Optimality of broken extremals

In this paper we analyse the optimality of broken Pontryagin extremal for an n-dimensional affine control system with a control parameter, taking values in a k- dimensional closed ball. We prove the optimality of broken normal extremals when n = 3 and the controllable vector fields form a contact distribution, and when the Lie algebra of the controllable fields is locally orthogonal to the singular locus and the drift does not belong to it. Moreover, if k = 2, we show the optimality of any broken extremal even abnormal when the controllable fields do not form a contact distribution in the point of singularity.Comment: arXiv admin note: text overlap with arXiv:1610.0675

Genome characteristics of primary carcinomas, local recurrences, carcinomatoses, and liver metastases from colorectal cancer patients

BACKGROUND: Colorectal cancer (CRC) is one of the most common causes of cancer-related deaths in the Western world, and despite the fact that metastases are usually the ultimate cause of deaths, the knowledge of the genetics of advanced stages of this disease is limited. In order to identify potential genetic abnormalities underlying the development of local and distant metastases in CRC patients, we have, by comparative genomic hybridization, compared the DNA copy number profiles of 10 primary carcinomas, 14 local recurrences, 7 peritoneal carcinomatoses, and 42 liver metastases from 61 CRC patients. RESULTS: The median number of aberrations among the primary carcinomas, local recurrences, carcinomatoses, and liver metastases was 10, 6, 13, and 14, respectively. Several genetic imbalances, such as gains of 7, 8q, 13q, and 20, and losses of 4q, 8p, 17p, and 18, were common in all groups. In contrast, gains of 5p and 12p were more common in the carcinomatoses than in other stages of the disease. With hierarchical cluster analysis, liver metastases could be divided into two main subgroups according to clusters of chromosome changes. CONCLUSIONS: Each stage of CRC progression is characterized by a particular genetic profile, and both carcinomatoses and liver metastases are more genetically complex than local recurrences and primary carcinomas. This is the first genome profiling of local recurrences and carcinomatoses, and gains of 5p and 12p seem to be particularly important for the spread of the CRC cells within the peritoneal cavity

Hypermethylated MAL gene – a silent marker of early colon tumorigenesis

Background Tumor-derived aberrantly methylated DNA might serve as diagnostic biomarkers for cancer, but so far, few such markers have been identified. The aim of the present study was to investigate the potential of the MAL (T-cell differentiation protein) gene as an early epigenetic diagnostic marker for colorectal tumors. Methods Using methylation-specific polymerase chain reaction (MSP) the promoter methylation status of MAL was analyzed in 218 samples, including normal mucosa (n = 44), colorectal adenomas (n = 63), carcinomas (n = 65), and various cancer cell lines (n = 46). Direct bisulphite sequencing was performed to confirm the MSP results. MAL gene expression was investigated with real time quantitative analyses before and after epigenetic drug treatment. Immunohistochemical analysis of MAL was done using normal colon mucosa samples (n = 5) and a tissue microarray with 292 colorectal tumors. Results Bisulphite sequencing revealed that the methylation was unequally distributed within the MAL promoter and by MSP analysis a region close to the transcription start point was shown to be hypermethylated in the majority of colorectal carcinomas (49/61, 80%) as well as in adenomas (45/63, 71%). In contrast, only a minority of the normal mucosa samples displayed hypermethylation (1/23, 4%). The hypermethylation of MAL was significantly associated with reduced or lost gene expression in in vitro models. Furthermore, removal of the methylation re-induced gene expression in colon cancer cell lines. Finally, MAL protein was expressed in epithelial cells of normal colon mucosa, but not in the malignant cells of the same type. Conclusion Promoter hypermethylation of MAL was present in the vast majority of benign and malignant colorectal tumors, and only rarely in normal mucosa, which makes it suitable as a diagnostic marker for early colorectal tumorigenesis

Identification of Highly Methylated Genes across Various Types of B-Cell Non-Hodgkin Lymphoma

<div><p>Epigenetic alterations of gene expression are important in the development of cancer. In this study, we identified genes which are epigenetically altered in major lymphoma types. We used DNA microarray technology to assess changes in gene expression after treatment of 11 lymphoma cell lines with epigenetic drugs. We identified 233 genes with upregulated expression in treated cell lines and with downregulated expression in B-cell lymphoma patient samples (n = 480) when compared to normal B cells (n = 5). The top 30 genes were further analyzed by methylation specific PCR (MSP) in 18 lymphoma cell lines. Seven of the genes were methylated in more than 70% of the cell lines and were further subjected to quantitative MSP in 37 B-cell lymphoma patient samples (diffuse large B-cell lymphoma (activated B-cell like and germinal center B-cell like subtypes), follicular lymphoma and Burkitt`s lymphoma) and normal B lymphocytes from 10 healthy donors. The promoters of <i>DSP</i>, <i>FZD8</i>, <i>KCNH2,</i> and <i>PPP1R14A</i> were methylated in 28%, 67%, 22%, and 78% of the 36 tumor samples, respectively, but not in control samples. Validation using a second series of healthy donor controls (n = 42; normal B cells, peripheral blood mononuclear cells, bone marrow, tonsils and follicular hyperplasia) and fresh-frozen lymphoma biopsies (n = 25), confirmed the results. The DNA methylation biomarker panel consisting of <i>DSP</i>, <i>FZD8</i>, <i>KCNH2,</i> and <i>PPP1R14A</i> was positive in 89% (54/61) of all lymphomas. Receiver operating characteristic analysis to determine the discriminative power between lymphoma and healthy control samples showed a c-statistic of 0.96, indicating a possible role for the biomarker panel in monitoring of lymphoma patients.</p></div