353 research outputs found
How long does it take to generate a group?
The diameter of a finite group with respect to a generating set is
the smallest non-negative integer such that every element of can be
written as a product of at most elements of . We denote this
invariant by \diam_A(G). It can be interpreted as the diameter of the Cayley
graph induced by on and arises, for instance, in the context of
efficient communication networks.
In this paper we study the diameters of a finite abelian group with
respect to its various generating sets . We determine the maximum possible
value of \diam_A(G) and classify all generating sets for which this maximum
value is attained. Also, we determine the maximum possible cardinality of
subject to the condition that \diam_A(G) is "not too small". Connections with
caps, sum-free sets, and quasi-perfect codes are discussed
The incidence of prostate cancer in Iran: Results of a population-based cancer registry
Background: Little is known about the epidemiology of prostate cancer in Iranian men. We carried out an active prostate cancer surveillance program in five provinces of Iran. Methods: Data used in this study were obtained from population-based cancer registries between 1996 and 2000. Results: The age-standardized incidence rate of prostate carcinoma in the five provinces was 5.1 per 100,000 person-years. No significant difference was seen in the age-standardized incidence rate of prostate cancer within the provinces studied. The mean±SD age of patients with prostate cancer was 67±13.5 years. Conclusion: The incidence of prostate cancer in Iran is very low as compared to the Western countries. This can partly be explained by lack of nationwide screening program, younger age structure and quality of cancer registration system in Iran
Resolving sets for Johnson and Kneser graphs
A set of vertices in a graph is a {\em resolving set} for if, for
any two vertices , there exists such that the distances . In this paper, we consider the Johnson graphs and Kneser
graphs , and obtain various constructions of resolving sets for these
graphs. As well as general constructions, we show that various interesting
combinatorial objects can be used to obtain resolving sets in these graphs,
including (for Johnson graphs) projective planes and symmetric designs, as well
as (for Kneser graphs) partial geometries, Hadamard matrices, Steiner systems
and toroidal grids.Comment: 23 pages, 2 figures, 1 tabl
On analog quantum algorithms for the mixing of Markov chains
The problem of sampling from the stationary distribution of a Markov chain
finds widespread applications in a variety of fields. The time required for a
Markov chain to converge to its stationary distribution is known as the
classical mixing time. In this article, we deal with analog quantum algorithms
for mixing. First, we provide an analog quantum algorithm that given a Markov
chain, allows us to sample from its stationary distribution in a time that
scales as the sum of the square root of the classical mixing time and the
square root of the classical hitting time. Our algorithm makes use of the
framework of interpolated quantum walks and relies on Hamiltonian evolution in
conjunction with von Neumann measurements.
There also exists a different notion for quantum mixing: the problem of
sampling from the limiting distribution of quantum walks, defined in a
time-averaged sense. In this scenario, the quantum mixing time is defined as
the time required to sample from a distribution that is close to this limiting
distribution. Recently we provided an upper bound on the quantum mixing time
for Erd\"os-Renyi random graphs [Phys. Rev. Lett. 124, 050501 (2020)]. Here, we
also extend and expand upon our findings therein. Namely, we provide an
intuitive understanding of the state-of-the-art random matrix theory tools used
to derive our results. In particular, for our analysis we require information
about macroscopic, mesoscopic and microscopic statistics of eigenvalues of
random matrices which we highlight here. Furthermore, we provide numerical
simulations that corroborate our analytical findings and extend this notion of
mixing from simple graphs to any ergodic, reversible, Markov chain.Comment: The section concerning time-averaged mixing (Sec VIII) has been
updated: Now contains numerical plots and an intuitive discussion on the
random matrix theory results used to derive the results of arXiv:2001.0630
Universal Geometric Graphs
We introduce and study the problem of constructing geometric graphs that have
few vertices and edges and that are universal for planar graphs or for some
sub-class of planar graphs; a geometric graph is \emph{universal} for a class
of planar graphs if it contains an embedding, i.e., a
crossing-free drawing, of every graph in .
Our main result is that there exists a geometric graph with vertices and
edges that is universal for -vertex forests; this extends to
the geometric setting a well-known graph-theoretic result by Chung and Graham,
which states that there exists an -vertex graph with edges
that contains every -vertex forest as a subgraph. Our bound on
the number of edges cannot be improved, even if more than vertices are
allowed.
We also prove that, for every positive integer , every -vertex convex
geometric graph that is universal for -vertex outerplanar graphs has a
near-quadratic number of edges, namely ; this almost
matches the trivial upper bound given by the -vertex complete
convex geometric graph.
Finally, we prove that there exists an -vertex convex geometric graph with
vertices and edges that is universal for -vertex
caterpillars.Comment: 20 pages, 8 figures; a 12-page extended abstracts of this paper will
appear in the Proceedings of the 46th Workshop on Graph-Theoretic Concepts in
Computer Science (WG 2020
Highly Luminescent Salts Containing Well-Shielded Lanthanide-Centered Complex Anions and Bulky Imidazolium Countercations
In this paper, we report on the syntheses, structures, and characterization of four molten salts containing imidazolium cations and europium(III)- or terbium(III)-centered complex anions. In the complex anions, the lanthanide centers are wrapped by four pseudodiketonate anionic ligands, which prevent them from contacting with high-frequency oscillators and allow them to show intense characteristic europium(III) or terbium(III) emission, small line widths, high color purity, high quantum yields (30â49%), and long decay times (\u3e2 ms)
Development of intuitive rules: Evaluating the application of the dual-system framework to understanding children's intuitive reasoning
This is an author-created version of this article. The original source of publication is Psychon Bull Rev. 2006 Dec;13(6):935-53
The final publication is available at www.springerlink.com
Published version: http://dx.doi.org/10.3758/BF0321390
Sensitivity of a tonne-scale NEXT detector for neutrinoless double beta decay searches
The Neutrino Experiment with a Xenon TPC (NEXT) searches for the neutrinoless
double-beta decay of Xe-136 using high-pressure xenon gas TPCs with
electroluminescent amplification. A scaled-up version of this technology with
about 1 tonne of enriched xenon could reach in less than 5 years of operation a
sensitivity to the half-life of neutrinoless double-beta decay decay better
than 1E27 years, improving the current limits by at least one order of
magnitude. This prediction is based on a well-understood background model
dominated by radiogenic sources. The detector concept presented here represents
a first step on a compelling path towards sensitivity to the parameter space
defined by the inverted ordering of neutrino masses, and beyond.Comment: 22 pages, 11 figure
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