Partition Statistics and Quasiharmonic Maass Forms

Andrews recently introduced k-marked Durfee symbols, which area generalization of partitions that are connected to momentsof Dyson's rank statistic. He used these connections to findidentities relating to their generating functions as well asto prove Ramanujan-type congruences for these objects and findrelations between them. In this paper, we show that the hypergeometricgenerating functions for these objects are natural examplesof quasimock theta functions, which are defined as the holomorphicparts of harmonic Maass forms and their derivatives. In particular,these generating functions may be viewed as analogs of Ramanujan'smock theta functions with arbitrarily high weight. We use theautomorphic properties to prove the existence of infinitelymany congruences for the Durfee symbols. Furthermore, we showthat as k varies, the modularity of the k-marked Durfee symbolsis precisely dictated by the case k = 2. Finally, we use thisrelation in order to prove the existence of general congruencesfor rank moments in terms of level one modular forms of boundedweight.     

Sequential Discrete p-Facility Models for Competitive Location Planning

Two new models for duopolistic competitive discrete location planning with sequential acting and variable delivered prices are introduced. If locations and prices are assumed to be set once and for all by the players, the resulting bilevel program is nonlinear. Under the assumption that further price adjustments are possible, i.e., that a Nash equilibrium in prices is reached, the model can be simplified to a linear discrete bilevel formulation. It is shown that in either situation players should not share any locations or markets if they strive for profit-maximization.For the situation with price adjustments, a heuristic solution procedure is suggested. In addition, the bilevel models are shown to serve as a basis from which different well-known location models – as, for example, the p-median problem, the preemptive location problem and the maximum covering problem – can be derived as special cases.     

Kinetics and isotype profile of antibody responses in rhesus macaques induced following vaccination with HPV 6, 11, 16 and 18 L1-virus-like particles formulated with or without Merck aluminum adjuvant

BACKGROUND: Human papillomaviruses (HPV) are the most common sexually transmitted viruses. Infection of the cervical epithelium by HPVs can lead to the development of cervical cancer. Recent advances in vaccine research have shown that immunization with papillomavirus-like particles (VLPs) containing the major structural viral protein, L1 from HPV 16 can provide protection from the establishment of a chronic HPV 16 infection and related cervical intraepithelial neoplasia (CIN) in baseline HPV 16 naive women. METHODS: To better understand the quantitative and qualitative effects of aluminum adjuvant on the immunogenic properties of an HPV 6, 11, 16 and 18L1 VLP vaccine, we used an HPV-specific, antibody isotyping assay and a competitive immunoassay that measures antibodies to neutralizing epitopes to profile sera from rhesus macaques immunized with the HPV L1 VLP vaccine formulated with or without aluminum adjuvant. RESULTS: Immunization with VLPs formulated with the aluminum adjuvant elicited a significantly stronger immune response with higher peak antibody titers both at four weeks post vaccination (12.7 to 41.9-fold higher) as well as in the persistent phase at week 52 (4.3 to 26.7-fold higher) than that of VLPs alone. Furthermore, the aluminum adjuvant formulated HPV VLP vaccine elicited a predominantly T helper type 2 response, with high levels of IgG1 and IgG4 and low levels of IgG2. The vaccine also elicited high levels of serum IgA, which may be important in providing mucosal immunity to impart protection in the anogenital tract. CONCLUSION: These results show that the HPV 6, 11, 16 and 18 L1-VLP vaccine formulated with Merck aluminum adjuvant elicits a robust and durable immune response and holds promise as a vaccine for preventing cervical cancer.     

Conformations and tautomers of 5a,6-anhydrotetracycline

Ab initio and density functional theory (DFT) calculations have been used to investigate the conformations and tautomeric forms of neutral anhydrotetracycline in aqueous solution.