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A remark on the connectedness of spheres in Cayley graphs
The aim of this small note is to prove an elementary yet useful properties of
finitely presented groups. Let G be a finitely generated group with one end.
Fix a (finite) generating set and let be the ball of radius around
. Let be the infinite connected component of the complement
of . Then G has connected spheres if there exists a such that
is connected for all . This note shows
that if G is finitely presented then it has connected spheres.Comment: 5p., 1 figur
Memorializing Genocide I: Earlier Holocaust Documentaries
In this essay, I discuss in detail two of the earliest such documentaries: Death Mills (1945), directed by Billy Wilder; and Nazi Concentration Camps (1945), directed by George Stevens. Both film-makers were able to get direct footage of the newly-liberated concentration camps from the U.S. Army. Wilder served as a Colonel in the U.S. Armyâs Psychological Warfare department in 1945 and was tasked with producing a documentary on the death camps as well as helping to restart Germanyâs film industry.
I next review the great French Holocaust documentary Night and Fog (1955), directed by Alain Resnais. This was a widely acclaimed film, winning the Prix Jean Vigo in 1956. Resnais employed a camp survivor (Jean Cayrol) to write the dialogue, and it is powerful, indeed, truly lyrical in places.
The last film I review in the essay is a generally overlooked British Thames Television documentary, Genocide: 1941-1945 (1974), directed by Michael Darlow (and narrated by Sir Laurence Oliver). It was the first of the major Holocaust documentaries to focus on the point that the Nazi genocide targeted first and foremost the Jewish people, and to explore the development of Nazi racial theory, and the rise of the SS
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Experimental evaluation of preprocessing algorithms for constraint satisfaction problems
This paper presents an experimental evaluation of two orthogonal schemes for preprocessing constraint satisfaction problems (CSPs). The first of these schemes involves a class of local consistency techniques that includes directional arc consistency, directional path consistency, and adaptive consistency. The other scheme concerns the prearrangement of variables in a linear order to facilitate an efficient search. In the first series of experiments, we evaluated the effect of each of the local consistency techniques on backtracking and its common enhancement, backjumping. Surprizingly, although adaptive consistency has the best worst-case complexity bounds, we have found that it exhibits the worst performance, unless the constraint graph was very sparse. Directional arc consistency (followed by either backjumping or backtracking) and backjumping (without any pre-processing) outperformed all other techniques; moreover, the former dominated the latter in computationally intensive situations. The second series of experiments suggests that maximum cardinality and minimum width arc the best pre-ordering (i.e., static ordering) strategies, while dynamic search rearrangement is superior to all the preorderings studied
Proceedings of the Biological Society of Washington.
v.5 (1888-1890
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