388 research outputs found
On the Origin of the Quantum Rules for Identical Particles
We present a proof of the Symmetrization Postulate for the special case of
noninteracting, identical particles. The proof is given in the context of the
Feynman formalism of Quantum Mechanics, and builds upon the work of Goyal,
Knuth and Skilling (Phys. Rev. A 81, 022109 (2010)), which shows how to derive
Feynman's rules from operational assumptions concerning experiments. Our proof
is inspired by an attempt to derive this result due to Tikochinsky (Phys. Rev.
A 37, 3553 (1988)), but substantially improves upon his argument, by clarifying
the nature of the subject matter, by improving notation, and by avoiding
strong, abstract assumptions such as analyticity.Comment: 8 pages, all figures embedded as TikZ. V2 clarified wording from V1
in response to reviewe
Finding Even Subgraphs Even Faster
Problems of the following kind have been the focus of much recent research in
the realm of parameterized complexity: Given an input graph (digraph) on
vertices and a positive integer parameter , find if there exist edges
(arcs) whose deletion results in a graph that satisfies some specified parity
constraints. In particular, when the objective is to obtain a connected graph
in which all the vertices have even degrees---where the resulting graph is
\emph{Eulerian}---the problem is called Undirected Eulerian Edge Deletion. The
corresponding problem in digraphs where the resulting graph should be strongly
connected and every vertex should have the same in-degree as its out-degree is
called Directed Eulerian Edge Deletion. Cygan et al. [\emph{Algorithmica,
2014}] showed that these problems are fixed parameter tractable (FPT), and gave
algorithms with the running time . They also asked, as
an open problem, whether there exist FPT algorithms which solve these problems
in time . In this paper we answer their question in the
affirmative: using the technique of computing \emph{representative families of
co-graphic matroids} we design algorithms which solve these problems in time
. The crucial insight we bring to these problems is to view
the solution as an independent set of a co-graphic matroid. We believe that
this view-point/approach will be useful in other problems where one of the
constraints that need to be satisfied is that of connectivity
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