209,239 research outputs found
Bernstein's problem on weighted polynomial approximation
We formulate and discuss a necessary and sufficient condition for polynomials
to be dense in a space of continuous functions on the real line, with respect
to Bernstein's weighted uniform norm. Equivalently, for a positive finite
measure on the real line we give a criterion for density of polynomials
in
Tensor products of Leavitt path algebras
We compute the Hochschild homology of Leavitt path algebras over a field .
As an application, we show that and have different
Hochschild homologies, and so they are not Morita equivalent; in particular
they are not isomorphic. Similarly, and
are distinguished by their Hochschild homologies and so they are not Morita
equivalent either. By contrast, we show that -theory cannot distinguish
these algebras; we have and
.Comment: 10 pages. Added hypothesis to Corolary 4.5; Example 5.2 expanded,
other cosmetic changes, including an e-mail address and some dashes. Final
version, to appear in PAM
Shellability of noncrossing partition lattices
We give a case-free proof that the lattice of noncrossing partitions
associated to any finite real reflection group is EL-shellable. Shellability of
these lattices was open for the groups of type and those of exceptional
type and rank at least three.Comment: 10 page
Data-Driven Prediction of Thresholded Time Series of Rainfall and SOC models
We study the occurrence of events, subject to threshold, in a representative
SOC sandpile model and in high-resolution rainfall data. The predictability in
both systems is analyzed by means of a decision variable sensitive to event
clustering, and the quality of the predictions is evaluated by the receiver
operating characteristics (ROC) method. In the case of the SOC sandpile model,
the scaling of quiet-time distributions with increasing threshold leads to
increased predictability of extreme events. A scaling theory allows us to
understand all the details of the prediction procedure and to extrapolate the
shape of the ROC curves for the most extreme events. For rainfall data, the
quiet-time distributions do not scale for high thresholds, which means that the
corresponding ROC curves cannot be straightforwardly related to those for lower
thresholds.Comment: 19 pages, 10 figure
Bifurcations from families of periodic solutions in piecewise differential systems
Consider a differential system of the form where
and are piecewise
functions and -periodic in the variable . Assuming that the unperturbed
system has a -dimensional submanifold of periodic solutions
with , we use the Lyapunov-Schmidt reduction and the averaging theory to
study the existence of isolated -periodic solutions of the above
differential system
Complex contact manifolds and S^{1} actions
We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex contact manifolds admitting holomorphic circle actions preserving the contact structure. Such vanishings are reminiscent of those of LeBrun and Salamon on Fano contact manifolds but under a symmetry assumption instead of a curvature condition
Structure theorems for subgroups of homeomorphisms groups
In this partly expository paper, we study the set A of groups of
orientation-preserving homeomorphisms of the circle S^1 which do not admit
non-abelian free subgroups. We use classical results about homeomorphisms of
the circle and elementary dynamical methods to derive various new and old
results about the groups in A. Of the known results, we include some results
from a family of results of Beklaryan and Malyutin, and we also give a new
proof of a theorem of Margulis. Our primary new results include a detailed
classification of the solvable subgroups of R. Thompson's group T .Comment: 31 pages, 3 figures; final version, to appear in "International
Journal of Algebra and Computation
Stochastic multi-scale models of competition within heterogeneous cellular populations: simulation methods and mean-field analysis
We propose a modelling framework to analyse the stochastic behaviour of
heterogeneous, multi-scale cellular populations. We illustrate our methodology
with a particular example in which we study a population with an
oxygen-regulated proliferation rate. Our formulation is based on an
age-dependent stochastic process. Cells within the population are characterised
by their age. The age-dependent (oxygen-regulated) birth rate is given by a
stochastic model of oxygen-dependent cell cycle progression. We then formulate
an age-dependent birth-and-death process, which dictates the time evolution of
the cell population. The population is under a feedback loop which controls its
steady state size: cells consume oxygen which in turns fuels cell
proliferation. We show that our stochastic model of cell cycle progression
allows for heterogeneity within the cell population induced by stochastic
effects. Such heterogeneous behaviour is reflected in variations in the
proliferation rate. Within this set-up, we have established three main results.
First, we have shown that the age to the G1/S transition, which essentially
determines the birth rate, exhibits a remarkably simple scaling behaviour. This
allows for a huge simplification of our numerical methodology. A further result
is the observation that heterogeneous populations undergo an internal process
of quasi-neutral competition. Finally, we investigated the effects of
cell-cycle-phase dependent therapies (such as radiation therapy) on
heterogeneous populations. In particular, we have studied the case in which the
population contains a quiescent sub-population. Our mean-field analysis and
numerical simulations confirm that, if the survival fraction of the therapy is
too high, rescue of the quiescent population occurs. This gives rise to
emergence of resistance to therapy since the rescued population is less
sensitive to therapy
What is the Jacobian of a Riemann surface with boundary?
We define the Jacobian of a Riemann surface with analytically parametrized
boundary components. These Jacobians belong to a moduli space of ``open abelian
varieties'' which satisfies gluing axioms similar to those of Riemann surfaces,
and therefore allows a notion of ``conformal field theory'' to be defined on
this space. We further prove that chiral conformal field theories corresponding
to even lattices factor through this moduli space of open abelian varieties.Comment: 27 pages. Minor explanation and motivation added
Computational explorations in Thompson's group F
We describe the results of some computational explorations in Thompson's
group F. We describe experiments to estimate the cogrowth of F with respect to
its standard finite generating set, designed to address the subtle and
difficult question whether or not Thompson's group is amenable. We also
describe experiments to estimate the exponential growth rate of F and the rate
of escape of symmetric random walks with respect to the standard generating
set.Comment: 16 pages, 2 figures, 5 table
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