1,286 research outputs found
Bounded Representations of Interval and Proper Interval Graphs
Klavik et al. [arXiv:1207.6960] recently introduced a generalization of
recognition called the bounded representation problem which we study for the
classes of interval and proper interval graphs. The input gives a graph G and
in addition for each vertex v two intervals L_v and R_v called bounds. We ask
whether there exists a bounded representation in which each interval I_v has
its left endpoint in L_v and its right endpoint in R_v. We show that the
problem can be solved in linear time for interval graphs and in quadratic time
for proper interval graphs.
Robert's Theorem states that the classes of proper interval graphs and unit
interval graphs are equal. Surprisingly the bounded representation problem is
polynomially solvable for proper interval graphs and NP-complete for unit
interval graphs [Klav\'{\i}k et al., arxiv:1207.6960]. So unless P = NP, the
proper and unit interval representations behave very differently.
The bounded representation problem belongs to a wider class of restricted
representation problems. These problems are generalizations of the
well-understood recognition problem, and they ask whether there exists a
representation of G satisfying some additional constraints. The bounded
representation problems generalize many of these problems
The Scottish Mental Survey 1932 linked to the Midspan studies: a prospective investigation of childhood intelligence and future health
The Scottish Mental Survey of 1932 (SMS1932) recorded mental ability test scores for nearly all of the age group of children born in 1921 and at school in Scotland on 1st June 1932. The Collaborative and Renfrew/Paisley studies, two of the Midspan studies, obtained health and social data by questionnaire and a physical examination in the 1970s. Some Midspan participants were born in 1921 and may have taken part in the SMS1932, so might have mental ability data available from childhood. The 1921-born Midspan participants were matched with the computerised SMS1932 database. The total numbers successfully matched were 1032 out of 1251 people (82.5%). Of those matched, 938 (90.9%) had a mental ability test score recorded. The mean score of the matched sample was 37.2 (standard deviation [SD] 13.9) out of a possible score of 76. The mean (SD) for the boys and girls respectively was 38.3 (14.2) and 35.7 (13.9). This compared with 38.6 (15.7) and 37.2 (14.3) for boys and girls in all of Scotland. Graded relationships were found between mental ability in childhood, and social class and deprivation category of residence in adulthood. Being in a higher social class or in a more affluent deprivation category was associated with higher childhood mental ability scores and the scores reduced with increasing deprivation. Future plans for the matched data include examining associations between childhood mental ability and other childhood and adult risk factors for disease in adulthood, and modelling childhood mental ability, alongside other factors available in the Midspan database, as a risk factor for specific illnesses, admission to hospital and mortality
Correlated variability of Mkn 421 at X-ray and TeV wavelengths on timescales of hours
Mkn 421 was observed for about two days with BeppoSAX, prior to and partly
overlapping the start of a 1 week continuous exposure with ASCA in April 1998,
as part of a world-wide multiwavelength campaign. A pronounced, well defined,
flare observed in X-rays was also observed simultaneously at TeV energies by
the Whipple Observatory's 10 m gamma-ray telescope. These data provide the
first evidence that the X-ray and TeV intensities are well correlated on
time-scales of hours.Comment: 4 pages, 1 figure, presented at the VERITAS Workshop on the TeV
Astrophysics of Extragalactic Object
Rapid Accurate Calculation of the s-Wave Scattering Length
Transformation of the conventional radial Schr\"odinger equation defined on
the interval into an equivalent form defined on the finite
domain allows the s-wave scattering length to be
exactly expressed in terms of a logarithmic derivative of the transformed wave
function at the outer boundary point , which corresponds to
. In particular, for an arbitrary interaction potential that dies off
as fast as for , the modified wave function obtained
by using the two-parameter mapping function has no singularities, and
For
a well bound potential with equilibrium distance , the optimal mapping
parameters are and . An
outward integration procedure based on Johnson's log-derivative algorithm
[B.R.\ Johnson, J.\ Comp.\ Phys., \textbf{13}, 445 (1973)] combined with a
Richardson extrapolation procedure is shown to readily yield high precision
-values both for model Lennard-Jones () potentials and for realistic
published potentials for the Xe--e, Cs_2(a\,^3\Sigma_u^+) and
He_2(X\,^1\Sigma_g^+) systems. Use of this same transformed
Schr{\"o}dinger equation was previously shown [V.V. Meshkov et al., Phys.\
Rev.\ A, {\bf 78}, 052510 (2008)] to ensure the efficient calculation of all
bound levels supported by a potential, including those lying extremely close to
dissociation.Comment: 12 pages, 9 figures, to appear in J. Chem. Phy
Spin-parity dependent tunneling of magnetization in single-molecule magnets
Single-molecule magnets facilitate the study of quantum tunneling of
magnetization at the mesoscopic level. The spin-parity effect is among the
fundamental predictions that have yet to be clearly observed. It is predicted
that quantum tunneling is suppressed at zero transverse field if the total spin
of the magnetic system is half-integer (Kramers degeneracy) but is allowed in
integer spin systems. The Landau-Zener method is used to measure the tunnel
splitting as a function of transverse field. Spin-parity dependent tunneling is
established by comparing the transverse field dependence of the tunnel
splitting of integer and half-integer spin systems.Comment: 4 pages, 6 figure
An Effective-Medium Tight-Binding Model for Silicon
A new method for calculating the total energy of Si systems is presented. The
method is based on the effective-medium theory concept of a reference system.
Instead of calculating the energy of an atom in the system of interest a
reference system is introduced where the local surroundings are similar. The
energy of the reference system can be calculated selfconsistently once and for
all while the energy difference to the reference system can be obtained
approximately. We propose to calculate it using the tight-binding LMTO scheme
with the Atomic-Sphere Approximation(ASA) for the potential, and by using the
ASA with charge-conserving spheres we are able to treat open system without
introducing empty spheres. All steps in the calculational method is {\em ab
initio} in the sense that all quantities entering are calculated from first
principles without any fitting to experiment. A complete and detailed
description of the method is given together with test calculations of the
energies of phonons, elastic constants, different structures, surfaces and
surface reconstructions. We compare the results to calculations using an
empirical tight-binding scheme.Comment: 26 pages (11 uuencoded Postscript figures appended), LaTeX,
CAMP-090594-
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