This important study presents a new method for longitudinally tracking cells in two-photon imaging data that addresses the specific challenges of imaging neurons in the developing cortex. It provides ...

To model electromagnetic wave propagation for coherent communications without polarization dependent losses, the unitary 2 ×2 Jones transfer matrix formalism is typically used. In this study, we ...

The complement of a knot is everything in three-dimensional space that isn’t the knot. It’s a topological object—if you wiggle the knot around, then its complement also squishes around.

Researchers have solved a long-standing problem in topology by helping classify four-dimensional shapes (4-manifolds) that allow certain types of deformations, known as quasiregular mappings, from ...

In contrast, quasiregular mappings can be found from a Euclidean space to several different spaces. Such manifolds are called ‘quasiregularly elliptic’.

Abstracts Dupin hypersurfaces in five dimensional Euclidean space parametrized by lines of curvature, with four distinct principal curvatures, are considered. A generic family of such hypersurfaces is ...

The aim of the paper is to show the fundamental advantage of the Euclidean Model of Space and Time (EMST) over Special Relativity (SR) in the field of wave description of matter. The EMST offers a ...

“The main result of my doctoral thesis complements the answer to Gromov’s question, as the result can be used to classify closed simply connected four-dimensional manifolds for which there is a ...

Euclidean geometry is the branch of mathematics describing shapes and the spatial relationships between objects in two-dimensional (2D) and three-dimensional (3D) settings. The rules of Euclidean ...

In 1843, William Rowan Hamilton had a four-dimensional flash of insight that still shapes our three-dimensional world.

An iterative procedure is described for determining half rotations in n-dimensional Euclidean space. The method is a variant of the cyclic Jacobi procedure and utilizes elementary plane rotations to ...