Nodal Cubics Through Eight Given Points

On a Pencil Op Nodal Cubics

Left-right asymmetry: nodal points.

The striking left-right asymmetry of visceral organs is known to depend on left- and right-side-specific cascades of gene expression during early embryogenesis. Now, developmental biologists are characterizing the earliest steps in asymmetry determination that dictate the sidedness of asymmetric gene expression. The proteins and structures involved control fascinating physiological processes, s...

Labeling points with given rectangles

In this paper, we consider the following problem: Given n pairs of a point and an axis-parallel rectangle in the plane, place each rectangle at each point in order that the point lies on the corner of the rectangle and the rectangles do not intersect. If the size of the rectangles may be enlarged or reduced at the same factor, maximize the factor. This paper generalizes the results of Formann a...

Computing some fundamental numbers of the variety of nodal cubics in P3

In this paper we obtain some fundamental numbers of the family Unod of non-degenerate nodal cubics in P3 involving, in addition to the characteristic conditions, other fundamental conditions, as for example that the node lies on a plane. Some of these numberswere first obtained by Schubert in his Kalkül der abzählenden Geometrie. In our approach we construct several compactifications of Unod, w...

Matching of Objects Nodal Points Improvement

The main objective of this work was to improve a previously developed object matching methodology. This overall methodology includes: a modeling phase; followed by a modal analysis; the construction of a matrix that relates both sets of objects points; and the matching phase. The previously implemented matching phase is based on a local search; with this solution the relation between objects no...