394 research outputs found
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
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
In search of the ice age tropics, a tribute to Prof. Daniel Livingstone and Prof. Paul Colinvaux
Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra
We give a method for computing upper and lower bounds for the volume of a
non-obtuse hyperbolic polyhedron in terms of the combinatorics of the
1-skeleton. We introduce an algorithm that detects the geometric decomposition
of good 3-orbifolds with planar singular locus and underlying manifold the
3-sphere. The volume bounds follow from techniques related to the proof of
Thurston's Orbifold Theorem, Schl\"afli's formula, and previous results of the
author giving volume bounds for right-angled hyperbolic polyhedra.Comment: 36 pages, 19 figure
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
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
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
Brachionus rotundiformis tschugunoff, 1921 from the brachionus plicatilis species complex (Rotifera: Monogononta): A new record from galápagos archipelago, Ecuador
The presence of the rotifer species Brachionus rotundiformis from the B. plicatilis species complex in Lake Arcturo, a saline lake in the Genovesa Island of the Galápagos Islands, is here reported. This is the first record of the species for the rotifer fauna of Ecuador as well as of the species complex to the Galápagos Islands. This finding is consistent with the idea of high dispersion capacity, and of cosmopolitan distribution of this species complex. Because Genovesa Island is uninhabited, passive transport by wind currents and zoochory by migrant birds seem to emerge as the most plausible factors in this process of colonization. Integrative studies on the morphological variations, genetic, molecular, and ecological aspects are still required to further understand the process of dispersion and the ecology of this member of the B. plicatilis species complex in this remote and isolated locality, and the exact taxonomical position of the island’s population to the other members of the complex.</p
Small grid embeddings of 3-polytopes
We introduce an algorithm that embeds a given 3-connected planar graph as a
convex 3-polytope with integer coordinates. The size of the coordinates is
bounded by . If the graph contains a triangle we can
bound the integer coordinates by . If the graph contains a
quadrilateral we can bound the integer coordinates by . The
crucial part of the algorithm is to find a convex plane embedding whose edges
can be weighted such that the sum of the weighted edges, seen as vectors,
cancel at every point. It is well known that this can be guaranteed for the
interior vertices by applying a technique of Tutte. We show how to extend
Tutte's ideas to construct a plane embedding where the weighted vector sums
cancel also on the vertices of the boundary face
Cancer risks in childhood and adolescence among the offspring of immigrants to Sweden
We used the nation-wide Swedish Family-Cancer Database to analyse the risk of nervous system tumours, leukaemia and non-Hodgkin's lymphoma in age groups 0–4 and 0–19 years among Swedish-born offspring of immigrants. The study included 850 000 individuals with an immigrant background, including European, Asian and American parents. We calculated standardised incidence ratios for the above three malignancies using Swedish offspring as a reference. Subjects were grouped by region or by selected countries of parental origin. No group differed significantly from Swedes in the occurrence of nervous system neoplasm or leukaemia. Offspring of Yugoslav fathers (SIR 2.27) and Turkish parents were at increased risk of non-Hodgkin's lymphoma. The highest risk was noted for non-Hodgkin's lymphoma among young offspring (0–4 years) of two Turkish parents (6.87). The currently available limited data on rates for childhood non-Hodgkin's lymphoma in these countries do not explain the risk in the offspring of immigrants. Yugoslavs and Turks are recent immigrant groups to Sweden, and their offspring have been subject to much population mixing, perhaps leading to recurring infections and immunological stimulation, which may contribute to their excess of lymphomas
- …