Approximate Entropy of Brain Network in the Study of Hemispheric Differences

Human brain, a dynamic complex system, can be studied with different approaches, including linear and nonlinear ones. One of the nonlinear approaches widely used in electroencephalographic (EEG) analyses is the entropy, the measurement of disorder in a system. The present study investigates brain networks applying approximate entropy (ApEn) measure for assessing the hemispheric EEG differences; reproducibility and stability of ApEn data across separate recording sessions were evaluated. Twenty healthy adult volunteers were submitted to eyes-closed resting EEG recordings, for 80 recordings. Significant differences in the occipital region, with higher values of entropy in the left hemisphere than in the right one, show that the hemispheres become active with different intensities according to the performed function. Besides, the present methodology proved to be reproducible and stable, when carried out on relatively brief EEG epochs but also at a 1-week distance in a group of 36 subjects. Nonlinear approaches represent an interesting probe to study the dynamics of brain networks. ApEn technique might provide more insight into the pathophysiological processes underlying age-related brain disconnection as well as for monitoring the impact of pharmacological and rehabilitation treatments.     

A variational method for the calculation of spin-rovibronic energy levels of triatomic molecules with three interacting electronic states

A general method is presented for the evaluation of the spin rovibronic energy levels of triatomic molecules with up to three interacting potential energy surfaces. The full theory is outlined in detail, both for singlet and for doublet electronic states and the method is then applied to the benchmark example of C₂H. High quality multireference configuration interaction calculations have been carried out to generate the 3-dimensional near-equilibrium adiabatic potential energy surfaces of the three lowest 1²A'(X²Σ⁺), 2²A'(A²Π), 1²A''(A²Π) electronic states of C₂H, and the pair of interacting states of A 0 symmetry have then been diabatized. Results are presented for J up to 7/2 and compared with gas-phase high resolution experimental results for energies up to 5600 cm¹.     

Dirac index classes and the noncommutative spectral flow

We present a detailed proof of the existence-theorem for noncommutative spectral sections (see the noncommutative spectral flow, unpublished preprint, 1997). We apply this result to various index-theoretic situations, extending to the noncommutative context results of Booss–Wojciechowski, Melrose–Piazza and Dai–Zhang. In particular, we prove a variational formula, in K_*(C_r^*(Γ)), for the index classes associated to 1-parameter family of Dirac operators on a Γ-covering with boundary; this formula involves a noncommutative spectral flow for the boundary family. Next, we establish an additivity result, in K_*(C_r^*(Γ)), for the index class defined by a Dirac-type operator associated to a closed manifold M and a map r:M→BΓ when we assume that M is the union along a hypersurface F of two manifolds with boundary M=M_{+ F} M₋. Finally, we prove a defect formula for the signature-index classes of two cut-and-paste equivalent pairs (M₁,r₁:M₁→BΓ) and (M₂,r₂:M₂→BΓ), where

M₁=M_{+ (F,φ1)} M₋, M₂=M_{+ (F,φ2)} M₋

and φ_jDiff(F). The formula involves the noncommutative spectral flow of a suitable 1-parameter family of twisted signature operators on F. We give applications to the problem of cut-and-paste invariance of Novikov's higher signatures on closed oriented manifolds.     

Primal separation for 0/1 polytopes

 The 0/1 primal separation problem is: Given an extreme point xˉ of a 0/1 polytope P and some point x ^*, find an inequality which is tight at xˉ, violated by x ^* and valid for P or assert that no such inequality exists. It is known that this separation variant can be reduced to the standard separation problem for P. We show that 0/1 optimization and 0/1 primal separation are polynomial time equivalent. This implies that the problems 0/1 optimization, 0/1 standard separation, 0/1 augmentation, and 0/1 primal separation are polynomial time equivalent. Then we provide polynomial time primal separation procedures for matching, stable set, maximum cut, and maximum bipartite graph problems, giving evidence that these algorithms are conceptually simpler and easier to implement than their corresponding counterparts for standard separation. In particular, for perfect matching we present an algorithm for primal separation that rests only on simple max-flow computations. In contrast, the known standard separation method relies on an explicit minimum odd cut algorithm. Consequently, we obtain a very simple proof that a maximum weight perfect matching of a graph can be computed in polynomial time. Received: August 20, 2001 / Accepted: April 2002 Published online: December 9, 2002 RID="⋆" ID="⋆" This research was developed while the author was on leave at the Istituto di Analisi dei Sistemi ed Informatica, Viale Manzoni 30, 00185 Roma, supported by the project TMR-DONET nr. ERB FMRX-CT98-0202 of the European Union. Mathematics Subject Classification (2000): 90C10, 90C60, 90C57     

Radon levels in underground workplaces – results of a nationwide survey in Italy

In Italy an extensive survey has been carried out with the aim to evaluate annual average radon concentration in underground workplaces.The survey covered 933 underground rooms located in 311 bank workplaces spread throughout in all Italian regions; at this scope the sampling was stratified random in order to be representative on national scale. The annual radon concentration was estimated by using passive radon dosemeters (NRPB/SSI type holder and CR-39 as detector): the devices were exposed for a period of about 3 months and 4 cycles were performed to cover a solar year. The radon levels in underground workplaces ranged from 27 to 4851 Bq/m³ with an overall mean value of 153 Bq/m³. As expected, radon distribution is not uniform throughout Italy: in several regions high radon annual averages have been found, confirming previous surveys.The analysis of data shows a high variability among regions and intra-region but low spread among rooms belonging to the same workplace.About 5% of underground workplaces displayed radon concentration exceeding 400 Bq/m³, and the 4.4% exceeds 500 Bq/m³, the national action level for the exposure to natural radioactivity in workplaces.     

Analysis of uncertainties affecting the Monte Carlo simulation of a neutron multiplicity counter

When applying numerical simulation to physical problems it is important to be able to clearly understand the quality that can be reached and the uncertainty associated with the modelling. In this paper we will deal with the Monte Carlo simulation of neutron coincidence and multiplicity counters. These instruments are intensively used in nuclear safeguards for the measurement and verification of the mass of fissile materials in nuclear installations. Their numerical simulation, either for detector design or for numerical calibration, is now used more and more frequently as support to inspections.Several benchmark exercises have been organised in order to assess the capabilities of Monte Carlo simulation to correctly predict realistic practical cases in neutron coincidence and multiplicity counting. Nevertheless most of them allowed reaching conclusions only on the overall uncertainties associated to the modelling through the comparison between calculated and measured integral data.In this paper we aim to analyse more deeply the sources of these uncertainties, separating the different possible causes and analysing parametrically the individual factors. We will include influencing factors deriving from the physical model of the detector, of the acquisition electronics, of the sample and from the nuclear data. The final total uncertainties are consistent with the results of the integral benchmarks.     

A high-voltage lithium-ion battery prepared using a Sn-decorated reduced graphene oxide anode and a LiNi<Subscript>0.5</Subscript>Mn<Subscript>1.5</Subscript>O<Subscript>4</Subscript> cathode

This paper describes the preparation and characterization of a high-voltage lithium-ion battery based on Sn-decorated reduced graphene oxide and LiNi_0.5Mn_1.5O₄ as the anode and cathode active materials, respectively. The Sn-decorated reduced graphene oxide is prepared using a microwave-assisted hydrothermal synthesis method followed by reduction at high temperature of a mixture of (C₆H₅)₂SnCl₂ and graphene oxide. The so-obtained anode material is characterized by thermogravimetric analysis, X-ray diffraction, scanning electron microscopy, and electron diffraction spectroscopy. The LiNi_0.5Mn_1.5O₄ is a commercially available product. The two materials are used to prepare composite electrodes, and their electrochemical properties are investigated by galvanostatic charge/discharge cycles at various current densities in lithium cells. The electrodes are then used to assemble a high-voltage lithium-ion cell, and the cell is tested to evaluate its performance as a function of discharge rate and cycle number.     

Power-law time distribution of large earthquakes

We study the statistical properties of time distribution of seismicity in California by means of a new method of analysis, the diffusion entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a given seismic sequence) and the next one does not obey Poisson statistics, as assumed by the current models. We prove that this distribution is an inverse power law with an exponent mu=2.06+/-0.01. We propose the long-range model, reproducing the main properties of the diffusion entropy and describing the seismic triggering mechanisms induced by large earthquakes.     

A Robertson-type uncertainty principle and quantum Fisher information

Let A₁,…,A_N be complex self-adjoint matrices and let ρ be a density matrix. The Robertson uncertainty principle

     

Immobilized TiO<Subscript>2</Subscript> nanoparticles produced by flame spray for photocatalytic water remediation

Anatase/rutile mixed-phase titanium dioxide (TiO₂) photocatalysts in the form of nanostructured powders with different primary particle size, specific surface area, and rutile content were produced from the gas-phase by flame spray pyrolysis (FSP) starting from an organic solution containing titanium (IV) isopropoxide as Ti precursor. Flame spray-produced TiO₂ powders were characterized by means of X-ray diffraction, Raman spectroscopy, and BET measurements. As-prepared powders were mainly composed of anatase crystallites with size ranging from 7 to 15 nm according to the synthesis conditions. TiO₂ powders were embedded in a multilayered fluoropolymeric matrix to immobilize the nanoparticles into freestanding photocatalytic membranes. The photocatalytic activity of the TiO₂-embedded membranes toward the abatement of hydrosoluble organic pollutants was evaluated employing the photodegradation of rhodamine B in aqueous solution as test reaction. The photoabatement rate of best performing membranes significantly overcomes that of membranes produced by the same method and incorporating commercial P25-TiO₂.