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Learning Generalizable Shape Completion with SIM(3) Equivariance
Yuqing Wang, Zhaiyu Chen, Xiao Xiang Zhu
https://arxiv.org/abs/2509.26631 https://arxiv.or…

Learning Generalizable Shape Completion with SIM(3) Equivariance
3D shape completion methods typically assume scans are pre-aligned to a canonical frame. This leaks pose and scale cues that networks may exploit to memorize absolute positions rather than inferring intrinsic geometry. When such alignment is absent in real data, performance collapses. We argue that robust generalization demands architectural equivariance to the similarity group, SIM(3), so the model remains agnostic to pose and scale. Following this principle, we introduce the first SIM(3)-equi…

Signless Laplacian characterization of cones over disjoint unions of cycles, edges and isolated vertices
Jiachang Ye, Jianguo Qian, Zoran Stanic
https://arxiv.org/abs/2509.25925

Signless Laplacian characterization of cones over disjoint unions of cycles, edges and isolated vertices
Two graphs are said to be $Q$-cospectral if they share the same signless Laplacian spectrum. A simple graph is said to be determined by its signless Laplacian spectrum (abbreviated as DQS) if there exists no other non-isomorphic simple graph with the same signless Laplacian spectrum. In this paper, we establish the following results: (1) Let$G \cong K_{1} \vee \bigl(C_{k} \cup qK_{2} \cup sK_{1}\bigr),$ with $q,s \geq 1$, $k \geq 4$, and at least $21$ vertices. If $k$ is odd, then $G$ is DQS.…

Moody Urbanity - Everyone 👺
情绪化城市 - 每个人 👺
📷 Pentax MX
🎞️ Orwo Wolfen P400
#filmphotography #Photography #blackandwhite

Fullmoon fun with a cheap cellphone ... the Flimserstein above Flims, Graubünden, Switzerland illuminated solely by #moonlight (the village is pretty dim) - 20 seconds at f/1.79 and ISO 1600; some stars are visible in the brightened sky.

A CSP approach to Graph Sandwich Problems
Manuel Bodirsky, Santiago Guzm\'an-Pro
https://arxiv.org/abs/2510.09128 https://arxiv.org/pdf/2510.09128

A CSP approach to Graph Sandwich Problems
The \emph{Sandwich Problem} (SP) for a graph class $\calC$ is the following computational problem. The input is a pair of graphs $(V,E_1)$ and $(V,E_2)$ where $E_1\subseteq E_2$, and the task is to decide whether there is an edge set $E$ where $E_1\subseteq E \subseteq E_2$ such that the graph $(V,E)$ belongs to $\calC$. In this paper we show that many SPs correspond to the constraint satisfaction problem (CSP) of an infinite $2$-edge-coloured graph $H$. We then notice that several known comple…

No Sign of a Magnetar Remnant Following the Kilonova-Producing Long GRB 211211A $\sim 1.7~$Years Later
Genevieve Schroeder (Cornell), Ben Margalit, Brian D. Metzger, Wen-fai Fong, Benjamin P. Gompertz, Kate D. Alexander, Edo Berger, Tanmoy Laskar, Gavin P. Lamb, Andrew Levan, Charles D. Kilpatrick, Jillian C. Rastinejad
https://arxiv.org/a…

No Sign of a Magnetar Remnant Following the Kilonova-Producing Long GRB 211211A $\sim 1.7~$Years Later
In addition to a $γ$-ray burst (GRB), the merger of two neutron stars may produce a temporarily or indefinitely stable neutron star remnant with a strong magnetic field (a "magnetar"). As this magnetar remnant spins down, it can deposit its rotational energy into the surrounding kilonova ejecta, producing synchrotron emission that peaks in the radio bands $\sim$months-years after the merger ("boosted kilonova"). The nearby ($z=0.0763$) long-duration GRB 211211A, which has an apparent kilonova …

From finding a spanning subgraph $H$ to an $H$-factor
Allan Lo
https://arxiv.org/abs/2509.18832 https://arxiv.org/pdf/2509.18832

R2GenKG: Hierarchical Multi-modal Knowledge Graph for LLM-based Radiology Report Generation
Futian Wang, Yuhan Qiao, Xiao Wang, Fuling Wang, Yuxiang Zhang, Dengdi Sun
https://arxiv.org/abs/2508.03426

R2GenKG: Hierarchical Multi-modal Knowledge Graph for LLM-based Radiology Report Generation
X-ray medical report generation is one of the important applications of artificial intelligence in healthcare. With the support of large foundation models, the quality of medical report generation has significantly improved. However, challenges such as hallucination and weak disease diagnostic capability still persist. In this paper, we first construct a large-scale multi-modal medical knowledge graph (termed M3KG) based on the ground truth medical report using the GPT-4o. It contains 2477 enti…

Efficient Algorithms for Partitioning Circulant Graphs with Optimal Spectral Approximation
Surya Teja Gavva, Peng Zhang
https://arxiv.org/abs/2509.11382 https://

Efficient Algorithms for Partitioning Circulant Graphs with Optimal Spectral Approximation
The Marcus-Spielman-Srivastava theorem (Annals of Mathematics, 2015) for the Kadison-Singer conjecture implies the following result in spectral graph theory: For any undirected graph $G = (V,E)$ with a maximum edge effective resistance at most $α$, there exists a partition of its edge set $E$ into $E_1 \cup E_2$ such that the two edge-induced subgraphs of $G$ spectrally approximates $(1/2)G$ with a relative error $O(\sqrtα)$. However, the proof of this theorem is non-constructive. It remains …