163,056 research outputs found
The inverse of the star-discrepancy problem and the generation of pseudo-random numbers
The inverse of the star-discrepancy problem asks for point sets of
size in the -dimensional unit cube whose star-discrepancy
satisfies where
is a constant independent of and . The first existence results in this
direction were shown by Heinrich, Novak, Wasilkowski, and Wo\'{z}niakowski in
2001, and a number of improvements have been shown since then. Until now only
proofs that such point sets exist are known. Since such point sets would be
useful in applications, the big open problem is to find explicit constructions
of suitable point sets .
We review the current state of the art on this problem and point out some
connections to pseudo-random number generators
Compositional Falsification of Cyber-Physical Systems with Machine Learning Components
Cyber-physical systems (CPS), such as automotive systems, are starting to
include sophisticated machine learning (ML) components. Their correctness,
therefore, depends on properties of the inner ML modules. While learning
algorithms aim to generalize from examples, they are only as good as the
examples provided, and recent efforts have shown that they can produce
inconsistent output under small adversarial perturbations. This raises the
question: can the output from learning components can lead to a failure of the
entire CPS? In this work, we address this question by formulating it as a
problem of falsifying signal temporal logic (STL) specifications for CPS with
ML components. We propose a compositional falsification framework where a
temporal logic falsifier and a machine learning analyzer cooperate with the aim
of finding falsifying executions of the considered model. The efficacy of the
proposed technique is shown on an automatic emergency braking system model with
a perception component based on deep neural networks
Some Results on the Complexity of Numerical Integration
This is a survey (21 pages, 124 references) written for the MCQMC 2014
conference in Leuven, April 2014. We start with the seminal paper of Bakhvalov
(1959) and end with new results on the curse of dimension and on the complexity
of oscillatory integrals. Some small errors of earlier versions are corrected
Sequential Quasi-Monte Carlo
We derive and study SQMC (Sequential Quasi-Monte Carlo), a class of
algorithms obtained by introducing QMC point sets in particle filtering. SQMC
is related to, and may be seen as an extension of, the array-RQMC algorithm of
L'Ecuyer et al. (2006). The complexity of SQMC is , where is
the number of simulations at each iteration, and its error rate is smaller than
the Monte Carlo rate . The only requirement to implement SQMC is
the ability to write the simulation of particle given as a
deterministic function of and a fixed number of uniform variates.
We show that SQMC is amenable to the same extensions as standard SMC, such as
forward smoothing, backward smoothing, unbiased likelihood evaluation, and so
on. In particular, SQMC may replace SMC within a PMCMC (particle Markov chain
Monte Carlo) algorithm. We establish several convergence results. We provide
numerical evidence that SQMC may significantly outperform SMC in practical
scenarios.Comment: 55 pages, 10 figures (final version
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