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.     

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.     

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.     

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.     

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.     

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.     

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.     

Solubilization of hydrophobic guest molecules in the monoolein discontinuous QL cubic mesophase and its soft nanoparticles

Hydrophobic bioactive guest molecules were solubilized in the discontinuous cubic mesophase (QL) of monoolein. Their effects on the mesophase structure and thermal behavior, and on the formation of soft nanoparticles upon dispersion of the bulk mesophase were studied. Four additives were analyzed. They were classified into two types based on their presumed location within the lipid bilayer and their influence on the phase behavior and structure. Differential scanning calorimetry (DSC), small-angle X-ray scattering (SAXS), polarized light microscopy, cryogenic-transmission electron microscopy (cryo-TEM), and dynamic light scattering (DLS) were used for the analysis. We found that carbamazepine and cholesterol (type I molecules) likely localize in the hydrophobic domains, but close to the hydrophobic-hydrophilic region. They induce strong perturbation to the mesophase packing by influencing both the order of the lipid acyl chains and interactions between lipid headgroups. This results in significant reduction of the phase transition enthalpy, and phase separation into lamellar and cubic mesophases above the maximum loading capacity. The inclusion of type I molecules in the mesophase also prevents the formation of soft nanoparticles with long-range internal order upon dispersion. In their presence, only vesicles or sponge-like nanoparticles form. Phytosterols and coenzyme Q10 (type II molecules) present only moderate effects. These molecules reside in the hydrophobic domains, where they cannot alter the lipid curvature or transform the QL mesophase into another phase. Therefore, above maximum loading, excess solubilizate precipitates in crystal forms. Moreover, when type II-loaded QL is dispersed, nanoparticles with long-range order and cubic symmetry (i.e., cubosomes) do form. A model for the growth of the ordered nanoparticles was developed from a series of intermediate structures identified by cryo-TEM. It proposes the development of the internal structure by fusion events between bilayer segments.     

On structural transitions in a discontinuous micellar cubic phase loaded with sodium diclofenac

An intermediate mesophase of lyotropic liquid crystalline structure from the ternary mixtures of glycerol monooleate, water, and ethanol was recently characterized in our lab. This mesophase, termed Q(L), consists of discrete discontinuous micelles arranged in a cubic array. The Q(L) phase can solubilize very significant loads of water-insoluble anti-inflamatory drug sodium diclofenac (Na-DFC). Close examination of the internal structures of the lyotropic liquid structure upon increasing the solubilization loads reveals the existence of three structural transitions controlled by the Na-DFC levels. Up to 0.4 wt% Na-DFC, the Q(L) structure remains intact with some influence on the hydration of the headgroups and on the intermicellar forces. However, at 0.8 to 1.2 wt% Na-DFC, the discontinuous micellar cubic phase is transformed into a more condensed mesophase of a bicontinuous cubic phase. At > or =1.2 wt% Na-DFC, the cubic phase is converted into a lamellar phase (L(alpha)). Within 5.5 to 7.3 wt% Na-DFC the mesophase is progressively transformed into a less ordered lamellar structure. At 12 wt% Na-DFC crystals tend to precipitate out. At low Na-DFC concentrations the drug behaves like a lyotropic or kosmotropic salt and can salt-out the surfactant from its water layer, but at higher levels it behaves like a hydrotropic, chaotropic salt and can salt-in the surfactant. The Na-DFC location and position within the interface as well as its polarization and partial ionization are strongly affected by its solubilization contents and the structure that it is inducing. In the cubic phase the drug is located less close to the hydration layer while once transition occurs it is exposed more to the water layer and the surfactant headgroups.     

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.