scholarly journals Maximum Entropy on the Mean approach to solve generalized inverse problems with an application in computational thermodynamics.

2021 ◽  
Author(s):  
Eva Lawrence ◽  
Fabrice Gamboa ◽  
Thierry Klein ◽  
Christine Guéneau
Keyword(s):  
Inverse Problems ◽  
Maximum Entropy ◽  
Convex Analysis ◽  
Generalized Inverse ◽  
Point Of View ◽  
Multidimensional Case ◽  
General Integral ◽  
The Mean ◽  
Entropy Maximisation ◽  
Analysis Point

In this paper, we study entropy maximisation problems in order to reconstruct functions or measures subject to very general integral constraints. Our work has a twofold purpose. We first make a global synthesis of entropy maximisation problems in the case of a single reconstruction (measure or function) from the convex analysis point of view, as well as in the framework of the embedding into the Maximum Entropy on the Mean (MEM) setting. We further propose an extension of the entropy methods for a multidimensional case.

Der Sommer und Herbst 2003 aus phänologischer Sicht | Summer and autumn 2003 from a phenological point of view

2004 ◽  
Vol 155 (5) ◽  
pp. 142-145 ◽  
Author(s):  
Claudio Defila
Keyword(s):  
Time Series ◽  
New Record ◽  
Point Of View ◽  
Late Spring ◽  
Mean Deviation ◽  
Leaf Shedding ◽  
The Mean ◽  
Very High ◽  
Selection Of

The record-breaking heatwave of 2003 also had an impact on the vegetation in Switzerland. To examine its influences seven phenological late spring and summer phases were evaluated together with six phases in the autumn from a selection of stations. 30% of the 122 chosen phenological time series in late spring and summer phases set a new record (earliest arrival). The proportion of very early arrivals is very high and the mean deviation from the norm is between 10 and 20 days. The situation was less extreme in autumn, where 20% of the 103 time series chosen set a new record. The majority of the phenological arrivals were found in the class «normal» but the class«very early» is still well represented. The mean precocity lies between five and twenty days. As far as the leaf shedding of the beech is concerned, there was even a slight delay of around six days. The evaluation serves to show that the heatwave of 2003 strongly influenced the phenological events of summer and spring.

scholarly journals BAYESIAN INFERENCE FOR THE TANGENT PORTFOLIO

2018 ◽  
Vol 21 (08) ◽  
pp. 1850054 ◽  
Author(s):  
DAVID BAUDER ◽  
TARAS BODNAR ◽  
STEPAN MAZUR ◽  
YAREMA OKHRIN
Keyword(s):  
Bayesian Inference ◽  
Point Of View ◽  
Posterior Distributions ◽  
Conditional Distributions ◽  
Linear Combinations ◽  
Conjugate Priors ◽  
Mean And Variance ◽  
The Mean ◽  
Stochastic Representations ◽  
Mean Vector

In this paper, we consider the estimation of the weights of tangent portfolios from the Bayesian point of view assuming normal conditional distributions of the logarithmic returns. For diffuse and conjugate priors for the mean vector and the covariance matrix, we derive stochastic representations for the posterior distributions of the weights of tangent portfolio and their linear combinations. Separately, we provide the mean and variance of the posterior distributions, which are of key importance for portfolio selection. The analytic results are evaluated within a simulation study, where the precision of coverage intervals is assessed.

scholarly journals The Regularized Weak Functional Matching Pursuit for linear inverse problems

2019 ◽  
Vol 27 (3) ◽  
pp. 317-340 ◽  
Author(s):  
Max Kontak ◽  
Volker Michel
Keyword(s):  
Inverse Problems ◽  
Matching Pursuit ◽  
A Priori ◽  
Computation Time ◽  
Point Of View ◽  
Computational Point ◽  
Linear Inverse Problems ◽  
Infinite Dimensional ◽  
Frame Condition ◽  
Ill Posed

Abstract In this work, we present the so-called Regularized Weak Functional Matching Pursuit (RWFMP) algorithm, which is a weak greedy algorithm for linear ill-posed inverse problems. In comparison to the Regularized Functional Matching Pursuit (RFMP), on which it is based, the RWFMP possesses an improved theoretical analysis including the guaranteed existence of the iterates, the convergence of the algorithm for inverse problems in infinite-dimensional Hilbert spaces, and a convergence rate, which is also valid for the particular case of the RFMP. Another improvement is the cancellation of the previously required and difficult to verify semi-frame condition. Furthermore, we provide an a-priori parameter choice rule for the RWFMP, which yields a convergent regularization. Finally, we will give a numerical example, which shows that the “weak” approach is also beneficial from the computational point of view. By applying an improved search strategy in the algorithm, which is motivated by the weak approach, we can save up to 90  of computation time in comparison to the RFMP, whereas the accuracy of the solution does not change as much.

scholarly journals HURWITZ THEOREM AND PARALLELIZABLE SPHERES FROM TENSOR ANALYSIS

2001 ◽  
Vol 16 (25) ◽  
pp. 4207-4222 ◽  
Author(s):  
J. A. NIETO ◽  
L. N. ALEJO-ARMENTA
Keyword(s):  
Clifford Algebra ◽  
Point Of View ◽  
Tensor Analysis ◽  
Tensor Algebra ◽  
Normed Algebra ◽  
Curved Spaces ◽  
Hurwitz Theorem ◽  
Analysis Point

By using tensor analysis, we find a connection between normed algebras and the parallelizability of the spheres S 1, S 3 and S 7. In this process, we discovered the analog of Hurwitz theorem for curved spaces and a geometrical unified formalism for the metric and the torsion. In order to achieve these goals we first develop a proof of Hurwitz theorem based on tensor analysis. It turns out that in contrast to the doubling procedure and Clifford algebra mechanism, our proof is entirely based on tensor algebra applied to the normed algebra condition. From the tersor analysis point of view our proof is straightforward and short. We also discuss a possible connection between our formalism and the Cayley–Dickson algebras and Hopf maps.

scholarly journals Uncertainty visualization of gaze estimation to support operator-controlled calibration

2018 ◽  
Vol 10 (5) ◽  
Author(s):  
Almoctar Hassoumi ◽  
Vsevolod Peysakhovich ◽  
Christophe Hurter
Keyword(s):  
Qualitative Evaluation ◽  
Point Of View ◽  
Angular Error ◽  
Qualitative Assessment ◽  
Gaze Estimation ◽  
Uncertainty Visualization ◽  
Estimation Uncertainty ◽  
The Mean ◽  
Gaze Position ◽  
Do So

      In this paper, we investigate how visualization assets can support the qualitative evaluation of gaze estimation uncertainty. Although eye tracking data are commonly available, little has been done to visually investigate the uncertainty of recorded gaze information. This paper tries to fill this gap by using innovative uncertainty computation and visualization. Given a gaze processing pipeline, we estimate the location of this gaze position in the world camera. To do so we developed our own gaze data processing which give us access to every stage of the data transformation and thus the uncertainty computation. To validate our gaze estimation pipeline, we designed an experiment with 12 participants and showed that the correction methods we proposed reduced the Mean Angular Error by about 1.32 cm, aggregating all 12 participants’ results. The Mean Angular Error is 0.25° (SD=0.15°) after correction of the estimated gaze. Next, to support the qualitative assessment of this data, we provide a map which codes the actual uncertainty in the user point of view. 

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