3,496 research outputs found
Structure of the Group of Balanced Labelings on Graphs, its Subgroups and Quotient Groups
We discuss functions from edges and vertices of an undirected graph to an
Abelian group. Such functions, when the sum of their values along any cycle is
zero, are called balanced labelings. The set of balanced labelings forms an
Abelian group. We study the structure of this group and the structure of two
closely related to it groups: the subgroup of balanced labelings which consists
of functions vanishing on vertices and the corresponding factor-group. This
work is completely self-contained, except the algorithm for obtaining the
3-edge-connected components of an undirected graph, for which we make
appropriate references to the literature.Comment: 22 page
Exact mean first-passage time on the T-graph
We consider a simple random walk on the T-fractal and we calculate the exact
mean time to first reach the central node . The mean is performed
over the set of possible walks from a given origin and over the set of starting
points uniformly distributed throughout the sites of the graph, except .
By means of analytic techniques based on decimation procedures, we find the
explicit expression for as a function of the generation and of the
volume of the underlying fractal. Our results agree with the asymptotic
ones already known for diffusion on the T-fractal and, more generally, they are
consistent with the standard laws describing diffusion on low-dimensional
structures.Comment: 6 page
Partial-Matching and Hausdorff RMS Distance Under Translation: Combinatorics and Algorithms
We consider the RMS distance (sum of squared distances between pairs of
points) under translation between two point sets in the plane, in two different
setups. In the partial-matching setup, each point in the smaller set is matched
to a distinct point in the bigger set. Although the problem is not known to be
polynomial, we establish several structural properties of the underlying
subdivision of the plane and derive improved bounds on its complexity. These
results lead to the best known algorithm for finding a translation for which
the partial-matching RMS distance between the point sets is minimized. In
addition, we show how to compute a local minimum of the partial-matching RMS
distance under translation, in polynomial time. In the Hausdorff setup, each
point is paired to its nearest neighbor in the other set. We develop algorithms
for finding a local minimum of the Hausdorff RMS distance in nearly linear time
on the line, and in nearly quadratic time in the plane. These improve
substantially the worst-case behavior of the popular ICP heuristics for solving
this problem.Comment: 31 pages, 6 figure
The scientific heritage of Richard Henry Dalitz, FRS (1925-2006)
Professor Richard H. Dalitz passed away on January 13, 2006. He was almost 81
years old and his outstanding contributions are intimately connected to some of
the major breakthroughs of the 20th century in particle and nuclear physics.
These outstanding contributions go beyond the Dalitz Plot, Dalitz Pair and CDD
poles that bear his name. He pioneered the theoretical study of strange baryon
resonances, of baryon spectroscopy in the quark model, and of hypernuclei, to
all of which he made lasting contributions. His formulation of the
" puzzle" led to the discovery that parity is not a symmetry of
the weak interactions. A brief scientific evaluation of Dalitz's major
contributions to particle and nuclear physics is hereby presented, followed by
the first comprehensive list of his scientific publications, as assembled from
several sources. The list is divided into two categories: the first, main part
comprises Dalitz's research papers and reviews, including topics in the history
of particle physics, biographies and reminiscences; the second part lists book
reviews, public lectures and obituaries authored by Dalitz, and books edited by
him. This provides the first necessary step towards a more systematic research
of the Dalitz heritage in modern physics.
The present 2016 edition updates the original 2006 edition, published in
Nucl. Phys. A 771 (2006) 2-7, doi:10.1016/j.nuclphysa.2006.03.007, and 8-25,
doi:10.1016/j.nuclphysa.2006.03.008, by including for the first time a dozen or
so of publications, found recently in a list submitted to the Royal Society by
Dalitz in 2004, that escaped our attention in the original version.Comment: updates the original edition by including several publications,
mostly in category III, that were unknown to us in 200
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