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Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
Track forecast errors were less than half of the 10-year average for 2005. Four- to five-day errors were slightly larger than the shorter-term overall; however, this was largely related to the west-southwest track shift across the Florida Panhandle rather than Katrina's path in the days leading up to landfall along the Gulf Coast. [52]
What would eventually become Katrina started as Tropical Depression Twelve which formed over the Bahamas at 5:00 p.m. EDT (2100 UTC) on August 23, 2005, partially from the remains of Tropical Depression Ten, which had dissipated due to the effects of a nearby upper trough.
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph.A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges.
By August 26, many of the computer models had shifted the potential path of Katrina 150 miles (240 km) westward from the Florida Panhandle, putting the city of New Orleans directly in the center of their track probabilities; the chances of a direct hit were forecast at 17%, with strike probability rising to 29% by August 28. [32]
A mapping : between total spaces of two fibrations : and : with the same base space is a fibration homomorphism if the following diagram commutes: . The mapping is a fiber homotopy equivalence if in addition a fibration homomorphism : exists, such that the mappings and are homotopic, by fibration homomorphisms, to the identities and . [2]: 405-406
German code breaking in World War II achieved some notable successes cracking British naval ciphers until well into the fourth year of the war, [1] using the extensive German radio intelligence operations during World War II.
Debris location relative to the known flight path (red), calculated flight path (yellow), and underwater search area since October 2014 (dark blue; 46% searched as of 29 July 2015). On 29 July, a piece of marine debris is found on Réunion—an island in the western Indian Ocean—that resembled an aircraft component.