We present a method for extracting iso-surfaces and their intersections in 4D. Our work is a signiicant extension of the 3D Marching Lines algorithm with new orientation and implementation considerations. As a practical tool, it can be applied to track eeciently space curves, de-ned by diierential invariants, across increasing scale.

in this short review we look at recent advances in schramm-loewner evolution (sle) theory and its application to critical phenomena. the application of sle goes beyond critical systems to other time dependent, scale invariant phenomena such as turbulence, sand-piles and watersheds. through the use of sle, the evolution of conformally invariant paths on the complex plane can be followed; hence a...

We classify invariant curves for birational surface maps that are expanding on cohomology. When the expansion is exponential, the arithmetic genus of an invariant curve is at most one. This implies severe constraints on both the type and number of irreducible components of the curve. In the case of an invariant curve with genus equal to one, we show that there is an associated invariant meromor...

To compensate for soft-tissue deformation during image-guided surgical procedures, non-rigid methods are often used as compensation. However, most of these algorithms first implement a rigid registration to provide an initial alignment. In liver tumor resections, the organ is deformed on a large scale, causing visual shape change on the organ. Unlike neurosurgery, there is no rigid reference av...

We prove that the focal set generated by the reflection of a point source off a translation invariant surface consists of two sets: a curve and a surface. The focal curve lies in the plane orthogonal to the symmetry direction containing the source, while the focal surface is translation invariant. This is done by constructing explicitly the focal set of the reflected line congruence (2-paramete...

In this paper we introduce the concept of generalized Baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. We give some inequalities for the generalized Baer-invariant of a pair of finite groups, when ? is considered to be the Schur-Baer variety. Further, we present a sufficient condition under which the order of the generalized Baer-invariant of a pair of finite ...

Magnetotelluric (MT) method is an electromagnetic technique that uses the earth natural field to map the electrical resistivity changes in subsurface structures. Because of the high penetration depth of the electromagnetic fields in this method (tens of meters to tens of kilometers), the MT data is used to investigate the shallow to deep subsurface geoelectrical structures and their dimensions....

Class II major histocompatibility complex antigens are intracellularly associated with a nonpolymorphic polypeptide referred to as the invariant chain. Before the class II heterodimer appears on the cell surface, the invariant chain dissociates but it has so far been unclear as to whether or not a proportion of the invariant chain also appears on the plasma membrane. We describe a study with th...

here, the concept of electric capacity on finsler spaces is introduced and the fundamentalconformal invariant property is proved, i.e. the capacity of a compact set on a connected non-compact finslermanifold is conformal invariant. this work enables mathematicians and theoretical physicists to become morefamiliar with the global finsler geometry and one of its new applications.