Targeted Metabolomics for Biomarker Discovery

Metabolomics is a truly interdisciplinary field of science, which combines analytical chemistry, platform technology, mass spectrometry, and NMR spectroscopy with sophisticated data analysis. Applied to biomarker discovery, it includes aspects of pathobiochemistry, systems biology/medicine, and molecular diagnostics and requires bioinformatics and multivariate statistics. While successfully established in the screening of inborn errors in neonates, metabolomics is now widely used in the characterization and diagnostic research of an ever increasing number of diseases. In this Review we highlight important technical prerequisites as well as recent developments in metabolomics and metabolomics data analysis with special emphasis on their utility in biomarker identification and qualification, as well as targeted metabolomics by employing high‐throughput mass spectrometry.     

Polarization squeezing in polarized light

It is shown that polarized light can be polarization squeezed only if it exhibits sub-Poissonian statistics with the Mandel's Q factor less than − 1/2.     

Deformed statistics Kullback-Leibler divergence minimization within a scaled Bregman framework

The generalized Kullback-Leibler divergence (K-Ld) in Tsallis statistics [constrained by the additive duality of generalized statistics (dual generalized K-Ld)] is here reconciled with the theory of Bregman divergences for expectations defined by normal averages, within a measure-theoretic framework. Specifically, it is demonstrated that the dual generalized K-Ld is a scaled Bregman divergence. The Pythagorean theorem is derived from the minimum discrimination information principle using the dual generalized K-Ld as the measure of uncertainty, with constraints defined by normal averages. The minimization of the dual generalized K-Ld, with normal averages constraints, is shown to exhibit distinctly unique features.     

Unification theory of classical statistical uncertainty relation and quantum uncertainty relation and its applications

General classical statistical uncertainty relation is deduced and generalized to quantum uncertainty relation. We give a general unification theory of the classical statistical and quantum uncertainty relations, and prove that the classical limit of quantum mechanics is just classical statistical mechanics. It is shown that the classical limit of the general quantum uncertainty relation is the general classical uncertainty relation. Also, some specific applications show that the obtained theory is self-consistent and coincides with those from physical experiments.     

An alternative approach to calculate the density of states in nonextensive statistical mechanics

A relation between the generalized partition function (Tsallis) and density of states is established by using the method of integral transform which enables reducing some integral equations into the algebraic equations. Inverse Mellin transformation of this equation gives the density of states. Similar relation is also hold the for standard partition function (Boltzmann-Gibbs) and the density of states. Using these relations, we recover the density of states for the classical ideal gas within both statistics.     

Self-organized critical model for protein folding

The major factor that drives a protein toward collapse and folding is the hydrophobic effect. At the folding process a hydrophobic core is shielded by the solvent-accessible surface area of the protein. We study the fractal behavior of 5526 protein structures present in the Brookhaven Protein Data Bank. Power laws of protein mass, volume and solvent-accessible surface area are measured independently. The present findings indicate that self-organized criticality is an alternative explanation for the protein folding. Also we note that the protein packing is an independent and constant value because the self-similar behavior of the volumes and protein masses have the same fractal dimension. This power law guarantees that a protein is a complex system. From the analyzed data, q-Gaussian distributions seem to fit well this class of systems.     

Modeling of the non-equilibrium effects by high electric fields in small semiconductor devices

For the purpose of the future theory of energy and momentum relaxation in semiconductor devices, the introduction of two temperatures and two mean velocities for electron and phonons is required. A new model, based on an asymptotic procedure for solving the generalized kinetic equations of electrons and phonons is proposed, which gives naturally the displaced Maxwellian at the leading order. After that, balance equations for the electron number, energy densities, and momentum densities are constructed, which now constitute a system of five equations for the chemical potential of electrons, the temperatures and the drift velocities. In the drift-diffusion approximation the constitutive laws are derived and the Onsager relations recovered.     

Thermal entanglement of Hubbard dimers in the nonextensive statistics

The thermal entanglement of the Hubbard dimer (two-site Hubbard model) has been studied with the nonextensive statistics. We have calculated the auto-correlation (O_q), pair correlation (L_q), concurrence (Γ_q) and conditional entropy (R_q) as functions of entropic index q and the temperature T. The thermal entanglement is shown to considerably depend on the entropic index. For q<1.0, the threshold temperature where Γ_q vanishes or R_q changes its sign is more increased and the entanglement may survive at higher temperatures than for q=1.0. Relations among L_q, Γ_q and R_q are investigated. The physical meaning of the entropic index q is discussed with the microcanonical and superstatistical approaches. The nonextensive statistics is applied also to Heisenberg dimers.     

The finite sample breakdown point of PCS

The Projection Congruent Subset (PCS) is a new method for finding multivariate outliers. PCS returns an outlyingness index which can be used to construct affine equivariant estimates of multivariate location and scatter. In this note, we derive the finite sample breakdown point of these estimators.