401. Rigidity of terminal simplices in persistent homologyAleksandra Franc, Žiga Virk, 2023, izvirni znanstveni članek Povzetek: 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 $n+1$.
Ključne besede: persistent homology, stability theorem, terminal simplex, rigidity
Objavljeno v DiRROS: 15.03.2024; Ogledov: 89; Prenosov: 46
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407. Trilinear embedding for divergence-form operators with complex coefficientsAndrea Carbonaro, Oliver Dragičević, Vjekoslav Kovač, Kristina Ana Škreb, 2023, izvirni znanstveni članek Povzetek: We prove a dimension-free $L^p(\Omega)\times L^q(\Omega)\times L^r(\Omega)\rightarrow L^1(\Omega\times (0,\infty))$ embedding for triples of elliptic operators in divergence form with complex coefficients and subject to mixed boundary conditions on $\Omega$, and for triples of exponents $p,q,r \in (1,\infty)$ mutually related by the identity $1/p+1/q+1/r=1$. Here $\Omega$ is allowed to be an arbitrary open subset of $\mathbb{R}^d$. Our assumptions involving the exponents and coefficient matrices are expressed in terms of a condition known as $p$-ellipticity. The proof utilizes the method of Bellman functions and heat flows. As a corollary, we give applications to (i) paraproducts and (ii) square functions associated with the corresponding operator semigroups, moreover, we prove (iii) inequalities of Kato-Ponce type for elliptic operators with complex coefficients. All the above results are the first of their kind for elliptic divergence-form operators with complex coefficients on arbitrary open sets. Furthermore, the approach to (ii),(iii) through trilinear embeddings seems to be new.
Ključne besede: elliptic differential operator, p-ellipticity, operator semigroup, multilinear estimate
Objavljeno v DiRROS: 15.03.2024; Ogledov: 87; Prenosov: 51
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408. A comparative analysis among quenched, tempered, and stepped cooled TIG welded SS-304 plates based on tensile strength, hardness, and microstructural appearanceSaurabh Dewangan, Saksham Saksham, Adhir Chandra Paul, Jaka Burja, 2023, izvirni znanstveni članek Ključne besede: welding, austenitic stainless steel, heat affected zone, mechanical properties
Objavljeno v DiRROS: 15.03.2024; Ogledov: 96; Prenosov: 48
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409. The cut method on hypergraphs for the Wiener indexSandi Klavžar, Gašper Domen Romih, 2023, izvirni znanstveni članek Povzetek: The cut method has been proved to be extremely useful in chemical graph theory. In this paper the cut method is extended to hypergraphs. More precisely, the method is developed for the Wiener index of $k$-uniform partial cube-hypergraphs. The method is applied to cube-hypergraphs and hypertrees. Extensions of the method to hypergraphs arising in chemistry which are not necessary $k$-uniform and/or not necessary linear are also developed.
Ključne besede: hypergraphs, Wiener index, cut method, partial cube-hypergraphs, hypertrees, phenylene, Clar structures
Objavljeno v DiRROS: 15.03.2024; Ogledov: 94; Prenosov: 46
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410. Faster distance-based representative skyline and k-center along pareto front in the planeSergio Cabello, 2023, izvirni znanstveni članek Povzetek: We consider the problem of computing the distance-based representative skyline in the plane, a problem introduced by Tao, Ding, Lin and Pei and independently considered by Dupin, Nielsen and Talbi in the context of multi-objective optimization. Given a set $P$ of $n$ points in the plane and a parameter $k$, the task is to select $k$ points of the skyline defined by $P$ (also known as Pareto front for $P$) to minimize the maximum distance from the points of the skyline to the selected points. We show that the problem can be solved in $O(n \log h)$ time, where $h$ is the number of points in the skyline of $P$. We also show that the decision problem can be solved in $O(n \log k)$ time and the optimization problem can be solved in $O(n \log k + n \log\log n)$ time. This improves previous algorithms and is optimal for a large range of values of $k$.
Ključne besede: geometric optimization, skyline, pareto front, clustering, k-center
Objavljeno v DiRROS: 15.03.2024; Ogledov: 79; Prenosov: 39
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