Tootfinder

Combinatorial Laplacians and relative Homology of complex pairs
Xiongfeng Zhan, Xueyi Huang, Lu Lu
https://arxiv.org/abs/2507.16381 https://

Combinatorial Laplacians and relative Homology of complex pairs
As a discretization of the Hodge Laplacian, the combinatorial Laplacian of simplicial complexes has garnered significant attention. In this paper, we study combinatorial Laplacians for complex pairs $(X, A)$, where $A$ is a subcomplex of a simplicial complex $X$. We establish a relative version of the matrix-tree theorem for complex pairs, which generalizes both the matrix-tree theorem for simplicial complexes proved by Duval, Klivans, and Martin (2009) and the result for Dirichlet eigenvalues …

Paris confirms strong interest in Ukraine arms co-production: https://benborges.xyz/2025/07/22/paris-confirms-strong-interest-in.html

Mutation of $n$-cotorsion pairs in extriangulated categories
Huimin Chang, Yu Liu, Panyue Zhou
https://arxiv.org/abs/2506.16188 https://

Mutation of $n$-cotorsion pairs in extriangulated categories
In this article, we introduce the notion of $n$-cotorsion pairs in extriangulated categories, which extends both the cotorsion pairs established by Nakaoka and Palu and the $n$-cotorsion pairs in triangulated categories developed by Chang and Zhou. We further prove that any mutation of an $n$-cotorsion pair remains an $n$-cotorsion pair. As applications, we provide a geometric characterization of $n$-cotorsion pairs in $n$-cluster categories of type $A_{\infty}$, and we realize mutations of $n$…

Complete systems of solutions, transmutations and Darboux transform for Sturm-Liouville equations in impedance form
V\'ictor A. Vicente-Ben\'itez
https://arxiv.org/abs/2506.16604

Complete systems of solutions, transmutations and Darboux transform for Sturm-Liouville equations in impedance form
We present the construction of a complete system of functions associated with the Sturm-Liouville equation in impedance form on a finite interval $I$, given an impedance function $a\in L^2(I)$. The system, known as the formal powers, is generated through recursive integration of the impedance function $a$ and its reciprocal. We establish the completeness of this system in the space $L^p$ with the weight function $a^2$. Under additional conditions on $a$, we extend the completeness of this compl…

Intermediate-temperature specific heat of solids and the rationale behind the Maier-Kelley empirical formula
Valmir Ribeiro, Fernando Parisio
https://arxiv.org/abs/2508.15009 ht…

Intermediate-temperature specific heat of solids and the rationale behind the Maier-Kelley empirical formula
The heat capacity of solids at intermediate-to-high temperatures is of fundamental importance to several fields ranging from geology to material science. It depends on a variety of factors, with anharmonicity and, ultimately, melting playing a pivotal role. In this work we develop a first-principles model from an analytically tractable semi-harmonic oscillator Hamiltonian. The resulting specific heat expression depends not only on the Einstein temperature of the material but also on other physi…

The Digital Life of Parisian Parks: Multifunctionality and Urban Context Uncovered by Mobile Application Traffic
Andr\'e Felipe Zanella, Linus W. Dietz, Sanja \v{S}\'cepanovi\'c, Ke Zhou, Zbigniew Smoreda, Daniele Quercia
https://arxiv.org/abs/2508.15516

The Digital Life of Parisian Parks: Multifunctionality and Urban Context Uncovered by Mobile Application Traffic
Landscape architecture typically considers urban parks through the lens of form and function. While past research on equitable access has focused mainly on form, studies of functions have been constrained by limited scale and coarse measurement. Existing efforts have partially quantified functions through small-scale surveys and movement data (e.g., GPS) or general usage records (e.g., CDR), but have not captured the activities and motivations underlying park visits. As a result, our understand…

MCM: Mamba-based Cardiac Motion Tracking using Sequential Images in MRI
Jiahui Yin, Xinxing Cheng, Jinming Duan, Yan Pang, Declan O'Regan, Hadrien Reynaud, Qingjie Meng
https://arxiv.org/abs/2507.17678

MCM: Mamba-based Cardiac Motion Tracking using Sequential Images in MRI
Myocardial motion tracking is important for assessing cardiac function and diagnosing cardiovascular diseases, for which cine cardiac magnetic resonance (CMR) has been established as the gold standard imaging modality. Many existing methods learn motion from single image pairs consisting of a reference frame and a randomly selected target frame from the cardiac cycle. However, these methods overlook the continuous nature of cardiac motion and often yield inconsistent and non-smooth motion estim…

On Repetitive Finite Automata with Translucent Words
Franti\v{s}ek Mr\'az (Charles University in Prague), Friedrich Otto (Universit\"atKassel)
https://arxiv.org/abs/2507.15315

On Repetitive Finite Automata with Translucent Words
We introduce and study the repetitive variants of the deterministic and the nondeterministic finite automaton with translucent words (DFAwtw and NFAwtw). On seeing the right sentinel, a repetitive NFAwtw need not halt immediately, accepting or rejecting, but it may change into another state and continue with its computation. We establish that a repetitive DFAwtw already accepts a language that is not even semi-linear, which shows that the property of being repetitive increases the expressive ca…

Piecemaker: a resource-efficient entanglement distribution protocol
Luise Prielinger, Kenneth Goodenough, Guus Avis, Stefan Krastanov, Don Towsley, Gayane Vardoyan
https://arxiv.org/abs/2508.14737

Piecemaker: a resource-efficient entanglement distribution protocol
We introduce multipartite entanglement distribution protocols that use a quantum switch to deliver stabilizer states to a number of remote end users. As in existing schemes, the first step in our protocols involves Bell pair generation between the switch and each end user. However, unlike existing schemes that wait for all Bell pairs to be established before distributing the desired state -- for example, via a projective measurement -- our approach stores only a minimal subset of Bell pairs whi…

Symmetric powers of $S^{(n-1,1)}$ and $D^{(n-1,1)}$
Pavel Turek, Jialin Wang
https://arxiv.org/abs/2507.15505 https://arxiv.org/pdf/2…

Symmetric powers of $S^{(n-1,1)}$ and $D^{(n-1,1)}$
Let $p$ be a prime and $n\geq 2$ be a positive integer. We establish new formulae for the decompositions of the first $p-1$ symmetric powers of the Specht module $S^{(n-1,1)}$ and the irreducible module $D^{(n-1,1)}$ in characteristic $p$ as direct sums of Young permutation modules. As an application of the formulae, we show that these symmetric powers have Specht filtration and find the vertices of their indecomposable summands. Our main tool, constructed in this paper, is a lift of a splittin…