1. Estimation of task-related dynamic brain connectivity via data inflation and classification model explainabilityPeter Rogelj, 2025, original scientific article Abstract: Study of brain function often involves analyzing task-related switching between intrinsic brain networks, which connect various brain regions. Functional brain connectivity analysis methods aim to estimate these networks but are limited by the statistical constraints of windowing functions, which reduce temporal resolution and hinder explainability of highly dynamic processes. In this work, we propose a novel approach to functional connectivity analysis through the explainability of EEG classification. Unlike conventional methods that condense raw data into extracted features, our approach inflates raw EEG data by decomposition into meaningful components that explain processes in the application domain. To uncover the brain connectivity that affects classification decisions, we introduce a new method of dynamic influence data inflation (DIDI), which extracts signals representing interactions between electrode regions. These inflated data are then classified using an end-to-end neural network classifier architecture designed for raw EEG signals. Saliency map estimation from trained classifiers reveals the connectivity dynamics affecting classification decisions, which can be visualized as dynamic connectivity support maps for improved interpretability. The methodology is demonstrated on two publicly available datasets: one for imagined motor movement classification and the other for emotion classification. The results highlight the dual benefits of our approach: in addition to providing interpretable insights into connectivity dynamics it increases classification accuracy.
Keywords: EEG, functional connectivity, data inflation, classification, explainability, saliency maps
Published in RUP: 04.06.2025; Views: 1711; Downloads: 11
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3. The Sierpiński product of graphsJurij Kovič, Tomaž Pisanski, Sara Sabrina Zemljič, Arjana Žitnik, 2023, original scientific article Abstract: In this paper we introduce a product-like operation that generalizes the construction of the generalized Sierpiński graphs. Let ▫$G, \, H$▫ be graphs and let ▫$f: V(G) \to V(H)$▫ be a function. Then the Sierpiński product of graphs ▫$G$▫ and ▫$H$▫ with respect to ▫$f$▫, denoted by ▫$G\otimes_f H$▫, is defined as the graph on the vertex set ▫$V(G) \times V(H)$▫, consisting of ▫$|V(G)|$▫ copies of ▫$H$▫; for every edge ▫$\{g, g'\}$▫ of ▫$G▫$ there is an edge between copies ▫$gH$▫ and ▫$g'H$▫ of form ▫$\{(g, f(g'), (g', f(g))\}$▫. Some basic properties of the Sierpiński product are presented. In particular, we show that the graph ▫$G\otimes_f H$▫ is connected if and only if both graphs ▫$G$▫ and ▫$H$▫ are connected and we present some conditions that ▫$G, \, H$▫ must fulfill for ▫$G\otimes_f H$▫ to be planar. As for symmetry properties, we show which automorphisms of ▫$G$▫ and ▫$H$▫ extend to automorphisms of ▫$G\otimes_f H$▫. In several cases we can also describe the whole automorphism group of the graph ▫$G\otimes_f H$▫. Finally, we show how to extend the Sierpiński product to multiple factors in a natural way. By applying this operation ▫$n$▫ times to the same graph we obtain an alternative approach to the well-known ▫$n$▫-th generalized Sierpiński graph.
Keywords: Sierpiński graphs, graph products, connectivity, planarity, symmetry
Published in RUP: 06.11.2023; Views: 1713; Downloads: 4
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7. Nove karakterizacije v strukturni teoriji grafov : 1-popolno usmerljivi grafi, produktni grafi in cena povezanostiTatiana Romina Hartinger, 2017, doctoral dissertation Keywords: 1-perfectly orientable graph, structural characterization of families of graphs, chordal graph, interval graph, circular arc graph, cograph, block-cactus graph, cobipartite graph, K4-minor-free graph, outerplanar graph, graph product, Cartesian product, lexicographic product, direct product, strong product, price of connectivity, cycle transversal, path transversal
Published in RUP: 09.11.2017; Views: 5128; Downloads: 44
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8. On cyclic edge-connectivity of fullerenesKlavdija Kutnar, Dragan Marušič, 2008, original scientific article Abstract: A graph is said to be cyclically ▫$k$▫-edge-connected, if at least ▫$k$▫ edges must be removed to disconnect it into two components, each containing a cycle. Such a set of ▫$k$▫ edges is called a cyclic-k-edge cutset and it is called a trivial cyclic-k-edge cutset if at least one of the resulting two components induces a single ▫$k$▫-cycle. It is known that fullerenes, that is, 3-connected cubic planar graphs all of whose faces are pentagons and hexagons, are cyclically 5-edge-connected. In this article it is shown that a fullerene ▫$F$▫ containing a nontrivial cyclic-5-edge cutset admits two antipodal pentacaps, that is, two antipodal pentagonal faces whose neighboring faces are also pentagonal. Moreover, it is shown that ▫$F$▫ has a Hamilton cycle, and as a consequence at least ▫$15 \cdot 2^{n/20-1/2}$▫ perfect matchings, where ▫$n$▫ is the order of ▫$F$▫.
Keywords: graph, fullerene graph, cyclic edge-connectivity, hamilton cycle, perfect matching
Published in RUP: 03.04.2017; Views: 3286; Downloads: 143
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