[show abstract][hide abstract] ABSTRACT: Max-linear programs have been used to describe optimisation problems for multiprocessor interactive systems. In some instances the variables used in this model are required to be integer; however, no method seems to exist for finding integer solutions to max-linear programs.
For a generic class of matrices, we show that integer solutions to two-sided max-linear systems and programs can be found in polynomial time. For general matrices, we adapt the existing methods for finding real solutions to obtain algorithms for finding integer solutions.
[show abstract][hide abstract] ABSTRACT: Adhesion of tumor cells to matrix components and endothelial cells is essential for tumor metastasis. Investigation of the adhesion molecules required and the signals which induce tumor cell adhesion and migration are crucial in order to increase our understanding of this process. This chapter describes protocols which may be used to study tumor cell adhesion to purified matrix elements and tissue sections. It also details methods used to investigate cell adhesion to endothelial cells, both under static and flow conditions. In addition, there is a section detailing the use of endothelial cell cultures on three-dimensional collagen gels which are useful when studying adhesion to endothelial cells and onward invasion through a protein matrix.
Methods in molecular biology (Clifton, N.J.) 01/2014; 1070:57-75.
[show abstract][hide abstract] ABSTRACT: Blood platelets have recently been proposed to play a critical role in the development and repair of the lymphatic system. The platelet C-type lectin receptor CLEC-2 and its ligand, the transmembrane protein Podoplanin, which is expressed at high levels on lymphatic endothelial cells (LECs), are required to prevent mixing of the blood and lymphatic vasculatures during mid-gestation. A similar defect is seen in mice deficient in the tyrosine kinase Syk, which plays a vital role in mediating platelet activation by CLEC-2. Furthermore, blood-lymphatic mixing is also present in mice with platelet-/megakaryocyte-specific deletions of CLEC-2 and Syk, suggesting that the phenotype is platelet in origin. The molecular basis of this effect is not known, but it is independent of the major platelet receptors that support hemostasis, including integrin αIIbβ3 (GPIIb-IIIa). Radiation chimeric mice reconstituted with CLEC-2-deficient or Syk-deficient bone marrow exhibit blood-lymphatic mixing in the intestines, illustrating a role for platelets in repair and growth of the lymphatic system. In this review, we describe the events that led to the identification of this novel role of platelets and discuss possible molecular mechanisms and the physiological and pathophysiological significance.
Advances in anatomy, embryology, and cell biology 01/2014; 214:93-105.