1. Cycle separating cuts in possible counterexamples to the cycle double cover and the Berge-Fulkerson conjecturesEdita Máčajová, Giuseppe Mazzuoccolo, Gloria Tabarelli, 2026, izvirni znanstveni članek Opis: It is known that smallest counterexamples to the Cycle Double Cover Conjecture and Berge-Fulkerson Conjecture (if they exist) are cyclically 4- and 5-edge-connected, respectively. We further analyse small cycle separating cuts in possible counterexamples. We prove that if a smallest counterexample G to the CDC Conjecture contains a cycle separating 4-cut S, then the behaviour of the admissible CDC coverings along the dangling edges of the two 4-poles induced by S is uniquely determined among more than 2 a priori possibilities. Similarly, for the Berge-Fulkerson Conjecture, we prove that among more than 2 a priori possibilities, there are only 13 pairs of admissible sets that could occur along the dangling edges of a 5-cut in a smallest counterexample.
Ključne besede: snark, cyclic connectivity, cycle double cover, Berge-Fulkerson conjecture
Objavljeno v RUP: 03.03.2026; Ogledov: 144; Prenosov: 3
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3. Role of music therapy in the development of language skills in children with autism spectrum disorder : a systematic literature reviewLucija Mlakar, Vesna Posavčević, 2026, pregledni znanstveni članek Opis: Autism Spectrum Disorder (ASD) is a complex neurodevelopmental condition that typically emerges in early childhood, marked by difficulties in communication, social interaction, behaviour, and emotional regulation. Despite these challenges, many children with ASD demonstrate exceptional musical abilities, making music a powerful medium for enhancing self-expression, fostering social bonds, and supporting neurological development crucial for speech and social skills. Historically, minimally verbal children with ASD were often excluded from research due to the difficulty of assessment using standardised tools; however, recent advancements have enabled more inclusive studies. Over the past decade, naturalistic approaches have gained prominence, with music therapy emerging as a particularly promising intervention. A systematic literature review, based on original research sourced from PubMed, Sage, and ScienceDirect, examined six studies involving children aged two to twelve years with minimal verbal abilities and a clinical diagnosis of autism. These studies consistently found that music therapy significantly supports the development of language and social communication skills, while also enhancing fronto-temporal brain connectivity. The review contributes valuable insights into the current state of research, underscores the importance of early intervention and parental involvement, and lays the groundwork for further exploration into the role of music therapy in language development for children with ASD.
Ključne besede: autism spectrum disorder, children, minimal language abilities, social communication, fronto-temporal brain connectivity, music therapy, non-music therapy
Objavljeno v RUP: 28.01.2026; Ogledov: 335; Prenosov: 12
Celotno besedilo (3,34 MB)
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4. Estimation of task-related dynamic brain connectivity via data inflation and classification model explainabilityPeter Rogelj, 2025, izvirni znanstveni članek Opis: 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.
Ključne besede: EEG, functional connectivity, data inflation, classification, explainability, saliency maps
Objavljeno v RUP: 04.06.2025; Ogledov: 1966; Prenosov: 17
Celotno besedilo (1,74 MB)
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6. The Sierpiński product of graphsJurij Kovič, Tomaž Pisanski, Sara Sabrina Zemljič, Arjana Žitnik, 2023, izvirni znanstveni članek Opis: 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.
Ključne besede: Sierpiński graphs, graph products, connectivity, planarity, symmetry
Objavljeno v RUP: 06.11.2023; Ogledov: 2148; Prenosov: 7
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10. Nove karakterizacije v strukturni teoriji grafov : 1-popolno usmerljivi grafi, produktni grafi in cena povezanostiTatiana Romina Hartinger, 2017, doktorska disertacija Ključne besede: 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
Objavljeno v RUP: 09.11.2017; Ogledov: 5945; Prenosov: 44
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