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

Hot Quark Matter with an Axial Chemical Potential

We analyze the phase diagram of hot quark matter in presence of an axial chemical potential, $\mu_5$. The latter is introduced to mimic the chirality transitions induced, in hot Quantum Chromodynamics, by the strong sphaleron configurations. In particular, we study the curvature of the critical line at small $\mu_5$, the effects of a finite quark mass and of a vector interaction. Moreover, we build the mixed phase at the first order phase transition line, and draw the phase diagram in the chiral density and temperature plane. We finally compute the full topological susceptibility in presence of a background of topological charge.Comment: 12 pages, 7 figures. Few references added, short discussion included. Final version appearing on Phys. Rev.

A self‐consistent theory of nonequilibrium excitation transport in energetically disordered systems

The migration of incoherent excitations in energetically disordered systems is studied theoretically using a self‐consistent diagrammatic approximation. Spatial diffusion and energy relaxation observables are related to the solutions of a nonlinear integral equation. Extensive numerical illustrations are given for two‐component and multicomponent systems. In the latter, spatial transport is found to be highly dispersive (nondiffusive) over an extremely wide range of timescales, in accordance with results from simulations and experiments. The dependence of spatial and spectral transport properties upon the spatial range and the energy dependence of the intermolecular hopping rates is examined. Several measures of energy relaxation, including detailed probability distributions in energy space, relaxation‐time spectra, and the nonequilibrium entropy are calculated and compared. The intimate relationship between spatial transport and energy relaxation is discussed in detail.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70474/2/JCPSA6-82-8-3692-1.pd

A Program of Astronomy Research on the Moon and Its Logistics Implications

This study concerns itself with one aspect of possible post-Apollo space activity -- a program of astronomical research on the moon that culminates in the establishment of a lunar observatory. A mathematical model is utilized to analyze the logistics implications of conducting such an astronomical research program. The nature of the research equipment needed for the accomplishment of the program is outlined. Superposition of this research program upon a basic long-term lunar-base operations plan tentatively indicates that it could be feasible to conduct such a program of research during the 1970\u27s and 1980\u27s well within the constraints imposed by the logistics of presently planned spacecraft, boosters, and launching facilities. Although the best available numbers were used, the present study is viewed more as an exposition of a methodology than as the establishment of a conclusive result

Interactions between landscape changes and host communities can regulate echinococcus multilocularis transmission

An area close to the Qinghai-Tibet plateau region and subject to intensive deforestation contains a large focus of human alveolar echinococcosis while sporadic human cases occur in the Doubs region of eastern France. The current review analyses and compares epidemiological and ecological results obtained in both regions. Analysis of rodent species assemblages within quantified rural landscapes in central China and eastern France shows a significant association between host species for the pathogenic helminth Echinococcus multilocularis, with prevalences of human alveolar echinococcosis and with land area under shrubland or grassland. This suggests that at the regional scale landscape can affect human disease distribution through interaction with small mammal communities and their population dynamics. Lidicker's ROMPA hypothesis helps to explain this association and provides a novel explanation of how landscape changes may result in increased risk of a rodent-borne zoonotic disease

Interference as an Issue and a Resource in Wireless Networks

This dissertation will be focused on the phenomenon of interference in wireless net- works. On one hand, interference will be viewed as a negative factor that one should mitigate in order to improve the performance of a wireless network in terms of achiev- able rate, and on the other hand as an asset to increase the performance of a network in terms of security. The problems that will be investigated are, first, the character- isation of the performance of a communication network modelled as an interference channel (IC) when interference alignment (IA) is used to mitigate the interference with imperfect knowledge of the channel state, second, the characterisation of the secrecy in the Internet-of-Things (IoT) framework where some devices may use artificial noise to generate interference to potential eavesdroppers. Different scenarios will be studied in the case where interference is unwanted; the first one is when the channel error is bounded. A lower bound on the capacity achievable in this case is provided and a new performance metric namely the saturating SNR is derived. The derived lower bound is studied with respect to some parameters of the estimation strategy when using Least-Square estimation to estimate the channel ma- trices. The second scenario deals with unbounded Gaussian estimation errors, here the statistical distribution of the achievable rate is given along with a new performance metric called outage probability that simplifies the study of the IC with IA under im- perfect CSI. The results are used to optimise the network parameters and extend the analysis further to the case of cellular networks. In the wanted interference situation, the secrecy of the worst-case communication is studied and the conditions for secrecy are provided. Furthermore the average number of secure links achievable in the network is studied according to a theoretical model that is developed for the IoT case

Supersymmetric Model of Spin-1/2 Fermions on a Chain

In recent work, N=2 supersymmetry has been proposed as a tool for the analysis of itinerant, correlated fermions on a lattice. In this paper we extend these considerations to the case of lattice fermions with spin 1/2 . We introduce a model for correlated spin-1/2 fermions with a manifest N=4 supersymmetry, and analyze its properties. The supersymmetric ground states that we find represent holes in an anti-ferromagnetic background.Comment: 15 pages, 10 eps figure