Noncommutative Koszul Algebras from Combinatorial Topology

Associated to any uniform finite layered graph Gamma there is a noncommutative graded quadratic algebra A(Gamma) given by a construction due to Gelfand, Retakh, Serconek and Wilson. It is natural to ask when these algebras are Koszul. Unfortunately, a mistake in the literature states that all such algebras are Koszul. That is not the case and the theorem was recently retracted. We analyze the Koszul property of these algebras for two large classes of graphs associated to finite regular CW complexes, X. Our methods are primarily topological. We solve the Koszul problem by introducing new cohomology groups H_X(n,k), generalizing the usual cohomology groups H^n(X). Along with several other results, our methods give a new and primarily topological proof of a result of Serconek and Wilson and of Piontkovski.Comment: 22 pages, 1 figur

Spin-S bilayer Heisenberg models: Mean-field arguments and numerical calculations

Spin-S bilayer Heisenberg models (nearest-neighbor square lattice antiferromagnets in each layer, with antiferromagnetic interlayer couplings) are treated using dimer mean-field theory for general S and high-order expansions about the dimer limit for S=1, 3/2,...,4. We suggest that the transition between the dimer phase at weak intraplane coupling and the Neel phase at strong intraplane coupling is continuous for all S, contrary to a recent suggestion based on Schwinger boson mean-field theory. We also present results for S=1 layers based on expansions about the Ising limit: In every respect the S=1 bilayers appear to behave like S=1/2 bilayers, further supporting our picture for the nature of the order-disorder phase transition.Comment: 6 pages, Revtex 3.0, 8 figures (not embedded in text

Modeling Space-Time Data Using Stochastic Differential Equations

This paper demonstrates the use and value of stochastic differential equations for modeling space-time data in two common settings. The first consists of point-referenced or geostatistical data where observations are collected at fixed locations and times. The second considers random point pattern data where the emergence of locations and times is random. For both cases, we employ stochastic differential equations to describe a latent process within a hierarchical model for the data. The intent is to view this latent process mechanistically and endow it with appropriate simple features and interpretable parameters. A motivating problem for the second setting is to model urban development through observed locations and times of new home construction; this gives rise to a space-time point pattern. We show that a spatio-temporal Cox process whose intensity is driven by a stochastic logistic equation is a viable mechanistic model that affords meaningful interpretation for the results of statistical inference. Other applications of stochastic logistic differential equations with space-time varying parameters include modeling population growth and product diffusion, which motivate our first, point-referenced data application. We propose a method to discretize both time and space in order to fit the model. We demonstrate the inference for the geostatistical model through a simulated dataset. Then, we fit the Cox process model to a real dataset taken from the greater Dallas metropolitan area.Business Administratio

Absence of ZAP-70 prevents signaling through the antigen receptor on peripheral blood T cells but not on thymocytes.

Recently, a severe combined immunodeficiency syndrome with a deficiency of CD8+ peripheral T cells and a TCR signal transduction defect in peripheral CD4+ T cells was associated with mutations in ZAP-70. Since TCR signaling is required in developmental decisions resulting in mature CD4 (and CD8) T cells, the presence of peripheral CD4+ T cells expressing TCRs incapable of signaling in these patients is paradoxical. Here, we show that the TCRs on thymocytes, but not peripheral T cells, from a ZAP-70-deficient patient are capable of signaling. Moreover, the TCR on a thymocyte line derived from this patient can signal, and the homologous kinase Syk is present at high levels and is tyrosine phosphorylated after TCR stimulation. Thus, Syk may compensate for the loss of ZAP-70 and account for the thymic selection of at least a subset of T cells (CD4+) in ZAP-70-deficient patients

Quantum Sturm-Liouville Equation, Quantum Resolvent, Quantum Integrals, and Quantum KdV : the Fast Decrease Case

We construct quantum operators solving the quantum versions of the Sturm-Liouville equation and the resolvent equation, and show the existence of conserved currents. The construction depends on the following input data: the basic quantum field $O(k)$ and the regularization .Comment: minor correction

Ensuring a Consistent Supply of Anthrax Vaccine

During the recent anthrax attacks, the country's supply of anthrax vaccine was dangerously low. The reasons for this were (1) the failure of the FDA, the Defense Department, and its contractor, BioPort Corporation, to plan adequately to ensure the production of a consistent supply of the vaccine in accordance with the FDA regulatory process; and (2) the reliance of the Defense Department on a single private supplier of the vaccine with serious financial problems. Careful planning should be employed to prevent such a situation with other biological products which may be needed to save lives during bioterrorist attacks

Zero Curvature Formalism for Supersymmetric Integrable Hierarchies in Superspace

We generalize the Drinfeld-Sokolov formalism of bosonic integrable hierarchies to superspace, in a way which systematically leads to the zero curvature formulation for the supersymmetric integrable systems starting from the Lax equation in superspace. We use the method of symmetric space as well as the non-Abelian gauge technique to obtain the supersymmetric integrable hierarchies of the AKNS type from the zero curvature condition in superspace with the graded algebras, sl(n+1,n), providing the Hermitian symmetric space structure.Comment: LaTeX, 9 pg