arXiv research

The paper studies automorphisms of free groups with a North-South dynamics.

Let $\varphi$ be a hyperbolic outer automorphism of a non-abelian free group $F_N$ such that $\varphi$ and $\varphi^{-1}$ admit absolute train track representatives. We prove that $\varphi$ acts on the space of projectivized geodesic currents on $F_N$ with generalized uniform North-South dynamics.

We consider the action of a pseudo-Anosov mapping class on $\mathcal{PML}(S)$. This action has north-south dynamics and so, under iteration, laminations converge exponentially to the stable lamination. We study the rate of this convergence and give examples of families of pseudo-Anosov mapping classes where the rate go…

We prove uniform north-south dynamics type results for the action of $\varphi\in Out(F_{N})$ on the space of projectivized geodesic currents $\mathbb{P}Curr(S)=\mathbb{P}Curr(F_{N})$, where $\varphi$ is induced by a pseudo-Anosov homeomorphism on a compact surface S with boundary such that $π_{1}(S)=F_{N}$. As an appli…

In this paper we define currents relative to a free factor system. We prove that a fully irreducible outer automorphism relative to a free factor system acts with uniform north-south dynamics on a subspace of the space of projective relative currents.

We present two proofs of the fact, originally due to Reiner Martin, that any fully irreducible hyperbolic element of $Out(F_N)$ acts on the projectivized space of geodesic currents $\mathbb{P}Curr(F_N)$ with uniform north-south dynamics. The first proof, using purely train-track methods, provides an elaborated and corr…

In this paper we prove that a fully irreducible outer automorphism relative to a non-exceptional free factor system acts loxodromically on the relative free factor complex as defined by Handel and Mosher. We also prove a north-south dynamic result for the action of such outer automorphisms on the closure of relative ou…

The aim of this (mostly expository) article is twofold. We first explore a variety of length functions on the space of currents, and we survey recent work regarding applications of length functions to counting problems. Secondly, we use length functions to provide a proof of a folklore theorem which states that pseudo-…

We prove that all atoroidal automorphisms of $Out(F_N)$ act on the space of projectivized geodesic currents with generalized north-south dynamics. As an application, we produce new examples of non virtually cyclic, free and purely atoroidal subgroups of $Out(F_N)$ such that the corresponding free group extension is hyp…

Let $X$ be a proper geodesic metric space and let $G$ be a group of isometries of $X$ which acts geometrically. Cordes constructed the Morse boundary of $X$ which generalizes the contracting boundary for CAT(0) spaces and the visual boundary for hyperbolic spaces. We characterize Morse elements in $G$ by their fixed po…

A random walk on a countable group $G$ acting on a metric space $X$ gives a characteristic called the drift which depends only on the transition probability measure $μ$ of the random walk. The drift is the `translation distance' of the random walk. In this paper, we prove that the drift varies continuously with the tra…

Let $X$ be a proper CAT(0) space and let $G$ be a cocompact group of isometries of $X$ which acts properly discontinuously. Charney and Sultan constructed a quasi-isometry invariant boundary for proper CAT(0) spaces which they called the contracting boundary. The contracting boundary imitates the Gromov boundary for $δ…

The paper studies topological and dynamic properties of boundaries in geometric group actions.

Python tool creates machine-learning-ready solar dataset.

New findings on translation lengths in Teichmüller and curve graphs for pseudo-Anosovs.

Point cloud is the most fundamental representation of 3D geometric objects. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis require connectivity information. Therefore, it is desirable to develop a mesh st…

Study on 2-valued dynamics on complex plane, showing some dynamics can't be group actions.

The paper studies dynamic star-shaped risk measures and their representation.

Study circles to understand dynamics and rigidity in homogeneous spaces.

A Riemmanian foliated dynamical system of 3-dimension $(\mathrm{RFDS}^{3})$ is a closed Riemannian 3-manifold with additional structures: foliation, dynamical system. In the context of arithmetic topology, it is a geometric/analytic analogue of an arithmetic scheme with a conjectural dynamical system suggested by C. De…

Paper connects dynamics of mechanical systems to Reeb dynamics.

Two heuristics solve dynamic multiple travelling salesmen problems.

In this paper we present a theoretical framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures, and we establish a duality between them. We derive a representation theorem for dynamic coherent risk measures in terms of …

DOODL learns shared spectral dynamics across related dynamical systems.

We propose a new class of mappings, called Dynamic Limit Growth Indices, that are designed to measure the long-run performance of a financial portfolio in discrete time setup. We study various important properties for this new class of measures, and in particular, we provide necessary and sufficient condition for a Dyn…

In this paper we present a theoretical framework for determining dynamic ask and bid prices of derivatives using the theory of dynamic coherent acceptability indices in discrete time. We prove a version of the First Fundamental Theorem of Asset Pricing using the dynamic coherent risk measures. We introduce the dynamic …

Dynamical-VAE learns causal dynamics from POMDPs using future information.

Most real world phenomena such as sunlight distribution under a forest canopy, minerals concentration, stock valuation, exhibit nonstationary dynamics i.e. phenomenon variation changes depending on the locality. Nonstationary dynamics pose both theoretical and practical challenges to statistical machine learning algori…

Unified analysis of DLNs using DMFT reveals dynamics of loss convergence and generalization trade-offs.

dLDS models neural dynamics as sparse combinations of simpler components.

Reinforcement learning would enjoy better success on real-world problems if domain knowledge could be imparted to the algorithm by the modelers. Most problems have both hidden state and unknown dynamics. Partially observable Markov decision processes (POMDPs) allow for the modeling of both. Unfortunately, they do not p…

We consider trivializations of second iterated bundles of a Lie group that preserve lifted group structures. With such a trivialization, we elaborate Hamiltonian dynamics on cotangent, Lagrangian dynamics on tangent bundles and, both Hamiltonian and Lagrangian dynamics on Tulczyjew's symplectic space which is tangent o…

Framework for quantifying uncertainty in dynamic processes.

This survey clarifies dynamic network terminology and reviews GNN models for dynamic networks.

Framework infers Langevin dynamics from stochastic observations of latent systems.

The paper introduces a dynamic MVP model using high-frequency financial data.

The paper extends Vlasov kinetic theory to time-dependent dynamics using cosymplectic and cocontact manifolds.

NDS learns dynamical models with prior knowledge, improving accuracy and efficiency.

New method learns population dynamics from snapshots, outperforming existing models.

Paper uses Chebyshev Tensors for accurate dynamic sensitivities and ISDA SIMM computation.

Model dynamic customer sensitivities across categories.

Survey on computational models in dynamical systems, including new universality concepts.

FNSDA adapts to new dynamics via Fourier space adaptation.

Study on geometry and dynamics of transverse subgroups.

Dynamic risk assessment method for WUI fires improves upon static frameworks.

Develops a method to model neural dynamics with flexible yet interpretable latent states.

SINDy-PI robustly identifies implicit dynamics from noisy data.

D2PCCA integrates deep learning and probabilistic modeling for nonlinear dynamical systems.