scholarly journals HEISENBERG–PAULI–WEYL UNCERTAINTY INEQUALITY FOR THE DUNKL TRANSFORM ON ℝd

2012 ◽  
Vol 87 (2) ◽  
pp. 316-325 ◽  
Author(s):  
FETHI SOLTANI
Keyword(s):  
Dunkl Transform ◽  
Local Uncertainty ◽  
Global Uncertainty ◽  
Uncertainty Inequality

AbstractIn this paper, we give analogues of the local uncertainty inequality for the Dunkl transform on ℝd, and indicate how the local uncertainty inequality implies a global uncertainty inequality.

scholarly journals Global and local uncertainty principles for signals on graphs

2018 ◽  
Vol 7 ◽  
Author(s):  
Nathanael Perraudin ◽  
Benjamin Ricaud ◽  
David I Shuman ◽  
Pierre Vandergheynst
Keyword(s):  
Local Structure ◽  
Small Region ◽  
Uncertainty Principles ◽  
Missing Information ◽  
Spectral Filter ◽  
Time Frequency ◽  
Local Uncertainty ◽  
Linear Signal ◽  
Global And Local ◽  
Global Uncertainty

Uncertainty principles such as Heisenberg's provide limits on the time-frequency concentration of a signal, and constitute an important theoretical tool for designing linear signal transforms. Generalizations of such principles to the graph setting can inform dictionary design, lead to algorithms for reconstructing missing information via sparse representations, and yield new graph analysis tools. While previous work has focused on generalizing notions of spreads of graph signals in the vertex and graph spectral domains, our approach generalizes the methods of Lieb in order to develop uncertainty principles that provide limits on the concentration of the analysis coefficients of any graph signal under a dictionary transform. One challenge we highlight is that the local structure in a small region of an inhomogeneous graph can drastically affect the uncertainty bounds, limiting the information provided by global uncertainty principles. Accordingly, we suggest new notions of locality, and develop local uncertainty principles that bound the concentration of the analysis coefficients of each atom of a localized graph spectral filter frame in terms of quantities that depend on the local structure of the graph around the atom's center vertex. Finally, we demonstrate how our proposed local uncertainty measures can improve the random sampling of graph signals.

A brisk local uncertainty estimator for hydrologic simulations and predictions (Blue Cat)

2020 ◽  
Author(s):  
Demetris Koutsoyiannis ◽  
Alberto Montanari
Keyword(s):  
Integrated Approach ◽  
Uncertainty Estimation ◽  
Confidence Bands ◽  
New Approach ◽  
Uncertainty Estimator ◽  
Physically Based ◽  
Local Uncertainty ◽  
Physically Based Modelling ◽  
Global Uncertainty

<p>We propose a brisk method for uncertainty estimation in hydrology which maximizes the probabilistic efficiency of the estimated confidence bands over the whole range of the predicted variables. It is an innovative approach framed within the blueprint we proposed in 2012 for stochastic physically-based modelling of hydrological systems. We present the theoretical foundation which proves that global uncertainty can be estimated with an integrated approach by tallying the empirical joint distribution of predictions and predictands in the calibration phase. We also theoretically prove the capability of the method to correct the bias and to fit heteroscedastic uncertainty for any probability distribution of the modelled variable. The method allows the incorporation of physical understanding of the modelled process along with its sources of uncertainty. We present an application to a toy case to prove the capability of the method to correct the bias and the entire distribution function of the predicting model. We also present a case study of a real world catchment. We prepare open source software to allow reproducibility of the results and replicability to other catchments. We term the new approach with the acronym BLUE CAT: Brisk Local Uncertainty Estimation by Conditioning And Tallying.</p>

A note on continuous fractional wavelet transform in ℝn

2021 ◽  
Author(s):  
Amit K. Verma ◽  
Bivek Gupta
Keyword(s):  
Wavelet Transform ◽  
Reproducing Kernel ◽  
Morrey Space ◽  
Inner Product ◽  
Dimensional Euclidean Space ◽  
Reconstruction Formula ◽  
Local Uncertainty ◽  
Fractional Wavelet Transform ◽  
Uncertainty Inequality ◽  
Product Relation

In this paper, we study the continuous fractional wavelet transform (CFrWT) in [Formula: see text]-dimensional Euclidean space [Formula: see text] with scaling parameter [Formula: see text] such that [Formula: see text]. We obtain inner product relation and reconstruction formula for the CFrWT depending on two wavelets along with the reproducing kernel function, involving two wavelets, for the image space of CFrWT. We obtain Heisenberg’s uncertainty inequality and Local uncertainty inequality for the CFrWT. Finally, we prove the boundedness of CFrWT on the Morrey space [Formula: see text] and estimate [Formula: see text]-distance of the CFrWT of two argument functions with respect to different wavelets.

Monkey on My Back. An Autoethnographic Narrative of a Therapeutic Experience

2020 ◽  
Author(s):  
Adam Wiesner
Keyword(s):  
Personal Experience ◽  
Meaning Making ◽  
The Self ◽  
Symbolic Language ◽  
Discursive Practices ◽  
Therapeutic Experience ◽  
Postmodern Philosophy ◽  
The Moment ◽  
The Individual ◽  
Global Uncertainty

With a conscious attempt to contribute to contemporary discussions in mad/trans/queer/monster studies, the monograph approaches complex postmodern theories and contextualizes them from an autoethnographic methodological perspective. As the self-explanatory subtitle reads, the book introduces several topics as revelatory fields for the author’s self-exploration at the moment of an intense epistemological and ontological crisis. Reflexively written, it does not solely focus on a personal experience, as it also aims at bridging the gap between the individual and the collective in times of global uncertainty. There are no solid outcomes defined; nevertheless, the narrative points to a certain—more fluid—way out. Through introducing alternative ways of hermeneutics and meaning-making, the book offers a synthesis of postmodern philosophy and therapy, evolutionary astrology as a symbolic language, embodied inquiry, and Buddhist thought that together represent a critical attempt to challenge the pathologizing discursive practices of modern disciplines during the neoliberal capitalist era.

SAUDI ARABIA'S ECONOMIC POLICY AMID GLOBAL UNCERTAINTY

2020 ◽  
Vol 2 (7) ◽  
pp. 191-196
Author(s):  
K. V. TIMAKHOV ◽  
Keyword(s):  
Economic Policy ◽  
Persian Gulf ◽  
Scientific Interest ◽  
Kingdom Of Saudi Arabia ◽  
Globalizing World ◽  
Geographical Position ◽  
Coronavirus Infection ◽  
The Persian Gulf ◽  
Global Uncertainty ◽  
Further Development

The events that took place in the first half of 2020 once again demonstrated how countries in the modern globalizing world are interdependent and interconnected: what is happening in one part of the planet inevitably affects other states, regardless of their geographical position. The Kingdom of Saudi Arabia is no exception. The crisis that arose because of the outbreak of the coronavirus infection hit the country’s infant economic system, disrupting the government’s ambitious plans to modernize and transform the kingdom. In this connection, it is of great scientific interest to study changes in the internal political course of the monarchy of the Persian Gulf, consider and analyze feasible scenarios for the further development of the country.

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