Research
Research
Research
Research
13,212+ open-access research outputs.
Building on the genus-3 reduction $C_A : w^2 = \lambda^8 + A \lambda^4 + 1$ established in our companion paper (arXiv:2604.09328), we give an unconditional proof of the perfect-cuboid conjecture ("Con…
We investigate the behavior of discrete interface growth models belonging to the Edwards--Wilkinson (EW) and Kardar--Parisi--Zhang (KPZ) universality classes, when defined on a complete graph, a topol…
Partially ordered patterns (POPs) generalize classical permutation patterns and have been extensively studied in the contexts of permutations, words, compositions, and partitions. Burstein, Han, Kitae…
Radiology report generation (RRG) has emerged as a promising approach to alleviate radiologists' workload and reduce human errors by automatically generating diagnostic reports from medical images. A …
Tracing out a Galilean-invariant Caldeira-Leggett environment breaks Galilean boost covariance of the reduced dynamics, while spatial translations and rotations survive intact. An operator-level analy…
Remaining Useful Life (RUL) estimation is a critical component of Prognostics and Health Management (PHM), enabling proactive maintenance scheduling and reducing unplanned failures in industrial equip…
On-chip silicon photonic coupled cavity arrays (CCA) are a promising platform for quantum simulators, with access to high Quality (Q) factor resonators, tunability, and foundry compatibility. Furtherm…
We study properties of the following four classes of operators on the Fock space in $\mathbb C^n:$ 1) weakly localized operators; 2) sufficiently localized operators in the sense of Xia and Zheng; 3) …
Continuous data assimilation (CDA) nudges observational data into governing equations to recover the underlying flow and improve predictions. Existing rigorous CDA analyses focus primarily on incompre…
The radial profile of binary fraction may vary with environment and is of significant importance for studying the formation mechanisms of binary stars and their dynamical evolution within globular clu…
The dispersion of fast radio bursts (FRBs) measures the column density of free electrons, tracing the diffuse ionized gas that contains more than $90\%$ of all baryons. On linear scales the FRB disper…
Modeling the emergence of human-like lexicons in computational systems has advanced through the use of interacting neural agents, which simulate both learning and communicative pressures. The NeLLCom-…
This paper uncovers an exact $\chi^2$ dissipation identity for the Blahut--Arimoto (BA) flow and establishes its fundamental information-geometric structure. While prior works have analyzed BA converg…
We propose, analyze, and numerically validate a correction adaptive two-grid finite element method (CAT-GFEM) for nonselfadjoint or indefinite elliptic problems. In contrast to the adaptive two-grid f…
The core instrument of the SVOM Gamma-ray burst mission launched in June 2024 is the 4-150 keV 2-D coded mask camera ECLAIRs responsible for the autonomous trigger and localization of transient events…
A longest path in a graph is called a detour. Denote by $a(k,n)$ the minimum number of detours in a connected graph with minimum degree $k$ and order $n,$ and denote by $b(k,n)$ the minimum odd number…
Deep learning approaches have shown remarkable promise in turbulence closure modeling for large eddy simulations (LES). The differentiable physics paradigm uses the so-called a-posteriori approach for…
Let $A:=\mathbb{C}[z_+,z_-]\otimes \Lambda(\theta_1,\theta_2,\theta_3)$, with $z_\pm$ even and $\theta_1,\theta_2,\theta_3$ odd. For a reductive Lie algebra $\mathfrak g$, let $\mathfrak g[A]:=\mathfr…
We establish regularity results for viscosity solutions to a class of quasilinear parabolic equations exhibiting nonhomogeneous degeneracy or singularity (a double phase regime) of the form \[ u_t - \…
The main aim of this paper is to study chains of model structures arising from cotorsion pairs in extriangulated categories. Starting with a hereditary Hovey triple, we construct further hereditary Ho…
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