73,704 research outputs found
One-bit Distributed Sensing and Coding for Field Estimation in Sensor Networks
This paper formulates and studies a general distributed field reconstruction
problem using a dense network of noisy one-bit randomized scalar quantizers in
the presence of additive observation noise of unknown distribution. A
constructive quantization, coding, and field reconstruction scheme is developed
and an upper-bound to the associated mean squared error (MSE) at any point and
any snapshot is derived in terms of the local spatio-temporal smoothness
properties of the underlying field. It is shown that when the noise, sensor
placement pattern, and the sensor schedule satisfy certain weak technical
requirements, it is possible to drive the MSE to zero with increasing sensor
density at points of field continuity while ensuring that the per-sensor
bitrate and sensing-related network overhead rate simultaneously go to zero.
The proposed scheme achieves the order-optimal MSE versus sensor density
scaling behavior for the class of spatially constant spatio-temporal fields.Comment: Fixed typos, otherwise same as V2. 27 pages (in one column review
format), 4 figures. Submitted to IEEE Transactions on Signal Processing.
Current version is updated for journal submission: revised author list,
modified formulation and framework. Previous version appeared in Proceedings
of Allerton Conference On Communication, Control, and Computing 200
The computational content of Nonstandard Analysis
Kohlenbach's proof mining program deals with the extraction of effective
information from typically ineffective proofs. Proof mining has its roots in
Kreisel's pioneering work on the so-called unwinding of proofs. The proof
mining of classical mathematics is rather restricted in scope due to the
existence of sentences without computational content which are provable from
the law of excluded middle and which involve only two quantifier alternations.
By contrast, we show that the proof mining of classical Nonstandard Analysis
has a very large scope. In particular, we will observe that this scope includes
any theorem of pure Nonstandard Analysis, where `pure' means that only
nonstandard definitions (and not the epsilon-delta kind) are used. In this
note, we survey results in analysis, computability theory, and Reverse
Mathematics.Comment: In Proceedings CL&C 2016, arXiv:1606.0582
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