1. The distance function on Coxeter-like graphs and self-dual codesMarko Orel, Draženka Višnjić, 2025, original scientific article Abstract: Let $SGL_n(\mathbb{F}_2)$ be the set of all invertible $n\times n$ symmetric matrices over the binary field $\mathbb{F}_2$. Let $\Gamma_n$ be the graph with the vertex set $SGL_n(\mathbb{F}_2)$ where a pair of matrices $\{A,B\}$ form an edge if and only if $\textrm{rank}(A-B)=1$. In particular, $\Gamma_3$ is the well-known Coxeter graph. The distance function $d(A,B)$ in $\Gamma_n$ is described for all matrices $A,B\in SGL_n(\mathbb{F}_2)$. The diameter of $\Gamma_n$ is computed. For odd $n\geq 3$, it is shown that each matrix $A\in SGL_n(\mathbb{F}_2)$ such that $d(A,I)=\frac{n+5}{2}$ and $\textrm{rank}(A-I)=\frac{n+1}{2}$ where $I$ is the identity matrix induces a self-dual code in $\mathbb{F}_2^{n+1}$. Conversely, each self-dual code $C$ induces a family ${\cal F}_C$ of such matrices $A$. The families given by distinct self-dual codes are disjoint. The identification $C\leftrightarrow {\cal F}_C$ provides a graph theoretical description of self-dual codes. A result of Janusz (2007) is reproved and strengthened by showing that the orthogonal group ${\cal O}_n(\mathbb{F}_2)$ acts transitively on the set of all self-dual codes in $\mathbb{F}_2^{n+1}$.
Keywords: Coxeter graph, invertible symmetric matrices, binary field, rank, distance in graphs, alternate matrices, self-dual codes
Published in DiRROS: 31.01.2025; Views: 249; Downloads: 144
 Full text (1,96 MB)
This document has many files! More... |
2. Variety of general position problems in graphsJing Tian, Sandi Klavžar, 2025, original scientific article Abstract: Let $X$ be a vertex subset of a graph $G$. Then $u, v\in V(G)$ are $X$-positionable if $V(P)\cap X \subseteq \{u,v\}$ holds for any shortest $u,v$-path $P$. If each two vertices from $X$ are $X$-positionable, then $X$ is a general position set. The general position number of $G$ is the cardinality of a largest general position set of $G$ and has been already well investigated. In this paper a variety of general position problems is introduced based on which natural pairs of vertices are required to be $X$-positionable. This yields the total (resp. dual, outer) general position number. It is proved that the total general position sets coincide with sets of simplicial vertices, and that the outer general position sets coincide with sets of mutually maximally distant vertices. It is shown that a general position set is a dual general position set if and only if its complement is convex. Several sufficient conditions are presented that guarantee that a given graph has no dual general position set. The total general position number, the outer general position number, and the dual general position number of arbitrary Cartesian products are determined.
Keywords: general position, total general position, outer general position, dual general position, Cartesian product of graphs, strong resolving graph, convex subgraph
Published in DiRROS: 07.11.2024; Views: 394; Downloads: 295
Full text (377,60 KB)
This document has many files! More... |
3. A new approach to universal $F$-inverse monoids in enriched signatureGanna Kudryavtseva, Ajda Lemut Furlani, 2024, original scientific article Abstract: We show that the universal $X$-generated $F$-inverse monoid $F(G)$, where ▫$G$▫ is an $X$-generated group, introduced by Auinger, Szendrei and the first-named author, arises as a quotient inverse monoid of the Margolis-Meakin expansion $M(G, X\cup \overline{G})$ of $G$, with respect to the extended generating set $X\cup \overline{G}$, where $\overline{G}$ is a bijective copy of $G$ which encodes the ▫$m$▫-operation in $F(G)$. The construction relies on a certain dual-closure operator on the semilattice of all finite and connected subgraphs containing the origin of the Cayley graph ${\rm Cay}(G, X\cup {\overline{G}})$ and leads to a new and simpler proof of the universal property of $F(G)$.
Keywords: inverse monoid, F-inverse monoid, Margolis-Meakin expansion, group presentation, Cayley graph of a group, closure operator, dual-closure operator, partial action, partial action product
Published in DiRROS: 21.10.2024; Views: 355; Downloads: 174
Full text (347,64 KB)
This document has many files! More... |
4. Nanoscale transformations of amphiboles within human alveolar epithelial cellsRuggero Vigliaturo, Maja Jamnik, Goran Dražić, Marjetka Podobnik, Magda Tušek-Žnidarič, Giancarlo Della Ventura, Günther Redhammer, Nada Žnidaršič, Simon Caserman, Reto Gieré, 2022, original scientific article Abstract: Amphibole asbestos is related to lung fibrosis and several types of lung tumors. The disease-triggering mechanisms still challenge our diagnostic capabilities and are still far from being fully understood. The literature focuses primarily on the role and formation of asbestos bodies in lung tissues, but there is a distinct lack of studies on amphibole particles that have been internalized by alveolar epithelial cells (AECs). These internalized particles may directly interact with the cell nucleus and the organelles, exerting a synergistic action with asbestos bodies (AB) from a different location. Here we document the near-atomic- to nano-scale transformations induced by, and taking place within, AECs of three distinct amphiboles (anthophyllite, grunerite, “amosite”) with different Fe-content and morphologic features. We show that: (i) an Fe-rich layer is formed on the internalized particles, (ii) particle grain boundaries are transformed abiotically by the internal chemical environment of AECs and/or by a biologically induced mineralization mechanism, (iii) the Fe-rich material produced on the particle surface does not contain large amounts of P, in stark contrast to extracellular ABs, and (iv) the iron in the Fe-rich layer is derived from the particle itself. Internalized particles and ABs follow two distinct formation mechanisms reaching different physicochemical end-states.
Keywords: amphiboles, human alveolar epithelial cells, asbestos, lung cancer, nanoscale investigation, acS/TEM-EDXS, dual-EELS, asbestos-related tumors
Published in DiRROS: 16.07.2024; Views: 747; Downloads: 424
Full text (4,53 MB)
This document has many files! More... |
5. |
6. Variety of mutual-visibility problems in graphsSerafino Cicerone, Gabriele Di Stefano, Lara Drožđek, Jaka Hedžet, Sandi Klavžar, Ismael G. Yero, 2023, original scientific article Abstract: If $X$ is a subset of vertices of a graph $G$, then vertices $u$ and $v$ are $X$-visible if there exists a shortest $u,v$-path $P$ such that $V(P)\cap X \subseteq \{u,v\}$. If each two vertices from $X$ are $X$-visible, then $X$ is a mutual-visibility set. The mutual-visibility number of $G$ is the cardinality of a largest mutual-visibility set of $G$ and has been already investigated. In this paper a variety of mutual-visibility problems is introduced based on which natural pairs of vertices are required to be $X$-visible. This yields the total, the dual, and the outer mutual-visibility numbers. We first show that these graph invariants are related to each other and to the classical mutual-visibility number, and then we prove that the three newly introduced mutual-visibility problems are computationally difficult. According to this result, we compute or bound their values for several graphs classes that include for instance grid graphs and tori. We conclude the study by presenting some inter-comparison between the values of such parameters, which is based on the computations we made for some specific families.
Keywords: mutual-visibility, total mutual-visibility, dual mutual-visibility number, outer mutual-visibility, grid graphs, torus graphs, computational complexity
Published in DiRROS: 10.04.2024; Views: 905; Downloads: 389
Full text (456,36 KB)
This document has many files! More... |
7. Outerplane bipartite graphs with isomorphic resonance graphsSimon Brezovnik, Zhongyuan Che, Niko Tratnik, Petra Žigert Pleteršek, 2024, original scientific article Abstract: We present novel results related to isomorphic resonance graphs of 2-connected outerplane bipartite graphs. As the main result, we provide a structure characterization for 2-connected outerplane bipartite graphs with isomorphic resonance graphs. Three additional characterizations are expressed in terms of resonance digraphs, via local structures of inner duals, as well as using distributive lattices on the set of order ideals of posets defined on inner faces of 2-connected outerplane bipartite graphs.
Keywords: distributive lattice, inner dual, isomorphic resonance graphs, order ideal, 2-connected outerplane bipartite graph
Published in DiRROS: 13.03.2024; Views: 803; Downloads: 417
Full text (452,02 KB)
This document has many files! More... |
8. Grain size distribution of DP 600 steel using single-pass asymmetrical wedge testUrška Klančnik, Peter Fajfar, Jan Foder, Heinz Palkowski, Jaka Burja, Grega Klančnik, 2023, original scientific article Keywords: wedge test, hot-rolling, grain size distribution, dual-phase steel
Published in DiRROS: 07.02.2024; Views: 1117; Downloads: 463
Full text (4,64 MB)
This document has many files! More... |
9. Neuromuscular assessment of force development, postural, and gait performance under cognitive-motor dual-tasking in healthy older adults and early Parkinson's disease patients : study protocol for a cross-sectional Mobile Brain/Body Imaging (MoBI) studyUroš Marušič, Manca Peskar, Maja Maša Šömen, Miloš Kalc, Aleš Holobar, Klaus Gramann, Bettina Wollesen, Anna Wunderlich, Christoph M. Michel, Aleksandar Miladinović, Mauro Catalan, Alex B. Stella, Miloš Ajčević, Paolo Manganotti, 2023, original scientific article Abstract: Background: Neuromuscular dysfunction is common in older adults and more pronounced in neurodegenerative diseases. In Parkinson's disease (PD), a complex set of factors often prevents the effective performance of activities of daily living that require intact and simultaneous performance of the motor and cognitive tasks. Methods: The cross-sectional study includes a multifactorial mixed-measure design. Between-subject factor grouping the sample will be Parkinson’s Disease (early PD vs. healthy). The within-subject factors will be the task complexity (single- vs. dual-task) in each motor activity, i.e., overground walking, semi-tandem stance, and isometric knee extension, and a walking condition (wide vs. narrow lane) will be implemented for the overground walking activity only. To study dual-task (DT) effects, in each motor activity participants will be given a secondary cognitive task, i.e., a visual discrimination task for the overground walking, an attention task for the semi-tandem, and mental arithmetic for the isometric extension. Analyses of DT effects and underlying neuronal correlates will focus on both gait and cognitive performance where applicable. Based on an a priori sample size calculation, a total N = 42 older adults (55-75 years) will be recruited. Disease-specific changes such as laterality in motor unit behavior and cortical control of movement will be studied with high-density surface electromyography and electroencephalography during static and dynamic motor activities, together with whole-body kinematics. Discussion: This study will be one of the first to holistically address early PD neurophysiological and neuromuscular patterns in an ecologically valid environment under cognitive-motor DT conditions of different complexities. The outcomes of the study aim to identify the biomarker for early PD either at the electrophysiological, muscular or kinematic level or in the communication between these systems.
Keywords: Parkinson's disease, mobile brain imaging, body brain imaging, MoBi, dual tasking, neuromuscular function, older adults
Published in DiRROS: 15.09.2023; Views: 1159; Downloads: 550
Full text (1,36 MB)
This document has many files! More... |
10. Stroop in motion : neurodynamic modulation underlying interference control while sitting, standing, and walkingManca Peskar, Nina Omejc, Maja Maša Šömen, Aleksandar Miladinović, Klaus Gramann, Uroš Marušič, 2023, original scientific article Abstract: There is conflicting evidence about how interference control in healthy adults is affected by walking as compared to standing or sitting. Although the Stroop paradigm is one of the best-studied paradigms to investigate interference control, the neurodynamics associated with the Stroop task during walking have never been studied. We investigated three Stroop tasks using variants with increasing interference levels – word-reading, ink-naming, and the switching of the two tasks, combined in a systematic dual-tasking fashion with three motor conditions – sitting, standing, and treadmill walking. Neurodynamics underlying interference control were recorded using the electroencephalogram. Worsened performance was observed for the incongruent compared to congruent trials and for the switching Stroop compared to the other two variants. The early frontocentral event-related potentials (ERPs) associated with executive functions (P2, N2) differentially signaled posture-related workloads, while the later stages of information processing indexed faster interference suppression and response selection in walking compared to static conditions. The early P2 and N2 components as well as frontocentral Theta and parietal Alpha power were sensitive to increasing workloads on the motor and cognitive systems. The distinction between the type of load (motor and cognitive) became evident only in the later posterior ERP components in which the amplitude non-uniformly reflected the relative attentional demand of a task. Our data suggest that walking might facilitate selective attention and interference control in healthy adults. Existing interpretations of ERP components recorded in stationary settings should be considered with care as they might not be directly transferable to mobile settings.
Keywords: Stroop task, mobile brain imaging, mobile body imaging, event-related potential, dual tasking
Published in DiRROS: 29.03.2023; Views: 1154; Downloads: 681
Full text (5,29 MB)
This document has many files! More... |
