Negativity as a distance from a separable state

The computable measure of the mixed-state entanglement, the negativity, is shown to admit a clear geometrical interpretation, when applied to Schmidt-correlated (SC) states: the negativity of a SC state equals a distance of the state from a pertinent separable state. As a consequence, a SC state is separable if and only if its negativity vanishes. Another remarkable consequence is that the negativity of a SC can be estimated "at a glance" on the density matrix. These results are generalized to mixtures of SC states, which emerge in certain quantum-dynamical settings.Comment: 9 pages, 1 figur

Lake regionalization and diatom metacommunity structuring in tropical South America

Lakes and their topological distribution across Earth’s surface impose ecological and evolutionary constraints on aquatic metacommunities. In this study, we group similar lake ecosystems as metacommunity units influencing diatom community structure. We assembled a database of 195 lakes from the tropical Andes and adjacent lowlands (8°N–30°S and 58–79°W) with associated environmental predictors to examine diatom metacommunity patterns at two different levels: taxon and functional (deconstructed species matrix by ecological guilds). We also derived spatial variables that inherently assessed the relative role of dispersal. Using complementary multivariate statistical techniques (principal component analysis, cluster analysis, nonmetric multidimensional scaling, Procrustes, variance partitioning), we examined diatom–environment relationships among different lake habitats (sediment surface, periphyton, and plankton) and partitioned community variation to evaluate the influence of niche-and dispersal-based assembly processes in diatom metacommunity structure across lake clusters. The results showed a significant association between geographic clusters of lakes based on gradients of climate and landscape configuration and diatom assemblages. Six lake clusters distributed along a latitudinal gradient were identified as functional metacommunity units for diatom communities. Variance partitioning revealed that dispersal mechanisms were a major contributor to diatom metacommunity structure, but in a highly context-dependent fashion across lake clusters. In the Andean Altiplano and adjacent lowlands of Bolivia, diatom metacommunities are niche assembled but constrained by either dispersal limitation or mass effects, resulting from area, environmental heterogeneity, and ecological guild relationships. Topographic heterogeneity played an important role in structuring planktic diatom metacommunities. We emphasize the value of a guild-based metacommunity model linked to dispersal for elucidating mechanisms underlying latitudinal gradients in distribution. Our findings reveal the importance of shifts in ecological drivers across climatic and physiographically distinct lake clusters, providing a basis for comparison of broad-scale community gradients in lake-rich regions elsewhere. This may help guide future research to explore evolutionary constraints on the rich Neotropical benthic diatom species pool

On the Maximum Crossing Number

Research about crossings is typically about minimization. In this paper, we consider \emph{maximizing} the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009] conjectured that any graph has a \emph{convex} straight-line drawing, e.g., a drawing with vertices in convex position, that maximizes the number of edge crossings. We disprove this conjecture by constructing a planar graph on twelve vertices that allows a non-convex drawing with more crossings than any convex one. Bald et al. [Proc. COCOON, 2016] showed that it is NP-hard to compute the maximum number of crossings of a geometric graph and that the weighted geometric case is NP-hard to approximate. We strengthen these results by showing hardness of approximation even for the unweighted geometric case and prove that the unweighted topological case is NP-hard.Comment: 16 pages, 5 figure

Lake Regionalization and Diatom Metacommunity Structuring in Tropical South America

Lakes and their topological distribution across Earth\u27s surface impose ecological and evolutionary constraints on aquatic metacommunities. In this study, we group similar lake ecosystems as metacommunity units influencing diatom community structure. We assembled a database of 195 lakes from the tropical Andes and adjacent lowlands (8°N–30°S and 58–79°W) with associated environmental predictors to examine diatom metacommunity patterns at two different levels: taxon and functional (deconstructed species matrix by ecological guilds). We also derived spatial variables that inherently assessed the relative role of dispersal. Using complementary multivariate statistical techniques (principal component analysis, cluster analysis, nonmetric multidimensional scaling, Procrustes, variance partitioning), we examined diatom–environment relationships among different lake habitats (sediment surface, periphyton, and plankton) and partitioned community variation to evaluate the influence of niche‐ and dispersal‐based assembly processes in diatom metacommunity structure across lake clusters. The results showed a significant association between geographic clusters of lakes based on gradients of climate and landscape configuration and diatom assemblages. Six lake clusters distributed along a latitudinal gradient were identified as functional metacommunity units for diatom communities. Variance partitioning revealed that dispersal mechanisms were a major contributor to diatom metacommunity structure, but in a highly context‐dependent fashion across lake clusters. In the Andean Altiplano and adjacent lowlands of Bolivia, diatom metacommunities are niche assembled but constrained by either dispersal limitation or mass effects, resulting from area, environmental heterogeneity, and ecological guild relationships. Topographic heterogeneity played an important role in structuring planktic diatom metacommunities. We emphasize the value of a guild‐based metacommunity model linked to dispersal for elucidating mechanisms underlying latitudinal gradients in distribution. Our findings reveal the importance of shifts in ecological drivers across climatic and physiographically distinct lake clusters, providing a basis for comparison of broad‐scale community gradients in lake‐rich regions elsewhere. This may help guide future research to explore evolutionary constraints on the rich Neotropical benthic diatom species pool

Realizability of Polytopes as a Low Rank Matrix Completion Problem

This article gives necessary and sufficient conditions for a relation to be the containment relation between the facets and vertices of a polytope. Also given here, are a set of matrices parameterizing the linear moduli space and another set parameterizing the projective moduli space of a combinatorial polytope

Polytopality and Cartesian products of graphs

We study the question of polytopality of graphs: when is a given graph the graph of a polytope? We first review the known necessary conditions for a graph to be polytopal, and we provide several families of graphs which satisfy all these conditions, but which nonetheless are not graphs of polytopes. Our main contribution concerns the polytopality of Cartesian products of non-polytopal graphs. On the one hand, we show that products of simple polytopes are the only simple polytopes whose graph is a product. On the other hand, we provide a general method to construct (non-simple) polytopal products whose factors are not polytopal.Comment: 21 pages, 10 figure

Theory of commensurable magnetic structures in holmium

The tendency for the period of the helically ordered moments in holmium to lock into values which are commensurable with the lattice is studied theoretically as a function of temperature and magnetic field. The commensurable effects are derived in the mean-field approximation from numerical calculations of the free energy of various commensurable structures, and the results are compared with the extensive experimental evidence collected during the last ten years on the magnetic structures in holmium. In general the stability of the different commensurable structures is found to be in accord with the experiments, except for the tau=5/18 structure observed a few degrees below T_N in a b-axis field. The trigonal coupling recently detected in holmium is found to be the interaction required to explain the increased stability of the tau=1/5 structure around 42 K, and of the tau=1/4 structure around 96 K, when a field is applied along the c-axis.Comment: REVTEX, 31 pages, 7 postscript figure

Utilization of granular solidification during terrestrial locomotion of hatchling sea turtles

Biological terrestrial locomotion occurs on substrate materials with a range of rheological behaviour, which can affect limb-ground interaction, locomotor mode and performance. Surfaces like sand, a granular medium, can display solid or fluid-like behaviour in response to stress. Based on our previous experiments and models of a robot moving on granular media, we hypothesize that solidification properties of granular media allow organisms to achieve performance on sand comparable to that on hard ground. We test this hypothesis by performing a field study examining locomotor performance (average speed) of an animal that can both swim aquatically and move on land, the hatchling Loggerhead sea turtle (Caretta caretta). Hatchlings were challenged to traverse a trackway with two surface treatments: hard ground (sandpaper) and loosely packed sand. On hard ground, the claw use enables no-slip locomotion. Comparable performance on sand was achieved by creation of a solid region behind the flipper that prevents slipping. Yielding forces measured in laboratory drag experiments were sufficient to support the inertial forces at each step, consistent with our solidification hypothesis

Forty years of paleoecology in the Galapagos

The Galapagos Islands provided one of the first lowland paleoecological records from the Neotropics. Since the first cores were raised from the islands in 1966, there has been a substantial increase in knowledge of past systems, and development of the science of paleoclimatology. The study of fossil pollen, diatoms, corals and compound-specific isotopes on the Galapagos has contributed to the maturation of this discipline. As research has moved from questions about ice-age conditions and mean states of the Holocene to past frequency of El Niño Southern Oscillation, the resolution of fossil records has shifted from millennial to sub-decadal. Understanding the vulnerability of the Galapagos to climate change will be enhanced by knowledge of past climate change and responses in the islands

Irreducible triangulations of surfaces with boundary

A triangulation of a surface is irreducible if no edge can be contracted to produce a triangulation of the same surface. In this paper, we investigate irreducible triangulations of surfaces with boundary. We prove that the number of vertices of an irreducible triangulation of a (possibly non-orientable) surface of genus g>=0 with b>=0 boundaries is O(g+b). So far, the result was known only for surfaces without boundary (b=0). While our technique yields a worse constant in the O(.) notation, the present proof is elementary, and simpler than the previous ones in the case of surfaces without boundary