This multicenter study demonstrates a dramatic increase in the diagnosis of VTE at children's hospitals from 2001 to 2007.

Let V be a simple vertex operator algebra satisfying the following conditions: (i) V (n) = 0 for n < 0, V (0) = C1 and V ′ is isomorphic to V as a V -module. (ii) Every N-gradable weak V -module is completely reducible. (iii) V is C 2 -cofinite. (In the presence of Condition (i), Conditions (ii) and (iii) are equivalent to a single condition, namely, that every weak V -module is completely reducible.) Using the results obtained by the author in the formulation and proof of the general version of the Verlinde conjecture and in the proof of the Verlinde formula, we prove that the braided tensor category structure on the category of V -modules is rigid, balanced and nondegenerate. In particular, the category of V -modules has a natural structure of modular tensor category. We also prove that the tensor-categorical dimension of an irreducible V -module is the reciprocal of a suitable matrix element of the fusing isomorphism under a suitable basis. IntroductionIn the present paper, we prove the rigidity and modularity of the braided tensor category of modules for a vertex operator algebra satisfying certain natural conditions (see below). Finding proofs of these properties has been an open problem for many years. Our proofs in this paper are based on the results obatined by the author [H7] in the formulation and proof of the general version of the Verlinde conjecture and in the proof of the Verlinde formula.In MS2] also demonstrated that the theory of these polynomial equations is actually a conformal-field-theoretic analogue of the theory of the tensor categories. This work of Moore and Seiberg greatly advanced our understanding of the structure of conformal field theories and the name "modular tensor category" was suggested by I. Frenkel for the theory of these Moore-Seiberg equations. Later, the precise notion of modular tensor category was introduced to summarize the properties of these polynomial equations and has played a central role in the development of conformal field theories and three-dimensional topological field theories. See for example [T] and [BK] for the theory of modular tensor categories, their applications and references to many important works of mathematicians and physicists.Mathematically To prove that a semisimple braided tensor category actually carries a modular tensor category structure, we need to prove that it is rigid, balanced and nondegenerate. The balancing isomorphisms or twists in these braided tensor categories are actually trivial to construct and the balancing axioms are easy to prove. On the other hand, the rigidity has been an open problem for many years after the braided tensor category structure on the category of modules for a vertex operator algebra satisfying the conditions in [HL1]-[HL4] [H1] was constructed. The main difficulty is that from the construction, 2 it is not clear why the numbers determining the module maps given by the sequences in the axioms for the rigidity are not 0. The nondegeneracy of the semisimple braided tensor category of modules for a...

We show that if every module W for a vertex operator algebra V = n∈Z V (n) satisfies the condition dim W/C 1 (W ) < ∞, where C 1 (W ) is the subspace of W spanned by elements of the form u −1 w for u ∈ V + = n>0 V (n) and w ∈ W , then matrix elements of products and iterates of intertwining operators satisfy certain systems of differential equations. Moreover, for prescribed singular points, there exist such systems of differential equations such that the prescribed singular points are regular. The finiteness of the fusion rules is an immediate consequence of a result used to establish the existence of such systems. Using these systems of differential equations and some additional reductivity conditions, we prove that products of intertwining operators for V satisfy the convergence and extension property needed in the tensor product theory for V -modules. Consequently, when a vertex operator algebra V satisfies all the conditions mentioned above, we obtain a natural structure of vertex tensor category (consequently braided tensor category) on the category of V -modules and a natural structure of intertwining operator algebra on the direct sum of all (inequivalent) irreducible V -modules. IntroductionIn the present paper, we show that for a vertex operator algebra satisfying certain finiteness and reductivity conditions, matrix elements of products and iterates of intertwining operators satisfy certain systems of differential equations of regular singular points. Similar results are also obtained by Nagatomo and Tsuchiya in [NT] . In the construction of these structures from representations of vertex operator algebras, one of the most important steps is to prove the associativity of intertwining operators, or a weaker version which, in physicists' terminology, is called the (nonmeromorphic) operator product expansion of chiral vertex operators. It was proved in [H1] that if a vertex operator algebra V is rational in the sense of [HL1], every finitely-generated lower-truncated generalized V -module is a V -module and products of intertwining operators for V have a convergence and extension property (see Definition 3.2 for the precise description of the property), then the associativity of intertwining operators holds. Consequently the category of V -modules has a natural structure of vertex tensor category (and braided tensor category) and the direct sum of all (inequivalent) irreducible V -modules has a natural structure of intertwining operator algebra.The results above reduce the construction of vertex tensor categories and intertwining operator algebras (in particular, the proof of the associativity of intertwining operators) to the proofs of the rationality of vertex operator algebras (in the sense of [HL1]), the condition on finitely-generated lowertruncated generalized V -modules and the convergence and extension property. Note that this rationality and the condition on finitely-generated lowertruncated generalized V -modules are both purely representation-theoretic properties. These and other relat...

We solve the problem of constructing all chiral genus-one correlation functions from chiral genus-zero correlation functions associated to a vertex operator algebra satisfying the following conditions: (i) V (n) = 0 for n < 0 and V (0) = C1, (ii) every N-gradable weak Vmodule is completely reducible and (iii) V is C 2 -cofinite. We establish the fundamental properties of these functions, including suitably formulated commutativity, associativity and modular invariance. The method we develop and use here is completely different from the one previously used by Zhu and other people. In particular, we show that the q-traces of products of certain geometrically-modified intertwining operators satisfy modular invariant systems of differential equations which, for any fixed modular parameter, reduce to doubly-periodic systems with only regular singular points. Together with the results obtained by the author in the genus-zero case, the results of the present paper solves essentially the problem of constructing chiral genus-one weakly conformal field theories from the representations of a vertex operator algebra satisfying the conditions above.

Purpose National Cancer Institute (NCI)-funded cooperative oncology group trials have improved overall survival for children with cancer from 10% to 85% and have set standards of care for adults with malignancies. Despite these successes, cooperative oncology groups currently face substantial challenges. We are working to develop methods to improve the efficiency and effectiveness of these trials. Specifically, we merged data from the Children’s Oncology Group (COG) and the Pediatric Health Information Systems (PHIS) to improve toxicity monitoring, estimate treatment-associated resource utilization and costs, and to address important clinical epidemiology questions. Methods COG and PHIS data on patients enrolled on a Phase III COG trial for de novo acute myeloid leukemia (AML) at 43 PHIS hospitals were merged using a probabilistic algorithm. Resource utilization summary statistics were then tabulated for the first chemotherapy course based on PHIS data. Results Of 416 patients enrolled on the Phase III COG trial at PHIS centers, 392 (94%) were successfully matched. Of these, 378 (96%) had inpatient PHIS data available beginning at the date of study enrollment. For these, daily blood product usage and anti-infective exposures were tabulated and standardized costs were described. Conclusions These data demonstrate that patients enrolled in a cooperative group oncology trial can be successfully identified in an administrative data set, and that supportive care resource utilization can be described. Further work is required to optimize the merging algorithm, map resource utilization metrics to NCI Common Toxicity Criteria for monitoring toxicity, perform comparative effectiveness studies, and estimate the costs associated with protocol therapy.