Modular differential equations for characters of RCFT

We discuss methods, based on the theory of vector-valued modular forms, to determine all modular differential equations satisfied by the conformal characters of RCFT; these modular equations are related to the null vector relations of the operator algebra. Besides describing effective algorithmic procedures, we illustrate our methods on an explicit example.Comment: 13 page

constant domain exchanged fab enables specific light chain pairing in heterodimeric bispecific seed antibodies

Abstract Background Bispecific antibodies promise to broadly expand the clinical utility of monoclonal antibody technology. Several approaches for heterodimerization of heavy chains have been established to produce antibodies with two different Fab arms, but promiscuous pairing of heavy and light chains remains a challenge for their manufacturing. Methods We have designed a solution in which the CH1 and CL domain pair in one of the Fab fragments is replaced with a CH3-domain pair and heterodimerized to facilitate correct modified Fab-chain pairing in bispecific heterodimeric antibodies based on a strand-exchange engineered domain (SEED) scaffold with specificity for epithelial growth factor receptor and either CD3 or CD16 (FcγRIII). Results Bispecific antibodies retained binding to their target antigens and redirected primary T cells or NK cells to induce potent killing of target cells. All antibodies were expressed at a high yield in Expi293F cells, were detected as single sharp symmetrical peaks in size exclusion chromatography and retained high thermostability. Mass spectrometric analysis revealed specific heavy-to-light chain pairing for the bispecific SEED antibodies as well as for one-armed SEED antibodies co-expressed with two different competing light chains. Conclusion Incorporation of a constant domain-exchanged Fab fragment into a SEED antibody yields functional molecules with favorable biophysical properties. General significance Our results show that the novel engineered bispecific SEED antibody scaffold with an incorporated Fab fragment with CH3-exchanged constant domains is a promising tool for the generation of complete heterodimeric bispecific antibodies with correct light chain pairing

Sensitivity and Specificity of Multiple Kato-Katz Thick Smears and a Circulating Cathodic Antigen Test for Schistosoma mansoni Diagnosis Pre- and Post-repeated-Praziquantel Treatment

Two Kato-Katz thick smears (Kato-Katzs) from a single stool are currently recommended for diagnosing Schistosoma mansoni infections to map areas for intervention. This ‘gold standard’ has low sensitivity at low infection intensities. The urine point-of-care circulating cathodic antigen test (POC-CCA) is potentially more sensitive but how accurately they detect S. mansoni after repeated praziquantel treatments, their suitability for measuring drug efficacy and their correlation with egg counts remain to be fully understood. We compared the accuracies of one to six Kato-Katzs and one POC-CCA for the diagnosis of S. mansoni in primary-school children who have received zero to ten praziquantel treatments. We determined the impact each diagnostic approach may have on monitoring and evaluation (M&E) and drug-efficacy findings

A new proof of the Vorono\"i summation formula

We present a short alternative proof of the Vorono\"i summation formula which plays an important role in Dirichlet's divisor problem and has recently found an application in physics as a trace formula for a Schr\"odinger operator on a non-compact quantum graph \mathfrak{G} [S. Egger n\'e Endres and F. Steiner, J. Phys. A: Math. Theor. 44 (2011) 185202 (44pp)]. As a byproduct we give a new proof of a non-trivial identity for a particular Lambert series which involves the divisor function d(n) and is identical with the trace of the Euclidean wave group of the Laplacian on the infinite graph \mathfrak{G}.Comment: Enlarged version of the published article J. Phys. A: Math. Theor. 44 (2011) 225302 (11pp

Renormalization of Multiple qq-Zeta Values

In this paper we shall define the renormalization of the multiple $q$-zeta values (M$q$ZV) which are special values of multiple $q$-zeta functions $\zeta_q(s_1,...,s_d)$ when the arguments are all positive integers or all non-positive integers. This generalizes the work of Guo and Zhang (math.NT/0606076v3) on the renormalization of Euler-Zagier multiple zeta values. We show that our renormalization process produces the same values if the M$q$ZVs are well-defined originally and that these renormalizations of M$q$ZV satisfy the $q$-stuffle relations if we use shifted-renormalizations for all divergent $\zeta_q(s_1,...,s_d)$ (i.e., $s_1\le 1$). Moreover, when \qup our renormalizations agree with those of Guo and Zhang.Comment: 22 pages. This is a substantial revision of the first version. I provide a new and complete proof of the fact that our renormalizations satisfy the q-stuffle relations using the shifting principle of MqZV

A Cold Front in A3667: Hydrodynamics and Magnetic Field in the Intracluster Medium

This conference presentation discusses a Chandra observation of the cold front in Abell 3667. We first review our earlier results which include a measurement of the front velocity, M~1, using the ratio of exterior and interior gas pressures; observations of the hydrodynamic effects expected for a transonic front motion (weak bow shock and gas compression near the leading edge of the front); direct observation of the suppressed diffusion across the front, and estimate of the magnetic field strength near the front from suppression of the Kelvin-Helmholtz instabilities. The new results include using the 2-dimensional brightness distribution inside the cold front (a) to show that the front is stable and (b) to map the mass distribution in the gas cloud. This analysis confirms the existence of a dark matter subcluster traveling with the front. We also fix an algebraic error in our published calculations for the growth rate of the KH instability and discuss an additional effect which could stabilize the front against the small-scale perturbations. These updates only strengthen our conclusions regarding the importance of the magnetic fields for the front dynamics.Comment: Shortened version of the paper published in Astronomy Letters; based on talk at conference "High Energy Astrophysics 2001", Moscow, Dec 200

Field-induced quantum fluctuations in the heavy fermion superconductor CeCu2Ge2

Quantum-mechanical fluctuations in strongly correlated electron systems cause unconventional phenomena such as non-Fermi liquid behavior, and arguably high temperature superconductivity. Here we report the discovery of a field-tuned quantum critical phenomenon in stoichiometric CeCu2Ge2, a spin density wave ordered heavy fermion metal that exhibits unconventional superconductivity under ~ 10 GPa of applied pressure. Our finding of the associated quantum critical spin fluctuations of the antiferromagnetic spin density wave order, dominating the local fluctuations due to single-site Kondo effect, provide new information about the underlying mechanism that can be important in understanding superconductivity in this novel compound.Comment: Heavy Fermion, Quantum Critical Phenomeno

Discontinuous Molecular Dynamics for Semi-Flexible and Rigid Bodies

A general framework for performing event-driven simulations of systems with semi-flexible or rigid bodies interacting under impulsive torques and forces is outlined. Two different approaches are presented. In the first, the dynamics and interaction rules are derived from Lagrangian mechanics in the presence of constraints. This approach is most suitable when the body is composed of relatively few point masses or is semi-flexible. In the second method, the equations of rigid bodies are used to derive explicit analytical expressions for the free evolution of arbitrary rigid molecules and to construct a simple scheme for computing interaction rules. Efficient algorithms for the search for the times of interaction events are designed in this context, and the handling of missed interaction events is discussed.Comment: 16 pages, double column revte