165 papers
This paper presents an age-structured PDE model of the cell cycle to analyze how the availability of population summary data, such as FACS and FUCCI measurements, influences the identifiability of model parameters and determines the minimum data requirements for successfully fitting structured population models.
This paper investigates the growth rates, asymptotic behaviors, and Gauss congruences of Reidemeister and Nielsen coincidence numbers for endomorphisms of torsion-free nilpotent groups and maps on compact nilmanifolds, while also establishing the rationality of the Nielsen coincidence zeta function.
This paper constructs an instanton cochain complex using the eigenspaces of a deformed mapping cone Laplacian and proves its cochain isomorphism to the topologically defined mapping cone Thom-Smale complex, thereby establishing a bridge between analytic and topological approaches to the wedge by a smooth closed form.
This paper proves that for integer parameters , the -Brjuno function attains its unique global minimum at the fixed point , demonstrates the local stability of these minimizers for near , and proposes a conjecture regarding phase transitions in the minimizer's location as varies.
This paper establishes that dynamically convex, closed contact type hypersurfaces in enclosing the zero section possess at least closed Reeb orbits, and further guarantees the existence of at least two irrationally elliptic orbits under non-degeneracy and finiteness conditions.
This paper analyzes two coupled ODE models of political competition on probability simplices, demonstrating that a unique spectral threshold governs global stability and radicalization dynamics, where the baseline model precludes irreversible centrist decline while an extended model with disengaged voters reveals how cumulative structural shifts can trigger staircase radicalization.
This paper introduces combinatorics on words through the lens of low factor complexity in infinite words, exploring their minimal complexity, formalizing non-triviality, and presenting new algebraic proofs and consequences for classical theorems by Morse, Hedlund, and Tijdeman.
This paper establishes variational principles for pressure functions in discrete nonautonomous dynamical systems on compact metric spaces by applying methods from convex analysis to the thermodynamical formalism.
This paper introduces a new notion of -chains for continuous-time semiflows inspired by the shadow-orbit property and proves that, for systems with strong compact dynamics, this definition generates the same chain-recurrent structure as Conley's classical -chains.
This paper establishes the existence and uniqueness of solutions to rough differential equations driven by tempered fractional Brownian motion with Hurst index by canonically lifting the noise to a geometric rough path and employing a Doss-Sussmann transformation combined with a greedy stopping time sequence, while also deriving quantitative growth bounds for the solutions.
This paper demonstrates that entropy acts as a driving force in various evolution equations because it characterizes the invariant measure of an underlying stochastic process, thereby unifying diverse examples from stochastic processes, gradient flows, and GENERIC systems under a single principle.
This paper establishes an extreme value theorem for the geodesic flow on the hyperbolic surface associated with the theta group by introducing a spliced continued fraction algorithm, proving its dynamical equivalence to the flow's first return map, and deriving a Galambos-type extreme value law for maximal cusp excursions via spectral analysis of the transfer operator.
This paper investigates the topological, metric, and fractal properties of a specific family of homogeneous self-similar sets parameterized by , proving that each set is a Cantorval with a non-empty interior and fractal boundary, while also determining its Lebesgue measure and the Hausdorff dimension of its boundary.
This paper solves the topological classification of smooth structurally stable flows on closed four-dimensional manifolds with exactly two saddle equilibria and heteroclinic connections, demonstrating that while the number of such curves completely characterizes flows on , it yields a countable family of equivalence classes on for odd numbers of curves , contrasting with the finite classification found in the three-dimensional case.
This paper establishes that for sufficiently large , the non-real part of the closure of roots of restricted polynomials outside the unit disk is exactly the closure of a finite-capture locus, achieved by constructing canonical traps and proving uniform inclusion properties within a specific lens-shaped region.
This paper establishes a logarithmic Bott localization formula for global holomorphic sections of on a compact complex manifold with a simple normal crossings divisor, extending the theory to non-isolated zero schemes that are local complete intersections and providing a current-theoretic formulation that identifies the local residue with a Coleff-Herrera current.
This paper establishes a new theory of maximizing sets for dynamical systems with weak hyperbolicity, proving that typical Lipschitz functions possess unique periodic maximizing measures on shift spaces (including all sofic shifts) while identifying the specific structural conditions under which periodic optimization fails.
This paper establishes necessary conditions for the existence of tensor invariants in general nonlinear dynamical systems, with a specific focus on semi-quasihomogeneous systems, thereby extending the foundational work of Poincaré and Kozlov on integrability.
This paper establishes both Anderson localization and Hölder continuity of the integrated density of states for quasi-periodic Schrödinger operators on with non-constant analytic potentials and fixed Diophantine frequencies in the perturbative regime, utilizing a novel multi-scale analysis approach to control Green's functions.
This paper presents an English translation and digitization of Sophie Kowalevski's 1889 French publication on the rotation of a rigid body about a fixed point, which introduced the famous Kovalevskaya Top.