New Partition Identities From Cℓ(1)C_{\ell}^{(1)}-Modules

In this paper we conjecture combinatorial Rogers-Ramanujan type colored partition identities related to standard representations of the affine Lie algebra of type $C^{(1)}_\ell$, $\ell\geq2$, and we conjecture similar colored partition identities with no obvious connection to representation theory of affine Lie algebras.Comment: 19 page

Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, I: level one case

This is the first in a series of papers in which we study vertex-algebraic structure of Feigin-Stoyanovsky's principal subspaces associated to standard modules for both untwisted and twisted affine Lie algebras. A key idea is to prove suitable presentations of principal subspaces, without using bases or even ``small'' spanning sets of these spaces. In this paper we prove presentations of the principal subspaces of the basic A_1^(1)-modules. These convenient presentations were previously used in work of Capparelli-Lepowsky-Milas for the purpose of obtaining the classical Rogers-Ramanujan recursion for the graded dimensions of the principal subspaces.Comment: 20 pages. To appear in International J. of Mat

Constructing quantum vertex algebras

This is a sequel to \cite{li-qva}. In this paper, we focus on the construction of quantum vertex algebras over \C, whose notion was formulated in \cite{li-qva} with Etingof and Kazhdan's notion of quantum vertex operator algebra (over \C[[h]]) as one of the main motivations. As one of the main steps in constructing quantum vertex algebras, we prove that every countable-dimensional nonlocal (namely noncommutative) vertex algebra over \C, which either is irreducible or has a basis of PBW type, is nondegenerate in the sense of Etingof and Kazhdan. Using this result, we establish the nondegeneracy of better known vertex operator algebras and some nonlocal vertex algebras. We then construct a family of quantum vertex algebras closely related to Zamolodchikov-Faddeev algebras.Comment: 37 page

Tutorial in oral antithrombotic therapy: Biology and dental implications

Objectives: Recent developments of new direct oral anticoagulants that target specific clotting factors necessitate understanding of coagulation biology. The objective of this tutorial is to offer dental professionals a review of coagulation mechanisms and the pharmacodynamics of the conventional and new oral anticoagulants. Also, we summarized the dental implications of the conventional and new anticoagulants. Method : We searched Medline using search terms "antithrombotic", "antihemostasis" or "anticoagulation" and combined them with the search results of "dental", "oral surgery" or "periodontal". We restricted the results to "human" and "English". Results: The early coagulation cascade, the new cell-based coagulation model, the pharmacokinetics and pharmacodynamics of conventional antithrombotics, and new oral anticoagulants were reviewed. The new direct factor Xa inhibitors and the direct thrombin inhibitor (s), called direct oral anticoagulants (DOAs) have rapid onset of action, fast elimination on cessation, and fewer drug-drug or drug-food interactions than warfarin. However, the lack of antidotes raises concerns that some dental procedures may trigger serious hemorrhagic events. Additionally, careful perioperative withdrawal and resumption protocols for the DOAs are reviewed, because DOAs' blood levels are dependent on renal function. Also, various reversal strategies in the event of excessive bleedings are summarized. Perioperative management of dental patients taking new DOAs and conventional oral anticoagulants are also discussed. However, the perioperative strategies for DOAs are yet to be validated in randomized trials

Fusion rules and complete reducibility of certain modules for affine Lie algebras

We develop a new method for obtaining branching rules for affine Kac-Moody Lie algebras at negative integer levels. This method uses fusion rules for vertex operator algebras of affine type. We prove that an infinite family of ordinary modules for affine vertex algebra of type A investigated in Adamovi\'c and O. Per\v{s}e (2008) is closed under fusion. Then we apply these fusion rules on explicit bosonic realization of level -1 modules for the affine Lie algebra of type $A_{\ell-1}^{(1)}$, obtain a new proof of complete reducibility for these representations, and the corresponding decomposition for $\ell \ge 3$. We also obtain the complete reducibility of the associated level -1 modules for affine Lie algebra of type $C_{\ell}^{(1)}$. Next we notice that the category of $D_{2 \ell -1}^{(1)}$ modules at level $- 2 \ell +3$ obtained in Per\v{s}e (2012) has the isomorphic fusion algebra. This enables us to decompose certain $E_6 ^{(1)}$ and $F_4 ^{(1)}$--modules at negative levels.Comment: 18 pages; final version, to appear in Journal of Algebra and Its Application

The structure of parafermion vertex operator algebras

It is proved that the parafermion vertex operator algebra associated to the irreducible highest weight module for the affine Kac-Moody algebra A_1^{(1)} of level k coincides with a certain W-algebra. In particular, a set of generators for the parafermion vertex operator algebra is determined.Comment: 12 page

The N=1 triplet vertex operator superalgebras

We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras SW(m), $m \geq 1$, which are natural super analogs of the triplet vertex algebra family W(p), $p \geq 2$, important in logarithmic conformal field theory. We classify irreducible SW(m)-modules and discuss logarithmic modules. We also compute bosonic and fermionic formulas of irreducible SW(m) characters. Finally, we contemplate possible connections between the category of SW(m)-modules and the category of modules for the quantum group U^{small}_q(sl_2), q=e^{\frac{2 \pi i}{2m+1}}, by focusing primarily on properties of characters and the Zhu's algebra A(SW(m)). This paper is a continuation of arXiv:0707.1857.Comment: 53 pages; v2: references added; v3: a few changes; v4: final version, to appear in CM

The subconvexity problem for \GL_{2}

Generalizing and unifying prior results, we solve the subconvexity problem for the $L$-functions of \GL_{1} and \GL_{2} automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present method is the softness of our arguments; this is largely due to a consistent use of canonically normalized period relations, such as those supplied by the work of Waldspurger and Ichino--Ikeda.Comment: Almost final version to appear in Publ. Math IHES. References updated

Gastric atrophy and oesophageal squamous cell carcinoma: Possible interaction with dental health and oral hygiene habit

Background:Gastric fundal atrophy has been hypothesised to increase the risk of oesophageal squamous cell carcinoma (OSCC), but studies have shown inconsistent results.Methods:We measured serum pepsinogen I (PGI) and pepsinogen II (PGII) among 293 incident cases and 524 matched neighbourhood controls in a high-risk area of Northern Iran. Conditional logistic regression model was used to estimate odds ratios (ORs) and their 95% confidence intervals (CIs).Results:After controlling for age, sex, residence area and other potential confounders, gastric atrophy (defined by a validated criterion, PGI <55 μg dl-1) was associated with a two-fold increased risk (OR=2.01, 95% CI: 1.18, 3.45) of OSCC in the absence of nonatrophic pangastritis (defined as PGII <11.8 μg dl-1). Stratification by PGII decreased the misclassification errors due to cancer-induced gastritis. Presence of both poor dental health, indicated by higher than median sum of decayed, missing, and filled teeth (DMFT score), and gastric atrophy further increased the risk of OSCC (OR=4.15, 95% CI: 2.04, 8.42) with relative excess risk due to interaction (RERI) of 1.47 (95% CI: 1.15, 4.1). Coexistence of poor oral hygiene habit with gastric atrophy elevated OSCC risk eight times (OR=8.65, 95% CI: 3.65, 20.46) and the additive interaction index was marginally statistically significant (RERI=4.34, 95% CI: 1.07, 9.76).Conclusion:Gastric atrophy is a risk factor for OSCC, and poor dental health and oral hygiene habit may act synergistically in increasing the risk. © 2012 Cancer Research UK

Granulomatous cheilitis associated with exacerbations of Crohn's disease: a case report

<p>Abstract</p> <p>Introduction</p> <p>Crohn's disease is a disease involving the whole gastrointestinal tract from the mouth to the anus. Oral lesions are considered to be an important extraintestinal manifestation. Granulomatous cheilitis has been recognized as an early manifestation of Crohn's disease. It may follow, coincide with or precede the onset of Crohn's disease. The aim of this presentation is to describe a rare case of a patient with Crohn's disease in whom significant swelling of the lower lip not only preceded the diagnosis of Crohn's disease for two years, but it manifested as an early clinical index of the recurrence of the intestinal disease as well.</p> <p>Case presentation</p> <p>A man aged 25 was admitted in our department on August 1999 with chronic diarrhea and loss of weight. His bowel symptoms started in 1998 at the age of 24. However, two years previously (June 1996) he noticed a swelling of the lower lip, which contrasted significantly with the previously normal appearance of his mouth. A lip biopsy performed at that time was compatible with granulomatous cheilitis. Crohn's disease involving the terminal ileum and large bowel was diagnosed in 1998 and confirmed on the basis of colonoscopy, enteroclysis and histology findings of the small and large bowel. Conservative treatment resulted in clinical and laboratory improvement of the bowel symptoms and lip swelling. During the following years the disease was active with exacerbations and remissions of mild to moderate severity. The swelling of the lower lip occurred in parallel with the exacerbations of the bowel disease, returning to normal during periods of remission.</p> <p>Conclusion</p> <p>Significant swelling of the lower lip due to granulomatous cheilitis could be the first manifestation of Crohn's disease, preceding intestinal symptoms. Exacerbation of the lip lesion could be an early clinical sign of a relapse of the underlying intestinal disease.</p