On the Efficient Solution of Variational Inequalities; Complexity and Computational Efficiency

In this paper we combine ideas from cutting plane and interior point methods in order to solve variational inequality problems efficiently. In particular, we introduce a general framework that incorporates nonlinear as well as linear "smarter" cuts. These cuts utilize second order information on the problem through the use of a gap function. We establish convergence as well as complexity results for this framework. Moreover, in order to devise more practical methods, we consider an affine scaling method as it applies to symmetric, monotone variationalinequality problems and demonstrate its convergence. Finally, in order to further improve the computational efficiency of the methods in this paper, we combine the cutting plane approach with the affine scaling approach

Essays on variational inequalities and competitive supply chain models

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2004.Includes bibliographical references (p. 103-107).In the first part of the thesis we combine ideas from cutting plane and interior point methods to solve variational inequality problems efficiently. In particular, we introduce "smarter" cuts into two general methods for solving these problems. These cuts utilize second order information on the problem through the use of a gap function. We establish convergence results for both methods, as well as complexity results for one of the methods. Finally, we compare the performance of an approach that combines affine scaling and cutting plane methods with other methods for solving variational inequalities. The second part of the thesis considers a supply chain setting where several capacitated suppliers compete for orders from a single retailer in a multi-period environment. At each period the retailer places orders to the suppliers in response to the prices and capacities they announce. Our model allows the retailer to carry inventory. Furthermore, suppliers can expand their capacity at an additional cost; the retailer faces exogenous, price-dependent, stochastic demand. We analyze discrete as well as continuous time versions of the model: (i) we illustrate the existence of equilibrium policies; (ii) we characterize the structure of these policies; (iii) we consider coordination mechanisms; and (iv) we present some computational results. We also consider a modified model that uses option contracts and finally present some extensions.by Marina Zaretsky.Ph.D

HK3 overexpression associated with epithelial-mesenchymal transition in colorectal cancer

Abstract Background Colorectal cancer (CRC) is a common cancer worldwide. The main cause of death in CRC includes tumor progression and metastasis. At molecular level, these processes may be triggered by epithelial-mesenchymal transition (EMT) and necessitates specific alterations in cell metabolism. Although several EMT-related metabolic changes have been described in CRC, the mechanism is still poorly understood. Results Using CrossHub software, we analyzed RNA-Seq expression profile data of CRC derived from The Cancer Genome Atlas (TCGA) project. Correlation analysis between the change in the expression of genes involved in glycolysis and EMT was performed. We obtained the set of genes with significant correlation coefficients, which included 21 EMT-related genes and a single glycolytic gene, HK3. The mRNA level of these genes was measured in 78 paired colorectal cancer samples by quantitative polymerase chain reaction (qPCR). Upregulation of HK3 and deregulation of 11 genes (COL1A1, TWIST1, NFATC1, GLIPR2, SFPR1, FLNA, GREM1, SFRP2, ZEB2, SPP1, and RARRES1) involved in EMT were found. The results of correlation study showed that the expression of HK3 demonstrated a strong correlation with 7 of the 21 examined genes (ZEB2, GREM1, TGFB3, TGFB1, SNAI2, TWIST1, and COL1A1) in CRC. Conclusions Upregulation of HK3 is associated with EMT in CRC and may be a crucial metabolic adaptation for rapid proliferation, survival, and metastases of CRC cells

Genomewide Clonal Analysis of Lethal Mutations in the Drosophila melanogaster Eye: Comparison of the X Chromosome and Autosomes

Using a large consortium of undergraduate students in an organized program at the University of California, Los Angeles (UCLA), we have undertaken a functional genomic screen in the Drosophila eye. In addition to the educational value of discovery-based learning, this article presents the first comprehensive genomewide analysis of essential genes involved in eye development. The data reveal the surprising result that the X chromosome has almost twice the frequency of essential genes involved in eye development as that found on the autosomes