5,385 research outputs found
Algebraic Tail Decay of Condition Numbers for Random Conic Systems under a General Family of Input Distributions
We consider the conic feasibility problem associated with linear homogeneous systems of inequalities. The complexity of iterative algorithms for solving this problem depends on a condition number. When studying the typical behaviour of algorithms under stochastic input one is therefore naturally led to investigate the fatness of the distribution tails of the random condition number that ensues. We study an unprecedently general class of probability models for the random input matrix and show that the tails decay at algebraic rates with an exponent that naturally emerges when applying a theory of uniform absolute continuity which is also developed in this paper.\ud
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Raphael Hauser was supported through grant NAL/00720/G from the Nuffield Foundation and through grant GR/M30975 from the Engineering and Physical Sciences Research Council of the UK. Tobias Müller was partially supported by EPSRC, the Department of Statistics, Bekker-la-Bastide fonds, Dr Hendrik Muller's Vaderlandsch fonds, and Prins Bernhard Cultuurfonds
The diameter of KPKVB random graphs
We consider a model for complex networks that was recently proposed as a
model for complex networks by Krioukov et al. In this model, nodes are chosen
randomly inside a disk in the hyperbolic plane and two nodes are connected if
they are at most a certain hyperbolic distance from each other. It has been
previously shown that this model has various properties associated with complex
networks, including a power-law degree distribution and a strictly positive
clustering coefficient. The model is specified using three parameters : the
number of nodes , which we think of as going to infinity, and which we think of as constant. Roughly speaking controls the power
law exponent of the degree sequence and the average degree.
Earlier work of Kiwi and Mitsche has shown that when (which
corresponds to the exponent of the power law degree sequence being ) then
the diameter of the largest component is a.a.s.~polylogarithmic in .
Friedrich and Krohmer have shown it is a.a.s.~ and they
improved the exponent of the polynomial in in the upper bound. Here we
show the maximum diameter over all components is a.a.s.~ thus giving
a bound that is tight up to a multiplicative constant.Comment: very minor corrections since the last versio
Modelling Accretion in Transitional Disks
Transitional disks are protoplanetary disk around young stars that display
inner holes in the dust distribution within a few AU, which is accompanied
nevertheless by some gas accretion onto the central star. These cavities could
possibly be created by the presence of one or more massive planets. If the gap
is created by planets and gas is still present in it, then there should be a
flow of gas past the planet into the inner region. It is our goal to study the
mass accretion rate into the gap and in particular the dependency on the
planet's mass and the thermodynamic properties of the disk. We performed 2D
hydro simulations for disks with embedded planets. We added radiative cooling
from the disk surfaces, radiative diffusion in the disk midplane, and stellar
irradiation to the energy equation to have more realistic models. The mass flow
rate into the gap region depends, for given disk thermodynamics,
non-monotonically on the mass of the planet. Generally, more massive planets
open wider and deeper gaps which would tend to reduce the mass accretion into
the inner cavity. However, for larger mass planets the outer disk becomes
eccentric and the mass flow rate is enhanced over the low mass cases. As a
result, for the isothermal disks the mass flow is always comparable to the
expected mass flow of unperturbed disks M_d, while for more realistic radiative
disks the mass flow is very small for low mass planets (<= 4 M_jup) and about
50% for larger planet masses. For the radiative disks that critical planet mass
for the disk to become eccentric is much larger that in the isothermal case.
Massive embedded planets can reduce the mass flow across the gap considerably,
to values of about an order of magnitude smaller than the standard disk
accretion rate, and can be responsible for opening large cavities. The
remaining mass flow into the central cavity is in good agreement with the
observations.Comment: 10 pages, 29 figures, accepted for publication in Astronomy &
Astrophysic
Social welfare effects of tax-benefit reform under endogenous participation and unemployment
This paper analyzes the effects of tax-benefit reforms in a framework integrating endogenous labor supply and unemployment. There is a discrete distribution of individuals’ productivities and labor supply decisions are limited to the participation decision. Unemployment is modeled in a search and matching framework with individual wage bargaining. We adopt an ordinal approach to social welfare comparisons and explore numerically various reform policies. For Switzerland, a participation income is shown to be an “uncontroversial” tax reform, improving social welfare according to any social welfare criterion displaying inequality aversion.
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