Fast Fourier Transform

In contrast to acquisition-based noise reduction methods a postprocess based on anisotropic diffusion is proposed. Extensions of this technique support 3-D and multiecho magnetic resonance imaging (MRI), incorporating higher spatial and spectral dimensions. The procedure overcomes the major drawbacks of conventional filter methods, namely the blurring of object boundaries and the suppression of fine structural details. The simplicity of the filter algorithm permits an efficient implementation, even on small workstations. The efficient noise reduction and sharpening of object boundaries are demonstrated by applying this image processing technique to 2-D and 3-D spin echo and gradient echo MR data. The potential advantages for MRI, diagnosis, and computerized analysis are discussed in detail. >

Nonlinear anisotropic filtering of MRI data

In cardiac tissue, reduced membrane excitability and reduced gap junction coupling both slow conduction velocity of the action potential. However, the ionic mechanisms of slow conduction for the two conditions are very different. We explored, using a multicellular theoretical fiber, the ionic mechanisms and functional role of the fast sodium current, INa, and the L-type calcium current, ICa(L), during conduction slowing for the two fiber conditions. A safety factor for conduction (SF) was formulated and computed for each condition. Reduced excitability caused a lower SF as conduction velocity decreased. In contrast, reduced gap junction coupling caused a paradoxical increase in SF as conduction velocity decreased. The opposite effect of the two conditions on SF was reflected in the minimum attainable conduction velocity before failure: decreased excitability could reduce velocity to only one third of control (from 54 to 17 cm/s) before failure occurred, whereas decreased coupling could reduce velocity to as low as 0.26 cm/s before block. Under normal conditions and conditions of reduced excitability, ICa(L) had a minimal effect on SF and on conduction. However, ICa(L) played a major role in sustaining conduction when intercellular coupling was reduced. This phenomenon demonstrates that structural, nonmembrane factors can cause a switch of intrinsic membrane processes that support conduction. High intracellular calcium concentration, [Ca]i, lowered propagation safety and caused earlier block when intercellular coupling was reduced. [Ca]i affected conduction via calcium-dependent inactivation of ICa(L). The increase of safety factor during reduced coupling suggests a major involvement of uncoupling in stable slow conduction in infarcted myocardium, making microreentry possible. Reliance on ICa(L) for this type of conduction suggests ICa(L) as a possible target for antiarrhythmic drug therapy.

Ionic Mechanisms of Propagation in Cardiac Tissue Roles of the Sodium and L-type Calcium Currents During Reduced Excitability and Decreased Gap Junction Coupling

In 1867, Lord Kelvin proposed that atoms—then considered to be elementary particles—could be described as knotted vortex tubes in either1. For almost two decades, this idea motivated an extensive study of the mathematical properties of knots, and the results obtained at that time by Tait2 remain central to mathematical knot theory3,4. But despite the clear relevance of knots to a large number of physical, chemical and biological systems, the physical properties of knot-like structures have not been much investigated. This is largely due to the absence of a theoretical means for generating stable knots in the nonlinear field equations that can be used to describe such systems. Here we show that knot-like structures can emerge as stable, finite-energy solutions in one such class of equations—local, three-dimensional langrangian field-theory models. Our results point to several experimental and theoretical situations where such structures may be relevant, ranging from defects in liquid crystals and vortices in superfluid helium to the structure-forming role of cosmic strings in the early Universe.

Stable knot-like structures in classical field theory

In this paper, we present a new strategy for pricing average value options, i.e. options whose payoff depends on the average price of the underlying asset over a fixed period leading up to the maturity date. Such options are of particular interest and importance for thinly-traded assets (e.g. crude oil), since price manipulation is inhibited, and both the investor and issuer enjoy a welcome degree of protection from the vagaries of the market. These options are often implicit in a bond contract, although they also appear in a straightforward form. Our results suggest that the price of an average-value option will always be lower than that of a standard European option. Our pricing strategy involves Monte Carlo simulation with variance reduction elements and offers an enhanced pricing method to both arbitragers and hedgers, as well as to the issuers of such bonds.

A Pricing Method for Options Based on Average Asset Values

This short book gives a solid introduction to the field. After a review of direct methods for the solution of linear systems, following chapters introd and analyze the more commonly used finite difference methods for solving a variety of problems. Annotation copyright Book News, Inc. Portland, Or.

The numerical solution of ordinary and partial differential equations

The Numerical Solution of Ordinary and Partial Differential Equations

SUMMARY Temperature is one of the most important factors that controls the extent and location of the seismogenic coupled and transition, partially coupled segments of the subduction interplate fault. The width of the coupled fault inferred from the continuous GPS observations for the steady interseismic period and the transient width of the last slow aseismic slip event (M w ∼ 7.5) that occurred in the Guerrero subduction zone in 2001‐2002 extends up to 180‐220 km from the trench. Previous thermal models do not consider this extremely wide coupled interface in Guerrero subduction zone that is characterized by shallow subhorizontal plate contact. In this study, a finite element model is applied to examine the temperature constraints on the width of the coupled area. The numerical scheme solves a system of 2-D Stokes equation and 2-D steady-state heat transfer equations. The updip limit of the coupling zone is taken between 100 and 150 ◦ C, while the downdip limit is accepted at 450 ◦ C as the transition from partial coupling to stable sliding. From the entire coupled zone, the seismogenic zone extends only up to ∼82 km from the trench (inferred from the rupture width of large subduction thrust earthquakes), corresponding to the 250 ◦ C isotherm. Only a small amount of frictional heating is needed to fit the intersection of the 450 ◦ C isotherm and the subducting plate surface at 180‐205 km from the trench. The calculated geotherms in the subducting slab and the phase diagram for MORB are used to estimate the metamorphic sequences within the oceanic subducting crust. A certain correlation exists between the metamorphic sequences and the variation of the coupling along the interplate fault.

/pdf/thermal-structure-coupling-and-metamorphism-in-the-mexican-u0u6lfdpvv.pdf

Thermal structure, coupling and metamorphism in the Mexican subduction zone beneath Guerrero

http://usuarios.geofisica.unam.mx/vladimir/papers_pdf/Termo-Mech%20model%20Mexico%20PEPI2005.pdf

Granville Sewell

Papers

The numerical solution of ordinary and partial differential equations

The Numerical Solution of Ordinary and Partial Differential Equations

Thermal structure, coupling and metamorphism in the Mexican subduction zone beneath Guerrero

Thermo-mechanical model of the mantle wedge in Central Mexican subduction zone and a blob tracing approach for the magma transport

PDE2D: Easy-to-use software for general two-dimensional partial differential equations