The linear Tur\'an number of the 3-graph $P_5$
arXiv:2601.19068v1 Announce Type: new Abstract: We prove that for any linear 3-graph on $n$ vertices without a path of length 5, the number of edges...
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46,143 articles
Asymptotic inference for skewed stable Ornstein-Uhlenbeck process
arXiv:2601.19071v1 Announce Type: new Abstract: We consider the parametric estimation of the Ornstein-Uhlenbeck process driven by a non-Gaussian $\alpha$-stable L\'{e}vy process with the stable index...
Software
Biology
Strip-type operators and abstract Cauchy problems
arXiv:2601.19075v1 Announce Type: new Abstract: We consider the non-homogeneous abstract linear Schr\"odinger and wave equations with zero initial conditions, defined by operators of strip-type and...
Software
Mathematics
Tiling of Hyperbolic Surface by a Single Tile
arXiv:2601.19083v1 Announce Type: new Abstract: Tilings of a surface of negative Euler characteristic by n-gons with n\ge 7 is a finite problem. One extreme of...
Artificial Intelligence
A Probabilistic Interpretation of the Master Equation Arising from Mean Field Games with Jump Diffusion
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...
Software
Energy
Exact calculations beyond charge neutrality in timelike Liouville field theory
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...
Physics
Quantum Computing
Multiscale feedback drives viral evolution and epidemic dynamics
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...
Biology
Genetics
Quantitative light-particle limit for the Vlasov-Fokker-Planck-Navier-Stokes system
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...
Software
Physics
How Entanglement Reshapes the Geometry of Quantum Differential Privacy
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...
Quantum Computing
Cybersecurity
Stochastic Persistence in Infinite Dimensions
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...
Technology
Chemistry
Strengthening the balanced set condition for the distance-regular graph of the bilinear forms
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...
Biology
Derived graded modules
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...
A sixth-order compact time-splitting Fourier pseudospectral method
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...
Technology
Mathematics
Integral moment of the Riemann zeta function and Hecke $L$-functions, II
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...
Information-Theoretic Secure Aggregation over Regular Graphs
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...
Cybersecurity
On the SOS Rank of Simple and Diagonal Biquadratic Forms
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 $3 \times 3$...
Technology
Biology
Rotationally symmetric critical metrics for Laplace eigenvalues on tori in a conformal class
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....
Characterizations of higher derivations and higher differential torsion theories in Eilenberg-Moore categories of monads
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...
On a Class of Multi-Dimensional Non-linear Time-Fractional Fokker-Planck Equations Capturing Brownian Motion
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...
Software
Energy
Desingularizations of Conformally Kaehler, Einstein Orbifolds
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...
Nonlocal Kramers-Moyal formulas and data-driven discovery of stochastic dynamical systems with multiplicative L\'evy noise
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...
Mathematics
Climate & Environment
Movable-Antenna Empowered Backscatter ISAC: Toward Geometry-Adaptive, Low-Power Networks
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....
Software
Energy
The {\L}ojasiewicz-Simon inequality related to grain boundary motion and its applications
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...
Software
Mathematics
Unexpected Analytic Phenomena on Finsler Manifolds
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...
Software
Mathematics