Maximum entropy algorithm with inexact upper entropy bound based on Fup basis functions with compact support

The maximum entropy (MaxEnt) principle is a versatile tool for statistical inference of the probability density function (pdf) from its moments as a least-biased estimation among all other possible pdf’s. It maximizes Shannon entropy, satisfying the moment constraints. Thus, the MaxEnt algorithm transforms the original constrained optimization problem to the unconstrained dual optimization problem using Lagrangian multipliers. The Classic Moment Problem (CMP) uses algebraic power moments, causing typical conventional numerical methods to fail for higher-order moments (m>5–10)$(m>5''–''10)$ due to different sensitivities of Lagrangian multipliers and unbalanced nonlinearities. Classic MaxEnt algorithms overcome these difficulties by using orthogonal polynomials, which enable roughly the same sensitivity for all Lagrangian multipliers. In this paper, we employ an idea based on different principles, using Fup_n${\mathit{Fup}}_n$ basis functions with compact support, which can exactly describe algebraic polynomials, but only if the Fup order-n   is greater than or equal to the polynomial’s order. Our algorithm solves the CMP with respect to the moments of only low order Fup₂${\mathit{Fup}}_2$ basis functions, finding a Fup₂${\mathit{Fup}}_2$ optimal pdf with better balanced Lagrangian multipliers. The algorithm is numerically very efficient due to localized properties of Fup₂${\mathit{Fup}}_2$ basis functions implying a weaker dependence between Lagrangian multipliers and faster convergence. Only consequences are an iterative scheme of the algorithm where power moments are a sum of Fup₂${\mathit{Fup}}_2$ and residual moments and an inexact entropy upper bound. However, due to small residual moments, the algorithm converges very quickly as demonstrated on two continuous pdf examples – the beta distribution and a bi-modal pdf, and two discontinuous pdf examples – the step and double Dirac pdf. Finally, these pdf examples present that Fup MaxEnt algorithm yields smaller entropy value than classic MaxEnt algorithm, but differences are very small for all practical engineering purposes.     

Spectroscopic investigation and optical characterization of novel highly thulium doped tellurite glasses

In this paper, optical properties of 75TeO₂-20ZnO-5Na₂O host glass doped with concentration of Tm³⁺ up to 10 %mol were studied in order to assess the most suitable rare earth content for short cavity fiber lasers. Raman spectroscopy revealed a change in the glass structure while increasing Tm³⁺ content, similar to the well known addition of alkali ions in a glass. Influence of the fabrication process on the OH⁻ content was determined by FTIR measurements. Refractive index of Tm³⁺ doped tellurite glasses was measured at five different wavelengths ranging from 533 nm to 1533 nm. Lifetime and emission spectra measurements of the Tm³⁺ doped tellurite glasses are reported.     

Rapamycin biosynthesis: Elucidation of gene product function

The function of gene products involved in the biosynthesis of the clinically important polyketide rapamycin were elucidated by biotransformation and gene complementation.     

Development of an inorganic cations retention model in ion chromatography by means of artificial neural networks with different two-phase training algorithms

This paper describes development of artificial neural network (ANN) retention model, which can be used for method development in variety of ion chromatographic applications. By using developed retention model it is possible both to improve performance characteristic of developed method and to speed up new method development by reducing unnecessary experimentation. Multilayered feed forward neural network has been used to model retention behaviour of void peak, lithium, sodium, ammonium, potassium, magnesium, calcium, strontium and barium in relation with the eluent flow rate and concentration of methasulphonic acid (MSA) in eluent. The probability of finding the global minimum and fast convergence at the same time were enhanced by applying a two-phase training procedure. The developed two-phase training procedure consists of both first and second order training. Several training algorithms were applied and compared, namely: back propagation (BP), delta-bar-delta, quick propagation, conjugate gradient, quasi Newton and Levenberg-Marquardt. It is shown that the optimized two-phase training procedure enables fast convergence and avoids problems arisen from the fact that every new weight initialization can be regarded as a new starting position and yield irreproducible neural network if only second order training is applied. Activation function, number of hidden layer neurons and number of experimental data points used for training set were optimized in order to insure good predictive ability with respect to speeding up retention modelling procedure by reducing unnecessary experimental work. The predictive ability of optimized neural networks retention model was tested by using several statistical tests. This study shows that developed artificial neural network are very accurate and fast retention modelling tool applied to model varied inherent non-linear relationship of retention behaviour with respect to mobile phase parameters.     

High-resolution calorimetric investigation of the existence of a nematic phase for the dodecylcyanobiphenyl liquid crystal

We have employed high-resolution calorimetric techniques in order to investigate the unresolved issue of the existence of a nematic phase for the liquid crystal dodecylcyanobiphenyl. Various heating and cooling runs were performed on dodecylcyanobiphenyl samples of different origin and their analysis did not reveal any signature of a nematic phase. The calorimetric results are presented in detail and they are additionally supported by optical polarising microscopy observations.     

Quantum Mechanics: Myths and Facts

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of “myths”, that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.     

Evidence of supercritical behavior in liquid single crystal elastomers

Temperature profiles of the first and the second moment of the nematic order parameter distribution function, as determined from the deuteron nuclear magnetic resonance line shapes, as well as heat capacity response, provide support for the supercritical scenario of the nematic-paranematic phase transition in liquid single crystal elastomers. The relative strength of the locked-in internal mechanical field with respect to the critical field can be decreased by swelling the elastomer samples with low molecular mass nematogen. By increasing the concentration of the dopant, critical and below-critical behavior is promoted.