We consider the problem of approximate belief-state monitoring using particle filtering for the purposes of implementing a policy for a partially observable Markov decision process (POMDP). While particle fil­ tering has become a widely used tool in AI for monitor­ ing dynamical systems, rather scant attention has been paid to their use in the context of decision making. As­ suming the existenc...

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The efficiency of the multicanonical procedure can be significantly improved by applying an additional bias to the numerically generated sample space. However, results obtained by biasing in different sampling regions cannot in general be accurately combined, since their relative normalization coefficient is not known precisely. We demonstrate that for overlapping biasing regions a simple itera...

We introduce a strictly deterministic, meaning non-random, rendering method, which performs superior to state of the art Monte Carlo techniques. Its simple and elegant implementation on parallel computer architectures is capable of simulating anti-aliasing, motion blur, depth of field, area light sources, glossy reflection and transmission, participating media, and global illumination. We provi...

In this paper we investigate the efficient realization of sampling methods, based on solutions of certain adjoint problems. This adjoint approach does not require the explicit knowledge of a Green’s function for the background medium, and allows to sample for all points and all dipole directions simultaneously; thus several limitations of standard sampling methods are relieved. A detailed deriv...

Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled with replacement. In contrast, sampling without replacement is far less understood, yet in practice it is very common, often easier to implement, and usually performs better. In this paper, we provide competitive convergence guarantees for without-replacement sampling...

Random sampling can lead to algorithms where the Fourier reconstruction is almost perfect when the underlying spectrum of the signal is sparse or band-limited. Conversely, regular sampling often hampers the Fourier data recovery methods. However, two-dimensional (2D) signals which are band-limited in one spatial dimension can be recovered by designing a regular acquisition grid that minimizes t...

Applied mathematics is concerned with developing models with predictive capability, and with probing those models to obtain qualitative and quantitative insight into the phenomena being modelled. Statistics is data-driven and is aimed at the development of methodologies to optimize the information derived from data. The increasing complexity of phenomena that scientists and engineers wish to mo...

Millimeter-accuracy Ultra-Wideband (UWB) positioning systems using the Time Difference Of Arrival (TDOA) algorithm are able to be utilized in military and many other important applications. Previous research on UWB positioning system has achieved up to mm or sub-mm accuracy. However, one bottleneck in UWB system is at sampling high resolution UWB signals, as well as high resolution timing infor...