arXiv research

New algorithm learns linear dynamical systems from measurements.

Develops polynomial diffusion models for multi-factor commodity futures dynamics.

Combines Kleinian groups and polynomials into a dynamical system.

The paper studies random dynamical systems of polynomial automorphisms on C^2 and finds mean stability.

Chebyshev polynomials analyze Czech enterprises' stock dynamics.

Study shows polynomial-width neural networks can closely approximate infinite-width networks in polynomial time.

New connection found between complex polynomials and surface homeomorphisms.

We describe the polynomial time complexity algorithm for computing first coefficients of the skein (Homflypt) and Kauffman polynomial invariants of links, discovered by D.Vertigan in 1992 but never published.

New method learns low-dimensional models for systems with non-polynomial terms.

We investigate the random dynamics of polynomial maps on the Riemann sphere and the dynamics of semigroups of polynomial maps on the Riemann sphere. In particular, the dynamics of a semigroup $G$ of polynomials whose planar postcritical set is bounded and the associated random dynamics are studied. In general, the Juli…

New algorithm reduces dynamic regret for noisy gradient feedback with piecewise polynomial comparators.

Polynomial growth elements found in all subgroups of Out(F_n).

We introduce the notion of N-reduced dynamical cocycles and use these objects to define enhancements of the rack counting invariant for classical and virtual knots and links. We provide examples to show that the new invariants are not determined by the rack counting invariant, the Jones polynomial or the generalized Al…

Wide networks with polynomial activations have proven asymptotic behavior.

Abstract: Deltoid map connects complex dynamics and algebra.

Estimates hybrid dynamical systems with polynomial expansions and Markovian switching.

We investigate the dynamics of semigroups generated by a family of polynomial maps on the Riemann sphere such that the postcritical set in the complex plane is bounded. The Julia set of such a semigroup may not be connected in general. We show that for such a polynomial semigroup, if $A$ and $B$ are two connected compo…

The paper defines a path metric on a stable component of polynomial families.

CODE learns ODE dynamics from sparse data, outperforming neural and kernel methods.

We investigate i.i.d. random complex dynamical systems generated by probability measures on finite unions of the loci of holomorphic families of rational maps on the Riemann sphere. We show that under certain conditions on the families, for a generic system, (especially, for a generic random polynomial dynamical system…

We extend the exploration regarding dynamical approach of macroeconomic variables by tackling systematically expenditure using Statistical Physics models (for the first time to the best of our knowledge). Also, using polynomial distribution which characterizes the behavior of dynamical systems in certain situations, we…

New method uses higher-order Langevin dynamics for efficient parallel sampling.

Proposes a graph dynamics prior for more accurate relational inference.

Langevin dynamics fails to produce accurate samples even with small score function errors.

Study revisits Alexander-Conway and Kauffman bracket polynomials for pretzel links.

The study computes trace fields and minimal polynomials for specific knots and links.

We prove that stochastic gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system. Even though the objective function is non-convex, we provide polynomial running …

The Basilica Julia set is universally equivalent to other complex dynamics sets.

The extragradient method accelerates convergence in complex game dynamics.

Polynomial processes have the property that expectations of polynomial functions (of degree $n$, say) of the future state of the process conditional on the current state are given by polynomials (of degree $\leq n$) of the current state. Here we explore the application of polynomial processes in the context of structur…

The basin of infinity of a polynomial map $f : {\bf C} \arrow {\bf C}$ carries a natural foliation and a flat metric with singularities, making it into a metrized Riemann surface $X(f)$. As $f$ diverges in the moduli space of polynomials, the surface $X(f)$ collapses along its foliation to yield a metrized simplicial t…

As we have proved in [L], the geodesic flows associated with the flat metrics on T^2 minimize the polynomial entropy. In this paper, we show that, among the geodesic flows that are Bott integrable and dynamically coherent, the geodesic flows associated to flat metrics are local strict minima for the polynomial entropy.…

Develops analogs of character varieties for algebraic correspondences, proving boundedness and compactifications.

Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of semi-algebraic proof systems that manipulate polynomial inequalities via elementary inferen…

New theory shows EDMD works well in chaotic systems.

Paper connects knot invariants and Morse flow loops.

Ehlers-Kundt conjecture is a physical assertion about the fundamental role of plane waves for the description of gravitational waves. Mathematically, it becomes equivalent to a problem on the Euclidean plane ${\mathbb R}^2$ with a very simple formulation in Classical Mechanics: given a non-necessarily autonomous potent…

Universal preconditioning reduces sequential prediction regret.

We investigate the random dynamics of rational maps on the Riemann sphere and the dynamics of semigroups of rational maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, in most cases, the chaos of the averaged system disappears, due to the cooperation of the generators. We investi…

Improved RL algorithm stabilizes unknown linear systems with polynomial regret.

New method uses Hermite polynomials for American option valuation.

New moving average adapts weight dynamically based on polynomial and wavefunction.

In the setting of polynomial jump-diffusion dynamics, we provide an explicit formula for computing correlators, namely, cross-moments of the process at different time points along its path. The formula appears as a linear combination of exponentials of the generator matrix, extending the well-known moment formula for p…

Combining diffusion models with Langevin dynamics improves posterior sampling efficiency.

Bayesian optimization with RPCE reduces MAP estimation for structural dynamics models.

Bayesian method synthesizes barrier certificates for unknown systems with latent states.

We investigate random complex dynamics of rational or polynomial maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, generically, the chaos of the averaged system disappears at any point in the Riemann sphere due to the automatic coopeartion of many kinds of maps in the system, ev…

The Tits alternative for Out(F_n) is reduced to the case where all elements in the subgroup under consideration grow polynomially.