A Convex Model for Edge-Histogram Specification with Applications to Edge-preserving Smoothing

The goal of edge-histogram specification is to find an image whose edge image has a histogram that matches a given edge-histogram as much as possible. Mignotte has proposed a non-convex model for the problem [M. Mignotte. An energy-based model for the image edge-histogram specification problem. IEEE Transactions on Image Processing, 21(1):379--386, 2012]. In his work, edge magnitudes of an input image are first modified by histogram specification to match the given edge-histogram. Then, a non-convex model is minimized to find an output image whose edge-histogram matches the modified edge-histogram. The non-convexity of the model hinders the computations and the inclusion of useful constraints such as the dynamic range constraint. In this paper, instead of considering edge magnitudes, we directly consider the image gradients and propose a convex model based on them. Furthermore, we include additional constraints in our model based on different applications. The convexity of our model allows us to compute the output image efficiently using either Alternating Direction Method of Multipliers or Fast Iterative Shrinkage-Thresholding Algorithm. We consider several applications in edge-preserving smoothing including image abstraction, edge extraction, details exaggeration, and documents scan-through removal. Numerical results are given to illustrate that our method successfully produces decent results efficiently

Integrated Solutions Development Capital Solutions Interim Report Volume I: Report

This report analyzes the water quality, flood, erosion, and integrated scores of multiple Austin watersheds, including Waller Creek.Waller Creek Working Grou

Prospect and Markowitz Stochastic Dominance

Levy and Levy (2002, 2004) develop the Prospect and Markowitz stochastic dominance theory with S-shaped and reverse S-shaped utility functions for investors. In this paper, we extend Levy and Levy's Prospect Stochastic Dominance theory (PSD) and Markowitz Stochastic Dominance theory (MSD) to the first three orders and link the corresponding S-shaped and reverse S-shaped utility functions to the first three orders. We also provide experiments to illustrate each case of the MSD and PSD to the first three orders and demonstrate that the higher order MSD and PSD cannot be replaced by the lower order MSD and PSD. Prospect theory has been regarded as a challenge to the expected utility paradigm. Levy and Levy (2002) prove that the second order PSD and MSD satisfy the expected utility paradigm. In our paper we take Levy and Levy's results one step further by showing that both PSD and MSD of any order are consistent with the expected utility paradigm. Furthermore, we formulate some other properties for the PSD and MSD including the hierarchy that exists in both PSD and MSD relationships; arbitrage opportunities that exist in the first orders of both PSD and MSD; and that for any two prospects under certain conditions, their third order MSD preference will be ???the opposite??? of or ???the same??? as their counterpart third order PSD preference. By extending Levy and Levy's work, we provide investors with more tools for empirical analysis, with which they can identify the first order PSD and MSD prospects and discern arbitrage opportunities that could increase his/her utility as well as wealth and set up a zero dollar portfolio to make huge profit. Our tools also enable investors to identify the third order PSD and MSD prospects and make better choices.Prospect stochastic dominance, Markowitz stochastic dominance, risk seeking, risk averse, S-shaped utility function, reverse S-shaped utility function

On the Estimation of Cost of Capital and its Reliability

Gordon and Shapiro (1956) first equated the price of a share with the present value of future dividends and derived the well-known relationship. Since then, there have been many improvements on the theory. For example, Thompson (1985, 1987) combined the "dividend yield plus growth" method with Box-Jenkins time series analysis of past dividend experience to estimate the cost of capital and its "reliability" for individual firms. Thompson and Wong (1991, 1996) proved the existence and uniqueness of the cost of capital and provided formula to estimate both the cost of capital and its reliability. However, their approaches cannot be used if the "reliability" does not exist or if there are multiple solutions for the "reliability". In this paper, we extend their theory by proving the existence and uniqueness of this reliability. In addition, we propose the estimators for the reliability and prove that the estimators converge to a true parameter. The estimation approach is further simplified, hence rendering computation easier. In addition, the properties of the cost of capital and its reliability will be analyzed with illustrations of several commonly used Box-Jenkins models.

An RBF scheme for option pricing in exponential Levy models

We use Radial Basis Function (RBF) interpolation to price options in exponential Lévy models by numerically solving the fundamental pricing PIDE (Partial integro-differential equations). Our RBF scheme can handle arbitrary singularities of the Lévy measure in 0 without introducing further approximations, making it simpler to implement than competing methods. In numerical experiments using processes from the CGMY-KoBoL class, the scheme is found to be second order convergent in the number of interpolation points, including for processes of unbounded variation