From Bandits to Experts: A Tale of Domination and Independence

We consider the partial observability model for multi-armed bandits, introduced by Mannor and Shamir. Our main result is a characterization of regret in the directed observability model in terms of the dominating and independence numbers of the observability graph. We also show that in the undirected case, the learner can achieve optimal regret without even accessing the observability graph before selecting an action. Both results are shown using variants of the Exp3 algorithm operating on the observability graph in a time-efficient manner

Moving and oblique observations of beams and plates

We study the observability of the one-dimensional Schr{\"o}dinger equation and of the beam and plate equations by moving or oblique observations. Applying different versions and adaptations of Ingham's theorem on nonharmonic Fourier series, we obtain various observability and non-observability theorems. Several open problems are also formulated at the end of the paper

Asymptotics for optimal design problems for the Schr\"odinger equation with a potential

We study the problem of optimal observability and prove time asymptotic observability estimates for the Schr\"odinger equation with a potential in $L^{\infty}(\Omega)$, with $\Omega\subset \mathbb{R}^d$, using spectral theory. An elegant way to model the problem using a time asymptotic observability constant is presented. For certain small potentials, we demonstrate the existence of a nonzero asymptotic observability constant under given conditions and describe its explicit properties and optimal values. Moreover, we give a precise description of numerical models to analyze the properties of important examples of potentials wells, including that of the modified harmonic oscillator

Observability of Boolean control networks: A unified approach based on the theories of finite automata

The problem on how to determine the observability of Boolean control networks (BCNs) has been open for five years already. In this paper, we propose a unified approach to determine all the four types of observability of BCNs in the literature. We define the concept of weighted pair graphs for BCNs. In the sense of each observability, we use the so-called weighted pair graph to transform a BCN to a finite automaton, and then we use the automaton to determine observability. In particular, the two types of observability that rely on initial states and inputs in the literature are determined. Finally, we show that no pairs of the four types of observability are equivalent, which reveals the essence of nonlinearity of BCNs.Comment: 8 pages, 9 figures, in press in IEEE Transactions on Automatic Control, 201

Automated Observability Investigation of Analog Electronic Circuits using SPICE

In the present paper, a computer-aided approach to fault observability investigation of linear analog circuits is developed. The method is based on sensitivity investigation of the test characteristics in the frequency domain. The test frequencies are selected maximizing the sensitivity of the magnitude of the test characteristics. Applying postprocessing of the simulation results using macrodefinitions in the graphical analyzer Probe, a fault observability investigation of the circuit is performed. A number of sensitivity measures are defined in Probe for observability investigation of multiple faults using pre-defined macrodefinitions. The sensitivity of S-parameters is obtained in order to investigate the fault observability at RF