Multiresolution approximation of the vector fields on T^3

Multiresolution approximation (MRA) of the vector fields on T^3 is studied. We introduced in the Fourier space a triad of vector fields called helical vectors which derived from the spherical coordinate system basis. Utilizing the helical vectors, we proved the orthogonal decomposition of L^2(T^3) which is a synthesis of the Hodge decomposition of the differential 1- or 2-form on T^3 and the Beltrami decomposition that decompose the space of solenoidal vector fields into the eigenspaces of curl operator. In the course of proof, a general construction procedure of the divergence-free orthonormal complete basis from the basis of scalar function space is presented. Applying this procedure to MRA of L^2(T^3), we discussed the MRA of vector fields on T^3 and the analyticity and regularity of vector wavelets. It is conjectured that the solenoidal wavelet basis must break r-regular condition, i.e. some wavelet functions cannot be rapidly decreasing function because of the inevitable singularities of helical vectors. The localization property and spatial structure of solenoidal wavelets derived from the Littlewood-Paley type MRA (Meyer's wavelet) are also investigated numerically.Comment: LaTeX, 33 Pages, 3 figures. submitted to J. Math. Phy

Bayesian value-of-infomation analysis: an application to a policy model of Alzheimer's disease

A framework is presented that distinguishes the conceptually separate decisions of which treatment strategy is optimal from the question of whether more information is required to inform this choice in the future. The authors argue that the choice of treatment strategy should be based on expected utility, and the only valid reason to characterize the uncertainty surrounding outcomes of interest is to establish the value of acquiring additional information. A Bayesian decision theoretic approach is demonstrated through a probabilistic analysis of a published policy model of Alzheimer’s disease. The expected value of perfect information is estimated for the decision to adopt a new pharmaceutical for the population of patients with Alzheimer’s disease in the United States. This provides an upper bound on the value of additional research. The value of information is also estimated for each of the model inputs. This analysis can focus future research by identifying those parameters where more precise estimates would be most valuable and indicating whether an experimental design would be required. We also discuss how this type of analysis can also be used to design experimental research efficiently (identifying optimal sample size and optimal sample allocation) based on the marginal cost and marginal benefit of sample information. Value-of-information analysis can provide a measure of the expected payoff from proposed research, which can be used to set priorities in research and development. It can also inform an efficient regulatory framework for new healthcare technologies: an analysis of the value of information would define when a claim for a new technology should be deemed substantiated and when evidence should be considered competent and reliable when it is not cost-effective to gather any more information

Maximally entangled fermions

Fermions play an essential role in many areas of quantum physics and it is desirable to understand the nature of entanglement within systems that consists of fermions. Whereas the issue of separability for bipartite fermions has extensively been studied in the present literature, this paper is concerned with maximally entangled fermions. A complete characterization of maximally entangled quasifree (gaussian) fermion states is given in terms of the covariance matrix. This result can be seen as a step towards distillation protocols for maximally entangled fermions.Comment: 13 pages, 1 figure, RevTex, minor errors are corrected, section "Conclusions" is adde

Structure transitions induced by the Hall term in homogeneous and isotropic magnetohydrodynamic turbulence

Hall effects on local structures in homogeneous, isotropic, and incompressible magnetohydrodynamic turbulence are studied numerically. The transition of vortices from sheet-like to tubular structures induced by the Hall term is found, while the kinetic energy spectrum does not distinguish the two types of structures. It is shown by the use of the sharp low-pass filter that the transition occurs not only in the scales smaller than the ion skin depth but also in a larger scale. The transition is related with the forward energy transfer in the spectral space. Analyses by the use of the sharp low-pass filter show that the nonlinear energy transfer associated with the Hall term is dominated by the forward transfer and relatively local in the wave number space. A projection of the simulation data to a Smagorinsky-type sub-grid-scale model shows that the high wave number component of the Hall term may possibly be replaced by the model effectively

Strongly thixotropic viscosity behavior of dimethylsulfoxide solution of polyrotaxane comprising alpha-cyclodextrin and low molecular weight poly(ethylene glycol)

ArticlePOLYMER. 48(24): 7139-7144 (2007)journal articl

Bayesian Value-of-Information Analysis: An Application to a Policy Model of Alzheimer's Disease

A framework is presented which distinguishes the conceptually separate decisions of which treatment strategy is optimal from the question of whether more information is required to inform this choice in the future. The authors argue that the choice of treatment strategy should be based on expected utility and the only valid reason to characterise the uncertainty surrounding outcomes of interest is to establish the value of acquiring additional information. A Bayesian decision theoretic approach is demonstrated though a probabilistic analysis of a published policy model of Alzheimer’s disease. The expected value of perfect information is estimated for the decision to adopt a new pharmaceutical for the population of US Alzheimer’s disease patients. This provides an upper bound on the value of additional research. The value of information is also estimated for each of the model inputs. This analysis can focus future research by identifying those parameters where more precise estimates would be most valuable, and indicating whether an experimental design would be required. We also discuss how this type of analysis can also be used to design experimental research efficiently (identifying optimal sample size and optimal sample allocation) based on the marginal cost and marginal benefit of sample information. Value-of-information analysis can provide a measure of the expected payoff from proposed research, which can be used to set priorities in research and development. It can also inform an efficient regulatory framework for new health care technologies: an analysis of the value of information would define when a claim for a new technology should be deemed “substantiated” and when evidence should be considered “competent and reliable” when it is not cost-effective to gather anymore information.stochastic CEA; Bayesian decision theory; value of information.

Instanton Calculus in R-R 3-form Background and Deformed N=2 Super Yang-Mills Theory

We study the ADHM construction of instantons in N=2 supersymmetric Yang-Mills theory deformed in constant Ramond-Ramond (R-R) 3-form field strength background in type IIB superstrings. We compare the deformed instanton effective action with the effective action of fractional D3/D(-1) branes at the orbifold singularity of C^2/Z_2 in the same R-R background. We find discrepancy between them at the second order in deformation parameters, which comes from the coupling of the translational zero modes of the D(-1)-branes to the R-R background. We improve the deformed action by adding a term with space-time dependent gauge coupling. Although the space-time action differs from the action in the omega-background, both actions lead to the same instanton equations of motion at the lowest order in gauge coupling.Comment: 27 pages, version to appear in JHE