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

Contagion on complex networks with persuasion

The threshold model has been widely adopted as a classic model for studying contagion processes on social networks. We consider asymmetric individual interactions in social networks and introduce a persuasion mechanism into the threshold model. Specifically, we study a combination of adoption and persuasion in cascading processes on complex networks. It is found that with the introduction of the persuasion mechanism, the system may become more vulnerable to global cascades, and the effects of persuasion tend to be more significant in heterogeneous networks than those in homogeneous networks: a comparison between heterogeneous and homogeneous networks shows that under weak persuasion, heterogeneous networks tend to be more robust against random shocks than homogeneous networks; whereas under strong persuasion, homogeneous networks are more stable. Finally, we study the effects of adoption and persuasion threshold heterogeneity on systemic stability. Though both heterogeneities give rise to global cascades, the adoption heterogeneity has an overwhelmingly stronger impact than the persuasion heterogeneity when the network connectivity is sufficiently dense.Comment: 12 pages, 7 figure

SIRT3 Protects Rotenone-induced Injury in SH-SY5Y Cells by Promoting Autophagy through the LKB1-AMPK-mTOR Pathway.

SIRT3 is a class III histone deacetylase that modulates energy metabolism, genomic stability and stress resistance. It has been implicated as a potential therapeutic target in a variety of neurodegenerative diseases, including Parkinson's disease (PD). Our previous study demonstrates that SIRT3 had a neuroprotective effect on a rotenone-induced PD cell model, however, the exact mechanism is unknown. In this study, we investigated the underlying mechanism. We established a SIRT3 stable overexpression cell line using lentivirus infection in SH-SY5Y cells. Then, a PD cell model was established using rotenone. Our data demonstrate that overexpression of SIRT3 increased the level of the autophagy markers LC3 II and Beclin 1. After addition of the autophagy inhibitor 3-MA, the protective effect of SIRT3 diminished: the cell viability decreased, while the apoptosis rate increased; α-synuclein accumulation enhanced; ROS production increased; antioxidants levels, including SOD and GSH, decreased; and MMP collapsed. These results reveal that SIRT3 has neuroprotective effects on a PD cell model by up-regulating autophagy. Furthermore, SIRT3 overexpression also promoted LKB1 phosphorylation, followed by activation of AMPK and decreased phosphorylation of mTOR. These results suggest that the LKB1-AMPK-mTOR pathway has a role in induction of autophagy. Together, our findings indicate a novel mechanism by which SIRT3 protects a rotenone-induced PD cell model through the regulation of autophagy, which, in part, is mediated by activation of the LKB1-AMPK-mTOR pathway