Enumeration of PLCP-orientations of the 4-cube

The linear complementarity problem (LCP) provides a unified approach to many problems such as linear programs, convex quadratic programs, and bimatrix games. The general LCP is known to be NP-hard, but there are some promising results that suggest the possibility that the LCP with a P-matrix (PLCP) may be polynomial-time solvable. However, no polynomial-time algorithm for the PLCP has been found yet and the computational complexity of the PLCP remains open. Simple principal pivoting (SPP) algorithms, also known as Bard-type algorithms, are candidates for polynomial-time algorithms for the PLCP. In 1978, Stickney and Watson interpreted SPP algorithms as a family of algorithms that seek the sink of unique-sink orientations of $n$-cubes. They performed the enumeration of the arising orientations of the $3$-cube, hereafter called PLCP-orientations. In this paper, we present the enumeration of PLCP-orientations of the $4$-cube.The enumeration is done via construction of oriented matroids generalizing P-matrices and realizability classification of oriented matroids.Some insights obtained in the computational experiments are presented as well

Complete combinatorial characterization of greedy-drawable trees

A (Euclidean) greedy drawing of a graph is a drawing in which, for any two vertices $s,t$ ($s \neq t$), there is a neighbor vertex of $s$ that is closer to $t$ than to $s$ in the Euclidean distance. Greedy drawings are important in the context of message routing in networks, and graph classes that admit greedy drawings have been actively studied. N\"{o}llenburg and Prutkin (Discrete Comput. Geom., 58(3), pp.543-579, 2017) gave a characterization of greedy-drawable trees in terms of an inequality system that contains a non-linear equation. Using the characterization, they gave a linear-time recognition algorithm for greedy-drawable trees of maximum degree $\leq 4$. However, a combinatorial characterization of greedy-drawable trees of maximum degree 5 was left open. In this paper, we give a combinatorial characterization of greedy-drawable trees of maximum degree $5$, which leads to a complete combinatorial characterization of greedy-drawable trees. Furthermore, we give a characterization of greedy-drawable pseudo-trees.Comment: 26 pages, 30 fugure

Economic Impacts of a New Road Network in San-En Region, Japan: A Spatial Computable General Equilibrium Model

In this paper, we aim to evaluate impacts of a new road network on the regional economy in San-en, Japan. San-en area is a boundary region between Aichi and Shizuoka Prefectures where the industrial sector is concentrated. The regional economy in San-en strongly depends on the regional transportation networks. Recently, a new road construction is planned in the region. The efficiency of road investment is expected for the regional economy. We construct a spatial computable general equilibrium model to evaluate the border economy. The spatial economic impacts of a new road construction are analyzed by the numerical simulation under several scenarios.

Impact of polyplex micelles installed with cyclic RGD peptide as ligand on gene delivery to vascular lesions

Gene therapy is expected to open a new strategy for the treatment of refractory vascular diseases, so the development of appropriate gene vectors for vascular lesions is needed. To realize this requirement with a non-viral approach, cyclo(RGDfK) peptide (cRGD) was introduced to block copolymer, poly(ethylene glycol)-block-polycation carrying ethylenediamine units (PEG-PAsp(DET)). cRGD recognizes αvβ3 and αvβ5 integrins, which are abundantly expressed in vascular lesions. cRGD-conjugated PEG-PAsp(DET) (cRGD-PEG-PAsp(DET)) formed polyplex micelles through complexation with plasmid DNA (pDNA), and the cRGD-PEG-PAsp(DET) micelles achieved significantly more efficient gene expression and cellular uptake as compared with PEG-PAsp(DET) micelles in endothelial cells and vascular smooth muscle cells. Intracellular tracking of pDNA showed that cRGD-PEG-PAsp(DET) micelles were internalized via caveolae-mediated endocytosis, which is associated with a pathway avoiding lysosomal degradation, and that PEG-PAsp(DET) micelles were transported to acidic endosomes and lysosomes via clathrin-mediated endocytosis. Further, in vivo evaluation in rat carotid artery with a neointimal lesion revealed that cRGD-PEG-PAsp(DET) micelles realized sustained gene expression, while PEG-PAsp(DET) micelles facilitated rapid but transient gene expression. These findings suggest that introduction of cRGD to polyplex micelles might create novel and useful functions for gene transfer and contribute to the establishment of efficient gene therapy for vascular diseases