3,818 research outputs found
Rank Reduction of Correlation Matrices by Majorization
A novel algorithm is developed for the problem of finding a low-rank correlation matrix nearest to a given correlation matrix. The algorithm is based on majorization and, therefore, it is globally convergent. The algorithm is computationally efficient, is straightforward to implement, and can handle arbitrary weights on the entries of the correlation matrix. A simulation study suggests that majorization compares favourably with competing approaches in terms of the quality of the solution within a fixed computational time. The problem of rank reduction of correlation matrices occurs when pricing a derivative dependent on a large number of assets, where the asset prices are modelled as correlated log-normal processes. Mainly, such an application concerns interest rates.rank, correlation matrix, majorization, lognormal price processes
Dimensionality of Local Minimizers of the Interaction Energy
In this work we consider local minimizers (in the topology of transport
distances) of the interaction energy associated to a repulsive-attractive
potential. We show how the imensionality of the support of local minimizers is
related to the repulsive strength of the potential at the origin.Comment: 27 page
Nonlocal interactions by repulsive-attractive potentials: radial ins/stability
In this paper, we investigate nonlocal interaction equations with
repulsive-attractive radial potentials. Such equations describe the evolution
of a continuum density of particles in which they repulse each other in the
short range and attract each other in the long range. We prove that under some
conditions on the potential, radially symmetric solutions converge
exponentially fast in some transport distance toward a spherical shell
stationary state. Otherwise we prove that it is not possible for a radially
symmetric solution to converge weakly toward the spherical shell stationary
state. We also investigate under which condition it is possible for a
non-radially symmetric solution to converge toward a singular stationary state
supported on a general hypersurface. Finally we provide a detailed analysis of
the specific case of the repulsive-attractive power law potential as well as
numerical results. We point out the the conditions of radial ins/stability are
sharp.Comment: 42 pages, 7 figure
Alien Registration- Laflamme, Raoul J. (Exeter, Penobscot County)
https://digitalmaine.com/alien_docs/10018/thumbnail.jp
Des possibilités d'emploi des composés organostanniques contre la pourriture brune des cabosses de cacaoyer due au PHYTOPHTHORA PALMIVORA (Butl.) Butl. au Cameroun Oriental
Critical interfaces and duality in the Ashkin Teller model
We report on the numerical measures on different spin interfaces and FK
cluster boundaries in the Askhin-Teller (AT) model. For a general point on the
AT critical line, we find that the fractal dimension of a generic spin cluster
interface can take one of four different possible values. In particular we
found spin interfaces whose fractal dimension is d_f=3/2 all along the critical
line. Further, the fractal dimension of the boundaries of FK clusters were
found to satisfy all along the AT critical line a duality relation with the
fractal dimension of their outer boundaries. This result provides a clear
numerical evidence that such duality, which is well known in the case of the
O(n) model, exists in a extended CFT.Comment: 5 pages, 4 figure
Vibrational Exciton Density of States in Solid Benzene
Computer‐aided calculations, based on experimentally‐fitted pairwise interaction terms, give the complete exciton density‐of‐states profile for the entire Brillouin zone. The restricted Frenkel model, with short‐range interactions, is the key assumption. Results are given and discussed for the out‐of‐plane a2ua2u normal mode ν11ν11(C6H6 and C6D6), for ν12(b1u)ν12(b1u), and for ν15(b2u)ν15(b2u). The wide range of parameters used makes this investigation pertinent to other vibrational and electronic exciton bands of benzene and any other molecular crystal with the same interchange symmetry. Also, Van Hove singularities are found to be more important for symmetry‐based critical points than for “accidental” critical points. Present‐day experimental and theoretical intermolecular excitation exchange interaction terms are compared.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71006/2/JCPSA6-53-9-3674-1.pd
Visualization of steps and surface reconstructions in Helium Ion Microscopy with atomic precision
Helium Ion Microscopy is known for its surface sensitivity and high lateral
resolution. Here, we present results of a Helium Ion Microscopy based
investigation of a surface confined alloy of Ag on Pt(111). Based on a change
of the work function of 25\,meV across the atomically flat terraces we can
distinguish Pt rich from Pt poor areas and visualize the single atomic layer
high steps between the terraces. Furthermore, dechanneling contrast has been
utilized to measure the periodicity of the hcp/fcc pattern formed in the 2--3
layers thick Ag/Pt alloy film. A periodicity of 6.65\,nm along the
surface direction has been measured. In terms of
crystallography a hcp domain is obtained through a lateral displacement of a
part of the outermost layer by of a nearest neighbour spacing
along . This periodicity is measured with atomic
precision: coincidence between the Ag and the Pt lattices is observed for 23 Ag
atoms on 24 Pt atoms. The findings are perfectly in line with results obtained
with Low Energy Electron Microscopy and Phase Contrast Atomic Force Microscopy.Comment: 15 pages, 7 figure
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