Bichromatic Pair Research Articles

Constrained many-to-many point matching in two dimensions

In the minimum-weight many-to-many point matching problem, we are given a set R of red points and a set B of blue points in the plane, of total size N, and we want to pair up each point in R to one or more points in B and vice versa so that the sum of distances between the paired points is minimized. This problem can be solved in O(N3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(N^3)$$\\end{document} time by using a reduction to the minimum-weight perfect matching problem, and thus, it is not fast enough to be used for on-line systems where a large number of tunes need to be compared. Motivated by similarity problems in music theory, in this paper we study several constrained minimum-weight many-to-many point matching problems in which the allowed pairings are given by geometric restrictions, i.e., a bichromatic pair can be matched if and only if the corresponding points satisfy a specific condition of closeness. We provide algorithms to solve these constrained versions in O(N) time when the sets R and B are given ordered by abscissa.

Ion trap quantum gates with amplitude-modulated laser beams

In ion traps, entangling gate operations can be realized by a bichromatic pair of laser beams that collectively interact with the ions. In this paper, a new method of modelling the laser–ion interaction is introduced that turns out to be superior to standard techniques for the description of gate operations on optical qubits. The treatment allows for a comparison of the performance of gates based on σz⊗σz and σϕ⊗σϕ interactions on optical transitions where the bichromatic laser field can be realized by an amplitude-modulated laser resonant with the qubit transition. Shaping the amplitude of the bichromatic laser pulse is shown to make the gates more robust against experimental imperfections.

A Simple Randomized Sieve Algorithm for the Closest-Pair Problem

We present a linear time randomized sieve algorithm for the closest-pair problem. The algorithm and its analysis are simple. The algorithm is extended to obtain a randomized linear time approximation algorithm for the closest bichromatic pair problem.

FINDING k FARTHEST PAIRS AND k CLOSEST/FARTHEST BICHROMATIC PAIRS FOR POINTS IN THE PLANE

We study the problem of enumerating k farthest pairs for n points in the plane and the problem of enumerating k closest/farthest bichromatic pairs of n red and n blue points in the plane. We propose a new technique for geometric enumeration problems which iteratively reduces the search space by a half and provides efficient algorithms. As applications of this technique, we develop algorithms, using higher order Voronoi diagrams, for the above problems, which run in O(min{n2, n log n+k4/3log n/log1/3 k}) time and O(n+k4/3/log1/3 k+k log n) space for general Lp metric with p≠2, and O(min{n2, n log n+k4/3}) time and O(n+k4/3+k log n) space for L2 metric. For the problem of enumerating k closest/farthest bichromatic pairs, we shall also discuss the case where we have different numbers of red and blue points. To the authors’ knowledge, no nontrivial algorithms have been known for these problems and our algorithms are faster than trivial ones when k=o(n3/2).

Spectral study of bichromatics: Biuret-protein and glucose-hexokinase reactions as visible-ultraviolet models for turbidity

A model was devised for the study of the analytical effectiveness of bichromatic spectral measurements when faced with a severe interference such as turbidity. This was accomplished by using the biuret reaction of serum proteins to investigate the midvisible range and the 340-nm spectral peak of the NADPH produced in a hexokinase-based glucose reaction for the ultraviolet range. Two different bichromatic pairs that are currently used for the biuret reaction were compared in which the side-wavelengths were on either the blue or the red side of the peak maximum (540–650 and 550-510 nm, respectively), while the most common ultraviolet wavelength pair (340–383 nm) was used for the glucose reaction. Single wavelength absorbance peak measurements were also included in this study in which Intralipid, a total parenteral nutrition solution, served as a controlled source of the interference, turbidity. By using single wavelength measurements for comparison to bichromatic determination, one could determine if advantages accrue to one or the other in the face of light scatter. Although Intralipid does not mimic natural hyperlipemia perfectly, choosing it allowed us to use uncontaminated preparations as a baseline to which we could compare the same specimens deliberately contaminated with known amounts of turbid substances. The concentrations obtained in this manner showed marked deviations from those values for protein and glucose known to be present in the studied turbid mixtures. These findings indicate that there may be shortcomings to bichromatics if it is used as a means of correcting for interference when the constraints inherent in such a process are not observed. The limitations of the bichromatic measurement process that should be kept in mind are discussed here.