6,290 research outputs found
Risk Minimization, Regret Minimization and Progressive Hedging Algorithms
This paper begins with a study on the dual representations of risk and regret
measures and their impact on modeling multistage decision making under
uncertainty. A relationship between risk envelopes and regret envelopes is
established by using the Lagrangian duality theory. Such a relationship opens a
door to a decomposition scheme, called progressive hedging, for solving
multistage risk minimization and regret minimization problems. In particular,
the classical progressive hedging algorithm is modified in order to handle a
new class of linkage constraints that arises from reformulations and other
applications of risk and regret minimization problems. Numerical results are
provided to show the efficiency of the progressive hedging algorithms.Comment: 21 pages, 2 figure
A Novel Euler's Elastica based Segmentation Approach for Noisy Images via using the Progressive Hedging Algorithm
Euler's Elastica based unsupervised segmentation models have strong
capability of completing the missing boundaries for existing objects in a clean
image, but they are not working well for noisy images. This paper aims to
establish a Euler's Elastica based approach that properly deals with random
noises to improve the segmentation performance for noisy images. We solve the
corresponding optimization problem via using the progressive hedging algorithm
(PHA) with a step length suggested by the alternating direction method of
multipliers (ADMM). Technically, all the simplified convex versions of the
subproblems derived from the major framework of PHA can be obtained by using
the curvature weighted approach and the convex relaxation method. Then an
alternating optimization strategy is applied with the merits of using some
powerful accelerating techniques including the fast Fourier transform (FFT) and
generalized soft threshold formulas. Extensive experiments have been conducted
on both synthetic and real images, which validated some significant gains of
the proposed segmentation models and demonstrated the advantages of the
developed algorithm
Statistical Properties of Multiple Optical Emission Components in Gamma-Ray Bursts and Implications
Well-sampled optical lightcurves of 146 gamma-ray bursts (GRBs) are complied
from the literature. Multiple optical emission components are extracted with
power-law function fits to these lightcurves. We present a systematical
analysis for statistical properties and their relations to prompt gamma-ray
emission and X-ray afterglow for each component. We show that peak luminosity
in the prompt and late flares are correlated and the evolution of the peak
luminosity may signal the evolution of the accretion rate. No tight correlation
between the shallow decay phase/plateau and prompt gamma-ray emission is found.
Assuming that they are due to a long-lasting wind injected by a compact object,
we show that the injected behavior favors the scenarios of a long-lasting wind
after the main burst episode. The peak luminosity of the afterglow onset is
tightly correlated with Eiso, and it is dimmer as peaking later. Assuming that
the onset bump is due to the fireball deceleration by the external medium, we
examine the Gamma_0-Eiso relation and find that it is confirmed with the
current sample. Optical re-brightening is observed in 30 GRBs in our sample. It
shares the same relation between the width and the peak time as found in the
onset bump, but no clear correlation between the peak luminosity and Eiso as
observed in the onset bumps is found. Although its peak luminosity also decays
with time, the slope is much shallower than that of the onset peak. We get L
t^{-1}_{p}$, being consistent with off-axis observations to an expanding
external fireball in a wind-like circum medium. The late re-brightening may
signal another jet component. Mixing of different emission components may be
the reason for the observed chromatic breaks in different energy bands.Comment: 10 pages, 5 figures, to be published by IJMPD (Proceedings of "The
Third Galileo - Xu Guangqi meeting", Beijing, October 11-15, 2011
Research on the Application of Blockchain in SMEs Credit Risk
The credit of an enterprise is related to its own development. This paper mainly discusses the relationship between the credit risk of small and medium enterprises (SMEs) and the application degree of blockchain. 64 listed companies with block chain technology as the core theme are selected to analyze their comprehensive financial data. Factor analysis is used to quantitatively evaluate the application degree of blockchain in SMEs, and then the Logistic model is used to evaluate the credit risk of SMEs. Finally, combining the application degree of blockchain in small and medium-sized enterprises and the credit risk assessment of these two groups of data. It confirms the conclusion that the higher the degree of blockchain application, the closer the supply chain finance relationship, and the better the credit status
- …