3,300 research outputs found
Bandlimited Spatial Field Sampling with Mobile Sensors in the Absence of Location Information
Sampling of physical fields with mobile sensor is an emerging area. In this
context, this work introduces and proposes solutions to a fundamental question:
can a spatial field be estimated from samples taken at unknown sampling
locations?
Unknown sampling location, sample quantization, unknown bandwidth of the
field, and presence of measurement-noise present difficulties in the process of
field estimation. In this work, except for quantization, the other three issues
will be tackled together in a mobile-sampling framework. Spatially bandlimited
fields are considered. It is assumed that measurement-noise affected field
samples are collected on spatial locations obtained from an unknown renewal
process. That is, the samples are obtained on locations obtained from a renewal
process, but the sampling locations and the renewal process distribution are
unknown. In this unknown sampling location setup, it is shown that the
mean-squared error in field estimation decreases as where is the
average number of samples collected by the mobile sensor. The average number of
samples collected is determined by the inter-sample spacing distribution in the
renewal process. An algorithm to ascertain spatial field's bandwidth is
detailed, which works with high probability as the average number of samples
increases. This algorithm works in the same setup, i.e., in the presence of
measurement-noise and unknown sampling locations.Comment: Submitted to IEEE Trans on Signal Processin
Adaptive Resolution Simulation in Equilibrium and Beyond
In this paper, we investigate the equilibrium statistical properties of both
the force and potential interpolations of adaptive resolution simulation
(AdResS) under the theoretical framework of grand-canonical like AdResS
(GC-AdResS). The thermodynamic relations between the higher and lower
resolutions are derived by considering the absence of fundamental conservation
laws in mechanics for both branches of AdResS. In order to investigate the
applicability of AdResS method in studying the properties beyond the
equilibrium, we demonstrate the accuracy of AdResS in computing the dynamical
properties in two numerical examples: The velocity auto-correlation of pure
water and the conformational relaxation of alanine dipeptide dissolved in
water. Theoretical and technical open questions of the AdResS method are
discussed in the end of the paper
Quantum enhanced estimation of a multi-dimensional field
We present a framework for the quantum enhanced estimation of multiple
parameters corresponding to non-commuting unitary generators. Our formalism
provides a recipe for the simultaneous estimation of all three components of a
magnetic field. We propose a probe state that surpasses the precision of
estimating the three components individually and discuss measurements that come
close to attaining the quantum limit. Our study also reveals that too much
quantum entanglement may be detrimental to attaining the Heisenberg scaling in
quantum metrology.Comment: 9 pages, 1 figur
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