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

Novel potential causative genes in carotid paragangliomas

Abstract Background Carotid paragangliomas (CPGLs) are rare neuroendocrine tumors that arise from the paraganglion at the bifurcation of the carotid artery and are responsible for approximately 65% of all head and neck paragangliomas. CPGLs can occur sporadically or along with different hereditary tumor syndromes. Approximately 30 genes are known to be associated with CPGLs. However, the genetic basis behind the development of these tumors is not fully elucidated, and the molecular mechanisms underlying CPGL pathogenesis remain unclear. Methods Whole exome and transcriptome high-throughput sequencing of CPGLs was performed on an Illumina platform. Exome libraries were prepared using a Nextera Rapid Capture Exome Kit (Illumina) and were sequenced under 75 bp paired-end model. For cDNA library preparation, a TruSeq Stranded Total RNA Library Prep Kit with Ribo-Zero Gold (Illumina) was used; transcriptome sequencing was carried out with 100 bp paired-end read length. Obtained data were analyzed using xseq which estimates the influence of mutations on gene expression profiles allowing to identify potential causative genes. Results We identified a total of 16 candidate genes (MYH15, CSP1, MYH3, PTGES3L, CSGALNACT2, NMD3, IFI44, GMCL1, LSP1, PPFIBP2, RBL2, MAGED1, CNIH3, STRA6, SLC6A13, and ATM) whose variants potentially influence their expression (cis-effect). The strongest cis-effect of loss-of-function variants was found in MYH15, CSP1, and MYH3, and several likely pathogenic variants in these genes associated with CPGLs were predicted. Conclusions Using the xseq probabilistic model, three novel potential causative genes, namely MYH15, CSP1, and MYH3, were identified in carotid paragangliomas

Mutational load in carotid body tumor

Abstract Background Carotid body tumor (CBT) is a rare neoplasm arising from paraganglion located near the bifurcation of the carotid artery. There is great intra-tumor heterogeneity, and CBT development could be associated with both germline and somatic allelic variants. Studies on the molecular genetics of CBT are limited, and the molecular mechanisms of its pathogenesis are not fully understood. This work is focused on the estimation of mutational load (ML) in CBT. Methods Using the NextSeq 500 platform, we performed exome sequencing of tumors with matched lymph node tissues and peripheral blood obtained from six patients with CBT. To obtain reliable results in tumors with low ML, we developed and successfully applied a complex approach for the analysis of sequencing data. ML was evaluated as the number of somatic variants per megabase (Mb) of the target regions covered by the Illumina TruSeq Exome Library Prep Kit. Results The ML in CBT varied in the range of 0.09–0.28/Mb. Additionally, we identified several pathogenic/likely pathogenic somatic and germline allelic variants across six patients studied (including TP53 variants). Conclusions Using the developed approach, we estimated the ML in CBT, which is much lower than in common malignant tumors. Identified variants in known paraganglioma/pheochromocytoma-causative genes and novel genes could be associated with the pathogenesis of CBT. The obtained results expand our knowledge of the mutation process in CBT as well as the biology of tumor development

The CIMP-high phenotype is associated with energy metabolism alterations in colon adenocarcinoma

Abstract Background CpG island methylator phenotype (CIMP) is found in 15–20% of malignant colorectal tumors and is characterized by strong CpG hypermethylation over the genome. The molecular mechanisms of this phenomenon are not still fully understood. The development of CIMP is followed by global gene expression alterations and metabolic changes. In particular, CIMP-low colon adenocarcinoma (COAD), predominantly corresponded to consensus molecular subtype 3 (CMS3, “Metabolic”) subgroup according to COAD molecular classification, is associated with elevated expression of genes participating in metabolic pathways. Methods We performed bioinformatics analysis of RNA-Seq data from The Cancer Genome Atlas (TCGA) project for CIMP-high and non-CIMP COAD samples with DESeq2, clusterProfiler, and topGO R packages. Obtained results were validated on a set of fourteen COAD samples with matched morphologically normal tissues using quantitative PCR (qPCR). Results Upregulation of multiple genes involved in glycolysis and related processes (ENO2, PFKP, HK3, PKM, ENO1, HK2, PGAM1, GAPDH, ALDOA, GPI, TPI1, and HK1) was revealed in CIMP-high tumors compared to non-CIMP ones. Most remarkably, the expression of the PKLR gene, encoding for pyruvate kinase participating in gluconeogenesis, was decreased approximately 20-fold. Up to 8-fold decrease in the expression of OGDHL gene involved in tricarboxylic acid (TCA) cycle was observed in CIMP-high tumors. Using qPCR, we confirmed the increase (4-fold) in the ENO2 expression and decrease (2-fold) in the OGDHL mRNA level on a set of COAD samples. Conclusions We demonstrated the association between CIMP-high status and the energy metabolism changes at the transcriptomic level in colorectal adenocarcinoma against the background of immune pathway activation. Differential methylation of at least nine CpG sites in OGDHL promoter region as well as decreased OGDHL mRNA level can potentially serve as an additional biomarker of the CIMP-high status in COAD

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

Exome analysis of carotid body tumor

Abstract Background Carotid body tumor (CBT) is a form of head and neck paragangliomas (HNPGLs) arising at the bifurcation of carotid arteries. Paragangliomas are commonly associated with germline and somatic mutations involving at least one of more than thirty causative genes. However, the specific functionality of a number of these genes involved in the formation of paragangliomas has not yet been fully investigated. Methods Exome library preparation was carried out using Nextera® Rapid Capture Exome Kit (Illumina, USA). Sequencing was performed on NextSeq 500 System (Illumina). Results Exome analysis of 52 CBTs revealed potential driver mutations (PDMs) in 21 genes: ARNT, BAP1, BRAF, BRCA1, BRCA2, CDKN2A, CSDE1, FGFR3, IDH1, KIF1B, KMT2D, MEN1, RET, SDHA, SDHB, SDHC, SDHD, SETD2, TP53BP1, TP53BP2, and TP53I13. In many samples, more than one PDM was identified. There are also 41% of samples in which we did not identify any PDM; in these cases, the formation of CBT was probably caused by the cumulative effect of several not highly pathogenic mutations. Estimation of average mutation load demonstrated 6–8 mutations per megabase (Mb). Genes with the highest mutation rate were identified. Conclusions Exome analysis of 52 CBTs for the first time revealed the average mutation load for these tumors and also identified potential driver mutations as well as their frequencies and co-occurrence with the other PDMs

Additional file 1: Table S1. of HK3 overexpression associated with epithelial-mesenchymal transition in colorectal cancer

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Additional file 3: Table S3. of HK3 overexpression associated with epithelial-mesenchymal transition in colorectal cancer

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