Statistics of Natural Images and Models

Large calibrated datasets of `random' natural images have recently become available. These make possible precise and intensive statistical studies of the local nature of images. We report results ranging from the simplest single pixel intensity to joint distribution of 3 Haar wavelet responses. Some of these statistics shed light on old issues such as the near scale-invariance of image statistics and some are entirely new. We fit mathematical models to some of the statistics and explain others in terms of local image featuresMathematic

Statistics of Range Images

The statistics of range images from natural environments is a largely unexplored field of research. It closely relates to the statistical modeling of the scene geometry in natural environments, and the modeling of optical natural images. We have used a 3D laser range-finder to collect range images from mixed forest scenes. The images are here analyzed with respect to different statisticsMathematic

Occlusion Models for Natural Images: A Statistical Study of a Scale-Invariant Dead Leaves Model

We develop a scale-invariant version of Matheron's “dead leaves model” for the statistics of natural images. The model takes occlusions into account and resembles the image formation process by randomly adding independent elementary shapes, such as disks, in layers. We compare the empirical statistics of two large databases of natural images with the statistics of the occlusion model, and find an excellent qualitative, and good quantitative agreement. At this point, this is the only image model which comes close to duplicating the simplest, elementary statistics of natural images—such as, the scale invariance property of marginal distributions of filter responses, the full co-occurrence statistics of two pixels, and the joint statistics of pairs of Haar wavelet responses.Mathematic

Dynamics and control of active sites in hierarchically nanostructured cobalt phosphide/chalcogenide-based electrocatalysts for water splitting

The rational design of efficient electrocatalysts for industrial water splitting is essential to generate sustainable hydrogen fuel. However, a comprehensive understanding of the complex catalytic mechanisms under harsh reaction conditions remains a major challenge. We apply a self-templated strategy to introduce hierarchically nanostructured “all-surface” Fe-doped cobalt phosphide nanoboxes (Co@CoFe–P NBs) as alternative electrocatalysts for industrial-scale applications. Operando Raman spectroscopy and X-ray absorption spectroscopy (XAS) experiments were carried out to track the dynamics of their structural reconstruction and the real catalytically active intermediates during water splitting. Our operando analyses reveal that partial Fe substitution in cobalt phosphides promotes a structural reconstruction into P–Co–O–Fe–P configurations with low-valence metal centers (M0/M+) during the hydrogen evolution reaction (HER). Results from density functional theory (DFT) demonstrate that these in situ reconstructed configurations significantly enhance the HER performance by lowering the energy barrier for water dissociation and by facilitating the adsorption/desorption of HER intermediates (H*). The competitive activity in the oxygen evolution reaction (OER) arises from the transformation of the reconstructed P–Co–O–Fe–P configurations into oxygen-bridged, high-valence CoIV–O–FeIV moieties as true active intermediates. In sharp contrast, the formation of such CoIII/IV–O–FeIII/IV moieties in Co–FeOOH is hindered under the same conditions, which outlines the key advantages of phosphide-based electrocatalysts. Ex situ studies of the as-synthesized reference cobalt sulfides (Co–S), Fe doped cobalt selenides (Co@CoFe–Se), and Fe doped cobalt tellurides (Co@CoFe–Te) further corroborate the observed structural transformations. These insights are vital to systematically exploit the intrinsic catalytic mechanisms of non-oxide, low-cost, and robust overall water splitting electrocatalysts for future energy conversion and storage

Sobol′’s sensitivity analysis for a distributed hydrological model of Yichun River Basin, China

Copyright © 2013 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Hydrology. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Hydrology Vol. 480 (2013), DOI: 10.1016/j.jhydrol.2012.12.005This paper aims to provide an enhanced understanding of the parameter sensitivities of the Soil and Water Assessment Tool (SWAT) using a variance-based global sensitivity analysis, i.e., Sobol′’s method. The Yichun River Basin, China, is used as a case study, and the sensitivity of the SWAT parameters is analyzed under typical dry, normal and wet years, respectively. To reduce the number of model parameters, some spatial model parameters are grouped in terms of data availability and multipliers are then applied to parameter groups, reflecting spatial variation in the distributed SWAT model. The SWAT model performance is represented using two statistical metrics – Root Mean Square Error (RMSE) and Nash–Sutcliffe Efficiency (NSE) and two hydrological metrics – RunOff Coefficient Error (ROCE) and Slope of the Flow Duration Curve Error (SFDCE). The analysis reveals the individual effects of each parameter and its interactions with other parameters. Parameter interactions contribute to a significant portion of the variation in all metrics considered under moderate and wet years. In particular, the variation in the two hydrological metrics is dominated by the interactions, illustrating the necessity of choosing a global sensitivity analysis method that is able to consider interactions in the SWAT model identification process. In the dry year, however, the individual effects control the variation in the other three metrics except SFDCE. Further, the two statistical metrics fail to identify the SWAT parameters that control the flashiness (i.e., variability of mid-flows) and overall water balance. Overall, the results obtained from the global sensitivity analysis provide an in-depth understanding of the underlying hydrological processes under different metrics and climatic conditions in the case study catchment.National Natural Science Foundation of Chin

ESTIMATING UNIVARIATE DISTRIBUTIONS VIA RELATIVE ENTROPY MINIMIZATION: CASE STUDIES ON FINANCIAL AND ECONOMIC DATA

We use minimum relative entropy (MRE) methods to estimate univariate probability density functions for a varied set of financial and economic variables, including S&P500 index returns, individual stock returns, power price returns and a number of housing-related economic variables. Some variables have fat tail distributions, others have finite support. Some variables have point masses in their distributions and others have multimodal distributions. We indicate specifically how the MRE approach can be tailored to the stylized facts of the variables that we consider and benchmark the MRE approach against alternative approaches. We find, for a number of variables, that the MRE approach outperforms the benchmark methods.Kullback-Leibler relative entropy, maximum likelihood, probability distribution, fat-tailed, point mass, stock return distribution, stock index return distribution, financial data, economic data, California Housing Data

Statistics of range images

The statistics of range images from natural environments is a largely unexplored eldofresearch. It closely relates to the statistical modeling of the scene geometry in natural environments, and the modeling of optical natural images. We have use d a 3D laser range- nder to collect range images from mixed forest scenes. The images are hereanalyzed with respect to di erent statistics.