Characterization of spherical particles using high-order neural networks and scanning flow cytometry

We retrieve the radius R, real n and imaginary k parts of the refractive index of homogeneous spherical particles using angular distribution of the light-scattering intensity. To solve the inverse light-scattering problem we use a high-order neural-network technique. The effect of network parameters on optimization is examined. The technique is evaluated for noise-corrupted input data at 0.6 μm<R<10.6 μm, 1.02<n<1.38, and 0<k<0.03. The errors of retrieval for nonabsorbing particles do not exceed 0.05 μm for radius and 0.015 for refractive index. The experimental verification is fulfilled by experimental data retrieved by means of a scanning flow cytometer. The light-scattering profiles of polystyrene beads and spherized red blood cells are processed with the high-order neural networks and a non-linear regression at Mie theory. The parameters retrieved by the high-order neural networks correlate well with the parameters retrieved by the least-square method.     

Farthest-point queries with geometric and combinatorial constraints

In this paper we discuss farthest-point problems in which a set or sequence S of n points in the plane is given in advance and can be preprocessed to answer various queries efficiently. First, we give a data structure that can be used to compute the point farthest from a query line segment in O(log²n) time. Our data structure needs O(nlogn) space and preprocessing time. To the best of our knowledge no solution to this problem has been suggested yet. Second, we show how to use this data structure to obtain an output-sensitive query-based algorithm for polygonal path simplification. Both results are based on a series of data structures for fundamental farthest-point queries that can be reduced to each other.     

About Regularity of Collections of Sets

The paper continues investigations of stationarity and regularity properties of collections of sets in normed spaces. It contains a summary of different characterizations (both primal and dual) of regularity and a list of sufficient conditions for a collection of sets to be regular.     

H MAS NMR monitoring of the C-labeled carbon scrambling for propane in zeolite H-ZSM-5

It has been demonstrated that ¹H MAS NMR spectroscopy can be used as a tool for in situ monitoring the reaction kinetics of ¹³C-labeled carbon scrambling in alkane molecules adsorbed on zeolite catalysts at the reaction temperature of 540–570 K. The accuracy of the results and the time resolution are improved compared to ¹³C MAS NMR spectroscopy.     

Finite-gap Solutions of the Fuchsian Equations

We find a new class of Fuchsian equations, with algebro-geometric solutions associated to a hyperelliptic curve. A method for calculating its arithmetic genus and branching points is suggested. Numerous examples are given.