165 papers
This paper proposes a robust geometric early warning indicator based on the width of the stochastic separatrix in a two-state ecosystem model, which successfully predicts rapid under-ice phytoplankton blooms in the Arctic where conventional critical slowing down signals fail due to strong noise or limited data.
This paper introduces the sampling logit equilibrium (SLE), a stationary concept for population games where agents use finite samples of opponents' plays to inform logit-based decisions, demonstrating that large-sample behavior approximates a logit equilibrium in a virtual game with payoff distortions caused by sampling noise.
For the planar three-body problem with positive masses, non-zero angular momentum, and fixed negative energy, the paper proves the existence of global solutions that maintain an arbitrarily large potential energy by featuring a single close approach to triple collision while evolving into a tight binary configuration with the third body diverging to infinity.
This paper presents a scalable Python-based algorithm that automates the identification and classification of homeostatic mechanisms in complex biological input-output networks by extending theoretical frameworks to handle multiple inputs and directly enumerating homeostatic subnetworks from connectivity structures, thereby overcoming the combinatorial and accessibility limitations of previous graph-theoretical approaches.
This paper reviews and contrasts the long-time behavior of initial-boundary value problems for systems admitting Lax Pair formulations, illustrating cases where integrability ensures regular asymptotic behavior alongside instances where irregular, fractal-like chaos emerges, while connecting these findings to perturbed Lax Pair theory on the real line.
This paper argues that conserved quantities in mass-action networks are dual to internal cycles and proposes conjectured duality relationships between preclusters, maximal invariant polyhedral supports, and siphons.
This paper derives upper PAC generalization bounds for neural oscillators based on second-order ODEs and MLPs, demonstrating that their estimation errors grow polynomially with model size and time while showing that constraining MLP Lipschitz constants via regularization enhances generalization performance in modeling nonlinear structural systems.
This paper introduces the BOUNDS method and the Augmented Information Kalman Filter (AI-KF) to systematically discover active sensing motifs and dynamically fuse neural network with model-based estimation, thereby improving state estimation for nonlinear autonomous systems in GPS-denied environments.
This paper constructs fractional Sobolev spaces with variable orders on arbitrary time scales and their product domains, establishing their functional-analytic properties and trace frameworks to derive Euler-Lagrange equations for variational problems involving variable-order Riemann-Liouville and Caputo fractional operators.
This paper introduces a novel, exactly solvable ordinary differential equation model incorporating an Allee effect to study rate-induced tipping, featuring finite-time extinction, a derived integral inequality for tipping conditions, a superior numerical method, and a practical application to the historical rise and fall of Japanese inland fisheries.
This paper investigates the conditions under which smooth maps are modulary dense on compact manifolds, specifically analyzing the validity and failure of this property in the context of the Lavrentiev gap.
This paper clarifies the abstract geometrical formulation of thermodynamics on non-compact symmetric spaces used in Cartan Neural Networks by proving that only Kähler spaces support Gibbs distributions, explicitly characterizing their generalized temperature spaces via adjoint orbits, and demonstrating the equivalence between various information and thermodynamical geometries while establishing the covariance of these distributions under the full symmetry group.
This paper establishes that for endomorphisms of projective spaces or automorphisms of compact Kähler manifolds, the pull-backs of currents under iterates converge exponentially fast to Green currents when tested against -Hölder continuous observables with bounded mass.
This paper advances the dimension theory of sets and measures by weakening Hochman's exponential separation condition, demonstrating the equivalence of modified and original definitions for homogeneous self-similar IFS on , and proving the density of specific subsets defined by Assouad, Hausdorff, and dimensions within their respective spaces.
This paper establishes that the harmonic map heat flow from a compact Riemannian manifold into the moduli space of unit-area flat tori is stable, ergodic, and converges to the normalized hyperbolic measure, with the relative entropy decaying to zero to quantify this information-theoretic equilibrium.
This paper establishes a unified framework for proving the almost everywhere pointwise convergence of sparse ergodic averages in for both deterministic and random sequences within specific parameter ranges, while providing new quantitative convergence estimates that improve upon previous non-quantitative results.
This paper characterizes the amenability of countable Borel equivalence relations via the uniform Liouville property, investigates Kesten's property for return probabilities on topological groups, and constructs an amenable contractible Polish group lacking this property by linking it to anti-concentration inequalities in measurable lamplighter groups.
This paper introduces a task-relative taxonomy of actuator inputs in feedback-linearizable nonlinear systems, defining "dexterity" inputs that can be deactivated to gracefully downgrade tasks while preserving linearization on shared outputs through a unified controller based on dynamic prolongation.
This paper proposes a d-dimensional generalization of the Kuramoto model on matrix-weighted networks, deriving necessary conditions for global synchronization and proving via a Master Stability Function approach that the synchronous solution is locally stable for any positive coupling strength on connected networks.
This paper integrates Chemical Reaction Network theory and Mathematical Epidemiology to generalize the Next Generation Matrix theorem and apply a symbolic-numeric approach, utilizing the Epid-CRN Mathematica package, for analyzing the stability and bifurcation of positive ordinary differential equations.