Szilvia Nagy

Elementary formula for entanglement entropies of fermionic systems

A generalized skew information is defined and a generalized uncertainty relation is established with the help of a trace inequality which was recently proven by Fujii. In addition, we prove the trace inequality conjectured by Luo and Zhang. Finally, we point out that Theorem 1 in S. Luo and Q. Zhang, IEEE Trans. Inf. Theory, vol. 50, pp. 1778-1782, no. 8, Aug. 2004 is incorrect in general, by giving a simple counter-example.An elementary formula for the von Neumann and Renyi entropies describing quantum correlations in two-fermionic systems having four single-particle states is presented. An interesting geometric structure of fermionic entanglement is revealed. A connection with the generalized Pauli principle is established.

Refinement trajectory and determination of eigenstates by a wavelet based adaptive method

The detail structure of the wave function is analyzed at various refinement levels using the methods of wavelet analysis. The eigenvalue problem of a model system is solved in granular Hilbert spaces, and the trajectory of the eigenstates is traced in terms of the resolution. An adaptive method is developed for identifying the fine structure localization regions, where further refinement of the wave function is necessary.

Comparison of accuracy between FSL’s FIRST and Freesurfer for caudate nucleus and putamen segmentation

Although several methods have been developed to automatically delineate subcortical gray matter structures from MR images, the accuracy of these algorithms has not been comprehensively examined. Most of earlier studies focused primarily on the hippocampus. Here, we assessed the accuracy of two widely used non-commercial programs (FSL-FIRST and Freesurfer) for segmenting the caudate and putamen. T1-weighted 1 mm3 isotropic resolution MR images were acquired for thirty healthy subjects (15 females). Caudate nucleus and putamen were segmented manually by two independent observers and automatically by FIRST and Freesurfer (v4.5 and v5.3). Utilizing manual labels as reference standard the following measures were studied: Dice coefficient (D), percentage volume difference (PVD), absolute volume difference as well as intraclass correlation coefficient (ICC) for consistency and absolute agreement. For putamen segmentation, FIRST achieved higher D, lower PVD and higher ICC for absolute agreement with manual tracing than either version of Freesurfer. Freesurfer overestimated the putamen, while FIRST was not statistically different from manual tracing. The ICC for consistency with manual tracing was similar between the two methods. For caudate segmentation, FIRST and Freesurfer performed more similarly. In conclusion, Freesurfer and FIRST are not equivalent when comparing to manual tracing. FIRST was superior for putaminal segmentation.

An economic prediction of refinement coefficients in wavelet-based adaptive methods for electron structure calculations.

The wave function of a many electron system contains inhomogeneously distributed spatial details, which allows to reduce the number of fine detail wavelets in multiresolution analysis approximations. Finding a method for decimating the unnecessary basis functions plays an essential role in avoiding an exponential increase of computational demand in wavelet‐based calculations. We describe an effective prediction algorithm for the next resolution level wavelet coefficients, based on the approximate wave function expanded up to a given level. The prediction results in a reasonable approximation of the wave function and allows to sort out the unnecessary wavelets with a great reliability.

Heat treatment parameters effecting the fractal dimensions of AuGe metallization on GaAs

Correlation was detected between the thermal treatment parameters of the AuGe–GaAs system and surface fractal structure. Structural entropic calculations were used to confirm the results obtained by fractal calculations.

Adaptive local refinement of the electron density, one-particle density matrices, and electron orbitals by hierarchical wavelet decomposition

The common experience that the distribution and interaction of electrons widely vary by scanning over various parts of a molecule is incorporated in the atomic-orbital expansion of wave functions. The application of Gaussian-type atomic orbitals suffers from the poor representation of nuclear cusps, as well as asymptotic regions, whereas Slater-type orbitals lead to unmanageable computational difficulties. In this contribution we show that using the toolkit of wavelet analysis it is possible to find an expansion of the electron density and density operators which is sufficiently precise, but at the same time avoids unnecessary complications at smooth and slightly detailed parts of the system. The basic idea of wavelet analysis is a coarse description of the system on a rough grid and a consecutive application of refinement steps by introducing new basis functions on a finer grid. This step could highly increase the number of required basis functions, however, in this work we apply an adaptive refinement only in those regions of the molecule, where the details of the electron structure require it. A molecule is split into three regions with different detail characteristics. The neighborhood of a nuclear cusp is extremely well represented by a moderately fine wavelet expansion; the domains of the chemical bonds are reproduced at an even coarser resolution level, whereas the asymptotic tails of the electron structure are surprisingly precise already at a grid distance of 0.5 a.u. The strict localization property of wavelet functions leads to an especially simple calculation of the electron integrals.

An economic prediction of the finer resolution level wavelet coefficients in electronic structure calculations

In wavelet based electronic structure calculations, introducing a new, finer resolution level is usually an expensive task, this is why often a two-level approximation is used with very fine starting resolution level. This process results in large matrices to calculate with and a large number of coefficients to be stored. In our previous work we have developed an adaptively refined solution scheme that determines the indices, where the refined basis functions are to be included, and later a method for predicting the next, finer resolution coefficients in a very economic way. In the present contribution, we would like to determine whether the method can be applied for predicting not only the first, but also the other, higher resolution level coefficients. Also the energy expectation values of the predicted wave functions are studied, as well as the scaling behaviour of the coefficients in the fine resolution limit.

Age at onset and seizure frequency affect white matter diffusion coefficient in patients with mesial temporal lobe epilepsy

In mesial temporal lobe epilepsy with hippocampal sclerosis (MTLE-HS), structural abnormalities are present not only in the hippocampus but also in the white matter with ipsilateral predominance. Although the timing of epilepsy onset is commonly associated with clinical and semiological dissimilarities, limited data exist regarding white matter diffusion changes with respect to age at epilepsy onset. The aim of this study was to investigate diffusion changes in the white matter of patients with unilateral MTLE-HS with respect to clinical parameters and to compare them with an age- and sex-matched healthy control group. Apparent diffusion coefficients (ADCs) were derived using monoexponential approaches from 22 (11 early and 11 late age at onset) patients with unilateral MTLE-HS and 22 age- and sex-matched control subjects after acquiring diffusion-weighted images on a 3T MRI system. Data were analyzed using two-tailed t-tests and multiple linear regression models. In the group with early onset MTLE-HS, ADC was significantly elevated in the ipsilateral hemispheric (p=0.04) and temporal lobe white matter (p=0.01) compared with that in controls. These differences were not detectable in late onset MTLE-HS patients. Apparent diffusion coefficient of the group with early onset MTLE-HS was negatively related to age at epilepsy onset in the ipsilateral hemispheric white matter (p=0.03) and the uncinate fasciculus (p=0.03), while in patients with late onset MTLE-HS, ADC was no longer dependent on age at epilepsy onset itself but rather on the seizure frequency in the ipsilateral uncinate fasciculus (p=0.03). Such diffusivity pattern has been associated with chronic white matter degeneration, reflecting myelin loss and higher extracellular volume which are more pronounced in the frontotemporal regions and also depend on clinical features. In the group with early onset MTLE-HS, the timing of epilepsy seems to be the major cause of white matter abnormalities while in late onset disease, it has a secondary role in provoking diffusion changes.

Problematic internet use is associated with structural alterations in the brain reward system in females.

Neuroimaging findings suggest that excessive Internet use shows functional and structural brain changes similar to substance addiction. Even though it is still under debate whether there are gender differences in case of problematic use, previous studies by-passed this question by focusing on males only or by using gender matched approach without controlling for potential gender effects. We designed our study to find out whether there are structural correlates in the brain reward system of problematic Internet use in habitual Internet user females. T1-weighted Magnetic Resonance (MR) images were collected in 82 healthy habitual Internet user females. Structural brain measures were investigated using both automated MR volumetry and voxel based morphometry (VBM). Self-reported measures of problematic Internet use and hours spent online were also assessed. According to MR volumetry, problematic Internet use was associated with increased grey matter volume of bilateral putamen and right nucleus accumbens while decreased grey matter volume of orbitofrontal cortex (OFC). Similarly, VBM analysis revealed a significant negative association between the absolute amount of grey matter OFC and problematic Internet use. Our findings suggest structural brain alterations in the reward system usually related to addictions are present in problematic Internet use.

Wavelet based fuzzy rule bases in pre-qualification of access networks' wire pairs

Even though the penetration of the fibre optical cables into telecommunication access networks seems to be accelerated, most of the customers are connected to the central office or to the telecommunication nodes by the copper wire pairs of the old telephone network. Until the replacement of the lines, their needs for modern high speed data communications services can be fulfilled by these symmetrical wire pairs. Equipment manufacturers produce equipments of the latest technologies for these networks (e.g. VDSL2), however pre-qualification of wire pairs of access networks is also essential, as the estimation of the performance gives the possibility to optimize the offered ensemble of services for telecommunications service providers. Our previous performance evaluation method based on fuzzy rule bases at discrete values of the insertion loss at 6 characteristic frequencies is improved by wavelet analysis. We have also proved, that the fine structure of the insertion loss spectrum does not play role in the achievable data transfer rate of the lines.