8,213 research outputs found
Scalable Verification of Markov Decision Processes
Markov decision processes (MDP) are useful to model concurrent process
optimisation problems, but verifying them with numerical methods is often
intractable. Existing approximative approaches do not scale well and are
limited to memoryless schedulers. Here we present the basis of scalable
verification for MDPSs, using an O(1) memory representation of
history-dependent schedulers. We thus facilitate scalable learning techniques
and the use of massively parallel verification.Comment: V4: FMDS version, 12 pages, 4 figure
GPU-accelerated discontinuous Galerkin methods on hybrid meshes
We present a time-explicit discontinuous Galerkin (DG) solver for the
time-domain acoustic wave equation on hybrid meshes containing vertex-mapped
hexahedral, wedge, pyramidal and tetrahedral elements. Discretely energy-stable
formulations are presented for both Gauss-Legendre and Gauss-Legendre-Lobatto
(Spectral Element) nodal bases for the hexahedron. Stable timestep restrictions
for hybrid meshes are derived by bounding the spectral radius of the DG
operator using order-dependent constants in trace and Markov inequalities.
Computational efficiency is achieved under a combination of element-specific
kernels (including new quadrature-free operators for the pyramid), multi-rate
timestepping, and acceleration using Graphics Processing Units.Comment: Submitted to CMAM
Smart Sampling for Lightweight Verification of Markov Decision Processes
Markov decision processes (MDP) are useful to model optimisation problems in
concurrent systems. To verify MDPs with efficient Monte Carlo techniques
requires that their nondeterminism be resolved by a scheduler. Recent work has
introduced the elements of lightweight techniques to sample directly from
scheduler space, but finding optimal schedulers by simple sampling may be
inefficient. Here we describe "smart" sampling algorithms that can make
substantial improvements in performance.Comment: IEEE conference style, 11 pages, 5 algorithms, 11 figures, 1 tabl
Microevolution of Helicobacter pylori during prolonged infection of single hosts and within families
Our understanding of basic evolutionary processes in bacteria is still very limited. For example, multiple recent dating estimates are based on a universal inter-species molecular clock rate, but that rate was calibrated using estimates of geological dates that are no longer accepted. We therefore estimated the short-term rates of mutation and recombination in Helicobacter pylori by sequencing an average of 39,300 bp in 78 gene fragments from 97 isolates. These isolates included 34 pairs of sequential samples, which were sampled at intervals of 0.25 to 10.2 years. They also included single isolates from 29 individuals (average age: 45 years) from 10 families. The accumulation of sequence diversity increased with time of separation in a clock-like manner in the sequential isolates. We used Approximate Bayesian Computation to estimate the rates of mutation, recombination, mean length of recombination tracts, and average diversity in those tracts. The estimates indicate that the short-term mutation rate is 1.4×10−6 (serial isolates) to 4.5×10−6 (family isolates) per nucleotide per year and that three times as many substitutions are introduced by recombination as by mutation. The long-term mutation rate over millennia is 5–17-fold lower, partly due to the removal of non-synonymous mutations due to purifying selection. Comparisons with the recent literature show that short-term mutation rates vary dramatically in different bacterial species and can span a range of several orders of magnitude
A genomic approach to examine the complex evolution of laurasiatherian mammals
Recent phylogenomic studies have failed to conclusively resolve certain branches of the placental mammalian tree, despite the evolutionary analysis of genomic data from 32 species. Previous analyses of single genes and retroposon insertion data yielded support for different phylogenetic scenarios for the most basal divergences. The results indicated that some mammalian divergences were best interpreted not as a single bifurcating tree, but as an evolutionary network. In these studies the relationships among some orders of the super-clade Laurasiatheria were poorly supported, albeit not studied in detail. Therefore, 4775 protein-coding genes (6,196,263 nucleotides) were collected and aligned in order to analyze the evolution of this clade. Additionally, over 200,000 introns were screened in silico, resulting in 32 phylogenetically informative long interspersed nuclear elements (LINE) insertion events.
The present study shows that the genome evolution of Laurasiatheria may best be understood as an evolutionary network. Thus, contrary to the common expectation to resolve major evolutionary events as a bifurcating tree, genome analyses unveil complex speciation processes even in deep mammalian divergences. We exemplify this on a subset of 1159 suitable genes that have individual histories, most likely due to incomplete lineage sorting or introgression, processes that can make the genealogy of mammalian genomes complex.
These unexpected results have major implications for the understanding of evolution in general, because the evolution of even some higher level taxa such as mammalian orders may sometimes not be interpreted as a simple bifurcating pattern
A Parallel Two-Pass MDL Context Tree Algorithm for Universal Source Coding
We present a novel lossless universal source coding algorithm that uses
parallel computational units to increase the throughput. The length- input
sequence is partitioned into blocks. Processing each block independently of
the other blocks can accelerate the computation by a factor of , but
degrades the compression quality. Instead, our approach is to first estimate
the minimum description length (MDL) source underlying the entire input, and
then encode each of the blocks in parallel based on the MDL source. With
this two-pass approach, the compression loss incurred by using more parallel
units is insignificant. Our algorithm is work-efficient, i.e., its
computational complexity is . Its redundancy is approximately
bits above Rissanen's lower bound on universal coding performance,
with respect to any tree source whose maximal depth is at most
Sequential Monte Carlo Methods for Protein Folding
We describe a class of growth algorithms for finding low energy states of
heteropolymers. These polymers form toy models for proteins, and the hope is
that similar methods will ultimately be useful for finding native states of
real proteins from heuristic or a priori determined force fields. These
algorithms share with standard Markov chain Monte Carlo methods that they
generate Gibbs-Boltzmann distributions, but they are not based on the strategy
that this distribution is obtained as stationary state of a suitably
constructed Markov chain. Rather, they are based on growing the polymer by
successively adding individual particles, guiding the growth towards
configurations with lower energies, and using "population control" to eliminate
bad configurations and increase the number of "good ones". This is not done via
a breadth-first implementation as in genetic algorithms, but depth-first via
recursive backtracking. As seen from various benchmark tests, the resulting
algorithms are extremely efficient for lattice models, and are still
competitive with other methods for simple off-lattice models.Comment: 10 pages; published in NIC Symposium 2004, eds. D. Wolf et al. (NIC,
Juelich, 2004
Convergence Rates of Gaussian ODE Filters
A recently-introduced class of probabilistic (uncertainty-aware) solvers for
ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to
initial value problems. These methods model the true solution and its first
derivatives \emph{a priori} as a Gauss--Markov process ,
which is then iteratively conditioned on information about . This
article establishes worst-case local convergence rates of order for a
wide range of versions of this Gaussian ODE filter, as well as global
convergence rates of order in the case of and an integrated Brownian
motion prior, and analyses how inaccurate information on coming from
approximate evaluations of affects these rates. Moreover, we show that, in
the globally convergent case, the posterior credible intervals are well
calibrated in the sense that they globally contract at the same rate as the
truncation error. We illustrate these theoretical results by numerical
experiments which might indicate their generalizability to .Comment: 26 pages, 5 figure
Write Channel Model for Bit-Patterned Media Recording
We propose a new write channel model for bit-patterned media recording that
reflects the data dependence of write synchronization errors. It is shown that
this model accommodates both substitution-like errors and insertion-deletion
errors whose statistics are determined by an underlying channel state process.
We study information theoretic properties of the write channel model, including
the capacity, symmetric information rate, Markov-1 rate and the zero-error
capacity.Comment: 11 pages, 12 figures, journa
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