136,225 research outputs found
A connection between concurrency and language theory
We show that three fixed point structures equipped with (sequential)
composition, a sum operation, and a fixed point operation share the same valid
equations. These are the theories of (context-free) languages, (regular) tree
languages, and simulation equivalence classes of (regular) synchronization
trees (or processes). The results reveal a close relationship between classical
language theory and process algebra
Exploiting Chordality in Optimization Algorithms for Model Predictive Control
In this chapter we show that chordal structure can be used to devise
efficient optimization methods for many common model predictive control
problems. The chordal structure is used both for computing search directions
efficiently as well as for distributing all the other computations in an
interior-point method for solving the problem. The chordal structure can stem
both from the sequential nature of the problem as well as from distributed
formulations of the problem related to scenario trees or other formulations.
The framework enables efficient parallel computations.Comment: arXiv admin note: text overlap with arXiv:1502.0638
Collapsing lattice animals and lattice trees in two dimensions
We present high statistics simulations of weighted lattice bond animals and
lattice trees on the square lattice, with fugacities for each non-bonded
contact and for each bond between two neighbouring monomers. The simulations
are performed using a newly developed sequential sampling method with
resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used
for linear chain polymers. We determine with high precision the line of second
order transitions from an extended to a collapsed phase in the resulting
2-dimensional phase diagram. This line includes critical bond percolation as a
multicritical point, and we verify that this point divides the line into two
different universality classes. One of them corresponds to the collapse driven
by contacts and includes the collapse of (weakly embeddable) trees, but the
other is {\it not yet} bond driven and does not contain the Derrida-Herrmann
model as special point. Instead it ends at a multicritical point where a
transition line between two collapsed phases (one bond-driven and the other
contact-driven) sparks off. The Derrida-Herrmann model is representative for
the bond driven collapse, which then forms the fourth universality class on the
transition line (collapsing trees, critical percolation, intermediate regime,
and Derrida-Herrmann). We obtain very precise estimates for all critical
exponents for collapsing trees. It is already harder to estimate the critical
exponents for the intermediate regime. Finally, it is very difficult to obtain
with our method good estimates of the critical parameters of the
Derrida-Herrmann universality class. As regards the bond-driven to
contact-driven transition in the collapsed phase, we have some evidence for its
existence and rough location, but no precise estimates of critical exponents.Comment: 11 pages, 16 figures, 1 tabl
Macro-evolutionary models and coalescent point processes: The shape and probability of reconstructed phylogenies
Forward-time models of diversification (i.e., speciation and extinction)
produce phylogenetic trees that grow "vertically" as time goes by. Pruning the
extinct lineages out of such trees leads to natural models for reconstructed
trees (i.e., phylogenies of extant species). Alternatively, reconstructed trees
can be modelled by coalescent point processes (CPP), where trees grow
"horizontally" by the sequential addition of vertical edges. Each new edge
starts at some random speciation time and ends at the present time; speciation
times are drawn from the same distribution independently. CPP lead to extremely
fast computation of tree likelihoods and simulation of reconstructed trees.
Their topology always follows the uniform distribution on ranked tree shapes
(URT). We characterize which forward-time models lead to URT reconstructed
trees and among these, which lead to CPP reconstructed trees. We show that for
any "asymmetric" diversification model in which speciation rates only depend on
time and extinction rates only depend on time and on a non-heritable trait
(e.g., age), the reconstructed tree is CPP, even if extant species are
incompletely sampled. If rates additionally depend on the number of species,
the reconstructed tree is (only) URT (but not CPP). We characterize the common
distribution of speciation times in the CPP description, and discuss incomplete
species sampling as well as three special model cases in detail: 1) extinction
rate does not depend on a trait; 2) rates do not depend on time; 3) mass
extinctions may happen additionally at certain points in the past
Phylogenetic analysis accounting for age-dependent death and sampling with applications to epidemics
The reconstruction of phylogenetic trees based on viral genetic sequence data
sequentially sampled from an epidemic provides estimates of the past
transmission dynamics, by fitting epidemiological models to these trees. To our
knowledge, none of the epidemiological models currently used in phylogenetics
can account for recovery rates and sampling rates dependent on the time elapsed
since transmission.
Here we introduce an epidemiological model where infectives leave the
epidemic, either by recovery or sampling, after some random time which may
follow an arbitrary distribution.
We derive an expression for the likelihood of the phylogenetic tree of
sampled infectives under our general epidemiological model. The analytic
concept developed in this paper will facilitate inference of past
epidemiological dynamics and provide an analytical framework for performing
very efficient simulations of phylogenetic trees under our model. The main idea
of our analytic study is that the non-Markovian epidemiological model giving
rise to phylogenetic trees growing vertically as time goes by, can be
represented by a Markovian "coalescent point process" growing horizontally by
the sequential addition of pairs of coalescence and sampling times.
As examples, we discuss two special cases of our general model, namely an
application to influenza and an application to HIV. Though phrased in
epidemiological terms, our framework can also be used for instance to fit
macroevolutionary models to phylogenies of extant and extinct species,
accounting for general species lifetime distributions.Comment: 30 pages, 2 figure
The Time Machine: A Simulation Approach for Stochastic Trees
In the following paper we consider a simulation technique for stochastic
trees. One of the most important areas in computational genetics is the
calculation and subsequent maximization of the likelihood function associated
to such models. This typically consists of using importance sampling (IS) and
sequential Monte Carlo (SMC) techniques. The approach proceeds by simulating
the tree, backward in time from observed data, to a most recent common ancestor
(MRCA). However, in many cases, the computational time and variance of
estimators are often too high to make standard approaches useful. In this paper
we propose to stop the simulation, subsequently yielding biased estimates of
the likelihood surface. The bias is investigated from a theoretical point of
view. Results from simulation studies are also given to investigate the balance
between loss of accuracy, saving in computing time and variance reduction.Comment: 22 Pages, 5 Figure
The recursion hierarchy for PCF is strict
We consider the sublanguages of Plotkin's PCF obtained by imposing some bound
k on the levels of types for which fixed point operators are admitted. We show
that these languages form a strict hierarchy, in the sense that a fixed point
operator for a type of level k can never be defined (up to observational
equivalence) using fixed point operators for lower types. This answers a
question posed by Berger. Our proof makes substantial use of the theory of
nested sequential procedures (also called PCF B\"ohm trees) as expounded in the
recent book of Longley and Normann
Fast Parallel Operations on Search Trees
Using (a,b)-trees as an example, we show how to perform a parallel split with
logarithmic latency and parallel join, bulk updates, intersection, union (or
merge), and (symmetric) set difference with logarithmic latency and with
information theoretically optimal work. We present both asymptotically optimal
solutions and simplified versions that perform well in practice - they are
several times faster than previous implementations
Sequential Design for Computer Experiments with a Flexible Bayesian Additive Model
In computer experiments, a mathematical model implemented on a computer is
used to represent complex physical phenomena. These models, known as computer
simulators, enable experimental study of a virtual representation of the
complex phenomena. Simulators can be thought of as complex functions that take
many inputs and provide an output. Often these simulators are themselves
expensive to compute, and may be approximated by "surrogate models" such as
statistical regression models. In this paper we consider a new kind of
surrogate model, a Bayesian ensemble of trees (Chipman et al. 2010), with the
specific goal of learning enough about the simulator that a particular feature
of the simulator can be estimated. We focus on identifying the simulator's
global minimum. Utilizing the Bayesian version of the Expected Improvement
criterion (Jones et al. 1998), we show that this ensemble is particularly
effective when the simulator is ill-behaved, exhibiting nonstationarity or
abrupt changes in the response. A number of illustrations of the approach are
given, including a tidal power application.Comment: 21 page
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