A quick guide to defect orbifolds

We provide a lightning review of the construction of (generalised) orbifolds [arXiv:0909.5013, arXiv:1210.6363] of two-dimensional quantum field theories in terms of topological defects, along the lines of [arXiv:1307.3141]. This universal perspective has many applications, some of which we sketch in the examples of 2d Yang-Mills theory, Landau-Ginzburg models, and rational CFT.Comment: 11 pages, contribution to the String-Math 2013 proceeding

An Explorative Analysis of ABCG2/TOP-1 mRNA Expression as a Biomarker Test for FOLFIRI Treatment in Stage III Colon Cancer Patients: Results from Retrospective Analyses of the PETACC-3 Trial

Biomarker-guided treatment for patients with colon cancer is needed. We tested ABCG2 and topoisomerase 1 (TOP1) mRNA expression as predictive biomarkers for irinotecan benefit in the PETACC-3 patient cohort. The present study included 580 patients with mRNA expression data from Stage III colon cancer samples from the PETACC-3 study, which randomized the patients to Fluorouracil/leucovorin (5FUL) +/- irinotecan. The primary end-points were recurrence free survival (RFS) and overall survival (OS). Patients were divided into one group with high ABCG2 expression (above median) and low TOP-1 expression (below 75 percentile) ("resistant") (n = 216) and another group including all other combinations of these two genes ("sensitive") (n = 364). The rationale for the cut-offs were based on the distribution of expression levels in the PETACC-3 Stage II set of patients, where ABCG2 was unimodal and TOP1 was bimodal with a high expression level mode in the top quarter of the patients. Cox proportional hazards regression was used to estimate the hazard ratios and the association between variables and end-points and log-rank tests to assess the statistical significance of differences in survival between groups. Kaplan-Meier estimates of the survival functions were used for visualization and estimation of survival rates at specific time points. Significant differences were found for both RFS (Hazard ratio (HR): 0.63 (0.44-0.92); p = 0.016) and OS (HR: 0.60 (0.39-0.93); p = 0.02) between the two biomarker groups when the patients received FOLFIRI (5FUL+irinotecan). Considering only the Microsatellite Stable (MSS) and Microsatellite Instability-Low (MSI-L) patients (n = 470), the differences were even more pronounced. In contrast, no significant differences were observed between the groups when patients received 5FUL alone. This study shows that the combination of ABCG2 and TOP1 gene expression significantly divided the Stage III colon cancer patients into two groups regarding benefit from adjuvant treatment with FOLFIRI but not 5FUL

Triangle-generation in topological D-brane categories

Tachyon condensation in topological Landau-Ginzburg models can generally be studied using methods of commutative algebra and properties of triangulated categories. The efficiency of this approach is demonstrated by explicitly proving that every D-brane system in all minimal models of type ADE can be generated from only one or two fundamental branes.Comment: 34 page

Rigidity and defect actions in Landau-Ginzburg models

Studying two-dimensional field theories in the presence of defect lines naturally gives rise to monoidal categories: their objects are the different (topological) defect conditions, their morphisms are junction fields, and their tensor product describes the fusion of defects. These categories should be equipped with a duality operation corresponding to reversing the orientation of the defect line, providing a rigid and pivotal structure. We make this structure explicit in topological Landau-Ginzburg models with potential x^d, where defects are described by matrix factorisations of x^d-y^d. The duality allows to compute an action of defects on bulk fields, which we compare to the corresponding N=2 conformal field theories. We find that the two actions differ by phases.Comment: 53 pages; v2: clarified exposition of pivotal structures, corrected proof of theorem 2.13, added remark 3.9; version to appear in CM

On the monoidal structure of matrix bi-factorisations

We investigate tensor products of matrix factorisations. This is most naturally done by formulating matrix factorisations in terms of bimodules instead of modules. If the underlying ring is C[x_1,...,x_N] we show that bimodule matrix factorisations form a monoidal category. This monoidal category has a physical interpretation in terms of defect lines in a two-dimensional Landau-Ginzburg model. There is a dual description via conformal field theory, which in the special case of W=x^d is an N=2 minimal model, and which also gives rise to a monoidal category describing defect lines. We carry out a comparison of these two categories in certain subsectors by explicitly computing 6j-symbols.Comment: 43 pages; v2: corrected a mistake in sec. 1 and app. A.1, the results are unaffected; v3: minor change

The potential role of Alu Y in the development of resistance to SN38 (Irinotecan) or oxaliplatin in colorectal cancer

BACKGROUND: Irinotecan (SN38) and oxaliplatin are chemotherapeutic agents used in the treatment of colorectal cancer. However, the frequent development of resistance to these drugs represents a considerable challenge in the clinic. Alus as retrotransposons comprise 11% of the human genome. Genomic toxicity induced by carcinogens or drugs can reactivate Alus by altering DNA methylation. Whether or not reactivation of Alus occurs in SN38 and oxaliplatin resistance remains unknown. RESULTS: We applied reduced representation bisulfite sequencing (RRBS) to investigate the DNA methylome in SN38 or oxaliplatin resistant colorectal cancer cell line models. Moreover, we extended the RRBS analysis to tumor tissue from 14 patients with colorectal cancer who either did or did not benefit from capecitabine + oxaliplatin treatment. For the clinical samples, we applied a concept of ‘DNA methylation entropy’ to estimate the diversity of DNA methylation states of the identified resistance phenotype-associated methylation loci observed in the cell line models. We identified different loci being characteristic for the different resistant cell lines. Interestingly, 53% of the identified loci were Alu sequences- especially the Alu Y subfamily. Furthermore, we identified an enrichment of Alu Y sequences that likely results from increased integration of new copies of Alu Y sequence in the drug-resistant cell lines. In the clinical samples, SOX1 and other SOX gene family members were shown to display variable DNA methylation states in their gene regions. The Alu Y sequences showed remarkable variation in DNA methylation states across the clinical samples. CONCLUSION: Our findings imply a crucial role of Alu Y in colorectal cancer drug resistance. Our study underscores the complexity of colorectal cancer aggravated by mobility of Alu elements and stresses the importance of personalized strategies, using a systematic and dynamic view, for effective cancer therapy. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12864-015-1552-y) contains supplementary material, which is available to authorized users

Topoisomerase I copy number alterations as biomarker for irinotecan efficacy in metastatic colorectal cancer

BACKGROUND: No biomarker exists to guide the optimal choice of chemotherapy for patients with metastatic colorectal cancer. We examined the copy numbers (CN) of topoisomerase I (TOP1) as well as the ratios of TOP1/CEN-20 and TOP1/CEN-2 as biomarkers for irinotecan efficacy in patients with metastatic colorectal cancer. METHODS: From a national cohort, we identified 163 patients treated every third week with irinotecan 350 mg/m(2) as second-line therapy. Among these 108 were eligible for analyses and thus entered the study. Primary tumors samples were collected and tissue microarray (TMA) blocks were produced. FISH analysis was performed using two probe-mixes: TOP1/CEN-20 and TOP1/CEN-2. Only samples harboring all three signals (TOP1, CEN-20 and CEN-2) using FISH were included in the analyses. RESULTS: In the TOP1/CEN-20 probe-mix the median TOP1- and CEN-20 CN were 4.46 (range: 1.5–9.5) and 2.00 (range: 0.55–4.55), respectively. The median TOP1- and CEN-2 CN in the TOP1/CEN-2 probe-mix, were 4.57 (range: 1.82–10.43) and 1.98 (range: 1.22–6.14), respectively. The median TOP1/CEN-20 ratio and TOP1/CEN-2 ratio were 1.25 (range: 0.92–2.90) and 2.05 (range: 1.00–6.00), respectively. None of the markers TOP1 CN, TOP1/CEN-20-ratio or TOP1/CEN-2-ratio were associated with progression free survival, overall survival or baseline characteristics. Yet, we observed a borderline association for a stepwise increase of the TOP1 CN in relation to objective response as hazard ratio were 1.35 (95% CI 0.96–1.90; p = 0.081). CONCLUSIONS: We verified a borderline significant association between increasing TOP1 CN and objective response as previously reported. Applying the probes representing CEN-20 and CEN-2, in order to investigate the ratios of TOP1/CEN-20 and TOP1/CEN-2 provided no further information in search of a biomarker driven patient stratification. Other biomarkers to be paired with TOP1 CN are therefore highly warranted