An experience of a Geometry Lab based on Mathematica for a Geometry course for Computer Science students, intended to be a basis for later courses in Computer Graphics, CAD and CAGD, is presented. Students combine their knowledge of basic geometry topics like polyhedra, curve and surface generation, aane and perspective transformations, among others, by means of lists manipulation and a clever ...

Over the past decade, several technologies have emerged to access nucleic acid-tagged libraries and select the fittest compound within such libraries. This perspective focuses on recent development with PNA-tagged small molecules displayed on DNA templates for screening purposes and to probe the optimal geometry in multivalent interactions. WINSSINGER, Nicolas. DNA display of PNA-tagged ligands...

Verification and historical perspective are presented on the gyrokinetic particle simulations that discovered the device size scaling of turbulent transport and indentified the geometry model as the source of the long-standing disagreement between gyrokinetic particle and continuum simulations.

Perceptual geometry refers to the interdisciplinary research whose objectives focuses on study of geometry from the perspective of visual perception, and in turn, applies such geometric findings to the ecological study of vision. Perceptual geometry attempts to answer fundamental questions in perception of form and representation of space through synthesis of cognitive and biological theories o...

Many of the tools of higher dimensional complex birational algebraic geometry—including singularities of pairs, multiplier ideals, and log canonical thresholds— have ”characteristic p” analogs arising from ideas in tight closure theory. Tight closure, introduced by Hochster and Huneke in [17], is a closure operation performed on ideals in commutative rings of prime characteristic, and has an in...

I explore the terrain that lies between architecture and geometry, from the perspective of a structural scientist with no professional architectural expertise. The divide between these disciplines perhaps stems from an ancient dichotomy between the art versus engineering schools of architecture, fertilised by the current dogma that art and science can never meet. Architects stand to gain much f...

This work presents an automatic hybrid matching of central catadioptric and perspective images. It is based on the hybrid epipolar geometry. The goal is to obtain correspondences between an omnidirectional image and a conventional perspective image taken from different points of view. Mixing both kind of images has multiple applications, since an omnidirectional image captures many information ...