Segregation in the Falicov--Kimball Model

The Falicov–Kimball model is a simple quantum lattice model that describes light and heavy electrons interacting with an on-site repulsion; alternatively, it is a model of itinerant electrons and fixed nuclei. It can be seen as a simplification of the Hubbard model; by neglecting the kinetic (hopping) energy of the spin up particles, one gets the Falicov–Kimball model. We show that away from half-filling, i.e. if the sum of the densities of both kinds of particles differs from 1, the particles segregate at zero temperature and for large enough repulsion. In the language of the Hubbard model, this means creating two regions with a positive and a negative magnetization. Our key mathematical results are lower and upper bounds for the sum of the lowest eigenvalues of the discrete Laplace operator in an arbitrary domain, with Dirichlet boundary conditions. The lower bound consists of a bulk term, independent of the shape of the domain, and of a term proportional to the boundary. Therefore, one lowers the kinetic energy of the itinerant particles by choosing a domain with a small boundary. For the Falicov- Kimball model, this corresponds to having a single “compact” domain that has no heavy particles. Received: 21 June 2001 / Accepted: 4 January 2002     

Unitary Correlations and the Fejér Kernel

Let M be a unitary matrix with eigenvalues t _j , and let f be a function on the unit circle. Define X _f (M)=f(t _j ). We derive exact and asymptotic formulae for the covariance of X _f and X _g with respect to the measures |(M)|²dM where dM is Haar measure and an irreducible character. The asymptotic results include an analysis of the Fejér kernel which may be of independent interest.     

Gluing and Wormholes for the Einstein Constraint Equations

 We establish a general gluing theorem for constant mean curvature solutions of the vacuum Einstein constraint equations. This allows one to take connected sums of solutions or to glue a handle (wormhole) onto any given solution. Away from this handle region, the initial data sets we produce can be made as close as desired to the original initial data sets. These constructions can be made either when the initial manifold is compact or asymptotically Euclidean or asymptotically hyperbolic, with suitable corresponding conditions on the extrinsic curvature. In the compact setting a mild nondegeneracy condition is required. In the final section of the paper, we list a number ways this construction may be used to produce new types of vacuum spacetimes. Received: 4 October 2001 / Accepted: 26 July 2002 Published online: 29 October 2002 RID="*" ID="*" Supported by the NSF under Grant PHY-0099373 RID="**" ID="**" Supported by the NSF under Grant DMS-9971975 and at MSRI by NSF grant DMS-9701755 RID="***" ID="***" Supported by the NSF under Grant DMS-9704515     

Toward a Comparison of Classical and New Privacy Mechanism

In the last decades, the development of interconnectivity, pervasive systems, citizen sensors, and Big Data technologies allowed us to gather many data from different sources worldwide. This phenomenon has raised privacy concerns around the globe, compelling states to enforce data protection laws. In parallel, privacy-enhancing techniques have emerged to meet regulation requirements allowing companies and researchers to exploit individual data in a privacy-aware way. Thus, data curators need to find the most suitable algorithms to meet a required trade-off between utility and privacy. This crucial task could take a lot of time since there is a lack of benchmarks on privacy techniques. To fill this gap, we compare classical approaches of privacy techniques like Statistical Disclosure Control and Differential Privacy techniques to more recent techniques such as Generative Adversarial Networks and Machine Learning Copies using an entire commercial database in the current effort. The obtained results allow us to show the evolution of privacy techniques and depict new uses of the privacy-aware Machine Learning techniques.     

Performance of Portfolios Based on the Expected Utility-Entropy Fund Rating Approach

Yang and Qiu proposed and reframed an expected utility–entropy (EU-E) based decision model. Later on, a similar numerical representation for a risky choice was axiomatically developed by Luce et al. under the condition of segregation. Recently, we established a fund rating approach based on the EU-E decision model and Morningstar ratings. In this paper, we apply the approach to US mutual funds and construct portfolios using the best rating funds. Furthermore, we evaluate the performance of the fund ratings based on the EU-E decision model against Morningstar ratings by examining the performance of the three models in portfolio selection. The conclusions show that portfolios constructed using the ratings based on the EU-E models with moderate tradeoff coefficients perform better than those constructed using Morningstar. The conclusion is robust to different rebalancing intervals.     

X‐ray absorption study of the local structure at the NiO/oxide interfaces

This work reports an X‐ray absorption near‐edge structure (XANES) spectroscopy study at the Ni K‐edge in the early stages of growth of NiO on non‐ordered SiO₂, Al₂O₃ and MgO thin films substrates. Two different coverages of NiO on the substrates have been studied. The analysis of the XANES region shows that for high coverages (80 Eq‐ML) the spectra are similar to that of bulk NiO, being identical for all substrates. In contrast, for low coverages (1 Eq‐ML) the spectra differ from that of large coverages indicating that the local order around Ni is limited to the first two coordination shells. In addition, the results also suggest the formation of cross‐linking bonds Ni—O—M (M = Si, Al, Mg) at the interface.     

In vivo magnetic resonance microscopy of Drosophilae at 9.4 T

In preclinical research, genetic studies have made considerable progress as a result of the development of transgenic animal models of human diseases. Consequently, there is now a need for higher resolution MRI to provide finer details for studies of small animals (rats, mice) or very small animals (insects). One way to address this issue is to work with high-magnetic-field spectrometers (dedicated to small animal imaging) with strong magnetic field gradients. It is also necessary to develop a complete methodology (transmit/receive coil, pulse sequence, fixing system, air supply, anesthesia capabilities, etc.). In this study, we developed noninvasive protocols, both in vitro and in vivo (from coil construction to image generation), for drosophila MRI at 9.4 T. The 10*10*80-μm resolution makes it possible to visualize whole drosophila (head, thorax, abdomen) and internal organs (ovaries, longitudinal and transverse muscles, bowel, proboscis, antennae and optical lobes). We also provide some results obtained with a Drosophila model of muscle degeneration. This opens the way for new applications of structural genetic modification studies using MRI of drosophila.     

Carbon-13 NMR Spectra of Some Group VIIB Transition Metal Thiocarbonyl and Selenocarbonyl Complexes

Recently, we reported the discovery of the first examples of transition metal selenocarbonyl complexes, (n⁵-C₅H₅) Mn (CO)₂ (CSe) and (n⁶-C₆H₅CO₂CH₂(CO)₂ (CSe).¹ These complexes are particularly interesting because, unlike CO and CS, the diatomic CSe molecule has so far eluded isolation even at very low temperatures,² and so these complexes represent the stabilization of a chemically unstable species through coordination to a metal (cf. metal carbene complexes). We have also synthesized several thiocarbonyl complexes of the same type,^3,4 as well as the analogous rhenium selenocarbonyl complexes.⁴ While many detailed studies of the ¹³C nmr spectra of transition metal carbonyls have appeared in the literature over the past few years, there have been no such studies for the closely related thiocarbonyls and selenocarbonyls, although a few isolated data have been reported recently for metal thiocarbonyls.^5,6 In this communication, we report the ¹³C nmr spectra of the isoelectronic series of complexes, (n⁵-C₅H₄R) M(COI)₂ (CX) (M = Mn, R = H, CH₃; M = Re, R = H; X = O,S, Se).