Any finite set of lines in the real projective plane determines a cell complex; these complexes and their combinatorial properties have been a subject of study at least since 1826 [9]. More recently, Levi [6] considered a topological generalization of this notion, defined as follows: Consider a simple closed curve in RP2 which does not separate RP2; this is called a pseudoline. (It is clear tha...

We introduce a new combinatorial object, the double-permutation sequence, and use it to encode a family of mutually disjoint compact convex sets in the plane in a way that captures many of its combinatorial properties. We use this encoding to give a new proof of the Edelsbrunner-Sharir theorem that a collection of n compact convex sets in the plane cannot be met by straight lines in more than 2...

Fish respire through gills, which have evolved to extract aqueous oxygen. Fish gills consist of filaments with well-ordered lamellar structures, which play a role in maximizing oxygen diffusion. It is interesting that when we anatomically observe the gills of various fish species, gill interlamellar distances (d) vary little among them, despite large variations in body mass (Mb). Noting that th...

At first glance, the trailing tentacles of a jellyfish appear to be randomly arranged. However, close examination of medusae has revealed that the arrangement and developmental order of the tentacles obey a mathematical rule. Here, we show that medusa jellyfish adopt the best strategy to achieve the most uniform distribution of a variable number of tentacles. The observed order of tentacles is ...

We study the problem of arranging circuit components on a straight line so as to minimize the total wire length needed to realize the inter component nets. Branch-and-bound and dynamic programming algorithms that find optimal solutions are presented. In addition, heuristic approaches including some that employ the Monte Carlo method are developed and an experimental evaluation provided.

We study the optimal linear arrangement (OLA) problem on interval graphs. Several linear layout problems that are NP-hard on general graphs are solvable in polynomial time on interval graphs. We prove that, quite surprisingly, optimal linear arrangement of interval graphs is NP-hard. The same result holds for permutation graphs. We present a lower bound and a simple and fast 2-approximation alg...

the present study is concerned with the simultaneous optimization of the size of components and the arrangement of connections for performance-based seismic design of low-rise spsws. design variables include the size of beams and columns, the thickness of the infill panels, the type of each beam-to-column connection and the type of each infill-to-boundary frame connection. the objective functio...