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Boundary behaviour of layer potentials for the multi-term time-fractional diffusion equation
Karolina Pawlak
https://arxiv.org/abs/2506.15356 https://

Boundary behaviour of layer potentials for the multi-term time-fractional diffusion equation
This paper investigates the boundary behaviour of layer potentials for the multi-term time-fractional diffusion equation (MTFDE) across the moving boundary. First, we establish the jump relation for the double-layer potential associated with the fundamental solution of the inhomogeneous MTFDE. Second, we prove the continuity of the double-layer potential generated by the kernel corresponding to the homogeneous MTFDE. Krasnoschok obtained similar results for the time-fractional diffusion equatio…

Spectral Contraction of Boundary-Weighted Filters on delta-Hyperbolic Graphs
Le Vu Anh, Mehmet Dik, Nguyen Viet Anh
https://arxiv.org/abs/2506.15464 https:…

Spectral Contraction of Boundary-Weighted Filters on delta-Hyperbolic Graphs
Hierarchical graphs often exhibit tree-like branching patterns, a structural property that challenges the design of traditional graph filters. We introduce a boundary-weighted operator that rescales each edge according to how far its endpoints drift toward the graph's Gromov boundary. Using Busemann functions on delta-hyperbolic networks, we prove a closed-form upper bound on the operator's spectral norm: every signal loses a curvature-controlled fraction of its energy at each pass. The result …

Fokker-Planck Score Learning: Efficient Free-Energy Estimation under Periodic Boundary Conditions
Daniel Nagel, Tristan Bereau
https://arxiv.org/abs/2506.15653

Fokker-Planck Score Learning: Efficient Free-Energy Estimation under Periodic Boundary Conditions
Accurate free-energy estimation is essential in molecular simulation, yet the periodic boundary conditions (PBC) commonly used in computer simulations have rarely been explicitly exploited. Equilibrium methods such as umbrella sampling, metadynamics, and adaptive biasing force require extensive sampling, while non-equilibrium pulling with Jarzynski's equality suffers from poor convergence due to exponential averaging. Here, we introduce a physics-informed, score-based diffusion framework: by ma…

Moment-enhanced shallow water equations for non-slip boundary conditions
Shiping Zhou, Juntao Huang, Andrew J. Christlieb
https://arxiv.org/abs/2506.14785 …

Moment-enhanced shallow water equations for non-slip boundary conditions
The shallow water equations often assume a constant velocity profile along the vertical axis. However, this assumption does not hold in many practical applications. To better approximate the vertical velocity distribution, models such as the shallow water moment expansion models have been proposed. Nevertheless, under non-slip bottom boundary conditions, both the standard shallow water equation and its moment-enhanced models struggle to accurately capture the vertical velocity profile due to th…

Atomic-scale insights on grain boundary segregation in a cathode battery material
Inger-Emma Nylund, Elise R. Eilertsen, Constantinos A. Hatzoglou, Kaja Eggen Aune, Ruben Bj{\o}rge, Antonius T. J. van Helvoort, Ann Mari Svensson, Paraskevas Kontis
https://arxiv.org/abs/2506.13940

Atomic-scale insights on grain boundary segregation in a cathode battery material
The grain boundary segregation of the Co-free pristine spinel LiNi0.5Mn1.5O4 cathode material has been studied by transmission electron microscopy and atom probe tomography. The segregation of Mn and the depletion of Ni at grain boundaries was observed by electron energy loss spectroscopy. These observations were also confirmed by atom probe tomography at other grain boundaries, which also revealed segregation of O and depletion of Li at grain boundaries. In addition, both methods revealed the …

Bidirectional Biometric Authentication Using Transciphering and (T)FHE
Joon Soo Yoo, Tae Min Ahn, Ji Won Yoon
https://arxiv.org/abs/2506.12802 https://

Bidirectional Biometric Authentication Using Transciphering and (T)FHE
Biometric authentication systems pose privacy risks, as leaked templates such as iris or fingerprints can lead to security breaches. Fully Homomorphic Encryption (FHE) enables secure encrypted evaluation, but its deployment is hindered by large ciphertexts, high key overhead, and limited trust models. We propose the Bidirectional Transciphering Framework (BTF), combining FHE, transciphering, and a non-colluding trusted party to enable efficient and privacy-preserving biometric authentication. T…

Higher loops in AdS: applications to boundary CFT
Simone Giombi, Zimo Sun
https://arxiv.org/abs/2506.14699 https://arxiv.org/pdf/2506…

Higher loops in AdS: applications to boundary CFT
The Euclidean Anti-de Sitter (AdS) space provides a natural framework for studying boundary conformal field theory (BCFT). We analyze the conformal boundary conditions of the critical O$(N)$ model in $d=4-ε$ dimensions using the $ε$-expansion, and extract some BCFT observables through higher-loop calculations in AdS. Specifically, in the so-called "ordinary" universality class, we determine the free energy to four-loop order and the one-point function of the lightest O$(N)$ singlet operator t…

CXL-GPU: Pushing GPU Memory Boundaries with the Integration of CXL Technologies
Donghyun Gouk, Seungkwan Kang, Seungjun Lee, Jiseon Kim, Kyungkuk Nam, Eojin Ryu, Sangwon Lee, Dongpyung Kim, Junhyeok Jang, Hanyeoreum Bae, Myoungsoo Jung
https://arxiv.org/abs/2506.15601

CXL-GPU: Pushing GPU Memory Boundaries with the Integration of CXL Technologies
This work introduces a GPU storage expansion solution utilizing CXL, featuring a novel GPU system design with multiple CXL root ports for integrating diverse storage media (DRAMs and/or SSDs). We developed and siliconized a custom CXL controller integrated at the hardware RTL level, achieving two-digit nanosecond roundtrip latency, the first in the field. This study also includes speculative read and deterministic store mechanisms to efficiently manage read and write operations to hide the endp…

Enstrophy dynamics for flow past a solid body with no-slip boundary condition
Aleksei Gorshkov
https://arxiv.org/abs/2506.15317 https://

Enstrophy dynamics for flow past a solid body with no-slip boundary condition
In the paper we study the impact of the boundary vorticity distribution on the dynamics of enstrophy for flows around streamlined body. A new energy identity is derived in the article, which includes the boundary values of the vortex function. For the Stokes system the dissipativity of enstrophy is proved. For the Navier-Stokes system a new equation of the enstrophy dynamics is obtained.