5,590 research outputs found
The Fastest Mixing Markov Process on a Graph and a Connection to a Maximum Variance Unfolding Problem
We consider a Markov process on a connected graph, with edges labeled with transition rates between the adjacent vertices. The distribution of the Markov process converges to the uniform distribution at a rate determined by the second smallest eigenvalue lambda_2 of the Laplacian of the weighted graph. In this paper we consider the problem of assigning transition rates to the edges so as to maximize lambda_2 subject to a linear constraint on the rates. This is the problem of finding the fastest mixing Markov process (FMMP) on the graph. We show that the FMMP problem is a convex optimization problem, which can in turn be expressed as a semidefinite program, and therefore effectively solved numerically. We formulate a dual of the FMMP problem and show that it has a natural geometric interpretation as a maximum variance unfolding (MVU) problem, , the problem of choosing a set of points to be as far apart as possible, measured by their variance, while respecting local distance constraints. This MVU problem is closely related to a problem recently proposed by Weinberger and Saul as a method for "unfolding" high-dimensional data that lies on a low-dimensional manifold. The duality between the FMMP and MVU problems sheds light on both problems, and allows us to characterize and, in some cases, find optimal solutions
Study of the weak annihilation contributions in charmless decays
In this paper, in order to probe the spectator-scattering and weak
annihilation contributions in charmless (where stands for a
light vector meson) decays, we perform the -analyses for the end-point
parameters within the QCD factorization framework, under the constraints from
the measured , , and
decays. The fitted results indicate that the end-point
parameters in the factorizable and nonfactorizable annihilation topologies are
non-universal, which is also favored by the charmless and (where
stands for a light pseudo-scalar meson) decays observed in the previous
work. Moreover, the abnormal polarization fractions measured by the LHCb
collaboration can be reconciled through the weak annihilation corrections.
However, the branching ratio of decay exhibits a
tension between the data and theoretical result, which dominates the
contributions to in the fits. Using the fitted end-point
parameters, we update the theoretical results for the charmless
decays, which will be further tested by the LHCb and Belle-II experiments in
the near future.Comment: 31 pages, 4 figures, 6 table
A Duality View of Spectral Methods for Dimensionality Reduction
We present a unified duality view of several recently emerged spectral methods for nonlinear dimensionality reduction, including Isomap, locally linear embedding, Laplacian eigenmaps, and maximum variance unfolding. We discuss the duality theory for the maximum variance unfolding problem, and show that other methods are directly related to either its primal formulation or its dual formulation, or can be interpreted from the optimality conditions. This duality framework reveals close connections between these seemingly quite different algorithms. In particular, it resolves the myth about these methods in using either the top eigenvectors of a dense matrix, or the bottom eigenvectors of a sparse matrix — these two eigenspaces are exactly aligned at primaldual optimality
Valley Carrier Dynamics in Monolayer Molybdenum Disulphide from Helicity Resolved Ultrafast Pump-probe Spectroscopy
We investigate the valley related carrier dynamics in monolayer MoS2 using
helicity resolved non-degenerate ultrafast pump-probe spectroscopy at the
vicinity of the high-symmetry K point under the temperature down to 78 K.
Monolayer MoS2 shows remarkable transient reflection signals, in stark contrast
to bilayer and bulk MoS2 due to the enhancement of many-body effect at reduced
dimensionality. The helicity resolved ultrafast time-resolved result shows that
the valley polarization is preserved for only several ps before scattering
process makes it undistinguishable. We suggest that the dynamical degradation
of valley polarization is attributable primarily to the exciton trapping by
defect states in the exfoliated MoS2 samples. Our experiment and a
tight-binding model analysis also show that the perfect valley CD selectivity
is fairly robust against disorder at the K point, but quickly decays from the
high-symmetry point in the momentum space in the presence of disorder.Comment: 15 pages,Accepted by ACS Nan
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