Study non-transitive pseudo-Anosov flows using group actions.
problem Characterize pseudo-Anosov flows in 3-manifolds.
method Extend pseudo-Anosov action to non-transitive flows, use group actions on orbit spaces and boundary at infinity.
result Pseudo-Anosov flows in 3-manifolds are determined by their group actions on boundary at infinity.
Study of isometries on hyperbolic 3-manifold cusps.
problem Understanding transitivity in hyperbolic 3-manifold actions.
method Analyzing multiply transitive actions of isometries on cusps.
result Proved a conjecture about the maximum transitivity and upper bounds on cusps.
Study groups acting on trees with specific local actions, proving cohomology vanishing or infinite.
problem Understanding bounded cohomology of groups with prescribed local actions.
method Proving vanishing or infinite bounded cohomology based on the 2-transitivity of F ′ F' F ′ . result Vanishing or infinite bounded cohomology depending on F ′ F' F ′ 's 2-transitivity. This paper studies actions of solvable Lie groups on nilpotent Lie groups.
problem Characterizing which solvable Lie groups can act simply transitively on nilpotent Lie groups.
method Using Lie algebra properties and semisimple splitting, the paper provides methods to check for such actions.
result A full description of possibilities for actions up to dimension 4.
To any connected and simply connected nilpotent Lie group N, one can associate its group of affine transformations Aff(N). In this paper, we study simply transitive actions of a given nilpotent Lie group G on another nilpotent Lie group N, via such affine transformations. We succeed in translating the existence questio…
A transitive smooth action of a connected Lie group G on a manifold M is called almost primitive (resp. primitive) if G doesn't contain any proper subgroup (resp. any proper normal subgroup) whose induced action on M is transitive as well. The aim of the present work is to investigate some combinatory properties of sym…
Semisimple Lie groups act transitively on pseudo-Riemannian manifolds, making them flat.
problem Understanding actions of semisimple Lie groups on pseudo-Riemannian manifolds.
method Analyzing the pseudo-Riemannian Lichnerowicz conjecture in homogeneous settings.
result Compact pseudo-Riemannian manifolds on which a semisimple group acts conformally, essentially and transitively, are conformally flat.
PQR estimates reward functions from actions and states without assuming state-only rewards.
problem Estimating reward functions from actions and states without state-only assumptions.
method Deep learning approach that sequentially estimates policy, Q-function, and reward.
result PQR uniquely recovers true reward with known transitions and bounds error with unknown transitions.
This paper shows how post-Lie algebra structures can be induced by simply transitive NIL-affine actions.
problem Understanding which solvable Lie groups can act simply transitively on nilpotent Lie groups.
method Introducing post-Lie algebra structures and showing their correspondence with simply transitive actions.
result Simply transitive NIL-affine actions induce complete post-Lie algebra structures in the 2-step nilpotent case.
A new RL paradigm reduces state-action-value function approximation inefficiency.
problem Challenges in state-action-value function approximation for RL.
method State Action Separable Reinforcement Learning (sasRL) decouples action space from value function learning.
result sasRL achieves up to 75% better performance than state-of-the-art MDP-based RL algorithms.
Study of pseudo-Riemannian manifolds with M{ö}bius group actions.
problem Characterizing pseudo-Riemannian manifolds with specific group actions.
method Analyzing the action of the conformal group on compact manifolds.
result If the non-compact semi-simple part of the conformal group is M{ö}bius, the manifold is conformally flat.
We classify the polar actions on the complex hyperbolic plane up to orbit equivalence. Apart from the trivial and transitive polar actions, there are five polar actions of cohomogeneity one and four polar actions of cohomogeneity two.
Classifies Lie algebras actions on 3D spaces, focusing on solvable groups.
problem Classifying transitive actions of Lie algebras on 3D spaces.
method Local equivalence and structure of one-dimensional invariant foliations.
result Cannot extend classification to solvable case.
DPN combines model-based and model-free reinforcement learning for efficient planning.
problem Efficiently plan actions in reinforcement learning environments.
method Combines model-based and model-free reinforcement learning, dynamically constructing plans using a learned state-transition model.
result Reduces the number of state transitions during planning by up to 96%, improving data efficiency and performance.
Cusped hyperbolic 3-manifolds can have up to 4 cusps under certain group actions.
problem Understanding the maximum number of cusps in hyperbolic 3-manifolds under group actions.
method Analyzing the isometry group actions on cusps of hyperbolic 3-manifolds.
result Constructing a family of manifolds with no upper bound on the number of cusps for k = 2 k=2 k = 2 . Compact complex manifolds with specific group actions are conformally flat.
problem Compact complex manifolds with invariant conformal holomorphic structures.
method Study of manifolds with transitive and essentially acting complex semi-simple Lie groups.
result If a complex semi-simple Lie group acts transitively and essentially, the manifold is conformally flat.
Study of transitivity in partially hyperbolic maps with expanding linear part.
problem Transitivity of partially hyperbolic endomorphisms with expanding linear part.
method Use of Blichfedt's theorem to analyze dynamical information from homology action.
result Robust transitivity condition and complete dichotomy for special cases.
This work uses action equivariance to learn structured latent spaces for reinforcement learning.
problem Learning structured latent spaces for reinforcement learning.
method Introduced a contrastive loss function to enforce action equivariance on learned representations.
result Optimal policies in the abstract MDP can be successfully lifted to the original MDP.
Identifies latent actions and dynamics from offline data with diverse demonstrators.
problem Recovering latent actions and environment dynamics from action-free trajectories.
method Assumes distinct policies for each demonstrator, identifies latent transitions and policies via matrix factorization.
result Identifies latent transitions and demonstrator policies up to permutation.
Study shows optimal RL with transition look-ahead is NP-hard for ℓ ≥ 2 \ell \geq 2 ℓ ≥ 2 .
problem Optimal reinforcement learning with transition look-ahead is computationally hard.
method Proved NP-hardness for ℓ ≥ 2 \ell \geq 2 ℓ ≥ 2 using linear programming. result There is a precise boundary between tractable and intractable cases for RL with look-ahead.
We study higher rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by R k \R ^k R k with k ≥ 3 k \geq 3 k ≥ 3 whose one-parameter groups act transitively as well as nondegenerate totally nonsymplectic $\Zk$ -actions for k ≥ 3 k \geq 3 k ≥ 3 .
New proof shows almost all surface group actions are dense.
problem Transitivity of normal subgroups on character varieties.
method Proved almost minimal action of non-trivial normal subgroups.
result Almost all points in character variety have dense orbits.
Study shows how certain spaces can be mapped to R^n with specific properties.
problem Characterizing and mapping locally compact median spaces of finite rank.
method Analyzing the combinatorics of halfspaces and properties of isometric actions.
result Spaces with certain actions are isometric to R^n, and orbits are discrete.
Classifies special homogeneous curves with polynomial equations.
problem Identifying and classifying special homogeneous curves.
method Analyzing homogeneous polynomials and their level sets with group actions.
result All special homogeneous curves are classified.
Paper introduces a new value function for state transitions and optimal policy learning.
problem Learning optimal policies from state transitions and actions.
method Develops a forward dynamics model to maximize a novel value function Q ( s , s ′ ) Q(s, s') Q ( s , s ′ ) . result Demonstrates benefits in value function transfer, redundant action spaces, and off-policy learning.
Due to a result by Mackenzie, extensions of transitive Lie groupoids are equivalent to certain Lie groupoids which admit an action of a Lie group. This paper is a treatment of the equivariant connection theory and holonomy of such groupoids, and shows that such connections give rise to the transition data necessary for…
We describe an algorithm for the enumeration of (candidates of) vertex-transitive combinatorial d d d -manifolds. With an implementation of our algorithm, we determine, up to combinatorial equivalence, all combinatorial manifolds with a vertex-transitive automorphism group on n ≤ 13 n\leq 13 n ≤ 13 vertices. With the exception of act…
SR-GNN models sessions as graphs to predict user actions.
problem Predict user actions based on anonymous sessions.
method SR-GNN models sessions as graphs and uses attention networks.
result SR-GNN outperforms state-of-the-art methods consistently.
New maps on the plane with specific symmetry properties identified.
problem Characterizing maps with quasi-vertex-transitive properties.
method Analyzing the automorphism groups and vertex orbits of maps on the plane.
result Existence of quasi-vertex-transitive maps of certain types, but not vertex-transitive.
Proposes a new sampling method for deep Q-learning to improve efficiency and convergence.
problem Challenges in learning state-action value function from replay buffer.
method State distribution-aware sampling method to balance replay times for transitions.
result Reduces unnecessary TD updates and increases updates for uncertain state-action values.
Classifies symplectic half-flat 6-manifolds with a transitive group action.
problem Finding compact non-flat examples of symplectic half-flat 6-manifolds.
method Review of classical results and classification in noncompact setting.
result All invariant symplectic half-flat SU(3)-structures are Hermitian.
We classify the transitive, effective, holomorphic actions of connected complex Lie groups on complex surfaces.
This paper studies supergrassmannians as homogeneous spaces for super Lie groups.
problem Defining and understanding supergrassmannians as homogeneous spaces.
method Using the functor of point approach, the paper constructs the action of super Lie group GL(m|n) on G_{k|l}(m|n).
result Explicit construction of the action of super Lie group GL(m|n) on supergrassmannian G_{k|l}(m|n).
The paper constructs supergrassmannians using gluing and describes their actions.
problem Constructing and describing the actions of supergrassmannians.
method Gluing of superdomains and action of super Lie group G L ( e x t b f m → ) GL(\overrightarrow{ extbf{m}}) G L ( e x t b f m ) in functor of points language. result Concrete proof of the transitively of the action and gluing of local charts.
New findings on geometric structures and their homogeneity.
problem Understanding local homogeneity in geometric structures.
method Investigating various geometric structures and their actions.
result Smooth closed 3D Lorentz manifolds with topologically transitive actions are locally homogeneous.
Deep reinforcement learning method finds rare events in complex systems.
problem Computing transition pathways in high-dimensional systems.
method Formulated as a cost minimization problem, solved using DDPG with physical properties.
result Efficiently samples and computes globally optimal transition pathways.
Classifies special homogeneous surfaces with unique properties.
problem Classifying hyperbolic polynomials with specific actions.
method Analyzes hyperbolic level sets and restricts negative Hessians.
result Existence of a finite number of special homogeneous surfaces with unique curvature.
We classify compact homogeneous geometries of irreducible spherical type and rank at least 2 which admit a transitive action of a compact connected group, up to equivariant 2-coverings. We apply our classification to polar actions on compact symmetric spaces.
The equivalence of principal bundles with transitive Lie groupoids due to Ehresmann is a well known result. A remarkable generalisation of this equivalence, due to Mackenzie, is the equivalence of principal bundle extensions with those transitive Lie groupoids over the total space of a principal bundle, which also admi…
New findings reveal discount regularization can be seen as a strong prior, leading to poor performance in unevenly sampled data.
problem Discount regularization leads to poor performance in unevenly sampled data.
method Equivalence theorem showing discount regularization as a strong prior, setting regularization parameters locally for individual state-action pairs.
result Discount regularization can be seen as a strong prior, leading to poor performance in unevenly sampled data.
4-manifolds show every flat 3-manifold as cusp sections.
problem Realizing flat 3-manifolds as cusp sections of hyperbolic 4-manifolds.
method Transitive action on cusps, dense flat metrics realization.
result Existence of many cusp-transitive 4-manifolds.
We study the construction of quasimorphisms on groups acting on trees introduced by Monod and Shalom, that we call median quasimorphisms, and in particular we fully characterise actions on trees that give rise to non-trivial median quasimorphisms. Roughly speaking, either the action is highly transitive on geodesics, i…
This work tackles model-based RL by optimizing state-action queries to learn policies with minimal data.
problem Expensive state transitions in practical RL problems limit the use of standard RL algorithms.
method Bayesian optimal experimental design to guide selection of state-action queries.
result Data-efficient RL approach that learns optimal policies with up to 1,000x less data.
If X X X is a connected complex manifold with d X = 2 d_X = 2 d X = 2 that admits the holomorphic and transitive action of a (connected) Lie group G G G , then the action extends to an action of the complexification G ^ \hat{G} G ^ of G G G on X X X except when either the unit disk or else a strictly pseudoconcave homogeneous complex manifold is i…
Study on holomorphic discs in bundles over compact surfaces, proving Fredholm regularity under certain conditions.
problem Analyzing holomorphic discs with boundary on surfaces in vector bundles over compact manifolds.
method Proves Fredholm regularity for sections with a single complex point under specific conditions.
result Holomorphic discs are Fredholm regular under certain conditions, including neutral Kähler and symplectic actions.
Study shows certain surface homeomorphisms groups can't be precompact.
problem Understanding precompactness of groups of surface homeomorphisms.
method Analyzing subgroup properties and transitivity of homeomorphisms.
result No subgroup of surface homeomorphisms can be Roelcke precompact.
The paper explores the transitivity of orbifold diffeomorphisms.
problem Understanding the transitivity of orbifold diffeomorphisms.
method Investigates the group of compactly supported diffeomorphisms of orbifolds.
result The group of orbifold diffeomorphisms is n n n -transitive. New algorithms learn MDPs with continuous states and actions using Gaussian processes.
problem Online learning in unknown, episodic MDPs with continuous states and actions.
method Developed variants of UCRL and posterior sampling algorithms using Gaussian process priors.
result Sublinear regret bounds for learning MDPs with specific kernel structures.