Radiolabelling of TiO<Subscript>2</Subscript> nanoparticles for radiotracer studies

Industrially manufactured titanium dioxide nanoparticles have been successfully radiolabelled with ⁴⁸V by irradiation with a cyclotron-generated proton beam. Centrifugation tests showed that the ⁴⁸V radiolabels were stably bound within the nanoparticle structure in an aqueous medium, while X-ray diffraction indicated that no major structural modifications to the nanoparticles resulted from the proton irradiation. In vitro tests of the uptake of cold and radiolabelled nanoparticles using the human cell line Calu-3 showed no significant difference in the uptake between both batches of nanoparticles. The uptake was quantified by Inductively Coupled Plasma Mass Spectrometry and high resolution γ-ray spectrometry for cold and radiolabelled nanoparticles, respectively. These preliminary results indicate that alterations to the nanoparticles’ properties introduced by proton bombardment can be controlled to a sufficient extent that their further use as radiotracers for biological investigations can be envisaged and elaborated.     

Dynamic data structures for fat objects and their applications

We present several efficient dynamic data structures for point-enclosure queries, involving convex fat objects in or . Our planar structures are actually fitted for a more general class of objects – (β,δ)-covered objects – which are not necessarily convex, see definition below. These structures are more efficient than alternative known structures, because they exploit the fatness of the objects. We then apply these structures to obtain efficient solutions to two problems: (i) finding a perfect containment matching between a set of points and a set of convex fat objects, and (ii) finding a piercing set for a collection of convex fat objects, whose size is optimal up to some constant factor.     

Strong bulk-edge coupling in the compressible half-filled quantum Hall state

We study bulk and edge correlations in the compressible half-filled state, using a modified version of the plasma analogy. The corresponding plasma has anomalously weak screening properties, and as a consequence we find that the correlations along the edge do not decay algebraically as in the Laughlin (incompressible) case, while the bulk correlations decay in the same way. The results suggest that due to the strong coupling between charged modes on the edge and the neutral fermions in the bulk, reflected by the weak screening in the plasma analogue, the (attractive) correlation hole is not well defined on the edge. Hence, the system there can be modeled as a free Fermi gas of electrons. We finally comment on a possible scenario, in which the Laughlin-like dynamical edge correlations may nevertheless be realized.     

On the performance of the ICP algorithm

We present upper and lower bounds for the number of iterations performed by the Iterative Closest Point (ICP) algorithm. This algorithm has been proposed by Besl and McKay as a successful heuristic for matching of point sets in d-space under translation, but so far it seems not to have been rigorously analyzed. We consider two standard measures of resemblance that the algorithm attempts to optimize: The RMS (root mean squared distance) and the (one-sided) Hausdorff distance. We show that in both cases the number of iterations performed by the algorithm is polynomial in the number of input points. In particular, this bound is quadratic in the one-dimensional problem, under the RMS measure, for which we present a lower bound construction of Ω(nlogn) iterations, where n is the overall size of the input. Under the Hausdorff measure, this bound is only O(n) for input point sets whose spread is polynomial in n, and this is tight in the worst case.We also present several structural geometric properties of the algorithm under both measures. For the RMS measure, we show that at each iteration of the algorithm the cost function monotonically and strictly decreases along the vector Δt of the relative translation. As a result, we conclude that the polygonal path π, obtained by concatenating all the relative translations that are computed during the execution of the algorithm, does not intersect itself. In particular, in the one-dimensional problem all the relative translations of the ICP algorithm are in the same (left or right) direction. For the Hausdorff measure, some of these properties continue to hold (such as monotonicity in one dimension), whereas others do not.     

A Spray‐Based Technique for the Production of MnS Thin Films

A spray‐based technique, originally developed for the production of semiconductor nanocrystals, is utilized for the preparation of high‐quality nanocrystalline thin films, as demonstrated with manganese sulfide. The films are formed by the use of pneumatic‐assisted thermospray or pneumatic nebulizers. Our simple, low‐cost, and low‐temperature process results in a dense and phase‐pure grain structure. The concepts and benefits of this technique are described and discussed. The film characteristics show dependence on the experimental parameters, in particular the rate of solvent vaporization. Three alternative film formation mechanisms are suggested for cases with varied experimental conditions.     

Minimally corrected partial atomic charges for non-covalent electrostatic interactions

We develop a new scheme for determining molecular partial atomic charges (PACs) with external electrostatic potential (ESP) closely mimicking that of the molecule. The PACs are the ‘minimal corrections’ to a reference set of PACs necessary for reproducing exactly the tensor components of the Cartesian zero-, first- and second- molecular electrostatic multipoles. We evaluate the quality of ESP reproduction when ‘minimally correcting’ (MC) Mulliken, Hirshfeld or iterative-Hirshfeld reference PACs. In all these cases, the MC-PACs significantly improve the ESP while preserving the reference PACs’ invariance under the molecular symmetry operations. When iterative-Hirshfeld PACs are used as reference, the MC-PACs yield ESPs of comparable quality to those of the ChElPG charge fitting method.     

Fly Cheaply: On the Minimum Fuel Consumption Problem

In planning a flight, stops at intermediate airports are sometimes necessary to minimize fuel consumption, even if a direct flight is available. We investigate the problem of finding the cheapest path from one airport to another, given a set of n airports in ² and a function l: ² × ² → ⁺ representing the cost of a direct flight between any pair. Given a source airport s, the cheapest-path map is a subdivision of ² where two points lie in the same region iff their cheapest paths from s use the same sequence of intermediate airports. We show a quadratic lower bound on the combinatorial complexity of this map for a class of cost functions. Nevertheless, we are able to obtain subquadratic algorithms to find the cheapest path from s to all other airports for any well-behaved cost function l: our general algorithm runs in O(n^{4/3 +} ) time, and a simpler, more practical variant runs in O(n^{3/2 +} ) time, while a special class of cost functions requires just O(n log n) time.     

A near-linear algorithm for the planar segment-center problem

LetP be a set ofn points in the plane and lete be a segment of fixed length. The segment-center problem is to find a placement ofe (allowing translation and rotation) which minimizes the maximum euclidean distance frome to the points ofP. We present an algorithm that solves the problem in timeO(n ^1+ε), for any ε>0, improving the previous solution of Agarwalet al. [3] by nearly a factor ofO(n). Work on this paper by the second author has been supported by NSF Grants CCR-91-22103 and CCR-93-11127, and by grants from the U.S.-Israeli Binational Science Foundation, the G.I.F., the German-Israeli Foundation for Scientific Research and Development, and the Fund for Basic Research administered by the Israeli Academy of Sciences.     

Determinants of Laplacians on surfaces of finite volume

Determinants of the Laplace and other elliptic operators on compact manifolds have been an object of study for many years (see [MP, RS, Vor]). Up until now, however, the theory of determinants has not been extended to non-compact situations, since these typically involve a mixture of discrete and continuous spectra. Recent advances in this theory, which are partially motivated by developments in mathematical physics, have led to a connection, in the compact Riemann surface case, between determinants of Laplacians on spinors and the Selberg zeta function of the underlying surface (see [DP, Kie, Sar, Vor]).Our purpose in this paper is to introduce a notion of determinants on non-compact (finite volume) Riemann surfaces. These will be associated to the Laplacian shifted by a parameters(1–s), and will be defined in terms of a Dirichlet series (w, s) which is a sum that represents the discrete as well as the continuous spectrum. It will be seen to be regular atw=0, and our main theorem (see Sect. 1) will express exp as the Selberg zeta function of the surface times the appropriate -factor.A Sloan Fellow and partially supported by NSF grant DMS-8701865     

Spectroscopic investigations on II–VI-semiconductor nanocrystals and their assemblies

This review points out that (magneto-)optical measurements may help to shine light on the recombination processes taking place in semiconductor nanocrystals. The surface capping with thiols creates a CdS shell around CdTe cores and forms a Cd site that is not fourfold-coordinated at the surface. It is pointed out how specific cappings such as thio-amines and thio-acids assist in coupling NCs and how we may distinguish between NC–NC interactions via electrostatic and covalent linking with the aid of the optical measurements. Furthermore, with static and time-resolved ODMR studies on IR-active core-shell HgTe/Hg _x Cd_1−x Te(S) particles it is demonstrated how the nature of the recombination emission being associated with a Cd–Hg mixed site is elucidated and by this yielding structural information on the NC core-shell interface. With these examples we show that and how nanomaterials of probable technological interest are studied beneficially with advanced spectroscopic techniques.