are the main humoral mediator of mucosal immunity. Mucosally delivered vaccines, such as live attenuated influenza vaccine (LAIV), are able to mimic natural infection without causing disease or virus transmission and mainly elicit a local immune response. The measurement of sIgA concentrations in nasal swab/wash and saliva samples is therefore a valuable tool for evaluating their role in the effectiveness of such vaccines. Here, we describe two standardized assays (enzyme-linked immunosorbent assay and microneutralization) available for the quantification of sIgA and discuss the advantages and limitations of their use

Improved algorithm for quantum separability and entanglement detection

Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. It has recently been shown that this problem is NP-hard. There is a highly inefficient `basic algorithm' for solving the quantum separability problem which follows from the definition of a separable state. By exploiting specific properties of the set of separable states, we introduce a new classical algorithm that solves the problem significantly faster than the `basic algorithm', allowing a feasible separability test where none previously existed e.g. in 3-by-3-dimensional systems. Our algorithm also provides a novel tool in the experimental detection of entanglement.Comment: 4 pages, revtex4, no figure

Ultrastructural and Histological Analysis of Dark Spot Syndrome in Siderastrea siderea and Agaricia agaricites

Dark Spot Syndrome (DSS) typically manifests in scleractinian corals as lesions of varying color, size, shape and location that can result in skeletal changes and tissue death. A causative agent for DSS has not yet been identified. The objective of this study was histological and ultrastructural comparison of the cellular and skeletal characteristics of DSS-affected and healthy Siderastrea siderea and Agaricia agaricites. The greater resolution possible with transmission electron microscopy (TEM) revealed microbial activity and tissue changes not resolvable utilizing histology. DSS-affected tissue had less integrity, with increasing cellular degradation and vacuolization. A high concentration of electron dense inclusions, which appear to be zymogen granules, was concentrated in the calicodermis and adjacent gastrodermal layer. Numerous endolithic fungal cells were observed directly adjacent to the calicodermis in DSS-affected S. siderea. Numerous unidentified endolithic cells were observed directly adjacent to the calicodermis in DSS-affected A. agaricites. These observations suggest that the coral may be using a digestive enzyme as a defensive mechanism against endolithic cellular invasion