6,323 research outputs found
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
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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
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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 and the regularization .Comment: minor correction
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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
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