3,012 research outputs found
The Orevkov invariant of an affine plane curve
We show that although the fundamental group of the complement of an algebraic
affine plane curve is not easy to compute, it possesses a more accessible
quotient, which we call the Orevkov invariant.Comment: 20 page
The notion of -weak dependence and its applications to bootstrapping time series
We give an introduction to a notion of weak dependence which is more general
than mixing and allows to treat for example processes driven by discrete
innovations as they appear with time series bootstrap. As a typical example, we
analyze autoregressive processes and their bootstrap analogues in detail and
show how weak dependence can be easily derived from a contraction property of
the process. Furthermore, we provide an overview of classes of processes
possessing the property of weak dependence and describe important probabilistic
results under such an assumption.Comment: Published in at http://dx.doi.org/10.1214/06-PS086 the Probability
Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Effect of Al on the sharpness of the MgSiO_3 perovskite to post-perovskite phase transition
By means of static ab-initio computations we investigate the influence of Al on the recently discovered perovskite to post-perovskite phase transition in MgSiO_3. We examine three substitution mechanisms for Al in the two structures: MgSi → AlAl; SiSiO → AlAl□; and Si → AlH. The substitutions introducing oxygen vacancies (highly unfavorable, energetically) and water (favorable) both lower the 0 Kelvin transition pressure, whereas charge coupled substitution increases it relative to 105 GPa for pure MgSiO_3. From the transition pressures for 0, 6.25, and 100 mol% charge coupled Al_2O_3 incorporation and simple solution theories, we estimate the phase diagram of Al-bearing MgSiO_3 at low Al concentrations. Assuming the Clapeyron slope is independent of Al concentration, we find the perovskite-to-post-perovskite transition region to span 127–140 GPa, at 6.25 mol% Al_2O_3. When the upper pressure limit is bounded by the core-mantle boundary, the phase coexistence region has width 150 km
Monotone cellular automata in a random environment
In this paper we study in complete generality the family of two-state,
deterministic, monotone, local, homogeneous cellular automata in
with random initial configurations. Formally, we are given a set
of finite subsets of
, and an initial set
of `infected' sites, which we take to be random
according to the product measure with density . At time ,
the set of infected sites is the union of and the set of all
such that for some . Our
model may alternatively be thought of as bootstrap percolation on
with arbitrary update rules, and for this reason we call it
-bootstrap percolation.
In two dimensions, we give a classification of -bootstrap
percolation models into three classes -- supercritical, critical and
subcritical -- and we prove results about the phase transitions of all models
belonging to the first two of these classes. More precisely, we show that the
critical probability for percolation on is for all models in the critical class, and that it is
for all models in the supercritical class.
The results in this paper are the first of any kind on bootstrap percolation
considered in this level of generality, and in particular they are the first
that make no assumptions of symmetry. It is the hope of the authors that this
work will initiate a new, unified theory of bootstrap percolation on
.Comment: 33 pages, 7 figure
On the Sharpness and Bias of Quantum Effects
The question of quantifying the sharpness (or unsharpness) of a quantum
mechanical effect is investigated. Apart from sharpness, another property,
bias, is found to be relevant for the joint measurability or coexistence of two
effects. Measures of bias will be defined and examples given.Comment: Substantially expanded version, with new results and some proofs
correcte
Probability and moment inequalities for sums of weakly dependent random variables, with applications
AbstractDoukhan and Louhichi [P. Doukhan, S. Louhichi, A new weak dependence condition and application to moment inequalities, Stochastic Process. Appl. 84 (1999) 313–342] introduced a new concept of weak dependence which is more general than mixing. Such conditions are particularly well suited for deriving estimates for the cumulants of sums of random variables. We employ such cumulant estimates to derive inequalities of Bernstein and Rosenthal type which both improve on previous results. Furthermore, we consider several classes of processes and show that they fulfill appropriate weak dependence conditions. We also sketch applications of our inequalities in probability and statistics
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