3,947 research outputs found
Combinatorics of bicubic maps with hard particles
We present a purely combinatorial solution of the problem of enumerating
planar bicubic maps with hard particles. This is done by use of a bijection
with a particular class of blossom trees with particles, obtained by an
appropriate cutting of the maps. Although these trees have no simple local
characterization, we prove that their enumeration may be performed upon
introducing a larger class of "admissible" trees with possibly doubly-occupied
edges and summing them with appropriate signed weights. The proof relies on an
extension of the cutting procedure allowing for the presence on the maps of
special non-sectile edges. The admissible trees are characterized by simple
local rules, allowing eventually for an exact enumeration of planar bicubic
maps with hard particles. We also discuss generalizations for maps with
particles subject to more general exclusion rules and show how to re-derive the
enumeration of quartic maps with Ising spins in the present framework of
admissible trees. We finally comment on a possible interpretation in terms of
branching processes.Comment: 41 pages, 19 figures, tex, lanlmac, hyperbasics, epsf. Introduction
and discussion/conclusion extended, minor corrections, references adde
Some photometer results obtained on the NASA 1969 Airborne Auroral Expedition
The spectral features measured by a photometer onboard the Convair 990 Galileo, during the Auroral Expedition are given in tables. The measurements given cover flights 3 to 15
Distance statistics in large toroidal maps
We compute a number of distance-dependent universal scaling functions
characterizing the distance statistics of large maps of genus one. In
particular, we obtain explicitly the probability distribution for the length of
the shortest non-contractible loop passing via a random point in the map, and
that for the distance between two random points. Our results are derived in the
context of bipartite toroidal quadrangulations, using their coding by
well-labeled 1-trees, which are maps of genus one with a single face and
appropriate integer vertex labels. Within this framework, the distributions
above are simply obtained as scaling limits of appropriate generating functions
for well-labeled 1-trees, all expressible in terms of a small number of basic
scaling functions for well-labeled plane trees.Comment: 24 pages, 9 figures, minor corrections, new added reference
Force distributions in a triangular lattice of rigid bars
We study the uniformly weighted ensemble of force balanced configurations on
a triangular network of nontensile contact forces. For periodic boundary
conditions corresponding to isotropic compressive stress, we find that the
probability distribution for single-contact forces decays faster than
exponentially. This super-exponential decay persists in lattices diluted to the
rigidity percolation threshold. On the other hand, for anisotropic imposed
stresses, a broader tail emerges in the force distribution, becoming a pure
exponential in the limit of infinite lattice size and infinitely strong
anisotropy.Comment: 11 pages, 17 figures Minor text revisions; added references and
acknowledgmen
Rate-dependent propagation of cardiac action potentials in a one-dimensional fiber
Action potential duration (APD) restitution, which relates APD to the
preceding diastolic interval (DI), is a useful tool for predicting the onset of
abnormal cardiac rhythms. However, it is known that different pacing protocols
lead to different APD restitution curves (RCs). This phenomenon, known as APD
rate-dependence, is a consequence of memory in the tissue. In addition to APD
restitution, conduction velocity restitution also plays an important role in
the spatiotemporal dynamics of cardiac tissue. We present new results
concerning rate-dependent restitution in the velocity of propagating action
potentials in a one-dimensional fiber. Our numerical simulations show that,
independent of the amount of memory in the tissue, waveback velocity exhibits
pronounced rate-dependence and the wavefront velocity does not. Moreover, the
discrepancy between waveback velocity RCs is most significant for small DI. We
provide an analytical explanation of these results, using a system of coupled
maps to relate the wavefront and waveback velocities. Our calculations show
that waveback velocity rate-dependence is due to APD restitution, not memory.Comment: 17 pages, 7 figure
Complications After Systematic, Random and Image-guided Prostate Biopsy
CONTEXT: Prostate biopsy (PB) represents the gold standard method to confirm the presence of cancer. In addition to traditional random or systematic approaches, a magnetic resonance imaging (MRI)-guided technique has been introduced recently. OBJECTIVE: To perform a systematic review of complications after transrectal ultrasound (TRUS)-guided, transperineal, and MRI-guided PB. EVIDENCE ACQUISITION: We performed a systematic literature search of Web of Science, Embase, and Scopus databases up to October 2015, according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement. Complications and mortality following random, systematic, and image-guided PBs were reviewed. Eighty-five references were included. EVIDENCE SYNTHESIS: The most frequent complication after PB was minor and self-limiting bleeding (hematuria and hematospermia), regardless of the biopsy approach. Occurrence of rectal bleeding was comparable for traditional TRUS-guided and image-guided PBs. Almost 25% of patients experienced lower urinary tract symptoms, but only a few had urinary retention, with higher rates after a transperineal approach. Temporary erectile dysfunction was not negligible, with a return to baseline after 1-6 mo. The incidence of infective complications is increasing, with higher rates among men with medical comorbidities and older age. Transperineal and in-bore MRI-targeted biopsy may reduce the risk of severe infectious complications. Mortality after PB is uncommon, regardless of biopsy technique. CONCLUSIONS: Complications after PB are frequent but often self-limiting. The incidence of hospitalization due to severe infections is continuously increasing. The patient's general health status, risk factors, and likelihood of antimicrobial resistance should be carefully appraised before scheduling a PB. PATIENT SUMMARY: We reviewed the variety and incidence of complications after prostate biopsy. Even if frequent, complications seldom represent a problem for the patient. The most troublesome complications are infections. To minimize this risk, the patient's medical condition should be carefully evaluated before biopsy
Binding Energy and the Fundamental Plane of Globular Clusters
A physical description of the fundamental plane of Galactic globular clusters
is developed which explains all empirical trends and correlations in a large
number of cluster observables and provides a small but complete set of truly
independent constraints on theories of cluster formation and evolution in the
Milky Way. Within the theoretical framework of single-mass, isotropic King
models, it is shown that (1) 39 regular (non--core-collapsed) globulars with
measured core velocity dispersions share a common V-band mass-to-light ratio of
1.45 +/- 0.10, and (2) a complete sample of 109 regular globulars reveals a
very strong correlation between cluster binding energy and total luminosity,
regulated by Galactocentric position: E_b \propto (L^{2.05} r_{\rm gc}^{-0.4}).
The observational scatter about either of these two constraints can be
attributed fully to random measurement errors, making them the defining
equations of a fundamental plane for globular clusters. A third, weaker
correlation, between total luminosity and the King-model concentration
parameter, c, is then related to the (non-random) distribution of globulars on
the plane. The equations of the FP are used to derive expressions for any
cluster observable in terms of only L, r_{\rm gc}, and c. Results are obtained
for generic King models and applied specifically to the globular cluster system
of the Milky Way.Comment: 60 pages with 19 figures, submitted to Ap
Critical collapse of collisionless matter - a numerical investigation
In recent years the threshold of black hole formation in spherically
symmetric gravitational collapse has been studied for a variety of matter
models. In this paper the corresponding issue is investigated for a matter
model significantly different from those considered so far in this context. We
study the transition from dispersion to black hole formation in the collapse of
collisionless matter when the initial data is scaled. This is done by means of
a numerical code similar to those commonly used in plasma physics. The result
is that for the initial data for which the solutions were computed, most of the
matter falls into the black hole whenever a black hole is formed. This results
in a discontinuity in the mass of the black hole at the onset of black hole
formation.Comment: 22 pages, LaTeX, 7 figures (ps-files, automatically included using
psfig
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