Uniform oriented matroids without the isotopy property

We give an easy general construction for uniform oriented matroids with disconnected realization space. This disproves the longstanding isotopy conjecture for simple line arrangements or order types in the plane.The research of Bernd Sturmfels and Neil White was supported in part by the Institute for Mathematics and Its Applications with funds provided by the National Science Foundation.     

Cooling antiprotons in an ion trap

The measurement of the inertial mass of the antiproton and proposed antihydrogen formation experiments require antiprotons stored in ion traps, cooled to very low (4K) temperatures. Techniques to cool the trapped antiprotons from energies around 1 keV are discussed. Coupling to an external circuit produces cooling times of order 10³ s, which may be reduced somewhat with negative feedback. Adiabatic reduction of the trapping potential produces significant cooling when the particle energies are substantially less than the well depth. Most promising is cooling via energy-transferring collisions to a cooled cloud of electrons simultaneously trapped with the antiprotons. Electron cooling times are of order 1 s, and strongly depend on electron number and density.     

Recognition of the structural-functional organization of genetic sequences

The analysis problem for genetic sequences is formulated from the viewpoint of modern mathematical and information approaches. Statistical, correlative, entropic, and spectral approaches are considered. A brief introduction into the background of the problem is given. Genesis of a new interdisciplinary subject area, bioinformatics, a science considering application of computer methods in biological studies, is analyzed. New approaches to studying macromolecular systems on the basis of combined spectral-analytic technologies are proposed. Estimates of the algorithmic complexity of implementation of the proposed approaches are presented.     

Large deviation principle for enhanced Gaussian processes

We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N. We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced (fractional) Brownian motion, in Hölder- or modulus topology, appears as special case.     

Resonant-induced transparency and coupled modes in layered metamaterials

We present an overview of some of our work on transmission properties and mode characteristics of layered metamaterials and their potential applications. In particular, we will show how layered metamaterials exhibit unusual transmission properties and unconventional features of guided modes, such as resonance-induced transparency in multilayer structures and slope reversal of dispersion curves in coupled waveguides. PACS 78.67.-n; 73.21.Ac; 61.46.+w; 42.25.Bs; 42.82.Et     

MR imaging of teeth using a silent single point imaging technique

Magnetic resonance imaging (MRI) of teeth is an emerging application area which is still in development. Previous investigations did not fully focus on potential in vivo applications. Using ¹H and ³¹P MRI, we obtained ex vivo microimages of teeth with a silent single point imaging (SPI) technique. ¹H Images with an in-plane resolution of 310×310 μm² were obtained. Utilizing sine-shaped gradient ramps significantly reduced the sound pressure level of the experiment to that of background noise. ¹H magnetic resonance spectroscopy (MRS) was used to characterize the major components in the observed resonance. The spin–spin (T₂) relaxation times of water in enamel and dentin differed by at least one order of magnitude. Three-dimensional surface reconstruction of the data allowed for complete visualization of the tooth’s surface while volume reconstruction displayed the internal geometry. PACS 82.56.Na; 83.85.Fg; 87.61.-c; 87.19.-j; 43.50.Cb     

A neuron as a quantum-optical device: A model

Inversion in the structure of polyaminoacids and proteins is discussed, and the electrodynamic quantum-optical model of a neuron is constructed. The feasibility of the quantum-logical summation of exciting pulses by a nanomembrane is considered. The model is consistent with the physiology foundations and assumes implementation by means of techniques used in microelectronics, integrated optics, and nanooptics.     

On the Asymptotics of Fekete-Type Points for Univariate Radial Basis Interpolation

Suppose that K ^d is compact and that we are given a function fC(K) together with distinct points x_iK, 1in. Radial basis interpolation consists of choosing a fixed (basis) function g : ⁺→ and looking for a linear combination of the translates g(|x−x_j|) which interpolates f at the given points. Specifically, we look for coefficients c_j such that has the property that F(x_i)=f(x_i), 1in. The Fekete-type points of this process are those for which the associated interpolation matrix [g(|x_i−x_j|)]_1i,jn has determinant as large as possible (in absolute value). In this work, we show that, in the univariate case, for a broad class of functions g, among all point sequences which are (strongly) asymptotically distributed according to a weight function, the equally spaced points give the asymptotically largest determinant. This gives strong evidence that the Fekete points themselves are indeed asymptotically equally spaced.     

Asymptotic robustness of standard errors in multilevel structural equation models

Data in social and behavioral sciences are often hierarchically organized. Multilevel statistical methodology was developed to analyze such data. Most of the procedures for analyzing multilevel data are derived from maximum likelihood based on the normal distribution assumption. Standard errors for parameter estimates in these procedures are obtained from the corresponding information matrix. Because practical data typically contain heterogeneous marginal skewnesses and kurtoses, this paper studies how nonnormally distributed data affect the standard errors of parameter estimates in a two-level structural equation model. Specifically, we study how skewness and kurtosis in one level affect standard errors of parameter estimates within its level and outside its level. We also show that, parallel to asymptotic robustness theory in conventional factor analysis, conditions exist for asymptotic robustness of standard errors in a multilevel factor analysis model.     

Effect of electric current on the magnetic and magnetoelastic properties of amorphous ferromagnetic alloys

The magnetic and magnetoelastic parameters of Fe₆₄Co₂₁B₁₅ and Fe_81.5B_13.5Si₃C₂ amorphous ferromagnetic alloys treated by direct electric current in air are studied as functions of the applied magnetic field and current density. The samples of the alloy have the form of narrow strips with different lengths. It is found that the magnetoelastic parameters of the dc-treated alloys depend on the magnetic field in a qualitatively different way. From the behavior of the magnetic and magnetoelastic parameters of the alloys in the magnetic field a model of magnetization nonuniform distribution in amorphous ferromagnetic alloys subjected to dc treatment is proposed.