9,962 research outputs found
Active Sampling-based Binary Verification of Dynamical Systems
Nonlinear, adaptive, or otherwise complex control techniques are increasingly
relied upon to ensure the safety of systems operating in uncertain
environments. However, the nonlinearity of the resulting closed-loop system
complicates verification that the system does in fact satisfy those
requirements at all possible operating conditions. While analytical proof-based
techniques and finite abstractions can be used to provably verify the
closed-loop system's response at different operating conditions, they often
produce conservative approximations due to restrictive assumptions and are
difficult to construct in many applications. In contrast, popular statistical
verification techniques relax the restrictions and instead rely upon
simulations to construct statistical or probabilistic guarantees. This work
presents a data-driven statistical verification procedure that instead
constructs statistical learning models from simulated training data to separate
the set of possible perturbations into "safe" and "unsafe" subsets. Binary
evaluations of closed-loop system requirement satisfaction at various
realizations of the uncertainties are obtained through temporal logic
robustness metrics, which are then used to construct predictive models of
requirement satisfaction over the full set of possible uncertainties. As the
accuracy of these predictive statistical models is inherently coupled to the
quality of the training data, an active learning algorithm selects additional
sample points in order to maximize the expected change in the data-driven model
and thus, indirectly, minimize the prediction error. Various case studies
demonstrate the closed-loop verification procedure and highlight improvements
in prediction error over both existing analytical and statistical verification
techniques.Comment: 23 page
Closed-Loop Statistical Verification of Stochastic Nonlinear Systems Subject to Parametric Uncertainties
This paper proposes a statistical verification framework using Gaussian
processes (GPs) for simulation-based verification of stochastic nonlinear
systems with parametric uncertainties. Given a small number of stochastic
simulations, the proposed framework constructs a GP regression model and
predicts the system's performance over the entire set of possible
uncertainties. Included in the framework is a new metric to estimate the
confidence in those predictions based on the variance of the GP's cumulative
distribution function. This variance-based metric forms the basis of active
sampling algorithms that aim to minimize prediction error through careful
selection of simulations. In three case studies, the new active sampling
algorithms demonstrate up to a 35% improvement in prediction error over other
approaches and are able to correctly identify regions with low prediction
confidence through the variance metric.Comment: 8 pages, submitted to ACC 201
The stellar and sub-stellar IMF of simple and composite populations
The current knowledge on the stellar IMF is documented. It appears to become
top-heavy when the star-formation rate density surpasses about 0.1Msun/(yr
pc^3) on a pc scale and it may become increasingly bottom-heavy with increasing
metallicity and in increasingly massive early-type galaxies. It declines quite
steeply below about 0.07Msun with brown dwarfs (BDs) and very low mass stars
having their own IMF. The most massive star of mass mmax formed in an embedded
cluster with stellar mass Mecl correlates strongly with Mecl being a result of
gravitation-driven but resource-limited growth and fragmentation induced
starvation. There is no convincing evidence whatsoever that massive stars do
form in isolation. Various methods of discretising a stellar population are
introduced: optimal sampling leads to a mass distribution that perfectly
represents the exact form of the desired IMF and the mmax-to-Mecl relation,
while random sampling results in statistical variations of the shape of the
IMF. The observed mmax-to-Mecl correlation and the small spread of IMF
power-law indices together suggest that optimally sampling the IMF may be the
more realistic description of star formation than random sampling from a
universal IMF with a constant upper mass limit. Composite populations on galaxy
scales, which are formed from many pc scale star formation events, need to be
described by the integrated galactic IMF. This IGIMF varies systematically from
top-light to top-heavy in dependence of galaxy type and star formation rate,
with dramatic implications for theories of galaxy formation and evolution.Comment: 167 pages, 37 figures, 3 tables, published in Stellar Systems and
Galactic Structure, Vol.5, Springer. This revised version is consistent with
the published version and includes additional references and minor additions
to the text as well as a recomputed Table 1. ISBN 978-90-481-8817-
Conformance Testing as Falsification for Cyber-Physical Systems
In Model-Based Design of Cyber-Physical Systems (CPS), it is often desirable
to develop several models of varying fidelity. Models of different fidelity
levels can enable mathematical analysis of the model, control synthesis, faster
simulation etc. Furthermore, when (automatically or manually) transitioning
from a model to its implementation on an actual computational platform, then
again two different versions of the same system are being developed. In all
previous cases, it is necessary to define a rigorous notion of conformance
between different models and between models and their implementations. This
paper argues that conformance should be a measure of distance between systems.
Albeit a range of theoretical distance notions exists, a way to compute such
distances for industrial size systems and models has not been proposed yet.
This paper addresses exactly this problem. A universal notion of conformance as
closeness between systems is rigorously defined, and evidence is presented that
this implies a number of other application-dependent conformance notions. An
algorithm for detecting that two systems are not conformant is then proposed,
which uses existing proven tools. A method is also proposed to measure the
degree of conformance between two systems. The results are demonstrated on a
range of models
Invariant Manifolds and Rate Constants in Driven Chemical Reactions
Reaction rates of chemical reactions under nonequilibrium conditions can be
determined through the construction of the normally hyperbolic invariant
manifold (NHIM) [and moving dividing surface (DS)] associated with the
transition state trajectory. Here, we extend our recent methods by constructing
points on the NHIM accurately even for multidimensional cases. We also advance
the implementation of machine learning approaches to construct smooth versions
of the NHIM from a known high-accuracy set of its points. That is, we expand on
our earlier use of neural nets, and introduce the use of Gaussian process
regression for the determination of the NHIM. Finally, we compare and contrast
all of these methods for a challenging two-dimensional model barrier case so as
to illustrate their accuracy and general applicability.Comment: 28 pages, 13 figures, table of contents figur
The M4 Core Project with HST --- I. Overview and First-Epoch
We present an overview of the ongoing Hubble Space Telescope large program
GO-12911. The program is focused on the core of M4, the nearest Galactic
globular cluster, and the observations are designed to constrain the number of
binaries with massive companions (black holes, neutron stars, or white dwarfs)
by measuring the ``wobble'' of the luminous (main-sequence) companion around
the center of mass of the pair, with an astrometric precision of ~50
micro-arcseconds. The high spatial resolution and stable medium-band PSFs of
WFC3/UVIS will make these measurements possible. In this work we describe: (i)
the motivation behind this study, (ii) our observing strategy, (iii) the many
other investigations enabled by this unique data set, and which of those our
team is conducting, and (iv) a preliminary reduction of the first-epoch
data-set collected on October 10, 2012.Comment: 25 pages, 14 figures (9 at low resolution), 3 tables. Published in:
Astronomische Nachrichten, Volume 334, Issue 10, pages 1062-1085, December
2013. http://onlinelibrary.wiley.com/doi/10.1002/asna.201311911/abstrac
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