274,454 research outputs found
Entropy-power uncertainty relations : towards a tight inequality for all Gaussian pure states
We show that a proper expression of the uncertainty relation for a pair of
canonically-conjugate continuous variables relies on entropy power, a standard
notion in Shannon information theory for real-valued signals. The resulting
entropy-power uncertainty relation is equivalent to the entropic formulation of
the uncertainty relation due to Bialynicki-Birula and Mycielski, but can be
further extended to rotated variables. Hence, based on a reasonable assumption,
we give a partial proof of a tighter form of the entropy-power uncertainty
relation taking correlations into account and provide extensive numerical
evidence of its validity. Interestingly, it implies the generalized
(rotation-invariant) Schr\"odinger-Robertson uncertainty relation exactly as
the original entropy-power uncertainty relation implies Heisenberg relation. It
is saturated for all Gaussian pure states, in contrast with hitherto known
entropic formulations of the uncertainty principle.Comment: 15 pages, 5 figures, the new version includes the n-mode cas
Integrated Bayesian Framework for Remaining Useful Life Prediction.
International audienceIn this paper, a data-driven method for remaining useful life (RUL) prediction is presented. The method learns the relation between acquired sensor data and end of life time (EOL) to predict the RUL. The proposed method extracts monotonic trends from offline sensor signals, which are used to build reference models. From online signals the method represents the uncertainty about the current status, using discrete Bayesian filter. Finally, the method predicts RUL of the monitored component using integrated method based on K-nearest neighbor (k-NN) and Gaussian process regression (GPR). The performance of the algorithm is demonstrated using two real data sets from NASA Ames prognostics data repository. The results show that the algorithm obtain good results for both application
Talking About Uncertainty
In the first article we review existing theories of uncertainty. We devote particular attention to the relation between metacognition, uncertainty and probabilistic expectations. We also analyse the role of natural language and communication for the emergence and resolution of states of uncertainty. We hypothesize that agents feel uncertainty in relation to their levels of expected surprise, which depends on probabilistic expectations-gaps elicited during communication processes. Under this framework above tolerance levels of expected surprise can be considered informative signals. These signals can be used to coordinate, at the group and social level, processes of revision of probabilistic expectations. When above tolerance levels of uncertainty are explicated by agents through natural language, in communication networks and public information arenas, uncertainty acquires a systemic role of coordinating device for the revision of probabilistic expectations. The second article of this research seeks to empirically demonstrate that we can crowd source and aggregate decentralized signals of uncertainty, i.e. expected surprise, coming from market agents and civil society by using the web and more specifically Twitter as an information source that contains the wisdom of the crowds concerning the degree of uncertainty of targeted communities/groups of agents at a given moment in time. We extract and aggregate these signals to construct a set of civil society uncertainty proxies by country. We model the dependence among our civil society uncertainty indexes and existing policy and market uncertainty proxies, highlighting contagion channels and differences in their reactiveness to real-world events that occurred in the year 2016, like the EU-referendum vote and the US presidential elections. In the third article, we propose a new instrument, called Worldwide Uncertainty Network, to analyse the uncertainty contagion dynamics across time and areas of the world. Such an instrument can be used to identify the systemic importance of countries in terms of their civil society uncertainty social percolation role. Our results show that civil society uncertainty signals coming from the web may be fruitfully used to improve our understanding of uncertainty contagion and amplification mechanisms among countries and between markets, civil society and political systems
Uncertainty Relations for Shift-Invariant Analog Signals
The past several years have witnessed a surge of research investigating
various aspects of sparse representations and compressed sensing. Most of this
work has focused on the finite-dimensional setting in which the goal is to
decompose a finite-length vector into a given finite dictionary. Underlying
many of these results is the conceptual notion of an uncertainty principle: a
signal cannot be sparsely represented in two different bases. Here, we extend
these ideas and results to the analog, infinite-dimensional setting by
considering signals that lie in a finitely-generated shift-invariant (SI)
space. This class of signals is rich enough to include many interesting special
cases such as multiband signals and splines. By adapting the notion of
coherence defined for finite dictionaries to infinite SI representations, we
develop an uncertainty principle similar in spirit to its finite counterpart.
We demonstrate tightness of our bound by considering a bandlimited lowpass
train that achieves the uncertainty principle. Building upon these results and
similar work in the finite setting, we show how to find a sparse decomposition
in an overcomplete dictionary by solving a convex optimization problem. The
distinguishing feature of our approach is the fact that even though the problem
is defined over an infinite domain with infinitely many variables and
constraints, under certain conditions on the dictionary spectrum our algorithm
can find the sparsest representation by solving a finite-dimensional problem.Comment: Accepted to IEEE Trans. on Inform. Theor
Optimal measurement of visual motion across spatial and temporal scales
Sensory systems use limited resources to mediate the perception of a great
variety of objects and events. Here a normative framework is presented for
exploring how the problem of efficient allocation of resources can be solved in
visual perception. Starting with a basic property of every measurement,
captured by Gabor's uncertainty relation about the location and frequency
content of signals, prescriptions are developed for optimal allocation of
sensors for reliable perception of visual motion. This study reveals that a
large-scale characteristic of human vision (the spatiotemporal contrast
sensitivity function) is similar to the optimal prescription, and it suggests
that some previously puzzling phenomena of visual sensitivity, adaptation, and
perceptual organization have simple principled explanations.Comment: 28 pages, 10 figures, 2 appendices; in press in Favorskaya MN and
Jain LC (Eds), Computer Vision in Advanced Control Systems using Conventional
and Intelligent Paradigms, Intelligent Systems Reference Library,
Springer-Verlag, Berli
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