Trends in pedestrian injury mortality for children aged 0-4 and 5-14 for England and Wales, Denmark, Sweden, the USA, and New Zealand were examined from 1968 onwards. While there has been a reduction in the pedestrian mortality in all these countries, there are striking international differences in the extent of these reductions. Denmark has achieved the greatest fall in mortality with the smal...

First, notice that the smallest value1 of r is minx∈[−L,L−1] r[x] = r[−1] = δ0 + δ1 − UL and occurs at x = −1. Next, consider solving the taut string problem by enforcing only the constraint |s[−1] − r[−1]| ≤ λ. The cost of the taut string problem is minimum for the shortest path s through a point at x = −1. We can decompose such path into the concatenation of the shortest path from x = −L− 1 t...

A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph is (strongly) rainbow connected if there exists a (geodesic) rainbow path between every pair of vertices. The (strong) rainbow connectivity of a graph G, denoted by (src(G), respectively) rc(G) is the smallest number of colors required to edge color the graph such ...

This paper presents a disambiguation approach for t ransla t ing non-segmented-Kana into Kanji. The method consists of two steps. In the first step, an input sentence is analyzed morphologically and ambiguous morphemes are stored in a network form. In the second step, the best path, which is a string of morphemes, is selected by syntactic and semantic analysis based on case grammar. In order to...

The oriented diameter of a bridgeless graph G is min{diam(H) |H is an orientation of G}. A path in an edge-colored graph G, where adjacent edges may have the same color, is called rainbow if no two edges of the path are colored the same. The rainbow connection number rc(G) of G is the smallest integer k for which there exists a k-edge-coloring of G such that every two distinct vertices of G are...

Learning Real-Time A* (LRTA*) is a real-time search method that makes decisions fast and still converges to a shortest path when it solves the same planning task repeatedly. In this paper, we propose new methods to speed up its convergence. We show that LRTA* often converges significantly faster when it breaks ties towards successors with smallest f-values (a la A*) and even faster when it move...

The classical PERT approach uses the path with the largest expected duration as the critical path to estimate the probability of completing a network by a given deadline. However, in general, such a path is not the most critical path (MCP) and does not have the smallest estimate for the probability of completion time. The main idea of this paper is derived from the domination structure between ...

(b) In the relaxation we can get many fractional paths between each demand pair of total unit value. These paths can be read out of the solution in polynomial time in the following way. We find an edge e of the smallest positive flow value c, and subtract flow of this value from a cycle or a path going through e over edges of positive flow value. Repeating this procedure we will decompose the f...

An edge (vertex) coloured graph is rainbow-connected if there is a rainbow path between any two vertices, i.e. a path all of whose edges (internal vertices) carry distinct colours. Rainbow edge (vertex) connectivity of a graph G is the smallest number of colours needed for a rainbow edge (vertex) colouring of G. In this paper we propose a very simple approach to studying rainbow connectivity in...

We investigate limits of performance in reference-tracking and path-following and highlight an essential difference between them. For a class of nonlinear systems, we show that in reference-tracking, the smallest achievable L2 norm of the tracking error is equal to the least amount of control energy needed to stabilize the zero-dynamics of the error system. We then show that this fundamental pe...