A genetic algorithm with neural network fitness function evaluation for IMRT beam angle optimization

Intensity Modulated Radiotherapy Treatment (IMRT) is a technique used in the treatment of cancer, where the radiation beams are modulated by a multileaf collimator allowing the irradiation of the patient using non-uniform radiation fields from selected angles. Beam angle optimization consists in trying to find the best set of angles that should be used in IMRT planning. The choice of this set of angles is patient and pathology dependent and, in clinical practice, most of the times it is made using a trial and error procedure or simply using equidistantly distributed angles. In this paper we propose a genetic algorithm that aims at calculating good sets of angles in an automated way, given a predetermined number of angles. We consider the discretization of all possible angles in the interval [0 \(^{\circ }\) , 360 \(^{\circ }\) ], and each individual is represented by a chromosome with 360 binary genes. As the calculation of a given individual’s fitness is very expensive in terms of computational time, the genetic algorithm uses a neural network as a surrogate model to calculate the fitness of most of the individuals in the population. To explicitly consider the estimation error that can result from the use of this surrogate model, the fitness of each individual is represented by an interval of values and not by a single crisp value. The genetic algorithm is capable of finding improved solutions, when compared to the usual equidistant solution applied in clinical practice. The genetic algorithm will be described and computational results will be shown.     

Solvability of a mathematical model of dissociative adsorption and associative desorption type

A mathematical model of dissociative adsorption and associative desorption for diatomic molecules is generalized. The model is described by a coupled system of parabolic and ordinary differential equations. The existence and uniqueness theorem of the classical solution is proved.     

Development and validation of a fast isocratic liquid chromatography method for the simultaneous determination of norfloxacin,lomefloxacin and ciprofloxacin in human plasma

A simple and fast liquid chromatographic method coupled with fluorescence detection (LC‐FD) is reported, for the first time, for the simultaneous quantification of norfloxacin (NOR), ciprofloxacin (CIP) and lomefloxacin (LOM) in human plasma, using levofloxacin as internal standard (IS). Sample preparation consists of a single‐step precipitation of plasma proteins followed by vortex‐mixing and centrifugation. Chromatographic separation was achieved within 7 min on a reversed‐phase C₁₈ column with a mobile phase consisting of 0.1% aqueous formic acid (pH = 3.0, triethylamine)–methanol (82:18, v/v) pumped isocratically at 1.2 mL/min. The detector was set at excitation/emission wavelengths of 278/450 nm. Calibration curves were linear (r² ≥ 0.994) in the range of 0.02–5.0 µg/mL, and the limit of quantification was established at 0.02 µg/mL for all analytes (NOR, CIP and LOM). The overall precision did not exceed 8.19% and accuracy was within ±10.91%. NOR, CIP and LOM were extracted from human plasma with an overall mean recovery ranged from 90.1 to 111.5%. No interferences were observed at the retention times of the analytes and IS. This novel LC‐FD method enables the reliable determination of NOR, CIP and LOM in a single chromatographic run, which may be suitable to support human pharmacokinetic‐based studies with those antimicrobial agents. Copyright © 2010 John Wiley & Sons, Ltd.     

Differential invariants of the cotangent bundle

Vilnius Pedagigic Institute. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 30, No. 3, pp. 536–547, July–September, 1990.     

An O(h6) cubic spline interpolating procedure for harmonic functions

An O(h⁶) method for the interpolation of harmonic functions in rectangular domains is described and analyzed, The method is based on an earlier cubic spline technique [N. Papamichael and J.R. Whiteman, BIT 14 , 452–459 (1974)], and makes use of recent results concerning the a posteriori correction of interpolatory cubic splines.     

Cramér-Rao bound for the estimates of frequencies and damping factors of quasipolynomials in noise

Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 32, No. 3, pp. 417–425, July–September, 1992.     

A Mononuclear Uranium(IV) Single‐Molecule Magnet with an Azobenzene Radical Ligand

A tetravalent uranium compound with a radical azobenzene ligand, namely, [{(SiMe₂NPh)₃‐tacn}U^IV(η²‐N₂Ph₂^.)] ( 2 ), was obtained by one‐electron reduction of azobenzene by the trivalent uranium compound [U^III{(SiMe₂NPh)₃‐tacn}] ( 1 ). Compound 2 was characterized by single‐crystal X‐ray diffraction and ¹H NMR, IR, and UV/Vis/NIR spectroscopy. The magnetic properties of 2 and precursor 1 were studied by static magnetization and ac susceptibility measurements, which for the former revealed single‐molecule magnet behaviour for the first time in a mononuclear U^IV compound, whereas trivalent uranium compound 1 does not exhibit slow relaxation of the magnetization at low temperatures. A first approximation to the magnetic behaviour of these compounds was attempted by combining an effective electrostatic model with a phenomenological approach using the full single‐ion Hamiltonian.     

Discrete Universality in the Selberg Class

The Selberg class S consists of functions L(s) that are defined by Dirichlet series and satisfy four axioms (Ramanujan conjecture, analytic continuation, functional equation, and Euler product). It has been known that functions in S that satisfy the mean value condition on primes are universal in the sense of Voronin, i.e., every function in a sufficiently wide class of analytic functions can be approximated by the shifts L(s + iτ ), τ ∈ R. In this paper we show that every function in the same class of analytic functions can be approximated by the discrete shifts L(s + ikh), k = 0, 1,..., where h > 0 is an arbitrary fixed number.     

Standard operation protocol for analysis of lipid hydroperoxides in human serum using a fully automated method based on solid-phase extraction and liquid chromatography-mass spectrometry in selected reaction monitoring

Standard operating procedures (SOPs) are of paramount importance in the analytical field to ensure the reproducibility of the results obtained among laboratories. SOPs gain special interest when the aim is the analysis of potentially unstable compounds. An SOP for analysis of lipid hydroperoxides (HpETEs) is here reported after optimization of the critical steps to be considered in their analysis in human serum from sampling to final analysis. The method is based on automated hyphenation between solid-phase extraction (SPE) and liquid chromatography-mass spectrometry (LC-MS). The developed research involves: (i) optimization of the SPE and LC-MS steps with a proper synchronization; (ii) validation of the method-viz. accuracy study (estimated as 86.4% as minimum value), evaluation of sensitivity and precision, which ranged from 2.5 to 7.0 ng/mL (0.25-0.70 ng on column) as quantification limit and precision below 13.2%), and robustness study (reusability of the cartridge for 5 times without affecting the accuracy and precision of the method); (iii) stability study, involving freeze-thaw stability, short-term and long-term stability and stock solution stability tests. The results thus obtained allow minimizing both random and systematic variation of the metabolic profiles of the target compounds by correct application of the established protocol.