Algorithms for generalized halfspace range searching and other intersection searching problems

In a generalized intersection searching problem, a set S of colored geometric objects is to be preprocessed so that, given a query object q, the distinct colors of the objects of S that are intersected by q can be reported or counted efficiently. These problems generalize the well-studied standard intersection searching problems and have many applications. Unfortunately, the solutions known for the standard problems do not yield efficient solutions to the generalized problems. Recently, efficient solutions have been given for generalized problems where the input and query objects are iso-oriented (i.e., axes-parallel) or where the color classes satisfy additional properties (e.g., connectedness). In this paper, efficient algorithms are given for several generalized problems involving objects that are not necessarily iso-oriented. These problems include: generalized halfspace range searching in , for any fixed d ≥ 2, and segment intersection searching, triangle stabbing, and triangle range searching in for certain classes of line segments and triangles. The techniques used include: computing suitable sparse representations of the input, persistent data structures, and filtering search.     

Sparse geometric graphs with small dilation

Given a set S of n points in , and an integer k such that 0k<n, we show that a geometric graph with vertex set S, at most n−1+k edges, maximum degree five, and dilation O(n/(k+1)) can be computed in time O(nlogn). For any k, we also construct planar n-point sets for which any geometric graph with n−1+k edges has dilation Ω(n/(k+1)); a slightly weaker statement holds if the points of S are required to be in convex position.     

Salt effects on cloud points and viscosities of polymethacrylates with pendant oligo-oxyethylene chains

Comblike polymethacrylates with oligo-oxyethylene side chains were synthesized from the commercially available monomers CH₂ ? C (CH₃) COO (CH₂CH₂O)_nCH ₃, the average n being 4, 8, and 22. The three polymers exhibited lower critical solution temperatures in aqueous media. Cloud points were determined as a function of the nature and concentration of salt. For salts that destabilize the polymer solutions, the cloud points decrease linearly with salt concentration, the extent of the decrease being strongly anion dependent. Salt effects on the viscosity of the polymers were measured in water, methanol, and acetonitrile. In water the viscosity decreases on adding salt, but in methanol and acetonitrile the neutral polymers are converted to polycations as cations form stable adducts with the oligo-oxyethylene side chains. The increase in viscosity is both cation and anion dependent. The general behavior of the comblike polymers resembles that reported for aqueous or methanolic salt solutions of poly (ethylene oxide) and nonionic surfactants.     

Detection of fungal carbohydrate antigens by high-performance immunoaffinity chromatography using a protein A column with covalently linked immunoglobulin G.

Fungal carbohydrate antigens were analysed by high-performance immunoaffinity chromatography (HPIAC) with immunoglobulin G (IgG) antibodies raised against extracellular polysaccharides of Mucor racemosus. The protein A-IgG complex was covalently bound with dimethyl pimelimidate, which enabled the use of strong acidic buffers to release the tightly bound antigens from the column. Prior to pulsed-amperometric detection, an anion-micromembrane suppressor was used to raise the pH of the effluent to above 12 without dilution. The HPIAC system provides a sophisticated method for the rapid and sensitive detection of antigenic oligomeric carbohydrates in biological samples and is proposed as an alternative to quantitative enzyme-linked immunosorbent assay techniques.     

Innovative technique for the direct determination of proteins in calcified aortic valves

Aortal valve mineralization very frequently causes a genesis of aortic stenosis, which is the most often surgically treated heart disease. Hydroxyapatite deposits have been identified as one of the causes leading to the loss of elasticity of the aortic valves. It is known that phosphates/calcium is accumulated in valve tissues during mineralization, but the mechanism of this process remains unclear. The work is focused mainly on the study of protein composition of mineralized aortic valves by nano-liquid chromatography electrospray ionization in a quadrupole orthogonal acceleration time-of-flight mass spectrometry. New methodological approach based on direct enzymatic digestion of proteins contained in hydroxyapatite deposits was developed for the study of pathological processes connected with osteogenesis. Our objectives were to simplify the traditional analytical protocols of sample preparation and to analyze the organic components of the explanted aortic valves for significant degenerative aortic stenosis. The study of aortic valve mineralization on the molecular level should contribute to understanding this process, which should consequently lead to effective prevention as well as to new ways of treatment of this grave disease.

Ion binding properties of poly(ethylene oxide)-based networks in dioxane and toluene

Binding constants of alkali picrates to poly(ethylene oxide)-based networks were measured spectrophotometrically in dioxane at 25 and 40°C. The networks were synthesized from aliphatic tri- or tetrafunctional isocyanates and α,ω-diamino-poly-(ethylene glycol)s. The slopes of the Klotz binding plots appear to decrease in the lower picrate concentration range, suggesting that binding of the salt becomes more difficult at high picrate content. It was shown that under saturation conditions six to seven ethylene oxide units are required to bind a sodium picrate ion pair. The affinity of the PEO-resins for the alkali picrate can be enhanced by immobilizing a poly(crown ether) in the network. A number of competition experiments for sodium picrate in toluene was also carried out to obtain the affinity of soluble ligands for alkali salts. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 1819–1824, 1997     

Interactions between ions and free or immobilized ligands. Application of the competition method

Application of a competition method to determine affinities of ligands for ionic species in low polarity media is described. A soluble ligand, L, and a network-immobilized ligand, N, are allowed to interact with the counterion of an ionic chromophore A” according to the reaction NM⁺A⁻ + L → LM⁺A⁻ + N (K). K values were determined in toluene and in ether-type solvents for linear and macrocyclic polyethers and polyamines, as well as for other cation-complexing agents, by varying either N or L. In solvents such as dioxane, binding constants of M⁺A⁻ to N can be determined directly. Combined with K values they yield the complex formation constant, K_L, of the reaction M⁺A⁻ + L → LM+A⁻.     

Maintaining the minimal distance of a point set in polylogarithmic time

A dynamic data structure is given that maintains the minimal distance in a set ofn points ink-dimensional space inO((logn) ^k log logn) amortized time per update. The size of the data structure is bounded byO(n(logn) ^k ). Distances are measured in the MinkowskiL _t -metric, where 1 t . This is the first dynamic data structure that maintains the minimal distance in polylogarithmic time for fully on-line updates.This work was supported by the ESPRIT II Basic Research Actions Program, under Contract No. 3075 (project ALCOM).     

Effects of poly(2-vinylpyridine) as a template for the radical polymerization of methacrylic acid—III. Influence of monomer concentration

The template polymerization of methacrylic acid along atactic poly (2-vinylpyridine) was studied calorimetrically at various monomer concentrations from 0.1 to 9.0 M in DMF; the concentration of the P2VP template was fixed at 0.4 base M. Azobisisobutyronitrile and bis(p-tert-butylcyclohexyl)peroxydicarbonate were used as initiators at concentrations of 0.1 and 0.01 M, respectively. The temperature was 30°. The results could be well described by a generalized kinetic model in which the effect of preferential adsorption of monomer by the template, this adsorption being assumed to be of the Langmuir type, has been taken into account, i.e. the model incorporates propagation along the template not only by picking-up monomer from the surrounding solution (mechanism II) but also by zipping-up pre-adsorbed monomer (mechanism I).