980 research outputs found
Improved Tradeoffs for Leader Election
We consider leader election in clique networks, where nodes are connected
by point-to-point communication links. For the synchronous clique under
simultaneous wake-up, i.e., where all nodes start executing the algorithm in
round , we show a tradeoff between the number of messages and the amount of
time. More specifically, we show that any deterministic algorithm with a
message complexity of requires rounds, for . Our result holds even if
the node IDs are chosen from a relatively small set of size ,
as we are able to avoid using Ramsey's theorem. We also give an upper bound
that improves over the previously-best tradeoff. Our second contribution for
the synchronous clique under simultaneous wake-up is to show that is in fact a lower bound on the message complexity that holds for any
deterministic algorithm with a termination time . We complement this
result by giving a simple deterministic algorithm that achieves leader election
in sublinear time while sending only messages, if the ID space is
of at most linear size. We also show that Las Vegas algorithms (that never
fail) require messages. For the synchronous clique under
adversarial wake-up, we show that is a tight lower bound for
randomized -round algorithms. Finally, we turn our attention to the
asynchronous clique: Assuming adversarial wake-up, we give a randomized
algorithm that achieves a message complexity of and an
asynchronous time complexity of . For simultaneous wake-up, we translate
the deterministic tradeoff algorithm of Afek and Gafni to the asynchronous
model, thus partially answering an open problem they pose
Global parameter identification of stochastic reaction networks from single trajectories
We consider the problem of inferring the unknown parameters of a stochastic
biochemical network model from a single measured time-course of the
concentration of some of the involved species. Such measurements are available,
e.g., from live-cell fluorescence microscopy in image-based systems biology. In
addition, fluctuation time-courses from, e.g., fluorescence correlation
spectroscopy provide additional information about the system dynamics that can
be used to more robustly infer parameters than when considering only mean
concentrations. Estimating model parameters from a single experimental
trajectory enables single-cell measurements and quantification of cell--cell
variability. We propose a novel combination of an adaptive Monte Carlo sampler,
called Gaussian Adaptation, and efficient exact stochastic simulation
algorithms that allows parameter identification from single stochastic
trajectories. We benchmark the proposed method on a linear and a non-linear
reaction network at steady state and during transient phases. In addition, we
demonstrate that the present method also provides an ellipsoidal volume
estimate of the viable part of parameter space and is able to estimate the
physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems
Biology
An introspective algorithm for the integer determinant
We present an algorithm computing the determinant of an integer matrix A. The
algorithm is introspective in the sense that it uses several distinct
algorithms that run in a concurrent manner. During the course of the algorithm
partial results coming from distinct methods can be combined. Then, depending
on the current running time of each method, the algorithm can emphasize a
particular variant. With the use of very fast modular routines for linear
algebra, our implementation is an order of magnitude faster than other existing
implementations. Moreover, we prove that the expected complexity of our
algorithm is only O(n^3 log^{2.5}(n ||A||)) bit operations in the dense case
and O(Omega n^{1.5} log^2(n ||A||) + n^{2.5}log^3(n||A||)) in the sparse case,
where ||A|| is the largest entry in absolute value of the matrix and Omega is
the cost of matrix-vector multiplication in the case of a sparse matrix.Comment: Published in Transgressive Computing 2006, Grenade : Espagne (2006
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