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432. Genetic markers in oligodendroglial tumoursTomaž Velnar, Uroš Smrdel, Mara Popović, Gorazd Bunc, 2010, review article Abstract: Background. Oliogodendrogliomas are brain tumours composed of the cells resembling oligodendrocytes. They represent the third most common glial tumour, comprising 2.5% of all primary brain tumours and 5-20% of all gliomas. Conclusions. Oligodendroglial tumours with 1p and 19q loss demonstrate a better overall prognosis due to more indolent clinical behaviour and higher sensitivity to treatment. Additionally, 1p and 19q loss is a marker of clinical utility, helping to assess tumour sensitivity to chemotherapy and harbouring the potential for improving the diagnosis and survival of oligodendroglioma patients as well as future clinical practice.
Published in DiRROS: 15.03.2024; Views: 93; Downloads: 29
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435. Invariants of multi-linkoidsBoštjan Gabrovšek, Neslihan Gügümcü, 2023, original scientific article Abstract: In this paper, we extend the definition of a knotoid to multilinkoids that consist of a finite number of knot and knotoid components. We study invariants of multi-linkoids, such as the Kauffman bracket polynomial, ordered bracket polynomial, the Kauffman skein module, and the $T$-invariant in relation with generalized $\Theta$-graphs.
Keywords: knotoid, multi-linkoid, spatial graph, Kauffman bracket polynomial, Kauffman bracket skein module, theta-curve, theta-graph
Published in DiRROS: 15.03.2024; Views: 92; Downloads: 61
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438. Reflexivity of the space of transversal distributionsJure Kališnik, 2023, original scientific article Abstract: For any smooth, Hausdorff and second-countable manifold $N$ one can define the Fréchet space ${\mathcal C}^{\infty}(N)$ of smooth functions on $N$ and its strong dual ${\cal E}'(N)$ of compactly supported distributions on $N$. It is a standard result that the strong dual of ${\cal E}'(N)$ is naturally isomorphic to ${\mathcal C}^{\infty}(N)$, which implies that both ${\mathcal C}^{\infty}(N)$ and ${\cal E}'(N)$ are reflexive locally convex spaces. In this paper we generalise that result to the setting of transversal distributions on the total space of a surjective submersion $\pi : P\to M$. We show that the strong ${\mathcal C}^{\infty}_c(M)$-dual of the space ${\cal E}'_{\pi} (P)$ of $\pi$-transversal distributions is naturally isomorphic to the ${\mathcal C}^{\infty}_c(M)$-module ${\mathcal C}^{\infty}(P)$.
Keywords: distributions with compact support, Fréchet spaces, transversal distributions, homomorphisms of modules, reflexive modules
Published in DiRROS: 15.03.2024; Views: 101; Downloads: 47
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439. Rigidity of terminal simplices in persistent homologyAleksandra Franc, Žiga Virk, 2023, original scientific article Abstract: Given a filtration function on a finite simplicial complex, stability theorem of persistent homology states that the corresponding barcode is continuous with respect to changes in the filtration function. However, due to the discrete setting of simplicial complexes, the simplices terminating matched bars cannot change continuously for arbitrary perturbations of filtration functions. In this paper we provide a sufficient condition for rigidity of a terminal simplex, i.e., a condition on $\varepsilon > 0$ implying that the terminal simplex of a homology class or a bar in persistent homology remains constant through $\varepsilon$-perturbations of filtration function. The condition for a homology class or a bar in dimension $n$ depends only on the barcodes in dimensions $n$ and $n+1$.
Keywords: persistent homology, stability theorem, terminal simplex, rigidity
Published in DiRROS: 15.03.2024; Views: 101; Downloads: 52
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