Transfinite thin plate spline interpolation

Duchon's method of thin plate splines defines a polyharmonic interpolant to scattered data values as the minimizer of a certain integral functional. For transfinite interpolation, i.e. interpolation of continuous data prescribed on curves or hypersurfaces, Kounchev has developed the method of polysplines, which are piecewise polyharmonic functions of fixed smoothness across the given hypersurfaces and satisfy some boundary conditions. Recently, Bejancu has introduced boundary conditions of Beppo Levi type to construct a semi-cardinal model for polyspline interpolation to data on an infinite set of parallel hyperplanes. The present paper proves that, for periodic data on a finite set of parallel hyperplanes, the polyspline interpolant satisfying Beppo Levi boundary conditions is in fact a thin plate spline, i.e. it minimizes a Duchon type functional

Using X-ray Crystallography, Biophysics, and Functional Assays to Determine the Mechanisms Governing T-cell Receptor Recognition of Cancer Antigens.

Human CD8+ cytotoxic T lymphocytes (CTLs) are known to play an important role in tumor control. In order to carry out this function, the cell surface-expressed T-cell receptor (TCR) must functionally recognize human leukocyte antigen (HLA)-restricted tumor-derived peptides (pHLA). However, we and others have shown that most TCRs bind sub-optimally to tumor antigens. Uncovering the molecular mechanisms that define this poor recognition could aid in the development of new targeted therapies that circumnavigate these shortcomings. Indeed, present therapies that lack this molecular understanding have not been universally effective. Here, we describe methods that we commonly employ in the laboratory to determine how the nature of the interaction between TCRs and pHLA governs T-cell functionality. These methods include the generation of soluble TCRs and pHLA and the use of these reagents for X-ray crystallography, biophysical analysis, and antigen-specific T-cell staining with pHLA multimers. Using these approaches and guided by structural analysis, it is possible to modify the interaction between TCRs and pHLA and to then test how these modifications impact T-cell antigen recognition. These findings have already helped to clarify the mechanism of T-cell recognition of a number of cancer antigens and could direct the development of altered peptides and modified TCRs for new cancer therapies

Distinct Magnetic Phase Transition at the Surface of an Antiferromagnet

In the majority of magnetic systems the surface is required to order at the same temperature as the bulk. In the present Letter, we report a distinct and unexpected surface magnetic phase transition at a lower temperature than the Néel temperature. Employing grazing incidence x-ray resonant magnetic scattering, we have observed the near-surface behavior of uranium dioxide. UO2 is a noncollinear, triple-q, antiferromagnet with the U ions on a face-centered cubic lattice. Theoretical investigations establish that at the surface the energy increase—due to the lost bonds—is reduced when the spins near the surface rotate, gradually losing their component normal to the surface. At the surface the lowest-energy spin configuration has a double-q (planar) structure. With increasing temperature, thermal fluctuations saturate the in-plane crystal field anisotropy at the surface, leading to soft excitations that have ferromagnetic XY character and are decoupled from the bulk. The structure factor of a finite two-dimensional XY model fits the experimental data well for several orders of magnitude of the scattered intensity. Our results support a distinct magnetic transition at the surface in the Kosterlitz-Thouless universality class

q-Newton binomial: from Euler to Gauss

A counter-intuitive result of Gauss (formulae (1.6), (1.7) below) is made less mysterious by virtue of being generalized through the introduction of an additional parameter

A weakly stable algorithm for general Toeplitz systems

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm

A multiwavelength study of the supernova remnant G296.8-0.3

We report XMM-Newton observations of the Galactic supernova remnant G296.8-0.3, together with complementary radio and infrared data. The spatial and spectral properties of the X-ray emission, detected towards G296.8-0.3, was investigated in order to explore the possible evolutionary scenarios and the physical connexion with its unusual morphology detected at radio frequencies. G296.8-0.3 displays diffuse X-ray emission correlated with the peculiar radio morphology detected in the interior of the remnant and with the shell-like radio structure observed to the northwest side of the object. The X-ray emission peaks in the soft/medium energy range (0.5-3.0 keV). The X-ray spectral analysis confirms that the column density is high (NH \sim 0.64 x 10^{22} cm^{-2}) which supports a distant location (d>9 kpc) for the SNR. Its X-ray spectrum can be well represented by a thermal (PSHOCK) model, with kT \sim 0.86 keV, an ionization timescale of 6.1 x 10^{10} cm^{-3} s, and low abundance (0.12 Z_sun). The 24 microns observations show shell-like emission correlated with part of the northwest and southeast boundaries of the SNR. In addition a point-like X-ray source is also detected close to the geometrical center of the radio SNR. The object presents some characteristics of the so-called compact central objects (CCO). Its X-ray spectrum is consistent with those found at other CCOs and the value of NH is consistent with that of G296.8-0.3, which suggests a physical connexion with the SNR.Comment: Accepted for publication in Astrophysics & Space Scienc

Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals

High-order derivatives of analytic functions are expressible as Cauchy integrals over circular contours, which can very effectively be approximated, e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius of convergence is equal, numerical stability strongly depends on r. We give a comprehensive study of this effect; in particular we show that there is a unique radius that minimizes the loss of accuracy caused by round-off errors. For large classes of functions, though not for all, this radius actually gives about full accuracy; a remarkable fact that we explain by the theory of Hardy spaces, by the Wiman-Valiron and Levin-Pfluger theory of entire functions, and by the saddle-point method of asymptotic analysis. Many examples and non-trivial applications are discussed in detail.Comment: Version 4 has some references and a discussion of other quadrature rules added; 57 pages, 7 figures, 6 tables; to appear in Found. Comput. Mat

The Science of Sungrazers, Sunskirters, and Other Near-Sun Comets

This review addresses our current understanding of comets that venture close to the Sun, and are hence exposed to much more extreme conditions than comets that are typically studied from Earth. The extreme solar heating and plasma environments that these objects encounter change many aspects of their behaviour, thus yielding valuable information on both the comets themselves that complements other data we have on primitive solar system bodies, as well as on the near-solar environment which they traverse. We propose clear definitions for these comets: We use the term near-Sun comets to encompass all objects that pass sunward of the perihelion distance of planet Mercury (0.307 AU). Sunskirters are defined as objects that pass within 33 solar radii of the Sun’s centre, equal to half of Mercury’s perihelion distance, and the commonly-used phrase sungrazers to be objects that reach perihelion within 3.45 solar radii, i.e. the fluid Roche limit. Finally, comets with orbits that intersect the solar photosphere are termed sundivers. We summarize past studies of these objects, as well as the instruments and facilities used to study them, including space-based platforms that have led to a recent revolution in the quantity and quality of relevant observations. Relevant comet populations are described, including the Kreutz, Marsden, Kracht, and Meyer groups, near-Sun asteroids, and a brief discussion of their origins. The importance of light curves and the clues they provide on cometary composition are emphasized, together with what information has been gleaned about nucleus parameters, including the sizes and masses of objects and their families, and their tensile strengths. The physical processes occurring at these objects are considered in some detail, including the disruption of nuclei, sublimation, and ionisation, and we consider the mass, momentum, and energy loss of comets in the corona and those that venture to lower altitudes. The different components of comae and tails are described, including dust, neutral and ionised gases, their chemical reactions, and their contributions to the near-Sun environment. Comet-solar wind interactions are discussed, including the use of comets as probes of solar wind and coronal conditions in their vicinities. We address the relevance of work on comets near the Sun to similar objects orbiting other stars, and conclude with a discussion of future directions for the field and the planned ground- and space-based facilities that will allow us to address those science topics

The Transplanted Appropriate Adult Scheme in China

Borrowed from England and Wales, the Chinese Appropriate Adult Scheme involves a dynamic of selective adaptation. This article analyses two salient features of the appropriate adult scheme within the Chinese context, in comparison with its counterpart in England and Wales: its complementarity of the juvenile's parent, and the passive role that appropriate adults play during pretrial interrogations. Drawing upon empirical evidence, the article argues that the transplanted Chinese appropriate adult scheme has failed to oversee the legality of interrogations, nor does it provide adequate safeguards for juvenile suspects. The concept of vulnerability that lies at the heart of the appropriate adult safeguard in England and Wales appears to be lost in translation. Rather than providing a safeguard for juveniles at their most vulnerable, the appropriate adult is more concerned with indulging the needs of the interrogators in China