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Contributions to the Study of Contemporary Domination Invariants of Graphs
2019, doctoral dissertation

Abstract: This doctoral dissertation is devoted to contemporary domination concepts, such as the Grundy domination, the convex domination, the isometric domination and the total domination. Our main focus is to study their structure and algorithmic properties. Four Grundy domination invariants are presented, namely the Grundy domination number, the Grundy total domination number, the Z-Grundy domination number, and the L-Grundy domination number. Some bounds and properties of Grundy domination invariants are proven. All four Grundy domination parameters are studied on trees, bipartite distance-hereditary graphs, split graphs, interval graphs, Sierpi\'nski graphs, Kneser graphs and $P_4$-tidy graphs. Graphs with equal total domination number and Grundy total domination number are investigated. Convex domination and isometric domination are studied on (weak) dominating pair graphs. For the chordal dominating pair graphs we present a polynomial algorithm to compute the convex domination number, and prove the NP-completeness of the corresponding decision problem for the chordal weak dominating pair graphs. For the isometric domination number of weak dominating pair graphs an efficient algorithm is presented. Total domination is studied on the Cartesian product of graphs. We dedicate ourselves to graphs for which the equality holds in Ho's theorem, which states that the total domination number of the Cartesian product of any two graphs without isolated vertices is at least one half of the product of their total domination numbers.
Keywords: Grundy domination, Grundy total domination, Z-Grundy domination, L-Grundy domination, convex domination, isometric domination, total domination, trees, split graphs, interval graphs, Sierpi\'nski graphs, Kneser graphs, modular decomposition, dominating pair graphs, Cartesian product
Published in DKUM: 23.10.2019; Views: 914; Downloads: 11
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Synthesis and characterisation of hydroxylammonium fluorochromate
Matjaž Kristl, Mihael Drofenik, Ljubo Golič, Amalija Golobič, 2003, original scientific article

Abstract: Reactions in the system $Cr – NH_3OHF – HF – H_2O$ were investigated. Green crystals of a new compound with the formula $(NH_3OH)_3CrF_6$ have been isolated from the water solution and characterized by chemical analysis. The compound crystallizes as triclinic, P-1, with cell parameters: a = 6.5461(2) Å, b = 6.9347(2) Å, c = 9.4072(3) Å, α = 86.772(1)°, β = 83.804(1)°, γ = 70.283(1)°. The effective magnetic moment, $µ_{eff}$ = 3.82 BM, was calculated from magnetic susceptibility measurements in the temperature range 80-290 K. The thermal decomposition of the compound was studied by TG and DSC analysis. $(NH_3OH)_3CrF_6$ decomposes above 125 °C in three steps and the residue has been identified by X-ray powder diffraction as $α – Cr_2O_3$.
Keywords: inorganic chemistry, structural chemistry, crystalline structure, coordination compounds, synthesis, inorganic reactions, thermal decomposition, characterization of compounds, TG, DSC, X-ray diffraction, chromium complexes, hydroxylammonium fluoro chromates, crystals
Published in DKUM: 25.08.2017; Views: 1267; Downloads: 102
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Influence of temperature on the surface enhanced Raman scattering spectra of 2, 4, 6 - trinitrotoluene
Simon Hamler, 2015, master's thesis

Abstract: The detection of trace amounts of explosive like trinitrotoluene (TNT) is an important issue in the prevention of terrorist attacks. Surface enhanced Raman scattering (SERS) spectroscopy has become a powerful detection technique for identification of minute amounts of analytes. This thesis presents data of TNT in solution, deposited on a nanostructured gold surface, which is heated up to 60 °C. The observed changes in the microscopy images and in the SERS spectra are explained by evaporation, phase transition and decomposition of the TNT molecules. The impact of temperature dependence of SERS effect is studied on a chemisorbed 4-Nitrothiophenol monolayer. To minimize the evaporation of TNT molecules, a self-assembled monolayer of mercaptohexanol (MCH) was inserted between plasmonic surface and TNT.
Keywords: surface enhanced Raman spectroscopy, explosives, temperature dependence, microscopy, evaporation, phase transition, decomposition
Published in DKUM: 05.11.2015; Views: 1516; Downloads: 72
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Recognizing Cartesian products in linear time
Wilfried Imrich, Iztok Peterin, 2007, original scientific article

Abstract: We present an algorithm that determines the prime factors of connected graphs with respect to the Cartesian product in linear time and space. This improves a result of Aurenhammer et al. [Cartesian graph factorization at logarithmic cost per edge, Comput. Complexity 2 (1992) 331-349], who compute the prime factors in ▫$O(mlog n)$▫ time, where ▫$m$▫ denotes the number of vertices of ▫$G$▫ and ▫$n$▫ the number of edges. Our algorithm is conceptually simpler. It gains its efficiency by the introduction of edge-labellings.
Keywords: matematika, teorija grafov, kartezični produkt grafov, linearni algoritem, razcep, mathematics, graph theory, Cartesian product graphs, linear algorithm, decomposition
Published in DKUM: 10.07.2015; Views: 1076; Downloads: 123
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Real-time motor unit identification from high-density surface EMG
Vojko Glaser, Aleš Holobar, Damjan Zazula, 2013, original scientific article

Abstract: This study addresses online decomposition of high-density surface electromyograms (EMG) in real-time. The proposed method is based on previouslypublished Convolution Kernel Compensation (CKC) technique and sharesthe same decomposition paradigm, i.e. compensation of motor unit action potentials and direct identification of motor unit (MU) discharges. In contrast to previously published version of CKC, which operates in batch mode and requires ~ 10 s of EMG signal, the real-time implementation begins with batch processing of ~ 3 s of the EMG signal in the initialization stage and continues on with iterative updating of the estimators of MU discharges as blocks of new EMG samples become available. Its detailed comparison to previously validated batch version of CKC and asymptotically Bayesian optimal Linear Minimum Mean Square Error (LMMSE) estimator demonstrates high agreementin identified MU discharges among all three techniques. In the case of synthetic surface EMG with 20 dB signal-to-noise ratio, MU discharges were identified with average sensitivity of 98 %. In the case of experimental EMG, real-time CKC fully converged after initial 5 s of EMG recordings and real-time and batch CKC agreed on 90 % of MU discharges, on average. The real-time CKC identified slightly fewer MUs than its batch version (experimental EMG, 4 MUs versus 5 MUs identified by batch CKC, on average), but required only 0.6 s of processing time on regular personal computer for each second of multichannel surface EMG.
Keywords: discharge pattern, high-density EMG, surface EMG, motor unit, real time decomposition
Published in DKUM: 25.05.2015; Views: 1223; Downloads: 0

Noninvasive, accurate assessment of the behavior of representative populations of motor units in targeted reinnervated muscles
Dario Farina, Hubertus Rehbaum, Aleš Holobar, Ivan Vujaklija, Ning Jiang, Christian Hofer, Stefan Salminger, Hans-Willem van Vliet, Oskar Aszmann, 2014, original scientific article

Abstract: Targeted muscle reinnervation (TMR) redirects nerves that have lost their target, due to amputation, to remaining muscles in the region of the stump with the intent of establishing intuitive myosignals to control a complex prosthetic device. In order to directly recover the neural code underlying an attempted limb movement, in this paper, we present the decomposition of high-density surface electromyographic (EMG) signals detected from three TMR patients into the individual motor unit spike trains. The aim was to prove, for the first time, the feasibility of decoding the neural drive that would reach muscles of the missing limb in TMR patients, to show the accuracy of the decoding, and to demonstrate the representativeness of the pool of extracted motor units. Six to seven flexible EMG electrode grids of 64 electrodes each were mounted over the reinnervated muscles of each patient, resulting in up to 448 EMG signals. The subjects were asked to attempt elbow extension and flexion, hand open and close, wrist extension and flexion, wrist pronation and supination, of their missing limb. The EMG signals were decomposed using the Convolution Kernel Compensation technique and the decomposition accuracy was evaluated with a signal-based index of accuracy, called pulse-to-noise ratio (PNR). The results showed that the spike trains of 3 to 27 motor units could be identified for each task, with a sensitivity of the decomposition > 90%, as revealed by PNR. The motor unit discharge rates were within physiological values of normally innervated muscles. Moreover, the detected motor units showed a high degree of common drive so that the set of extracted units per task was representative of the behavior of the population of active units. The results open a path for a new generation of human-machine interfaces in which the control signals are extracted from noninvasive recordings and the obtained neural information is based directly on the spike trains of motor neurons.
Keywords: electromyographic, EMG, decomposition, high-density EMG, motor neuron, motor unit, myoelectronic control, neural drive to muscle, target muscle reinervation, TMR
Published in DKUM: 25.05.2015; Views: 1148; Downloads: 0

Characterization of reducible hexagons and fast decomposition of elementary benzenoid graphs
Andrej Taranenko, Aleksander Vesel, 2008, original scientific article

Abstract: A benzenoid graph is a finite connected plane graph with no cut vertices in which every interior region is bounded by a regular hexagon of a side length one. A benzenoid graph G is elementary if every edge belongs to a 1-factor of G. A hexagon h of an elementary benzenoid graph is reducible, if the removal of boundary edges and vertices of h results in an elementary benzenoid graph. We characterize the reducible hexagons of an elementary benzenoid graph. The characterization is the basis for an algorithm which finds the sequence of reducible hexagons that decompose a graph of this class in ▫$O(n^2)$▫ time. Moreover, we present an algorithm which decomposes an elementary benzenoid graph with at most one pericondensed component in linear time.
Keywords: mathematics, graph theory, benzenoid graphs, 1-factor, hexagons, reducible hexagons, reducible face decomposition
Published in DKUM: 07.06.2012; Views: 1537; Downloads: 84
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An approach to solving systems of polynomials via modular arithmetics with applications
Valery Romanovski, Mateja Prešern, 2011, original scientific article

Abstract: The objective of this paper is twofold. First, we describe a method to solve large systems of polynomial equations using modular arithmetics. Then, we apply the approach to the study of the problem of linearizability for a quadratic system of ordinary differential equations.
Keywords: mathematics, polynomials, decomposition
Published in DKUM: 07.06.2012; Views: 1269; Downloads: 85
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Polygon trapezoidation by sets of open trapezoids
Borut Žalik, Anton Jezernik, Krista Rizman Žalik, 2003, original scientific article

Abstract: A new efficient algorithm is described for the simple trapezoidation of polygons based on a sweep-line paradigm. As the sweep-line glides over the plane, a set of so-called open trapezoids is generated and maintained. It is shown that a boundary case (more polygon vertices are located on the sweep-line) can be solved safely and does not slow down the algorithm. If desired, the polygon holes can be trapezoidated simultaneously. This proposed algorithm when compared with the fastest known algorithm developed by Seidel resulted in more efficiency for different classes of polygons.
Keywords: polygon, polygon decomposition, trapezoidation, computational geometry
Published in DKUM: 01.06.2012; Views: 1538; Downloads: 120
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