Maximum entropy reconstruction and the observed symmetries of higher order galaxy covariance functions

1988 ◽  
Vol 333 ◽  
pp. 130
Author(s):  
Henry E. Kandrup
Keyword(s):  
Maximum Entropy ◽  
Higher Order ◽  
Maximum Entropy Reconstruction ◽  
Covariance Functions

Elimination of13Cα Splitting in Protein NMR Spectra by Deconvolution with Maximum Entropy Reconstruction

2003 ◽  
Vol 125 (9) ◽  
pp. 2382-2383 ◽  
Author(s):  
Nobuhisa Shimba ◽  
Alan S. Stern ◽  
Charles S. Craik ◽  
Jeffrey C. Hoch ◽  
Volker Dötsch
Keyword(s):  
Maximum Entropy ◽  
Nmr Spectra ◽  
Protein Nmr ◽  
Maximum Entropy Reconstruction

scholarly journals Higher Order Geometric Theory of Information and Heat Based on Poly-Symplectic Geometry of Souriau Lie Groups Thermodynamics and Their Contextures: The Bedrock for Lie Group Machine Learning

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 840 ◽  
Author(s):  
Frédéric Barbaresco
Keyword(s):  
Machine Learning ◽  
Maximum Entropy ◽  
Lie Groups ◽  
Lie Group ◽  
Data Analytics ◽  
Geometric Theory ◽  
Higher Order ◽  
Small Data ◽  
Algebra Structure ◽  
Fisher Metric

We introduce poly-symplectic extension of Souriau Lie groups thermodynamics based on higher-order model of statistical physics introduced by Ingarden. This extended model could be used for small data analytics and machine learning on Lie groups. Souriau geometric theory of heat is well adapted to describe density of probability (maximum entropy Gibbs density) of data living on groups or on homogeneous manifolds. For small data analytics (rarified gases, sparse statistical surveys, …), the density of maximum entropy should consider higher order moments constraints (Gibbs density is not only defined by first moment but fluctuations request 2nd order and higher moments) as introduced by Ingarden. We use a poly-sympletic model introduced by Christian Günther, replacing the symplectic form by a vector-valued form. The poly-symplectic approach generalizes the Noether theorem, the existence of moment mappings, the Lie algebra structure of the space of currents, the (non-)equivariant cohomology and the classification of G-homogeneous systems. The formalism is covariant, i.e., no special coordinates or coordinate systems on the parameter space are used to construct the Hamiltonian equations. We underline the contextures of these models, and the process to build these generic structures. We also introduce a more synthetic Koszul definition of Fisher Metric, based on the Souriau model, that we name Souriau-Fisher metric. This Lie groups thermodynamics is the bedrock for Lie group machine learning providing a full covariant maximum entropy Gibbs density based on representation theory (symplectic structure of coadjoint orbits for Souriau non-equivariant model associated to a class of co-homology).

scholarly journals Maximum Entropy Reconstruction Of Moment-Coded Images

1987 ◽  
Vol 26 (10) ◽  
Author(s):  
Nicolaos S. Tzannes ◽  
Peter A. Jonnard
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Reconstruction ◽  
Coded Images

Higher order auto‐spectra by maximum entropy method

Geophysics ◽  
1983 ◽  
Vol 48 (10) ◽  
pp. 1409-1410 ◽  
Author(s):  
Robert Owen Plaisted ◽  
Hugo Gustavo Peña
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Power Spectra ◽  
Higher Order ◽  
Linear Process ◽  
Entropy Method ◽  
Resolving Power ◽  
Energy Spectra ◽  
Nonlinear Interactions

Higher order auto‐spectra, in particular bispectra and perhaps trispectra, are being used increasingly for analyzing various nonlinear interactions in the ocean, e.g., Herring (1980) and McComas and Briscoe (1980). The resolution of these spectra, as with conventional energy spectra, is frequently limited because short data records must be used. The purpose of this note is to present a maximum entropy (MEM) representation for higher order auto‐spectra which has the advantage of the superior resolving power of the MEM technique under these circumstances. The derivation is a generalizaton of the power spectra derived for a linear process (Box and Jenkins, 1970). We derive an MEM representation for bispectra and show that this result can be generalized to auto‐spectra of any order.

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