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534. Role of isotropic lipid phase in the fusion of photosystem II membranesKinga Böde, Uroš Javornik, Ondřej Dlouhý, Ottó Zsiros, Avratanu Biswas, Ildikó Domonkos, Primož Šket, Václav Karlický, Bettina Ughy, Petar H. Lambrev, Vladimír Špunda, Janez Plavec, Győző Garab, 2024, original scientific article Published in DiRROS: 27.08.2024; Views: 232; Downloads: 182
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536. Graphs with total mutual-visibility number zero and total mutual-visibility in Cartesian productsJing Tian, Sandi Klavžar, 2024, original scientific article Abstract: If $G$ is a graph and $X\subseteq V(G)$, then $X$ is a total mutual-visibility set if every pair of vertices $x$ and $y$ of $G$ admits a shortest $x,y$-path $P$ with $V(P) \cap X \subseteq \{x,y\}$. The cardinality of a largest total mutual-visibility set of $G$ is the total mutual-visibility number $\mu_{\rm t}(G)$ of $G$. Graphs with $\mu_{\rm t}(G) = 0$ are characterized as the graphs in which no vertex is the central vertex of a convex $P_3$. The total mutual-visibility number of Cartesian products is bounded and several exact results proved. For instance, $\mu_{\rm t}(K_n\,\square\, K_m) = \max\{n,m\}$ and $\mu_{\rm t}(T\,\square\, H) = \mu_{\rm t}(T)\mu_{\rm t}(H)$, where $T$ is a tree and $H$ an arbitrary graph. It is also demonstrated that $\mu_{\rm t}(G\,\square\, H)$ can be arbitrary larger than $\mu_{\rm t}(G)\mu_{\rm t}(H)$.
Keywords: mutual-visibility set, total mutual-visibility set, bypass vertex, Cartesian product of graphs, trees
Published in DiRROS: 26.08.2024; Views: 212; Downloads: 103
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537. Persistent homology with selective Rips complexes detects geodesic circlesŽiga Virk, 2024, original scientific article Abstract: This paper introduces a method to detect each geometrically significant loop that is a geodesic circle (an isometric embedding of $S^1$) and a bottleneck loop (meaning that each of its perturbations increases the length) in a geodesic space using persistent homology. Under fairly mild conditions, we show that such a loop either terminates a 1- dimensional homology class or gives rise to a 2-dimensional homology class in persistent homology. The main tool in this detection technique are selective Rips complexes, new custom made complexes that function as an appropriate combinatorial lens for persistent homology to detect the above mentioned loops. The main argument is based on a new concept of a local winding number, which turns out to be an invariant of certain homology classes.
Keywords: simple closed geodesic, Rips complex, persistent homology, local winding number
Published in DiRROS: 26.08.2024; Views: 222; Downloads: 93
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538. Complexity of 2-rainbow total domination problemTadeja Kraner Šumenjak, Aleksandra Tepeh, 2024, original scientific article Abstract: In this paper,we extend the findings of recent studies on $k$-rainbow total domination by placing our focus on its computational complexity aspects. We show that the problem of determining whether a graph has a $2$-rainbow total dominating function of a given weight is NP-complete. This complexity result holds even when restricted to planar graphs. Along the way tight bounds for the $k$-rainbow total domination number of rooted product graphs are established. In addition, we obtain the closed formula for the $k$-rainbow total domination number of the corona product $G ∗ H$, provided that $H$ has enough vertices.
Keywords: domination, rainbow domination, rooted product, NP-complete
Published in DiRROS: 26.08.2024; Views: 233; Downloads: 102
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539. The remedy for a world without transcendence : Georges Bataille on sacrifice and the theology of transgressionLuka Trebežnik, 2024, original scientific article Abstract: Georges Bataille is undoubtedly a key reference for all relevant contemporary thoughts about sacrifice. This article attempts to follow his impulses and intuitions, which are often misunderstood because they are highly personal, provocative, and suggestive. The problem of sacrifice is approached in three concentric circles. The first presents a view from a distance, from the cosmic standpoint of “base materialism” and “general economy.” The second takes a closer look at the sacrificial site and deals with Bataille’s fascination with Aztec sacrificial culture. The concluding third part looks at sacrifice from the point of the altar, the place of communication and communal consumption of death, as a site of the emergence of the sacred and of community. In this way, the article seeks to highlight Bataille’s transgressive thinking as a worthwhile contribution to post-metaphysical theology.
Keywords: sacrifice, transgression, violence, sacred, communication, Aztecs, Bataille
Published in DiRROS: 26.08.2024; Views: 244; Downloads: 200
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540. Analysis of eigenvalue condition numbers for a class of randomized numerical methods for singular matrix pencilsDaniel Kressner, Bor Plestenjak, 2024, original scientific article Abstract: The numerical solution of the generalized eigenvalue problem for a singular matrix pencil is challenging due to the discontinuity of its eigenvalues. Classically, such problems are addressed by first extracting the regular part through the staircase form and then applying a standard solver, such as the QZ algorithm, to that regular part. Recently, several novel approaches have been proposed to transform the singular pencil into a regular pencil by relatively simple randomized modifications. In this work, we analyze three such methods by Hochstenbach, Mehl, and Plestenjak that modify, project, or augment the pencil using random matrices. All three methods rely on the normal rank and do not alter the finite eigenvalues of the original pencil. We show that the eigenvalue condition numbers of the transformed pencils are unlikely to be much larger than the ▫$\delta$▫-weak eigenvalue condition numbers, introduced by Lotz and Noferini, of the original pencil. This not only indicates favorable numerical stability but also reconfirms that these condition numbers are a reliable criterion for detecting simple finite eigenvalues. We also provide evidence that, from a numerical stability perspective, the use of complex instead of real random matrices is preferable even for real singular matrix pencils and real eigenvalues. As a side result, we provide sharp left tail bounds for a product of two independent random variables distributed with the generalized beta distribution of the first kind or Kumaraswamy distribution.
Keywords: singular pencil, singular generalized eigenvalue problem, eigenvalue condition number, randomized numerical method, random matrices
Published in DiRROS: 26.08.2024; Views: 219; Downloads: 96
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