7,578 research outputs found
Mass Spectra of N=2 Supersymmetric SU(n) Chern-Simons-Higgs Theories
An algebraic method is used to work out the mass spectra and symmetry
breaking patterns of general vacuum states in N=2 supersymmetric SU(n)
Chern-Simons-Higgs systems with the matter fields being in the adjoint
representation. The approach provides with us a natural basis for fields, which
will be useful for further studies in the self-dual solutions and quantum
corrections. As the vacuum states satisfy the SU(2) algebra, it is not
surprising to find that their spectra are closely related to that of angular
momentum addition in quantum mechanics. The analysis can be easily generalized
to other classical Lie groups.Comment: 17 pages, use revte
SACOC: A spectral-based ACO clustering algorithm
The application of ACO-based algorithms in data mining is growing over the last few years and several supervised and unsupervised learning algorithms have been developed using this bio-inspired approach. Most recent works concerning unsupervised learning have been focused on clustering, where ACO-based techniques have showed a great potential. At the same time, new clustering techniques that seek the continuity of data, specially focused on spectral-based approaches in opposition to classical centroid-based approaches, have attracted an increasing research interest–an area still under study by ACO clustering techniques. This work presents a hybrid spectral-based ACO clustering algorithm inspired by the ACO Clustering (ACOC) algorithm. The proposed approach combines ACOC with the spectral Laplacian to generate a new search space for the algorithm in order to obtain more promising solutions. The new algorithm, called SACOC, has been compared against well-known algorithms (K-means and Spectral Clustering) and with ACOC. The experiments measure the accuracy of the algorithm for both synthetic datasets and real-world datasets extracted from the UCI Machine Learning Repository
A Fast and Efficient Incremental Approach toward Dynamic Community Detection
Community detection is a discovery tool used by network scientists to analyze
the structure of real-world networks. It seeks to identify natural divisions
that may exist in the input networks that partition the vertices into coherent
modules (or communities). While this problem space is rich with efficient
algorithms and software, most of this literature caters to the static use-case
where the underlying network does not change. However, many emerging real-world
use-cases give rise to a need to incorporate dynamic graphs as inputs.
In this paper, we present a fast and efficient incremental approach toward
dynamic community detection. The key contribution is a generic technique called
, which examines the most recent batch of changes made to an
input graph and selects a subset of vertices to reevaluate for potential
community (re)assignment. This technique can be incorporated into any of the
community detection methods that use modularity as its objective function for
clustering. For demonstration purposes, we incorporated the technique into two
well-known community detection tools. Our experiments demonstrate that our new
incremental approach is able to generate performance speedups without
compromising on the output quality (despite its heuristic nature). For
instance, on a real-world network with 63M temporal edges (over 12 time steps),
our approach was able to complete in 1056 seconds, yielding a 3x speedup over a
baseline implementation. In addition to demonstrating the performance benefits,
we also show how to use our approach to delineate appropriate intervals of
temporal resolutions at which to analyze an input network
The Chern-Simons Coefficient in Supersymmetric Non-abelian Chern-Simons Higgs Theories
By taking into account the effect of the would be Chern-Simons term, we
calculate the quantum correction to the Chern-Simons coefficient in
supersymmetric Chern-Simons Higgs theories with matter fields in the
fundamental representation of SU(n). Because of supersymmetry, the corrections
in the symmetric and Higgs phases are identical. In particular, the correction
is vanishing for N=3 supersymmetric Chern-Simons Higgs theories. The result
should be quite general, and have important implication for the more
interesting case when the Higgs is in the adjoint representation.Comment: more references and explanation about rgularization dpendence are
included, 13 pages, 1 figure, latex with revte
Universal saturation of electron dephasing in three-dimensional disordered metals
We have systematically investigated the low-temperature electron dephasing
times in more than 40 three-dimensional polycrystalline impure
metals with distinct material characteristics. In all cases, a saturation of
the dephasing time is observed below about a (few) degree(s) Kelvin, depending
on samples. The value of the saturated dephasing time [] falls basically in the range 0.005 to 0.5 ns for
all samples. Particularly, we find that scales with the electron
diffusion constant as , with close to or
slightly larger than 1, for over two decades of from about 0.1 to 10
cm/s. Our observation suggests that the saturation behavior of
is universal and intrinsic in three-dimensional polycrystalline impure metals.
A complete theoretical explanation is not yet available.Comment: 4 pages, 3 eps figure
The ideal gas as an urn model: derivation of the entropy formula
The approach of an ideal gas to equilibrium is simulated through a
generalization of the Ehrenfest ball-and-box model. In the present model, the
interior of each box is discretized, {\it i.e.}, balls/particles live in cells
whose occupation can be either multiple or single. Moreover, particles
occasionally undergo random, but elastic, collisions between each other and
against the container walls. I show, both analitically and numerically, that
the number and energy of particles in a given box eventually evolve to an
equilibrium distribution which, depending on cell occupations, is binomial
or hypergeometric in the particle number and beta-like in the energy.
Furthermore, the long-run probability density of particle velocities is
Maxwellian, whereas the Boltzmann entropy exactly reproduces the
ideal-gas entropy. Besides its own interest, this exercise is also relevant for
pedagogical purposes since it provides, although in a simple case, an explicit
probabilistic foundation for the ergodic hypothesis and for the maximum-entropy
principle of thermodynamics. For this reason, its discussion can profitably be
included in a graduate course on statistical mechanics.Comment: 17 pages, 3 figure
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