János Pipek

6602171346

Publications - 12

On structural entropy and spatial filling factor analysis of colonoscopy pictures

Brigita Sziová János Pipek Szilvia Nagy

Publication Name: Entropy

Publication Date: 2019-03-01

Volume: 21

Issue: 3

Page Range: Unknown

Description:

Colonoscopy is the standard device for diagnosing colorectal cancer, which develops from little lesions on the bowel wall called polyps. The Rényi entropies-based structural entropy and spatial filling factor are two scale- and resolution-independent quantities that characterize the shape of a probability distribution with the help of characteristic curves of the structural entropy-spatial filling factor map. This alternative definition of structural entropy is easy to calculate, independent of the image resolution, and does not require the calculation of neighbor statistics, unlike the other graph-based structural entropies.The distant goal of this study was to help computer aided diagnosis in finding colorectal polyps by making the Rényi entropy based structural entropy more understood. The direct goal was to determine characteristic curves that can differentiate between polyps and other structure on the picture. After analyzing the distribution of colonoscopy picture color channels, the typical structures were modeled with simple geometrical functions and the structural entropy-spatial filling factor characteristic curves were determined for these model structures for various parameter sets. A colonoscopy image analying method, i.e., the line- or column-wise scanning of the picture, was also tested, with satisfactory matching of the characteristic curve and the image.

Open Access: Yes

DOI: 10.3390/e21030256

The coupled cluster method and entanglement in three fermion systems

Gábor Sárosi János Pipek Péter Lévay Szilvia Nagy

Publication Name: Journal of Mathematical Physics

Publication Date: 2017-01-01

Volume: 58

Issue: 1

Page Range: Unknown

Description:

The Coupled Cluster (CC) and full CI expansions are studied for three fermions with six and seven modes. Surprisingly the CC expansion is tailor made to characterize the usual stochastic local operations and classical communication (SLOCC) entanglement classes. It means that the notion of a SLOCC transformation shows up quite naturally as a one relating the CC and CI expansions, and going from the CI expansion to the CC one is equivalent to obtaining a form for the state where the structure of the entanglement classes is transparent. In this picture, entanglement is characterized by the parameters of the cluster operators describing transitions from occupied states to singles, doubles, and triples of non-occupied ones. Using the CC parametrization of states in the seven-mode case, we give a simple formula for the unique SLOCC invariant I. Then we consider a perturbation problem featuring a state from the unique SLOCC class characterized by I. For this state with entanglement generated by doubles, we investigate the phenomenon of changing the entanglement type due to the perturbing effect of triples. We show that there are states with real amplitudes such that their entanglement encoded into configurations of clusters of doubles is protected from errors generated by triples. Finally we put forward a proposal to use the parameters of the cluster operator describing transitions to doubles for entanglement characterization. Compared to the usual SLOCC classes, this provides a coarse grained approach to fermionic entanglement.

Open Access: Yes

DOI: 10.1063/1.4974510

Multiresolution modeling of cavity resonators in microwave systems

András Fehér Brigita Sziová János Pipek Szilvia Nagy

Publication Name: 2016 13th International Conference on Synthesis Modeling Analysis and Simulation Methods and Applications to Circuit Design Smacd 2016

Publication Date: 2016-07-25

Volume: Unknown

Issue: Unknown

Page Range: Unknown

Description:

Multiresolution analysis or wavelet analysis provides a toolbox not only for signal processing, but also for synthesis of complex systems. Wavelets can be used for modeling complex parts of microwave circuits, such as cavity resonators. The differential equations describing the physical behavior of the device can be discretized using multiple resolutions simultaneously, i.e., high resolutions, where the details of the geometry demand it, and low resolutions, where the geometry is smooth. Using wavelet analysis offers the possibility of systematic and adaptive refinement, where the result is not sufficiently precise. Our method gives an approximation for the error of the solution in order to make it possible to decide, whether refinements are necessary.

Open Access: Yes

DOI: 10.1109/SMACD.2016.7520651

Optimization of the prediction of second refined wavelet coefficients in electron structure calculations

Brigita Sziová János Pipek Szilvia Nagy

Publication Name: Open Physics

Publication Date: 2016-01-01

Volume: 14

Issue: 1

Page Range: 643-650

Description:

In wavelet-based solution of eigenvalue-type differential equations, like the Schrödinger equation, refinement in the resolution of the solution is a costly task, as the number of the potential coefficients in the wavelet expansion of the solution increases exponentially with the resolution. Predicting the magnitude of the next resolution level coefficients from an already existing solution in an economic way helps to either refine the solution,or to select the coefficients, which are to be included into the next resolution level calculations, or to estimate the magnitude of the error of the solution. However, after accepting a solution with a predicted refinement as a basis, the error can still be estimated by a second prediction, i.e., from a prediction to the second finer resolution level coefficients. These secondary predicted coefficients are proven to be oscillating around the values of the wavelet expansion coefficients of the exact solution. The optimal averaging of these coefficients is presented in the following paper using a sliding average with three optimized coefficients for simple, one-dimensional electron structures.

Open Access: Yes

DOI: 10.1515/phys-2016-0063

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

János Pipek Szilvia Nagy

Publication Name: Physical Chemistry Chemical Physics

Publication Date: 2015-01-01

Volume: 17

Issue: 47

Page Range: 31558-31565

Description:

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.

Open Access: Yes

DOI: 10.1039/c5cp01214g

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

János Pipek Szilvia Nagy

Publication Name: Journal of Computational Chemistry

Publication Date: 2013-03-05

Volume: 34

Issue: 6

Page Range: 460-465

Description:

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. © 2012 Wiley Periodicals, Inc.

Open Access: Yes

DOI: 10.1002/jcc.23154

Error estimation of wavelet based modeling of electromagnetic waves in waveguides and resonators

András Fehér János Pipek Szilvia Nagy

Publication Name: 2nd Middle East Conference on Antennas and Propagation Mecap 2013

Publication Date: 2012-01-01

Volume: Unknown

Issue: Unknown

Page Range: Unknown

Description:

Wavelets provide an effective toolbox for solving differential equations by representing the continuous functions by their wavelet expansion coefficients and the corresponding differential equations by discrete matrix equations. The wavelet basis functions are organized into resolution levels of different frequency terms at different locations, and the main advantage of the wavelet expansion representation is that the resolution level can be different at different locations, if the solution function contains higher frequency terms in one place and restricted to lower frequencies at other places. Wavelet based differential equation solving methods can be adaptive, it is possible to refine the solution locally, if the precision is not sufficient at some regions. In the present work a simple method for estimating the next resolution level wavelet coefficients is presented. Predicting the approximate value of these coefficients makes it possible to select the minimal set of wavelet basis functions for the next resolution level solution in a computationally economic way, or in the last resolution levels it can substitute the next level solution of the matrix equation. © 2012 IEEE.

Open Access: Yes

DOI: 10.1109/MECAP.2012.6618193

A wavelet-based adaptive method for determining eigenstates of electronic systems

János Pipek Szilvia Nagy

Publication Name: Theoretical Chemistry Accounts

Publication Date: 2010-03-01

Volume: 125

Issue: 3-6

Page Range: 471-479

Description:

The possibilities for reducing the necessary computation power in wavelet-based electronic structure calculations are studied. The expansion of the expectation values of energy operators, the integrals of basis functions are mostly system-independent, consequently it is not necessary to compute them in each calculations. Fixed building blocks, such as a parameterized expansion of the nuclear and electron-electron cusp can reduce the amount of necessary calculation. An algorithm for local expansion refinement is also given. It is possible to determine the significant expansion coefficients of a high resolution level without solving the Schrödinger equation using only lower resolution results. © Springer-Verlag 2009.

Open Access: Yes

DOI: 10.1007/s00214-009-0653-6

The kinetic energy operator in the subspaces of wavelet analysis

János Pipek Szilvia Nagy

Publication Name: Journal of Mathematical Chemistry

Publication Date: 2009-06-01

Volume: 46

Issue: 1

Page Range: 261-282

Description:

At any resolution level of wavelet expansions the physical observable of the kinetic energy is represented by an infinite matrix which is "canonically" chosen as the projection of the operator - Δ/2 onto the subspace of the given resolution. It is shown, that this canonical choice is not optimal, as the regular grid of the basis set introduces an artificial consequence of its periodicity, and it is only a particular member of possible operator representations. We present an explicit method of preparing a near optimal kinetic energy matrix which leads to more appropriate results in numerical wavelet based calculations. This construction works even in those cases, where the usual definition is unusable (i.e., the derivative of the basis functions does not exist). It is also shown, that building an effective kinetic energy matrix is equivalent to the renormalization of the kinetic energy by a momentum dependent effective mass compensating for artificial periodicity effects. © 2008 Springer Science+Business Media, LLC.

Open Access: Yes

DOI: 10.1007/s10910-008-9458-4

Artifacts of grid-based electron structure calculations

János Pipek Szilvia Nagy

Publication Name: Chemical Physics Letters

Publication Date: 2008-10-13

Volume: 464

Issue: 1-3

Page Range: 103-106

Description:

Electron structure calculations over equidistant grids represent physical observables by matrices usually chosen as the projection of the corresponding operator in the Schrödinger picture onto the subspace expanded by the basis set of the given grid resolution. It is shown that any matrix representation compatible with the translational symmetry of the lattice suffers from essential difficulties. Especially the momentum and related operators like the kinetic energy show anomalous behavior, moreover, the required canonical commutation relation can never be satisfied. © 2008 Elsevier B.V. All rights reserved.

Open Access: Yes

DOI: 10.1016/j.cplett.2008.08.091

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

Csaba Dominkovics János Pipek L. Dobos Gábor Harsányi I. Mojzes Szilvia Nagy

Publication Name: Applied Physics Letters

Publication Date: 2007-08-24

Volume: 91

Issue: 7

Page Range: Unknown

Description:

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. © 2007 American Institute of Physics.

Open Access: Yes

DOI: 10.1063/1.2768911

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

János Pipek Szilvia Nagy

Publication Name: Journal of Chemical Physics

Publication Date: 2006-11-13

Volume: 125

Issue: 17

Page Range: Unknown

Description:

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. © 2006 American Institute of Physics.

Open Access: Yes

DOI: 10.1063/1.2363368