Frames: a maximum entropy statistical estimate of the inverse problem

A maximum entropy statistical treatment of an inverse problem concerning frame theory is presented. The problem arises from the fact that a frame is an overcomplete set of vectors that defines a mapping with no unique inverse. Although any vector in the concomitant space can be expressed as a linear combination of frame elements, the coefficients of the expansion are not unique. Frame theory guarantees the existence of a set of coefficients which is “optimal” in a minimum norm sense. We show here that these coefficients are also “optimal” from a maximum entropy viewpoint.

Adaptive Approach for a Maximum Entropy Algorithm in Ecological Niche Modeling

This paper presents an Adaptive Maximum Entropy (AME) approach for modeling biological species. The Maximum Entropy algorithm (MaxEnt) is one of the most used methods in modeling biological species geographical distribution. The approach presented here is an alternative to the classical algorithm. Instead of using the same set features in the training, the AME approach tries to insert or to remove a single feature at each iteration. The aim is to reach the convergence faster without affect the performance of the generated models. The preliminary experiments were well performed. They showed an increasing on performance both in accuracy and in execution time. Comparisons with other algorithms are beyond the scope of this paper. Some important researches are proposed as future works.

Application of the maximum entropy method to the (2 + 1)D four-fermion model

We investigate spectral functions extracted using the maximum entropy method from correlators measured in lattice simulations of the (2+1)-dimensional four-fermion model. This model is particularly interesting because it has both a chirally broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are only resonances. In the broken phase we study the elementary fermion, pion, sigma, and massive pseudoscalar meson; our results confirm the Goldstone nature of the π and permit an estimate of the meson binding energy. We have, however, seen no signal of σ→ππ decay as the chiral limit is approached. In the symmetric phase we observe a resonance of nonzero width in qualitative agreement with analytic expectations; in addition the ultraviolet behavior of the spectral functions is consistent with the large nonperturbative anomalous dimension for fermion composite operators expected in this model.

The continuous wavelet transform as a maximum entropy solution of the corresponding inverse problem

The continuous wavelet transform is obtained as a maximumentropy solution of the corresponding inverse problem. It is well knownthat although a signal can be reconstructed from its wavelet transform,the expansion is not unique due to the redundancy of continuous wavelets.Hence, the inverse problem has no unique solution. If we want to recognizeone solution as "optimal", then an appropriate decision criterion hasto be adopted. We show here that the continuous wavelet transform is an"optimal" solution in a maximum entropy sense.

On the q=1/2 non-extensive maximum entropy distribution

A detailed mathematical analysis on the q = 1/2 non-extensive maximum entropydistribution of Tsallis' is undertaken. The analysis is based upon the splitting of such adistribution into two orthogonal components. One of the components corresponds to theminimum norm solution of the problem posed by the fulfillment of the a priori conditionson the given expectation values. The remaining component takes care of the normalizationconstraint and is the projection of a constant onto the Null space of the "expectation-values-transformation"

A non-extensive maximum entropy based regulations method for bad conditioned inverse problems

A regularization method based on the non-extensive maximum entropy principle is devised. Special emphasis is given to the q=1/2 case. We show that, when the residual principle is considered as constraint, the q=1/2 generalized distribution of Tsallis yields a regularized solution for bad-conditioned problems. The so devised regularized distribution is endowed with a component which corresponds to the well known regularized solution of Tikhonov (1977).

Maximum Entropy Discrimination

We present a general framework for discriminative estimation based on the maximum entropy principle and its extensions. All calculations involve distributions over structures and/or parameters rather than specific settings and reduce to relative entropy projections. This holds even when the data is not separable within the chosen parametric class, in the context of anomaly detection rather than classification, or when the labels in the training set are uncertain or incomplete. Support vector machines are naturally subsumed under this class and we provide several extensions. We are also able to estimate exactly and efficiently discriminative distributions over tree structures of class-conditional models within this framework. Preliminary experimental results are indicative of the potential in these techniques.

Vertical and horizontal processes in the global atmosphere and the maximum entropy production conjecture

The objective of this paper is to reconsider the Maximum Entropy Production conjecture (MEP) in the context of a very simple two-dimensional zonal-vertical climate model able to represent the total material entropy production due at the same time to both horizontal and vertical heat fluxes. MEP is applied first to a simple four-box model of climate which accounts for both horizontal and vertical material heat fluxes. It is shown that, under condition of fixed insolation, a MEP solution is found with reasonably realistic temperature and heat fluxes, thus generalising results from independent two-box horizontal or vertical models. It is also shown that the meridional and the vertical entropy production terms are independently involved in the maximisation and thus MEP can be applied to each subsystem with fixed boundary conditions. We then extend the four-box model by increasing its resolution, and compare it with GCM output. A MEP solution is found which is fairly realistic as far as the horizontal large scale organisation of the climate is concerned whereas the vertical structure looks to be unrealistic and presents seriously unstable features. This study suggest that the thermal meridional structure of the atmosphere is predicted fairly well by MEP once the insolation is given but the vertical structure of the atmosphere cannot be predicted satisfactorily by MEP unless constraints are imposed to represent the determination of longwave absorption by water vapour and clouds as a function of the state of the climate. Furthermore an order-of-magnitude estimate of contributions to the material entropy production due to horizontal and vertical processes within the climate system is provided by using two different methods. In both cases we found that approximately 40 mW m−2 K−1 of material entropy production is due to vertical heat transport and 5–7 mW m−2 K−1 to horizontal heat transport

Advanced mapping of environmental data: Geostatistics, Machine Learning and Bayesian Maximum Entropy

This book combines geostatistics and global mapping systems to present an up-to-the-minute study of environmental data. Featuring numerous case studies, the reference covers model dependent (geostatistics) and data driven (machine learning algorithms) analysis techniques such as risk mapping, conditional stochastic simulations, descriptions of spatial uncertainty and variability, artificial neural networks (ANN) for spatial data, Bayesian maximum entropy (BME), and more.

The second law of thermodynamics and the global climate system : A review of the maximum entropy production principle

The long-term mean properties of the global climate system and those of turbulent fluid systems are reviewed from a thermodynamic viewpoint. Two general expressions are derived for a rate of entropy production due to thermal and viscous dissipation (turbulent dissipation) in a fluid system. It is shown with these expressions that maximum entropy production in the Earth s climate system suggested by Paltridge, as well as maximum transport properties of heat or momentum in a turbulent system suggested by Malkus and Busse, correspond to a state in which the rate of entropy production due to the turbulent dissipation is at a maximum. Entropy production due to absorption of solar radiation in the climate system is found to be irrelevant to the maximized properties associated with turbulence. The hypothesis of maximum entropy production also seems to be applicable to the planetary atmospheres of Mars and Titan and perhaps to mantle convection. Lorenz s conjecture on maximum generation of available potential energy is shown to be akin to this hypothesis with a few minor approximations. A possible mechanism by which turbulent fluid systems adjust themselves to the states of maximum entropy production is presented as a selffeedback mechanism for the generation of available potential energy. These results tend to support the hypothesis of maximum entropy production that underlies a wide variety of nonlinear fluid systems, including our planet as well as other planets and stars

States of maximum entropy production in a onedimensional vertical model with convective adjustment

We investigate the hypothesis that the atmosphere is constrained to maximize its entropy production by using a one-dimensional (1-D) vertical model. We prescribe the lapse rate in the convective layer as that of the standard troposphere. The assumption that convection sustains a critical lapse rate was absent in previous studies, which focused on the vertical distribution of climatic variables, since such a convective adjustment reduces the degrees of freedom of the system and may prevent the application of the maximum entropy production (MEP) principle. This is not the case in the radiative–convective model (RCM) developed here, since we accept a discontinuity of temperatures at the surface similar to that adopted in many RCMs. For current conditions, the MEP state gives a difference between the ground temperature and the air temperature at the surface ≈10 K. In comparison, conventional RCMs obtain a discontinuity ≈2 K only. However, the surface boundary layer velocity in the MEP state appears reasonable (≈3 m s-¹). Moreover, although the convective flux at the surface in MEP states is almost uniform in optically thick atmospheres, it reaches a maximum value for an optical thickness similar to current conditions. This additional result may support the maximum convection hypothesis suggested by Paltridge (1978)

Maximum entropy, fractal dimension and lacunarity in quantification of cellular rejection in myocardial biopsy of patients submitted to heart transplantation

This paper presents a method for the quantification of cellular rejection in endomyocardial biopsies of patients submitted to heart transplant. The model is based on automatic multilevel thresholding, which employs histogram quantification techniques, histogram slope percentage analysis and the calculation of maximum entropy. The structures were quantified with the aid of the multi-scale fractal dimension and lacunarity for the identification of behavior patterns in myocardial cellular rejection in order to determine the most adequate treatment for each case.

Synthesis and crystal phase evaluation of hydroxylapatite using the rietveld-maximum entropy method

Bioceramic systems based on hydroxylapatite (HAP) are an important class of bioactive materials that may promote bone regeneration. The aim of this research was to evaluate how the stoichiometry of HAP influences its microstructural properties when diagnosed using the combined Rietveld method and Maximum entropy method (MEM). The Rietveld Method (RM) is recognizably a powerful tool used to obtain structural and microstructural information of polycrystalline samples analyzed by x-ray diffraction. Latterly have combined the RM with the maximum entropy method (MEM), with the goal of improve structural refinement results. The MEM provides high resolution maps of electron density and their analysis leave the accurate localization of atoms inside of unit cell. Like that, cycles Rietveld-MEM allow an excellent structural refinement In this work, a hydroxylapatite sample obtained by emulsion method had its structure refined using one cycle Rietveld-MEM with x-ray diffraction data. The indices obtained in initial refinement was Rwp = 7.50%, Re = 6.56%, S - 1.14% e RB = 1.03%. After MEM refinement and electron densities maps analysis to correction of atomics positions, the news indicators of Rietveld refinement quality was Rwp = 7.35%, Re = 6.56%, S = 1.12% and RB = 0.75%. The excellent result obtained to RB shows the efficiency of MEM as auxiliary in the refinement of structure of hydroxylapatite by RM.