173 papers
This paper demonstrates that spontaneous flow reversals in 2D active nematic turbulence are organized by a low-dimensional, symmetry-governed network of exact coherent structures and their invariant manifolds, which persist from the preturbulent regime into chaos to dictate the dynamics of flow switching.
This paper systematically analyzes how numerical ill-conditioning caused by multicollinearity in candidate function libraries undermines the robustness of sparse regression for discovering biological dynamics, demonstrating that while orthogonal polynomial bases can improve model recovery under specific data distributions, they often fail or perform worse than monomial libraries when data sampling deviates from their associated weight functions.
This paper proves that the Möbius Disjointness Conjecture holds for a specific class of irregular, distal flows on the infinite-dimensional torus defined by a skew-product transformation with -smooth coefficients.
This paper presents a conditional framework for the Collatz conjecture, derived from human-LLM collaboration, which proves structural properties of modular scrambling and burst-gap dynamics to suggest orbit contraction while leaving key hypotheses regarding burst and gap lengths as open problems.
This paper provides an affirmative resolution to "Open Question 1" posed by Feng and Wang regarding a symmetry conjecture on homogeneous iterated function systems.
This paper extends the Ziv-Merhav theorem on universal estimation of specific cross-entropy from multi-level Markov measures to a broader class of decoupled measures, including regular g-measures and equilibrium measures from statistical mechanics.
This paper introduces a graph-based framework for Thermodynamical Material Networks (TMNs) that models circular economy material flows using dynamic energy and mass balances, proposes new circularity indicators, and validates the approach through numerical simulations of fluid and solid material systems.
This study demonstrates that symmetric reservoir topologies significantly enhance prediction accuracy for low-dimensional nonlinear dynamical systems with limited input dimensions, whereas high-dimensional chaotic systems like turbulent shear flow exhibit minimal sensitivity to such structural symmetries.
This paper establishes a unified bounded-variation solution framework for prox-regular sweeping processes by proving the equivalence between a new integral formulation with a quadratic correction term and the standard differential-measure formulation, while also deriving a Brézis-Ekeland-Nayroles-type variational characterization that ensures stability under uniform limits.
This paper presents a formal control synthesis framework for continuous-state stochastic systems that minimizes a linear combination of system entropy (measured by KL divergence to uniform) and cumulative cost by deriving novel bounds on the entropy difference between continuous distributions and their finite-state abstractions, thereby enabling entropy-aware controllers with rigorous performance guarantees.
This paper establishes that mixed H2/H-infinity control exhibits benign nonconvexity where every stationary point is globally optimal, by characterizing the feasible set's topology and employing an Extended Convex Lifting framework to bridge nonconvex policy optimization with convex reformulations for scalable, data-driven applications.
This paper defines and analyzes the asymptotic behavior of the Archimedean height pairing for fiberwise cohomologically trivial differential forms on one-parameter degenerations of Riemann surfaces, utilizing Dai--Yoshikawa's results on small eigenvalues to extend the current-valued pairing of Filip--Tosatti to broader geometric settings.
This paper proposes a fast and provably correct method for approximating the persistence diagrams of sliding window embeddings of quasiperiodic functions by integrating the Three Gap Theorem from number theory with the Persistent Künneth formula from topological data analysis.
This study introduces Equilibrium-Informed Neural Networks (EINNs), a novel deep learning approach that reverses the traditional parameter-search process by inferring system parameters from candidate equilibrium states to efficiently detect critical bifurcation thresholds and tipping points in complex nonlinear dynamical systems.
This paper unconditionally proves the quantum unique ergodicity conjecture for Pitale lifts on hyperbolic 4-manifolds by employing a novel amplification method with favorable geometric properties to overcome the challenges posed by non-temperedness.
This paper applies the Chemical Reaction Network theory (CRNT) and the symbolic package EpidCRN to analyze multi-strain rumor spreading models on online social networks, revealing that stability transitions occur via "relay" mechanisms governed by siphon-induced transcritical bifurcations and invasion inequalities.
This paper presents an efficient algorithm that utilizes partial Gröbner basis computation and sparse interpolation to find simple generating sets for subfields of rational function fields, demonstrating improved performance and practical utility in applications like structural parameter identifiability.
This paper investigates the total population levels in heterogeneous environments with directed diffusion for any power-law relationship between intrinsic growth rate and carrying capacity, disproving the existence of a critical exponent that determines population prevalence over carrying capacity and analyzing how the total population depends on the diffusion coefficient under a generalized dispersal strategy.
This paper establishes that a -generic non-trivial sectional-hyperbolic chain-recurrent class satisfies a trichotomy, being either a homoclinic loop, a union of saddle connections between singularities, or robustly a homoclinic class, thereby providing a partial answer to questions posed in a 2021 publication.
This paper establishes the first rigorous Nekhoroshev-type stability results for ultra-differentiable solutions of non-local semilinear Schrödinger equations without external parameters by employing rational normal forms and a novel global vector field norm, achieving optimal stability times under Gevrey regularity assumptions.