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arXiv:2601.19084v1 Announce Type: new Abstract: In this paper we study the classical solution to the master equation arising from mean-field games (MFGs) driven by jump-diffusion...
arXiv:2601.19097v1 Announce Type: new Abstract: Timelike Liouville field theory (also known as imaginary Liouville theory or imaginary Gaussian multiplicative chaos) is expected to describe two-dimensional...
arXiv:2601.19101v1 Announce Type: new Abstract: We introduce a minimal multiscale framework that links within-host virus dynamics to population-level SIRS epidemiology through explicit, bidirectional coupling. At...
arXiv:2601.19110v1 Announce Type: new Abstract: We investigate the hydrodynamic limit of the Vlasov--Fokker--Planck--Navier--Stokes system in the light particle regime, where the particle relaxation takes place...
arXiv:2601.19126v1 Announce Type: new Abstract: Quantum differential privacy provides a rigorous framework for quantifying privacy guarantees in quantum information processing. While classical correlations are typically...
arXiv:2601.19145v1 Announce Type: new Abstract: Motivated by infinite-dimensional ecological and biological models such as reaction-diffusion SPDEs and stochastic functional differential equations, we develop a general...
arXiv:2601.19163v1 Announce Type: new Abstract: We consider a distance-regular graph $\Gamma=(X, \mathcal R)$ called the bilinear forms graph $H_q(D,N-D)$; we assume $N>2D\geq 6$ and $q...
arXiv:2601.19164v1 Announce Type: new Abstract: We introduce the notion of the $\infty$-category of (complete) derived $G$-graded modules over a $G$-graded ring $R$ for a torsion-free...
arXiv:2601.19172v1 Announce Type: new Abstract: In this paper, we propose a novel sixth-order compact time-splitting scheme, denoted as $ S_{6\text{c}}$, for solving the Dirac equation...
arXiv:2601.19177v1 Announce Type: new Abstract: In this paper, let $f$ be a Hecke cusp form for $SL(2,\mathbb{Z})$. We establish an asymptotic formula for the mixed...
arXiv:2601.19183v1 Announce Type: new Abstract: Large-scale decentralized learning frameworks such as federated learning (FL), require both communication efficiency and strong data security, motivating the study...
arXiv:2601.19195v1 Announce Type: new Abstract: We study the sum-of-squares (SOS) rank of simple and diagonal biquadratic forms. For simple biquadratic forms in $3 \times 3$...
arXiv:2601.19196v1 Announce Type: new Abstract: We study the problem of maximizing the first Laplace-Beltrami eigenvalue normalized by area in a conformal class on a torus....
arXiv:2601.19200v1 Announce Type: new Abstract: Let $T$ be a monad on a category $\mathscr{C}$. In this paper, we introduce the notion of higher derivations on...
arXiv:2601.19211v1 Announce Type: new Abstract: The time-fractional Fokker-Planck equation is a key model for characterizing anomalous diffusion, stochastic transport, and non-equilibrium statistical mechanics with applications...
arXiv:2601.19215v1 Announce Type: new Abstract: Let {(M,g_j)} be a sequence of smooth compact oriented Einstein 4-manifolds of fixed Einstein constant $\lambda > 0$ that Gromov-Hausdorff...
arXiv:2601.19223v1 Announce Type: new Abstract: Traditional data-driven methods, effective for deterministic systems or stochastic differential equations (SDEs) with Gaussian noise, fail to handle the discontinuous...
arXiv:2601.19224v1 Announce Type: new Abstract: Backscatter-based integrated sensing and communication (B-ISAC) elevates passive tags into information-bearing scatterers, offering an ultra-low-power path toward dual-function wireless systems....
arXiv:2601.19226v1 Announce Type: new Abstract: In this paper, we study the {\L}ojasiewicz-Simon gradient inequality for the mathematical model of grain boundary motion. We first derive...
arXiv:2601.19229v1 Announce Type: new Abstract: In the Riemannian setting, every flat Cartan--Hadamard manifold is isometric to Euclidean space, the canonical model that underlies the theory...
arXiv:2601.19230v1 Announce Type: new Abstract: The Graph Minors Structure Theorem (GMST) of Robertson and Seymour states that for every graph $H,$ any $H$-minor-free graph $G$...
arXiv:2601.19242v1 Announce Type: new Abstract: Given $\lambda\in (0,1/2)$, let \begin{equation*} C_\lambda=\set{(1-\lambda)\sum_{i=1}^\infty d_i\lambda^{i-1}:d_i\in\set{0,1}} \end{equation*} be the middle Cantor sets with convex hull $[0, 1]$. We are...
arXiv:2601.19250v1 Announce Type: new Abstract: Singular value decomposition (SVD) and matrix inversion are ubiquitous in scientific computing. Both tasks are computationally demanding for large scale...
arXiv:2601.19252v1 Announce Type: new Abstract: In this paper we characterize concircular helices in $R^3$ by means of a differential equation involving their curvature and torsion....