Communication in the Presence of Noise

Shannon, Claude E.

doi:10.1109/jrproc.1949.232969

Cited by 5,420 publications

(3,132 citation statements)

References 6 publications

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“…This is probably because of the coarser resolution. According to the sampling theorem (Shannon, 1949), undulations should be visible since the spatial resolution (≈ 7 m at 19 GHz and ≈ 14 m at 37 GHz) was less than half of the typical period of the undulations (≈ 40 m). The computation of the power spectra using irregular fast Fourier transform (Greengard and Lee, 2004, results not shown) shows peaks in the range of 30-60 m, but they are not significant.…”

Section: Long Transects and Ssm/i Observationsmentioning

confidence: 99%

Influence of meter-scale wind-formed features on the variability of the microwave brightness temperature around Dome C in Antarctica

et al. 2014

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Abstract. Space-borne passive microwave radiometers are widely used to retrieve information in snowy regions by exploiting the high sensitivity of microwave emission to snow properties. For the Antarctic Plateau, many studies presenting retrieval algorithms or numerical simulations have assumed, explicitly or not, that the subpixel-scale heterogeneity is negligible and that the retrieved properties were representative of whole pixels. In this paper, we investigate the spatial variations of brightness temperature over a range of a few kilometers in the Dome C area. Using ground-based radiometers towed by a vehicle, we collected brightness temperature at 11, 19 and 37 GHz at horizontal and vertical polarizations along transects with meter resolution. The most remarkable observation was a series of regular undulations of the signal with a significant amplitude reaching 10 K at 37 GHz and a quasi-period of 30-50 m. In contrast, the variability at longer length scales seemed to be weak in the investigated area, and the mean brightness temperature was close to SSM/I and WindSat satellite observations for all the frequencies and polarizations. To establish a link between the snow characteristics and the microwave emission undulations, we collected detailed snow grain size and density profiles at two points where opposite extrema of brightness temperature were observed. Numerical simulations with the DMRT-ML microwave emission model revealed that the difference in density in the upper first meter explained most of the brightness temperature variations. In addition, we found that these variations of density near the surface were linked to snow hardness. Patches of hard snow -probably formed by wind compaction -were clearly visible and covered as much as 39 % of the investigated area. Their brightness temperature was higher than in normal areas. This result implies that the microwave emission measured by satellites over Dome C is more complex than expected and very likely depends on the year-to-year areal proportion of the two different types of snow.

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Section: Long Transects and Ssm/i Observationsmentioning

confidence: 99%

Influence of meter-scale wind-formed features on the variability of the microwave brightness temperature around Dome C in Antarctica

et al. 2014

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“…In this case, they show that the system can produce time oscillations even in that region of parameter space where the corresponding deterministic system would display a steady state. The information capacity of oscillating systems affected by noise can be estimated by Shannon's theorem [27] …”

Section: Amount Of Information In Genetic Control Elementsmentioning

confidence: 99%

The dynamics of genetic control in the cell: the good and bad of being late

Tiana

Jensen

2013

Phil. Trans. R. Soc. A.

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One contribution of 15 to a Theme Issue 'Dynamics, control and information in delay-coupled systems' . The expression of genes in the cell is controlled by a complex interaction network involving proteins, RNA and DNA. The molecular events associated with the nodes of such a network take place on a variety of time scales, and thus cannot be regarded as instantaneous. In many cases, the cell is robust with respect to the delay in gene expression control, behaving as if it were instantaneous. However, there are specific cases in which delay gives rise to temporal oscillations. This is the case, for example, of the expression of tumoursuppressor protein p53, of protein Hes1, involved in the differentiation of stem cells, of NFkB and Wnt, in which case delay arises implicitly from the structure of the associated network. By means of delay rate equations, we study the kinetics of small regulatory networks, emphasizing the role of delay in an evolutionary context. These models suggest that oscillations are a typical outcome of the dynamics of regulatory networks, and evolution has to work to avoid them when not required (and not vice versa).

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“…Otherwise, i. e., if the real system might be infinitely far off from the model, safety guarantees are impossible. By the sampling theorem in signal processing [40], such constraints further enable compliance monitoring solely on the basis of sample points instead of the unobservable intermediate states about which no sensor data exists. 2 Extension In addition to providing proofs for the results, this article extends the short version [24] with support for a correct-by-construction approach to synthesize ModelPlex monitors by a systematic transformation in the differential dynamic logic axiomatization [33].…”

Section: Introductionmentioning

confidence: 99%

ModelPlex: verified runtime validation of verified cyber-physical system models

Mitsch

Platzer

2016

Form Methods Syst Des

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Formal verification and validation play a crucial role in making cyber-physical systems (CPS) safe. Formal methods make strong guarantees about the system behavior if accurate models of the system can be obtained, including models of the controller and of the physical dynamics. In CPS, models are essential; but any model we could possibly build necessarily deviates from the real world. If the real system fits to the model, its behavior is guaranteed to satisfy the correctness properties verified with respect to the model. Otherwise, all bets are off. This article introduces ModelPlex, a method ensuring that verification results about models apply to CPS implementations. ModelPlex provides correctness guarantees for CPS executions at runtime: it combines offline verification of CPS models with runtime validation of system executions for compliance with the model. ModelPlex ensures in a provably correct way that the verification results obtained for the model apply to the actual system runs by monitoring the behavior of the world for compliance with the model. If, at some point, the observed behavior no longer complies with the model so that offline verification results no longer apply, ModelPlex initiates provably safe fallback actions, assuming the system dynamics deviation is bounded. This article, furthermore, develops a systematic technique to synthesize provably correct monitors automatically from CPS proofs in differential dynamic logic by a correct-by-construction approach, leading to verifiably correct runtime model validation. Overall, ModelPlex generates provably correct monitor conditions that, if checked to hold at runtime, are provably guaranteed to imply that the offline safety verification results about the CPS model apply to the present run of the actual CPS implementation.

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Communication in the Presence of Noise

Cited by 5,420 publications

References 6 publications

Influence of meter-scale wind-formed features on the variability of the microwave brightness temperature around Dome C in Antarctica

Influence of meter-scale wind-formed features on the variability of the microwave brightness temperature around Dome C in Antarctica

The dynamics of genetic control in the cell: the good and bad of being late

ModelPlex: verified runtime validation of verified cyber-physical system models

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