Second order reductions of the WDVV Equations related to classical Lie algebras

We construct second order reductions of the generalized Witten-Dijkgraaf-Verlinde-Verlinde system based on simple Lie algebras. We discuss to what extent some of the symmetries of the WDVV system are preserved by the reduction.Comment: 6 pages, 1 tabl

Experiments with the WDVV equations for the gluino-condensate prepotential: the cubic (two-cut) case

We demonstrate by explicit calculation that the first two terms in the CIV-DV prepotential for the two-cut case satisfy the generalized WDVV equations, just as in all other known examples of hyperelliptic Seiberg-Witten models. The WDVV equations are non-trivial in this situation, provided the set of moduli is extended as compared to the Dijkgraaf-Vafa suggestion and includes also moduli, associated with the positions of the cuts (not only with their lengths). Expression for the extra modulus dictated by WDVV equation, however, appears different from a naive expectation implied by the Whitham theory. Moreover, for every value of the "quantum-deformation parameter" 1/g_3, we actually find an entire one-parameter family of solutions to the WDVV equations, of which the conventional prepotential is just a single point.Comment: 10 pages, Late

On Associativity Equations in Dispersionless Integrable Hierarchies

We discuss the origin of the associativity (WDVV) equations in the context of quasiclassical or Whitham hierarchies. The associativity equations are shown to be encoded in the dispersionless limit of the Hirota equations for KP and Toda hierarchies. We show, therefore, that any tau-function of dispersionless KP or Toda hierarchy provides a solution to associativity equations. In general, they depend on infinitely many variables. We also discuss the particular solution to the dispersionless Toda hierarchy that describes conformal mappings and construct a family of new solutions to the WDVV equations depending on finite number of variables.Comment: 16 pages, LaTe

DV and WDVV

We prove that the quasiclassical tau-function of the multi-support solutions to matrix models, proposed recently by Dijkgraaf and Vafa to be related to the Cachazo-Intrilligator-Vafa superpotentials of the N=1 supersymmetric Yang-Mills theories, satisfies the Witten-Dijkgraaf-Verlinde-Verlinde equations.Comment: 15 pages, 2 figure

A significant proportion of classic Hodgkin lymphoma recurrences represents clonally unrelated second primary lymphoma

Despite high cure rates in classic Hodgkin lymphoma (cHL), relapses are observed. Whether relapsed cHL represents second primary lymphoma or an underlying T-cell lymphoma (TCL) mimicking cHL is under-investigated. To analyze the nature of cHL recurrences, in-depth clonality testing of immunoglobulin (IG) and T-cell receptor (TR) rearrangements was performed in paired cHL diagnosis and recurrences of 60 patients, supported by targeted mutation analysis of lymphoma-associated genes. Clonal IG rearrangements were detected by next-generation sequencing (NGS) in 69/120 (58%) diagnosis and recurrence samples. The clonal relationship could be established in 34 cases, identifying clonally related relapsed cHL in 24/34 patients (71%). Clonally unrelated cHL was observed in 10/34 patients (29%) as determined by IG-NGS clonality assessment, and confirmed by the identification of predominantly mutually exclusive gene mutations in the paired cHL samples. In recurrences of &gt;2 years, ~60% of cHL patients for which the clonal relationship could be established showed a second primary cHL. Clonal TR gene rearrangements were identified in 14/125 samples (11%), and TCL-associated gene mutations were detected in 7/14 samples. Retrospective pathology review with integration of the molecular findings were consistent with an underlying TCL in 5 patients aged &gt;50 years. This study shows that cHL recurrences, especially after 2 years, sometimes represent a new primary cHL or TCL mimicking cHL, as uncovered by NGS-based IG/TR clonality testing and gene mutation analysis. Given the significant therapeutic consequences, molecular testing of a presumed relapse in cHL is crucial for subsequent appropriate treatment strategies adapted to the specific lymphoma presentation.</p

Patients with usual vulvar intraepithelial neoplasia-related vulvar cancer have an increased risk of cervical abnormalities

Contains fulltext : 81890.pdf (publisher's version ) (Closed access)BACKGROUND: Vulvar squamous cell carcinoma (SCC) originates the following two pathways, related to differentiated (d) vulvar intraepithelial neoplasia (VIN) or to human papillomavirus (HPV)-related usual (u) VIN. Multicentric HPV infections (cervix, vagina and vulva) are common. We hypothesise that patients with a uVIN-related vulvar SCC more often have cervical high-grade squamous intraepithelial lesions (HSILs) compared with women with dVIN-related vulvar SCC. METHODS: All vulvar SCCs (201) were classified to be dVIN- (n=164) or uVIN related (n=37). Data with regard to the smear history and cervical histology were retrieved from PALGA, the nationwide Netherlands database of histo- and cytopathology. For HSIL cervical smears of which histology was taken, HPV DNA analysis on both the vulvar and cervical specimens was performed. RESULTS: At least one smear was available in 145 (72%) of the 201 patients. Patients with a uVIN-related vulvar SCC more often had an HSIL compared with patients with a dVIN-related SCC (35 vs 2%, P<0.001). A total of 10 of the 13 HSILs were histologically assessed and identical HPV types were found in the vulva and cervix. CONCLUSION: These data emphasise the necessity to differentiate between dVIN- and uVIN-related vulvar tumours and to examine the entire lower female ano-genital tract once an uVIN-related lesion is found