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This exposition is an introduction to the main ideas of Kolmogorov complexity and surveys the wealth of useful applications of this elegant notion. We distinguish: I) Application of the fact that some strings are compressible. This includes a strong version of Godel' s incompleteness theorem. II) Lower bound arguments that rest on application of the fact that certain strings cannot be compressed at all. Applications range from Turing machines to electronic chips. III) Probability Theory and a priori probability. Applications range from foundational issues to the theory of learning and inductive inference in Artificial Intelligence. IV) Resource-bounded Kolmogorov complexity. Applications range from NP-completeness and the P versus NP question to cryptography.

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Recent advances in oncotherapies and immunotherapies have markedly expanded melanoma treatment options. Nevertheless, the benefits of these treatments are often short-lived due to the development of resistance. We have previously established the onco-protective effect of the K63-ubiquitin (K63-Ub) deubiquitinating enzyme CYLD. In this study, we studied the role of the K63-Ub ubiquitin enzyme UBE2N and its functionally essential partners, UBE2V1 and UBE2V2, in melanoma growth and progression. We found that UBE2N and UBE2V2 were expressed and activated at elevated levels in malignant melanoma cell lines compared to normal melanocytes. Inhibition of UBE2N either pharmacologically or genetically via CRIPSR-mediated gene deletion and shRNA-mediated gene-silencing markedly decreased melanoma cell growth and sensitized cells to decarbonize and radiation treatments in vitro. In addition, we found that knockdown of UBE2V2 but not UBE2V1 significantly increased melanoma cell apoptosis and inhibited cell growth and migration. Surprisingly, gene silencing of UBE2N and UBE2V2 increased activation of the AKT and JNK pathways, and sensitized A375 melanoma cells to AKT and JNK inhibitors. In agreement with the in vitro data, subcutaneous tumor growth analysis showed that A375 melanoma cells with UBE2N and UBE2V2 knockdowns displayed significantly reduced tumor growth compared with cells with UBE2V1 knockdown or non-silencing control. Moreover, tumors with UBE2N or UBE2V2 knockdown expressed markedly elevated levels of E-cadherin and cleaved caspase 3. Further examination of the lung tissues revealed that UBE2N or UBE2V2 knockdown abolished pulmonary metastasis. These results indicate that UBE2N and UBE2V2 are crucial for melanoma growth, progression, and survival. We are currently using proteomic approaches to understand the molecular mechanisms mediating these effects.

women(190.60AE63.12 VS 205.40AE41.07), although the result was not statistically different. Besides, women with PCOS tended to have lower alpha and beta diversity in gut microbiota. Spearman correlation analysis showed that metabolic disorders were associated with changes in gut microbiota: 0h insulin, 2h insulin, and HOMA-IR values were negatively correlated with species richness (r¼-0.369,-.0425,-0.356, p<0.05). The content of genus Desulfovibrio in patients with PCOS was positively correlated with 0h glucose, 0h insulin, HOMA-IR, LDL (r¼0.485, 0.604, 0.640, 0.472, p<0.05). Genus Streptococcu was positively correlated with BMI, 1h blood glucose, 2h blood glucose, 2h insulin, HOMA-IR, cholesterol (r¼0.492, 0.485, 0.548, 0.477, 0.458, 0.516, p<0.05). CONCLUSIONS: Our study demonstrated that women with PCOS had lower biodiversity in gut microbiota, of which were closely associated with insulin resistance and abnormal lipid metabolism. Our findings suggest that changes in the gut microbiome may influence the development and pathology of PCOS and its metabolic disorders as well.