The two-dimensional Single Large Object Placement Problem (SLOPP) problem consists of determining a cutting pattern of a set of n small rectangular piece types (little object) on a rectangular stock plate (large object) of length L and width W, as to maximize the sum of the profits of the pieces to be cut. Each piece type i, i = 1, . . ., m, is characterized by a length li, a width wi, a profit...

We investigate a new application of DC (Difference of Convex functions) programming and DCA (DC Algorithm) in solving the constrained two-dimensional non-guillotine cutting problem. This problem consists of cutting a number of rectangular pieces from a large rectangular object. The cuts are done under some constraints and the objective is to maximize the total value of the pieces cut. We reform...

Given a convex polyhedron with n vertices and F faces, what is the fewest number of pieces, each of which unfolds to a simple polygon, into which it may be cut by slices along edges? Shephard’s conjecture says that this number is always 1, but it’s still open. The fewest nets problem asks to provide upper bounds for the number of pieces in terms of n and/or F . We improve the previous best know...

It is shown that solutions to the 2nd order BFKL eigenvalue equation exist for arbitrary large real values of the complex angular momentum j. This corresponds to a cut in the complex j plane along the whole real axis, and it makes the use of the complex angular momentum variable for the calculation of the high-energy behavior somewhat questionable. The eigenfunctions contain non-perturbative pi...

Given n non-vertical pairwise disjoint triangles in 3-space, their vertical depth (above/below) relation may contain cycles. We show that, for any ε > 0, the triangles can be cut into O(n3/2+ε) pieces, where each piece is a connected semi-algebraic set whose description complexity depends only on the choice of ε, such that the depth relation among these pieces is now a proper partial order. Thi...

AIM Triple-negative breast cancer (TNBC), defined by the absence of receptors for estrogen, progesterone and human epithelial receptor 2 (HER2), is a recalcitrant disease in need of effective therapy. We previously isolated very-highly metastatic variants of the TNBC cell line MDA-MB-231 using serial orthotopic implantation of MDA-MB-231 human breast cancer cells in nude mice. MATERIALS AND M...

There are two general strategies for sequencing a complete genome. The method preferred by the Human Genome Project is the hierarchical shotgun sequencing method. In this approach, genomic DNA is cut into pieces of about 150 Mb and inserted into BAC vectors, transformed into E. coli where they are replicated and stored. The BAC inserts are isolated and mapped to determine the order of each clon...

Modular Kirigami is here defined as the symmetric assemblage, with artistic intent, of multiple copies of cut paper shapes. Intricate examples with icosahedral symmetry are presented. These consist purely of interlocked flat pieces of paper, with no folding and no adhesives.