553 research outputs found
On the number of simple arrangements of five double pseudolines
We describe an incremental algorithm to enumerate the isomorphism classes of
double pseudoline arrangements. The correction of our algorithm is based on the
connectedness under mutations of the spaces of one-extensions of double
pseudoline arrangements, proved in this paper. Counting results derived from an
implementation of our algorithm are also reported.Comment: 24 pages, 16 figures, 6 table
Lines pinning lines
A line g is a transversal to a family F of convex polytopes in 3-dimensional
space if it intersects every member of F. If, in addition, g is an isolated
point of the space of line transversals to F, we say that F is a pinning of g.
We show that any minimal pinning of a line by convex polytopes such that no
face of a polytope is coplanar with the line has size at most eight. If, in
addition, the polytopes are disjoint, then it has size at most six. We
completely characterize configurations of disjoint polytopes that form minimal
pinnings of a line.Comment: 27 pages, 10 figure
Drawing Arrangement Graphs In Small Grids, Or How To Play Planarity
We describe a linear-time algorithm that finds a planar drawing of every
graph of a simple line or pseudoline arrangement within a grid of area
O(n^{7/6}). No known input causes our algorithm to use area
\Omega(n^{1+\epsilon}) for any \epsilon>0; finding such an input would
represent significant progress on the famous k-set problem from discrete
geometry. Drawing line arrangement graphs is the main task in the Planarity
puzzle.Comment: 12 pages, 8 figures. To appear at 21st Int. Symp. Graph Drawing,
Bordeaux, 201
Stability and symmetry-breaking bifurcation for the ground states of a NLS with a interaction
We determine and study the ground states of a focusing Schr\"odinger equation
in dimension one with a power nonlinearity and a strong
inhomogeneity represented by a singular point perturbation, the so-called
(attractive) interaction, located at the origin. The
time-dependent problem turns out to be globally well posed in the subcritical
regime, and locally well posed in the supercritical and critical regime in the
appropriate energy space. The set of the (nonlinear) ground states is
completely determined. For any value of the nonlinearity power, it exhibits a
symmetry breaking bifurcation structure as a function of the frequency (i.e.,
the nonlinear eigenvalue) . More precisely, there exists a critical
value \om^* of the nonlinear eigenvalue \om, such that: if \om_0 < \om <
\om^*, then there is a single ground state and it is an odd function; if \om
> \om^* then there exist two non-symmetric ground states. We prove that before
bifurcation (i.e., for \om < \om^*) and for any subcritical power, every
ground state is orbitally stable. After bifurcation (\om =\om^*+0), ground
states are stable if does not exceed a value that lies
between 2 and 2.5, and become unstable for . Finally, for and \om \gg \om^*, all ground states are unstable. The branch of odd
ground states for \om \om^*,
obtaining a family of orbitally unstable stationary states. Existence of ground
states is proved by variational techniques, and the stability properties of
stationary states are investigated by means of the Grillakis-Shatah-Strauss
framework, where some non standard techniques have to be used to establish the
needed properties of linearization operators.Comment: 46 pages, 5 figure
Measurements of Scintillation Efficiency and Pulse-Shape for Low Energy Recoils in Liquid Xenon
Results of observations of low energy nuclear and electron recoil events in
liquid xenon scintillator detectors are given. The relative scintillation
efficiency for nuclear recoils is 0.22 +/- 0.01 in the recoil energy range 40
keV - 70 keV. Under the assumption of a single dominant decay component to the
scintillation pulse-shape the log-normal mean parameter T0 of the maximum
likelihood estimator of the decay time constant for 6 keV < Eee < 30 keV
nuclear recoil events is equal to 21.0 ns +/- 0.5 ns. It is observed that for
electron recoils T0 rises slowly with energy, having a value ~ 30 ns at Eee ~
15 keV. Electron and nuclear recoil pulse-shapes are found to be well fitted by
single exponential functions although some evidence is found for a double
exponential form for the nuclear recoil pulse-shape.Comment: 11 pages, including 5 encapsulated postscript figure
Atmospheric Heating and Wind Acceleration: Results for Cool Evolved Stars based on Proposed Processes
A chromosphere is a universal attribute of stars of spectral type later than
~F5. Evolved (K and M) giants and supergiants (including the zeta Aurigae
binaries) show extended and highly turbulent chromospheres, which develop into
slow massive winds. The associated continuous mass loss has a significant
impact on stellar evolution, and thence on the chemical evolution of galaxies.
Yet despite the fundamental importance of those winds in astrophysics, the
question of their origin(s) remains unsolved. What sources heat a chromosphere?
What is the role of the chromosphere in the formation of stellar winds? This
chapter provides a review of the observational requirements and theoretical
approaches for modeling chromospheric heating and the acceleration of winds in
single cool, evolved stars and in eclipsing binary stars, including physical
models that have recently been proposed. It describes the successes that have
been achieved so far by invoking acoustic and MHD waves to provide a physical
description of plasma heating and wind acceleration, and discusses the
challenges that still remain.Comment: 46 pages, 9 figures, 1 table; modified and unedited manuscript;
accepted version to appear in: Giants of Eclipse, eds. E. Griffin and T. Ake
(Berlin: Springer
Clinical perspectives on sampling and processing approaches for the management of infection in diabetic foot ulceration: A qualitative study
Diabetic foot ulcers (DFUs) often become infected and are treated with antimicrobials, with samples collected to inform care. Swab samples are easier than tissue sampling but report fewer organisms. Compared with culture and sensitivity (C&S) methods, molecular microbiology identifies more organisms. Clinician perspectives on sampling and processing are unknown. We explored clinician perspectives on DFU sampling—tissue samples/wound swabs—and on processing techniques, culture and sensitivity or molecular techniques. The latter provides information on organisms which have not survived transport to the laboratory for culture. We solicited feedback on molecular microbiology reports. Qualitative study using semi-structured interview, with analysis using a Framework approach. CODIFI2 clinicians from UK DFU clinics. Seven consultants agreed to take part. They reported, overall, a preference for tissue samples over swabbing. Clinicians were not confident replacing C&S with molecular microbiology as the approach to reporting was unfamiliar. The study was small and did not recruit any podiatrists or nurses, who may have discipline-specific attitudes or perspectives on DFU care. Both sampling approaches appear to be used by clinicians. Molecular microbiology reports would not be, at present, suitable for replacement of traditional culture and sensitivity
Newtonian Collapse of Scalar Field Dark Matter
In this letter, we develop a Newtonian approach to the collapse of galaxy
fluctuations of scalar field dark matter under initial conditions inferred from
simple assumptions. The full relativistic system, the so called
Einstein-Klein-Gordon, is reduced to the Schr\"odinger-Newton one in the weak
field limit. The scaling symmetries of the SN equations are exploited to track
the non-linear collapse of single scalar matter fluctuations. The results can
be applied to both real and complex scalar fields.Comment: 4 pages RevTex4 file, 4 eps figure
Graphs and Reflection Groups
It is shown that graphs that generalize the ADE Dynkin diagrams and have
appeared in various contexts of two-dimensional field theory may be regarded in
a natural way as encoding the geometry of a root system. After recalling what
are the conditions satisfied by these graphs, we define a bilinear form on a
root system in terms of the adjacency matrices of these graphs and undertake
the study of the group generated by the reflections in the hyperplanes
orthogonal to these roots. Some ``non integrally laced " graphs are shown to be
associated with subgroups of these reflection groups. The empirical relevance
of these graphs in the classification of conformal field theories or in the
construction of integrable lattice models is recalled, and the connections with
recent developments in the context of supersymmetric theories and
topological field theories are discussed.Comment: 42 pages TEX file, harvmac and epsf macros, AMS fonts optional,
uuencoded, 8 figures include
Bounding Helly numbers via Betti numbers
We show that very weak topological assumptions are enough to ensure the
existence of a Helly-type theorem. More precisely, we show that for any
non-negative integers and there exists an integer such that
the following holds. If is a finite family of subsets of such that for any
and every
then has Helly number at most . Here
denotes the reduced -Betti numbers (with singular homology). These
topological conditions are sharp: not controlling any of these first Betti numbers allow for families with unbounded Helly number.
Our proofs combine homological non-embeddability results with a Ramsey-based
approach to build, given an arbitrary simplicial complex , some well-behaved
chain map .Comment: 29 pages, 8 figure
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