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Spatially distributed networks of large size arise in a variety of science and engineering problems, such as wireless sensor networks and smart power grids. Most of their features can be described by properties of their state-space matrices whose entries have indices in the vertex set of a graph. In this paper, we introduce novel algebras of Beurling type that contain matrices on a connected simple graph having polynomial off-diagonal decay, and we show that they are Banach subalgebras of the space of all bounded operators on the space of all p-summable sequences. The $$\ell^p$$-stability of state-space matrices is an essential hypothesis for the robustness of spatially distributed networks. In this paper, we establish the equivalence among -stabilities of matrices in Beurling algebras for different exponents $$p$$, with quantitative analysis for the lower stability bounds. Admission of norm-control inversion plays a crucial role in some engineering practice. In this paper, we prove that matrices in Beurling subalgebras of have norm-controlled inversion and we find a norm-controlled polynomial with close to optimal degree. Polynomial estimate to powers of matrices is important for numerical implementation of spatially distributed networks. In this paper, we apply our results on norm-controlled inversion to obtain a polynomial estimate to powers of matrices in Beurling algebras. The polynomial estimate is a noncommutative extension about convolution powers of a complex function and is applicable to estimate the probability of hopping from one agent to another agent in a stationary Markov chain on a spatially distributed network.
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An asynchronous wireless network for capturing event-driven data from large populations of autonomous sensors
Abstract Networks of spatially distributed radiofrequency identification sensors could be used to collect data in wearable or implantable biomedical applications. However, the development of scalable networks remains challenging. Here we report a wireless radiofrequency network approach that can capture sparse event-driven data from large populations of spatially distributed autonomous microsensors. We use a spectrally efficient, low-error-rate asynchronous networking concept based on a code-division multiple-access method. We experimentally demonstrate the network performance of several dozen submillimetre-sized silicon microchips and complement this with large-scale in silico simulations. To test the notion that spike-based wireless communication can be matched with downstream sensor population analysis by neuromorphic computing techniques, we use a spiking neural network machine learning model to decode prerecorded open source data from eight thousand spiking neurons in the primate cortex for accurate prediction of hand movement in a cursor control task.
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- Award ID(s):
- 2322600
- PAR ID:
- 10581857
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Nature Electronics
- Volume:
- 7
- Issue:
- 4
- ISSN:
- 2520-1131
- Page Range / eLocation ID:
- 313 to 324
- Subject(s) / Keyword(s):
- wireless sensor networks
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1038/s41928-024-01134-y
