The paper studies automorphisms of free groups with a North-South dynamics.
problem Characterizing automorphisms of free groups with dynamical properties.
method Analyzes the action of outer automorphisms on a relative space of currents.
result Proves the existence of a preferred compact space on which automorphisms act with North-South dynamics.
Let φ be a hyperbolic outer automorphism of a non-abelian free group FN such that φ and φ−1 admit absolute train track representatives. We prove that φ acts on the space of projectivized geodesic currents on FN with generalized uniform North-South dynamics.
Defines currents relative to a free factor system and proves dynamics for fully irreducible automorphisms.
problem Understanding dynamics of fully irreducible automorphisms on projective relative currents.
method Defining currents relative to a free factor system and proving dynamics.
result Uniform north-south dynamics on a subspace of projective relative currents for fully irreducible automorphisms.
We consider the action of a pseudo-Anosov mapping class on 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…
New hyperbolic groups from ping-pong automorphisms.
problem Finding new hyperbolic groups from automorphisms.
method Proving generalized north-south dynamics and constructing new subgroups.
result Produced new examples of hyperbolic groups not convex cocompact.
Outer automorphisms act loxodromically on a complex.
problem Understanding the dynamics of outer automorphisms on relative free factor complexes.
method Proving loxodromic action and north-south dynamics.
result Fully irreducible outer automorphisms act loxodromically on the relative free factor complex.
We prove uniform north-south dynamics type results for the action of φ∈Out(FN) on the space of projectivized geodesic currents PCurr(S)=PCurr(FN), where φ is induced by a pseudo-Anosov homeomorphism on a compact surface S with boundary such that π1(S)=FN. As an appli…
We present two proofs of the fact, originally due to Reiner Martin, that any fully irreducible hyperbolic element of Out(FN) acts on the projectivized space of geodesic currents PCurr(FN) with uniform north-south dynamics. The first proof, using purely train-track methods, provides an elaborated and corr…
Explains length functions on currents and their applications to dynamics and counting.
problem Counting problems and dynamics on projective geodesic currents.
method Exploration of length functions and their applications to counting problems and dynamics.
result Proof of a folklore theorem about pseudo-Anosov homeomorphisms acting uniformly on projective geodesic currents.
The Morse boundary characterizes group dynamics and generalizes hyperbolic space results.
problem Characterizing group dynamics on Morse boundaries.
method Characterizing Morse elements by their fixed points on the Morse boundary and analyzing the dynamics of group actions.
result The action of G on ∂MX is minimal if G is not virtually cyclic. 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 proves continuity of drift in mapping class group.
problem Continuity of drift in mapping class group.
method Random walk analysis on mapping class group, continuity proof.
result Drift varies continuously with transition probability measures.
The paper studies topological and dynamic properties of boundaries in geometric group actions.
problem Understanding the topological and dynamic properties of boundaries in geometric group actions.
method Developed and studied sublinearly Morse and quasi-redirecting boundaries for proper geodesic spaces with geometric group actions.
result Proved that the action of a group on the boundaries is minimal and that the boundaries are topological spaces.
Python tool creates machine-learning-ready solar dataset.
problem Creating a usable dataset for space weather forecasting.
method Python tool generates dataset from SoHO and SDO images, applying pre-processing.
result Dataset is machine-learning ready, free of missing data, and temporally synced.
New findings on translation lengths in Teichmüller and curve graphs for pseudo-Anosovs.
problem Comparing translation lengths in Teichmüller and curve graphs for pseudo-Anosovs.
method Combining techniques for upper and lower bounds with Rauzy-Veech induction machinery.
result Minimal stable curve graph translation length is of order 1/g for fixed genus g.
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…
Paper shows leafwise cohomological expression for dynamical zeta functions.
problem Analyzing dynamical zeta functions on foliated dynamical systems.
method Leafwise cohomological approach.
result Leafwise cohomological expression of dynamical zeta functions.
Study on 2-valued dynamics on complex plane, showing some dynamics can't be group actions.
problem Whether 2-valued dynamics can be defined by the action of a 2-valued group.
method Construction of examples of dynamics that are or are not group actions.
result Some 2-valued dynamics on complex plane cannot be defined by the action of a 2-valued group.
The paper studies dynamic star-shaped risk measures and their representation.
problem Representing dynamic star-shaped risk measures and their properties.
method Representation theorems for dynamic monetary and star-shaped risk measures.
result Dynamic star-shaped risk measures can be represented as the lower envelope of a family of dynamic convex risk measures.
Study circles to understand dynamics and rigidity in homogeneous spaces.
problem Understanding dynamics and rigidity in infinite-volume homogeneous spaces.
method Addressing four questions about circle packings.
result Highlighting the interplay between dynamics, geometry, and rigidity.
Paper connects dynamics of mechanical systems to Reeb dynamics.
problem Understanding dynamics in mechanical systems with Poisson structures.
method Using Jacobi bundle metrics and linear Poisson structures.
result Extends classical results on Reeb dynamics to mechanical systems.
Two heuristics solve dynamic multiple travelling salesmen problems.
problem Dynamic routing with unknown customers.
method Balanced dynamic closest vehicle heuristic and balanced dynamic assignment vehicle heuristic.
result Continuous approximation models for strategic dynamic routing.
The paper provides a representation for dynamic risk measures and capital allocations.
problem Representation of dynamic risk measures and capital allocations under Itô-Lévy model.
method Representation theorem for dynamic capital allocation derived from BSDEs with quadratic-exponential growth.
result Derivation of a capital allocation representation for dynamic entropic risk measure and static coherent risk measure.
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.
problem Learning independent dynamical operators for each system limits discovery of shared structure.
method DOODL learns a dictionary of characteristic spectral dynamics on a manifold of related systems.
result DOODL achieves errors one to two orders of magnitude lower than independent operator estimation methods.
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…
Develops a new framework to understand MCMC dynamics as flows on Wasserstein space.
problem Lack of understanding general MCMC dynamics in terms of flows on Wasserstein space.
method Introduces novel concepts to recognize MCMC dynamics as fiber-gradient Hamiltonian flows on Wasserstein space.
result Enables ParVI simulation of MCMC dynamics, enriching ParVI family with more efficient dynamics.
SPICE estimates sparse linear dynamic networks without hyperparameters.
problem Estimating topology and dynamics of sparse linear dynamic networks.
method SPICE (Sparse Iterative Covariance Estimation) method in an iterative framework.
result Directly reveals the underlying topology of the network.
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.
problem Learning accurate state representations from partial observations in POMDPs.
method Dynamical Variational Auto-Encoder (DVAE) with hindsight framework.
result DVAE uncovers causal graph more effectively than history-based methods.
Dynamic systems linked to infinite permutation matrices.
problem Dynamic equivalence of control systems.
method Association of infinite permutation matrices.
result Relationship between dynamic equivalences and permutation matrices.
Unified analysis of DLNs using DMFT reveals dynamics of loss convergence and generalization trade-offs.
problem Understanding the overall dynamics of diagonal linear networks (DLNs) in neural network training.
method Dynamical Mean-Field Theory (DMFT) applied to DLNs.
result Derives low-dimensional effective process capturing high-dimensional gradient flow dynamics.
dLDS models neural dynamics as sparse combinations of simpler components.
problem Understanding complex neural dynamics at a population level.
method Proposes a decomposed dynamical system model trained through dictionary learning.
result Model efficiently captures and demix diverse neural dynamics.
Method learns to map dynamics of different systems.
problem Mapping dynamics of different systems.
method Learned latent dynamical system for mapping.
result Learned correspondences enable imagined motions and bisimulation.
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…
Framework for quantifying uncertainty in dynamic processes.
problem Quantifying uncertainty in dynamic stochastic processes.
method Define dynamic uncertainty sets and dynamic robust risk measures.
result Dynamic robust risk measures are time-consistent under specific uncertainty sets.
Model predicts market dynamics from demand uncertainty.
problem Market dynamics under uncertain demand forecasts.
method Simple dynamical model iterated with varying parameters.
result Reproduces equilibria, periodic, chaotic, and collapses.
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…
This survey clarifies dynamic network terminology and reviews GNN models for dynamic networks.
problem Ambiguity in dynamic network terminology and lack of GNN models for dynamic networks.
method Established consistent terminology and notation for dynamic networks, reviewed GNN models.
result Comprehensive survey of dynamic graph neural network models.
Framework infers Langevin dynamics from stochastic observations of latent systems.
problem Inferring non-stationary Langevin dynamics from indirect stochastic observations.
method Non-parametric framework explicitly modeling stochastic observation process and non-stationary latent dynamics.
result Correct inference of non-stationary dynamics requires accounting for non-equilibrium states and observation duration.
The paper introduces a dynamic MVP model using high-frequency financial data.
problem Capturing the dynamics of minimum variance portfolio weights in financial markets.
method Imposes autoregressive structure on MVP processes and uses CLIME and LASSO for estimation.
result Proposes DR-MVP model with established asymptotic properties.
The paper extends Vlasov kinetic theory to time-dependent dynamics using cosymplectic and cocontact manifolds.
problem Extending Vlasov kinetic theory to time-dependent dynamics.
method Introducing geometric kinetic theories within cosymplectic and cocontact manifolds.
result Alternative realizations of cosymplectic and cocontact kinetic theories linked via Poisson/momentum maps.
LEGEND learns complex dynamics from aggregate data.
problem Learning nonlinear dynamics from aggregate data with missing individual-level trajectories.
method LEGEND models hidden stochastic processes via hidden variables and learns dynamics directly on aggregate observations.
result LEGEND outperforms state-of-the-art baselines on various synthetic and real-world datasets.
Algorithm classifies causal systems into kinds based on shared dynamical symmetries.
problem Classifying causal systems into kinds without explicit models.
method Dynamical symmetry approach to classify systems by shared symmetries.
result Algorithm correctly sorts systems into dynamical kinds, robust under sampling error.
NDS learns dynamical models with prior knowledge, improving accuracy and efficiency.
problem Learning accurate dynamical models with limited data and varying dynamics.
method Neural Dynamical Systems (NDS) integrates prior knowledge in ODEs with neural networks to estimate parameters and predict states.
result NDS achieves higher accuracy and uses fewer samples compared to other methods.
New method learns population dynamics from snapshots, outperforming existing models.
problem Capturing periodic and other dynamical properties of population dynamics.
method Wasserstein Lagrangian Mechanics (WLM) for learning second-order dynamics from observed marginals.
result WLM outperforms existing methods across various dynamics, including vortex dynamics, embryonic development, and flocking.
The Dynamic Pricing Challenge revealed varying algorithm performance across different market dynamics.
problem Complexity of pricing and learning in competitive markets.
method Participants submitted pricing and demand learning algorithms for numerical performance analysis in simulated environments.
result Algorithm performance varies significantly across different market dynamics.
Paper uses Chebyshev Tensors for accurate dynamic sensitivities and ISDA SIMM computation.
problem Computing dynamic sensitivities and initial margin for financial instruments.
method Uses Chebyshev Tensors in Monte Carlo simulations to compute dynamic sensitivities and ISDA SIMM.
result High accuracy and computational gains for FX swaps and Spread Options.