227 research outputs found
Approximation of conformal mappings using conformally equivalent triangular lattices
Consider discrete conformal maps defined on the basis of two conformally
equivalent triangle meshes, that is edge lengths are related by scale factors
associated to the vertices. Given a smooth conformal map , we show that it
can be approximated by such discrete conformal maps . In
particular, let be an infinite regular triangulation of the plane with
congruent triangles and only acute angles (i.e.\ ). We scale this
tiling by and approximate a compact subset of the domain of
with a portion of it. For small enough we prove that there exists a
conformally equivalent triangle mesh whose scale factors are given by
on the boundary. Furthermore we show that the corresponding discrete
conformal maps converge to uniformly in with error of
order .Comment: 14 pages, 3 figures; v2 typos corrected, revised introduction, some
proofs extende
Multi-Armed Bandits for Correlated Markovian Environments with Smoothed Reward Feedback
We study a multi-armed bandit problem in a dynamic environment where arm
rewards evolve in a correlated fashion according to a Markov chain. Different
than much of the work on related problems, in our formulation a learning
algorithm does not have access to either a priori information or observations
of the state of the Markov chain and only observes smoothed reward feedback
following time intervals we refer to as epochs. We demonstrate that existing
methods such as UCB and -greedy can suffer linear regret in such
an environment. Employing mixing-time bounds on Markov chains, we develop
algorithms called EpochUCB and EpochGreedy that draw inspiration from the
aforementioned methods, yet which admit sublinear regret guarantees for the
problem formulation. Our proposed algorithms proceed in epochs in which an arm
is played repeatedly for a number of iterations that grows linearly as a
function of the number of times an arm has been played in the past. We analyze
these algorithms under two types of smoothed reward feedback at the end of each
epoch: a reward that is the discount-average of the discounted rewards within
an epoch, and a reward that is the time-average of the rewards within an epoch.Comment: Significant revision of prior version including deeper discussion of
related work, gap-independent regret bounds, and regret bounds for discounted
reward
Neoadjuvant chemoradiation and pancreaticoduodenectomy for initially locally advanced head pancreatic adenocarcinoma
International audienceThe most accepted treatment for locally advanced pancreatic adenocarcinoma (LAPA) is chemoradiotherapy (CRT). We sought to determine the benefit of pancreaticoduodenectomy (PD) in patients with LAPA initially treated by neoadjuvant CRT
Polya's inequalities, global uniform integrability and the size of plurisubharmonic lemniscates
First we prove a new inequality comparing uniformly the relative volume of a
Borel subset with respect to any given complex euclidean ball \B \sub \C^n
with its relative logarithmic capacity in \C^n with respect to the same ball
\B.
An analoguous comparison inequality for Borel subsets of euclidean balls of
any generic real subspace of \C^n is also proved.
Then we give several interesting applications of these inequalities.
First we obtain sharp uniform estimates on the relative size of \psh
lemniscates associated to the Lelong class of \psh functions of logarithmic
singularities at infinity on \C^n as well as the Cegrell class of
\psh functions of bounded Monge-Amp\`ere mass on a hyperconvex domain \W
\Sub \C^n.
Then we also deduce new results on the global behaviour of both the Lelong
class and the Cegrell class of \psh functions.Comment: 25 page
Now the wars are over: The past, present and future of Scottish battlefields
Battlefield archaeology has provided a new way of appreciating historic battlefields. This paper provides a summary of the long history of warfare and conflict in Scotland which has given rise to a large number of battlefield sites. Recent moves to highlight the archaeological importance of these sites, in the form
of Historic Scotland’s Battlefields Inventory are discussed, along with some of the problems associated with the preservation and management of these important
cultural sites
Forced Stratified Turbulence: Successive Transitions with Reynolds Number
Numerical simulations are made for forced turbulence at a sequence of
increasing values of Reynolds number, R, keeping fixed a strongly stable,
volume-mean density stratification. At smaller values of R, the turbulent
velocity is mainly horizontal, and the momentum balance is approximately
cyclostrophic and hydrostatic. This is a regime dominated by so-called pancake
vortices, with only a weak excitation of internal gravity waves and large
values of the local Richardson number, Ri, everywhere. At higher values of R
there are successive transitions to (a) overturning motions with local
reversals in the density stratification and small or negative values of Ri; (b)
growth of a horizontally uniform vertical shear flow component; and (c) growth
of a large-scale vertical flow component. Throughout these transitions, pancake
vortices continue to dominate the large-scale part of the turbulence, and the
gravity wave component remains weak except at small scales.Comment: 8 pages, 5 figures (submitted to Phys. Rev. E
Single and vertically coupled type II quantum dots in a perpendicular magnetic field: exciton groundstate properties
The properties of an exciton in a type II quantum dot are studied under the
influence of a perpendicular applied magnetic field. The dot is modelled by a
quantum disk with radius , thickness and the electron is confined in the
disk, whereas the hole is located in the barrier. The exciton energy and
wavefunctions are calculated using a Hartree-Fock mesh method. We distinguish
two different regimes, namely (the hole is located at the radial
boundary of the disk) and (the hole is located above and below the
disk), for which angular momentum transitions are predicted with
increasing magnetic field. We also considered a system of two vertically
coupled dots where now an extra parameter is introduced, namely the interdot
distance . For each and for a sufficient large magnetic field,
the ground state becomes spontaneous symmetry broken in which the electron and
the hole move towards one of the dots. This transition is induced by the
Coulomb interaction and leads to a magnetic field induced dipole moment. No
such symmetry broken ground states are found for a single dot (and for three
vertically coupled symmetric quantum disks). For a system of two vertically
coupled truncated cones, which is asymmetric from the start, we still find
angular momentum transitions. For a symmetric system of three vertically
coupled quantum disks, the system resembles for small the pillar-like
regime of a single dot, where the hole tends to stay at the radial boundary,
which induces angular momentum transitions with increasing magnetic field. For
larger the hole can sit between the disks and the state
remains the groundstate for the whole -region.Comment: 11 pages, 16 figure
The Archaeology of the Siege of Fort William, 1746
In August and September 2007, the Centre for Battlefield Archaeology and Glasgow University Archaeological Research Division (GUARD) conducted a programme of archaeological investigation of the remains of the old fort at Fort William and part of The Parade in the town of Fort William on the west coast of Scotland. The fieldwork involved geophysical survey at the fort and The Parade, followed by trial excavation of anomalies. Trial trenches at The Parade exposed several rich midden deposits and material providing evidence for the burning of the town of Maryburgh, as suggested in contemporary accounts in 1746. The results at the fort were not so positive, as most traces of the garrison were removed in the 19th and 20th centuries through its use as a railway yard; however, a trench outside the fort suggests survival of midden deposits pre-dating this period of destruction. This part-Heritage Lottery assisted project was a Highland 2007 initiative supported by Lochaber Community Fund and Highland Council, and included active participation on the part of the local community, including school groups and metal detectorists
Oka's inequality for currents and applications
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46241/1/208_2005_Article_BF01446636.pd
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