298 research outputs found
Online Independent Set Beyond the Worst-Case: Secretaries, Prophets, and Periods
We investigate online algorithms for maximum (weight) independent set on
graph classes with bounded inductive independence number like, e.g., interval
and disk graphs with applications to, e.g., task scheduling and spectrum
allocation. In the online setting, it is assumed that nodes of an unknown graph
arrive one by one over time. An online algorithm has to decide whether an
arriving node should be included into the independent set. Unfortunately, this
natural and practically relevant online problem cannot be studied in a
meaningful way within a classical competitive analysis as the competitive ratio
on worst-case input sequences is lower bounded by .
As a worst-case analysis is pointless, we study online independent set in a
stochastic analysis. Instead of focussing on a particular stochastic input
model, we present a generic sampling approach that enables us to devise online
algorithms achieving performance guarantees for a variety of input models. In
particular, our analysis covers stochastic input models like the secretary
model, in which an adversarial graph is presented in random order, and the
prophet-inequality model, in which a randomly generated graph is presented in
adversarial order. Our sampling approach bridges thus between stochastic input
models of quite different nature. In addition, we show that our approach can be
applied to a practically motivated admission control setting.
Our sampling approach yields an online algorithm for maximum independent set
with competitive ratio with respect to all of the mentioned
stochastic input models. for graph classes with inductive independence number
. The approach can be extended towards maximum-weight independent set by
losing only a factor of in the competitive ratio with denoting
the (expected) number of nodes
Group theoretic dimension of stationary symmetric \alpha-stable random fields
The growth rate of the partial maximum of a stationary stable process was
first studied in the works of Samorodnitsky (2004a,b), where it was
established, based on the seminal works of Rosi\'nski (1995,2000), that the
growth rate is connected to the ergodic theoretic properties of the flow that
generates the process. The results were generalized to the case of stable
random fields indexed by Z^d in Roy and Samorodnitsky (2008), where properties
of the group of nonsingular transformations generating the stable process were
studied as an attempt to understand the growth rate of the partial maximum
process. This work generalizes this connection between stable random fields and
group theory to the continuous parameter case, that is, to the fields indexed
by R^d.Comment: To appear in Journal of Theoretical Probability. Affiliation of the
authors are update
Stochastic stability versus localization in chaotic dynamical systems
We prove stochastic stability of chaotic maps for a general class of Markov
random perturbations (including singular ones) satisfying some kind of mixing
conditions. One of the consequences of this statement is the proof of Ulam's
conjecture about the approximation of the dynamics of a chaotic system by a
finite state Markov chain. Conditions under which the localization phenomenon
(i.e. stabilization of singular invariant measures) takes place are also
considered. Our main tools are the so called bounded variation approach
combined with the ergodic theorem of Ionescu-Tulcea and Marinescu, and a random
walk argument that we apply to prove the absence of ``traps'' under the action
of random perturbations.Comment: 27 pages, LaTe
Quenched invariance principle for random walks in balanced random environment
We consider random walks in a balanced random environment in ,
. We first prove an invariance principle (for ) and the
transience of the random walks when (recurrence when ) in an
ergodic environment which is not uniformly elliptic but satisfies certain
moment condition. Then, using percolation arguments, we show that under mere
ellipticity, the above results hold for random walks in i.i.d. balanced
environments.Comment: Published online in Probab. Theory Relat. Fields, 05 Oct 2010. Typo
(in journal version) corrected in (26
Glucose kinase of Streptomyces coelicolor A3(2): large-scale purification and biochemical analysis
Metals in Catalysis, Biomimetics & Inorganic Material
Comprehensive analysis of blood group antigen binding to classical and El Tor cholera toxin B-pentamers by NMR
Cholera is a diarrheal disease responsible for the deaths of thousands, possibly even hundreds of thousands of people every year, and its impact is predicted to further increase with climate change. It has been known for decades that blood group O individuals suffer more severe symptoms of cholera compared with individuals with other blood groups (A, B and AB). The observed blood group dependence is likely to be caused by the major virulence factor of Vibrio cholerae, the cholera toxin (CT). Here, we investigate the binding of ABH blood group determinants to both classical and El Tor CTB-pentamers using saturation transfer difference NMR and show that all three blood group determinants bind to both toxin variants. Although the details of the interactions differ, we see no large differences between the two toxin genotypes and observe very similar binding constants. We also show that the blood group determinants bind to a site distinct from that of the primary receptor, GM1. Transferred NOESY data confirm that the conformations of the blood group determinants in complex with both toxin variants are similar to those of reported X-ray and solution structures. Taken together, this detailed analysis provides a framework for the interpretation of the epidemiological data linking the severity of cholera infection and an individual's blood group, and brings us one step closer to understanding the molecular basis of cholera blood group dependence
A Pathwise Ergodic Theorem for Quantum Trajectories
If the time evolution of an open quantum system approaches equilibrium in the
time mean, then on any single trajectory of any of its unravelings the time
averaged state approaches the same equilibrium state with probability 1. In the
case of multiple equilibrium states the quantum trajectory converges in the
mean to a random choice from these states.Comment: 8 page
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