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

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 $\langle\overline{11}2\rangle$ 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 $1/\sqrt{3}$ of a nearest neighbour spacing along $\langle\overline{11}2\rangle$. 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