Extended use of IST

AbstractVan den Berg, I.P., Extended use of IST, Annals of Pure and Applied Logic 58 (1992) 73–92. Internal Set Theory is an axiomatic approach to nonstandard analysis, consisting of three axiom schemes, Transfer (T), Idealization (I), and Standardization (S). We show that the range of application of these axiom schemes may be enlarged with respect to the original formulation. Not only more kinds of formulas are allowed, but also different settings. Many examples illustrate these extensions. Most concern formal aspects of nonstandard asymptotics

Detecting In Vivo Free Radicals in Various Disease Models

In vivo free radical imaging in pre-clinical models of disease is now possible. Free radicals have traditionally been characterized by ESR or EPR spin trapping spectroscopy. The disadvantage of the ESR/EPR approach is that spin adducts are short-lived due to biological reductive and/or oxidative processes. Immuno-spin trapping (IST) involves the use of an antibody that recognizes macromolecular DMPO-spin adducts (anti-DMPO antibody), regardless of the oxidative/reductive state of trapped radical adducts. The IST approach has been extended to an in vivo application that combines IST with molecular magnetic resonance imaging (mMRI). This combined IST-mMRI approach involves the use of a spin trapping agent, DMPO, to trap free radicals in disease models, and administration of a mMRI probe, an anti-DMPO probe, that combines an antibody against DMPO-radical adducts and a MRI contrast agent, resulting in targeted free radical adduct detection. The combined IST-mMRI approach has been used in several rodent disease models, including diabetes, ALS, gliomas, and septic encephalopathy. The advantage of this approach is that heterogeneous levels of trapped free radicals can be detected directly in vivo and in situ to pin-point where free radicals are formed in different tissues. The approach can also be used to assess therapeutic agents that are either free radical scavengers or generate free radicals. The focus of this review will be on the different applications that have been studied, advantages and limitations, and future directions

Transport properties of a quantum wire: the role of extended time-dependent impurities

We study the transport properties of a quantum wire, described by the Tomonaga-Luttinger model, in the presence of a backscattering potential provided by several extended time-dependent impurities (barriers). Employing the B\" uttiker-Landauer approach, we first consider the scattering of noninteracting electrons ($g=1$) by a rectangular-like barrier and find an exact solution for the backscattering current, as well as a perturbative solution for a weak static potential with an arbitrary shape. We then include electron-electron interactions and use the Keldysh formalism combined with the bosonization technique to study oscillating extended barriers. We show that the backscattering current off time-dependent impurities can be expressed in terms of the current for the corresponding static barrier. Then we determine the backscattering current for a static extended potential, which, in the limit of noninteracting electrons ($g=1$), coincides with the result obtained using the B\" uttiker-Landauer formalism. In particular, we find that the conductance can be increased beyond its quantized value in the whole range of repulsive interactions $0<g<1$ already in the case of a single oscillating extended impurity, in contrast %contrary to the case of a point-like impurity, where this phenomenon occurs only for $0<g<1/2$.Comment: 9 pages, 5 figure

Do investment-specific technological changes matter for business fluctuations? Evidence from Japan

The observed decline in the relative price of investment goods to consumption goods in Japan suggests the existence of investment-specific technological (IST) changes. We examine whether IST changes are a major source of business fluctuations in Japan, by estimating a dynamic stochastic general equilibrium model with Bayesian methods. We show that IST changes are less important than neutral technological changes in explaining output fluctuations. We also demonstrate that investment fluctuations are mainly driven by shocks to investment adjustment costs. Such shocks represent variations of costs involved in changing investment spending, such as financial intermediation costs. We then find that the estimated series of the investment adjustment cost shock correlates strongly with the diffusion index of firms' financial position in the Tankan (Short-term Economic Survey of Enterprises in Japan). We thus argue that the large decline in investment growth in the early 1990s is due to an increase in investment adjustment costs stemming from firms' tight financial constraint after the collapse of Japan's asset price bubble

A course space construction based on local Dirichlet-to-Neumann maps

Coarse-grid correction is a key ingredient of scalable domain decomposition methods. In this work we construct coarse-grid space using the low-frequency modes of the subdomain Dirichlet-to-Neumann maps and apply the obtained two-level preconditioners to the extended or the original linear system arising from an overlapping domain decomposition. Our method is suitable for parallel implementation, and its efficiency is demonstrated by numerical examples on problems with large heterogeneities for both manual and automatic partitionings

An interior point algorithm for minimum sum-of-squares clustering

Copyright @ 2000 SIAM PublicationsAn exact algorithm is proposed for minimum sum-of-squares nonhierarchical clustering, i.e., for partitioning a given set of points from a Euclidean m-space into a given number of clusters in order to minimize the sum of squared distances from all points to the centroid of the cluster to which they belong. This problem is expressed as a constrained hyperbolic program in 0-1 variables. The resolution method combines an interior point algorithm, i.e., a weighted analytic center column generation method, with branch-and-bound. The auxiliary problem of determining the entering column (i.e., the oracle) is an unconstrained hyperbolic program in 0-1 variables with a quadratic numerator and linear denominator. It is solved through a sequence of unconstrained quadratic programs in 0-1 variables. To accelerate resolution, variable neighborhood search heuristics are used both to get a good initial solution and to solve quickly the auxiliary problem as long as global optimality is not reached. Estimated bounds for the dual variables are deduced from the heuristic solution and used in the resolution process as a trust region. Proved minimum sum-of-squares partitions are determined for the rst time for several fairly large data sets from the literature, including Fisher's 150 iris.This research was supported by the Fonds National de la Recherche Scientifique Suisse, NSERC-Canada, and FCAR-Quebec