304 research outputs found
Thin shell implies spectral gap up to polylog via a stochastic localization scheme
We consider the isoperimetric inequality on the class of high-dimensional
isotropic convex bodies. We establish quantitative connections between two
well-known open problems related to this inequality, namely, the thin shell
conjecture, and the conjecture by Kannan, Lovasz, and Simonovits, showing that
the corresponding optimal bounds are equivalent up to logarithmic factors. In
particular we prove that, up to logarithmic factors, the minimal possible ratio
between surface area and volume is attained on ellipsoids. We also show that a
positive answer to the thin shell conjecture would imply an optimal dependence
on the dimension in a certain formulation of the Brunn-Minkowski inequality.
Our results rely on the construction of a stochastic localization scheme for
log-concave measures.Comment: 33 page
State Estimation with Sets of Densities considering Stochastic and Systematic Errors
In practical applications, state estimation requires the consideration of stochastic and systematic errors. If both error types are present, an exact probabilistic description of the state estimate is not possible, so that common Bayesian estimators have to be questioned. This paper introduces a theoretical concept, which allows for incorporating unknown but bounded errors into a Bayesian inference scheme by utilizing sets of densities. In order to derive a tractable estimator, the Kalman filter is applied to ellipsoidal sets of means, which are used to bound additive systematic errors. Also, an extension to nonlinear system and observation models with ellipsoidal error bounds is presented. The derived estimator is motivated by means of two example applications
A Comparison of Stealthy Sensor Attacks on Control Systems
As more attention is paid to security in the context of control systems and
as attacks occur to real control systems throughout the world, it has become
clear that some of the most nefarious attacks are those that evade detection.
The term stealthy has come to encompass a variety of techniques that attackers
can employ to avoid detection. Here we show how the states of the system (in
particular, the reachable set corresponding to the attack) can be manipulated
under two important types of stealthy attacks. We employ the chi-squared fault
detection method and demonstrate how this imposes a constraint on the attack
sequence either to generate no alarms (zero-alarm attack) or to generate alarms
at a rate indistinguishable from normal operation (hidden attack)
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