Steven Senger

Swarm interpolation using an approximate chebyshev distribution

In this paper, we describe a novel swarming framework that guides autonomous mobile sensors into a flexible arrangement to interpolate values of a field in an unknown region. The algorithm is devised so that the sensor distribution will behave like a Chebyshev distribution, which can be optimal for certain ideal geometries. The framework is designed to dynamically adjust to changes in the region of interest, and operates well with very little a priori knowledge of the given region. For comparison, we interpolate a variety of nontrivial fields using a standard swarming algorithm that produces a uniform distribution and our new algorithm. We find that our new algorithm interpolates fields with greater accuracy.

Tracking Time-Dependent Scalar Fields with Swarms of Mobile Sensors

In previous work, we introduced a novel swarming interpolation framework and validated its effectiveness on static fields. In this paper, we show that a slightly revised version of this framework is able to track fields that translate, rotate, or expand over time, enabling interpolation of both static and dynamic fields. Our framework can be used to control autonomous mobile sensors into flexible spatial arrangements in order to interpolate values of a field in an unknown region. The key advantage to this framework is that the stable sensor distribution can be chosen to resemble a Chebyshev distribution, which can be optimal for certain ideal geometries.

Distance Graphs in Vector Spaces Over Finite Fields

In this chapter we systematically study various properties of the distance graph in \({\mathbb{F}}_{q}^{d}\), the d-dimensional vector space over the finite field \({\mathbb{F}}_{q}\) with q elements. In the process we compute the diameter of distance graphs and show that sufficiently large subsets of d-dimensional vector spaces over finite fields contain every possible finite configuration.

A low complexity replacement scheme for erased frame coefficients

One key property of frames is their resilience against erasures due to the possibility of generating stable, yet over-complete expansions. Blind reconstruction is one common methodology to reconstruct a signal when frame coefficients have been erased. In this paper we introduce several novel low complexity replacement schemes which can be applied to the set of faulty frame coefficients before blind reconstruction is performed, thus serving as a preconditioning of the received set of frame coefficients. One main idea is that frame coefficients associated with frame vectors close to the one erased should have approximately the same value as the lost one. It is shown that injecting such low complexity replacement schemes into blind reconstruction significantly reduce the worst-case reconstruction error. We then apply our results to the circle frames. If we allow linear combinations of different neighboring coefficients for the reconstruction of missing coefficients, we can even obtain perfect reconstruction for the circle frames under certain weak conditions on the set of erasures.