Lecture notes on group actions on injective spaces and Helly graphs.
problem Understanding group actions on specific metric spaces.
method Review of injective metric spaces and Helly graphs, elementary properties, constructions, and exercises.
result Presentation of various constructions of injective metric spaces and Helly graphs with interesting group actions.
A method to generate long-range human actions by leveraging graph convolutional networks and self-attention.
problem Generating long-range skeleton-based human actions is challenging due to small frame deviations.
method Proposes a variant of GCNs with self-attention to adaptively sparsify action graphs and capture structure information.
result Extensive experiments show superior performance compared to existing methods on human action datasets.
Characterizes geometric actions on graphs with flexible stabilizers.
problem Understanding geometric actions on flexible stabilizers.
method Defining generalized fine actions and proving relative quasi-convexity criteria.
result Characterizes Bowditch boundary points in relatively geometric actions.
The paper studies quaternionic structures on GKM graphs and their relation to torus actions on quaternionic projective spaces.
problem Understanding quaternionic structures on GKM graphs and their implications for torus actions.
method Introducing quaternionic structures on GKM graphs and analyzing their properties in the context of torus actions.
result Abstract GKM graphs with specific 2-face structures correspond to torus actions on quaternionic projective spaces or Grassmannians.
Study on finiteness property of right-angled Artin groups actions on extension graphs.
problem Finiteness property of hyperbolic simplicial actions on right-angled Artin groups.
method Analysis of right-angled Artin group actions on extension graphs, using asymptotic translation lengths and syllable lengths.
result Asymptotic translation lengths of elements in right-angled Artin groups are rational and have a common denominator under certain conditions.
KG-A2C agent learns natural language IF games by reasoning and constraining action spaces.
problem Challenges of natural language understanding, partial observability, and combinatorially large action spaces in IF games.
method Builds a dynamic knowledge graph while exploring, constraining actions using templates.
result Outperforms current IF agents across various games with larger action spaces.
We study two actions of big mapping class groups. The first is an action by isometries on a Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. The first two parts of the paper are devoted to the definition of objects and tools needed to int…
The paper uses action graphs to predict user engagement in Snapchat.
problem Understanding what motivates users to engage with mobile social apps.
method Formalized in-app action transition patterns as action graphs, analyzing their characteristics to predict future engagement.
result Action graphs can characterize user behavior patterns and inform future engagement.
Investigates sequential problems on graph structures and large action spaces.
problem Sequential decision-making on graph structures and large action spaces.
method Spectral bandits, side observations, influence maximization, kernel bandits, polymatroid bandits, function optimization, infinitely many-arms bandits.
result Contributions to graph and structured bandits.
Study circle actions on 4-manifolds, deriving formulas and graphs.
problem Understanding circle actions on 4-dimensional manifolds.
method Derive the Atiyah-Hirzebruch formula and associate graphs to fixed point data.
result Show existence of 4D oriented S^1-manifolds from satisfying graphs.
Study proves hyperfiniteness of mapping class group actions on surface graphs.
problem Hyperfiniteness of mapping class group actions on surface graphs.
method Infinite unicorn paths and Gromov boundaries of arc and curve graphs.
result Proves hyperfiniteness of orbit equivalence relations induced by mapping class group actions.
We consider stochastic multi-armed bandit problems with graph feedback, where the decision maker is allowed to observe the neighboring actions of the chosen action. We allow the graph structure to vary with time and consider both deterministic and Erdős-Rényi random graph models. For such a graph feedback model, we fir…
We study commensurating actions of groups and the associated properties FW and PW, in connection with wallings, median graphs, CAT(0) cubings and multi-ended Schreier graphs.
Graph theory connects automorphisms to cohomology.
problem Understanding automorphism actions on graph cohomology.
method Graph-theoretical interpretation of de Rham cohomology.
result Proves graph analogues of differential geometry results.
Graph neural Thompson Sampling improves online decision-making for graph data.
problem Online decision-making with graph-structured rewards.
method GNN-TS algorithm using GNN for mean reward estimation and graph neural tangent features for uncertainty.
result GNN-TS achieves a state-of-the-art regret bound of ildeO((ildedT)1/2). We study discrete, cocompact, isometric actions of groups on Hadamard spaces, and the induced actions on ideal boundaries. For a class of groups generalizing fundamental groups of three-dimensional graph manifolds, we find a set of invariants for the action which determine the boundary action up to equivariant homeomor…
New bound for group action length without diameter restriction.
problem Bounding minimal translation length for Artin groups.
method Graph theoretic properties of biconnected graphs.
result Upper bound of 2 for minimal translation length holds without diameter restriction.
We define a way of approximating actions on measure spaces using finite graphs; we then show that in quite general settings these graphs form a family of expanders if and only if the action is expanding in measure. This provides a somewhat unified approach to construct expanders. We also show that the graphs we obtain …
Abstract: Proves generic torus diffeomorphisms act parabolically and non-properly on fine curve graph and have generalized rotation sets.
problem Generic torus diffeomorphisms on fine curve graph.
method Proves generic torus diffeomorphisms act parabolically and non-properly on fine curve graph.
result Generic torus diffeomorphisms have generalized rotation sets of any point-symmetric compact convex homothety type.
Study GKM actions on special manifolds with interval orbit spaces.
problem Understanding GKM actions on specific types of manifolds.
method Analyzing group diagrams and orbit spaces; describing GKM graphs.
result Necessary and sufficient conditions for GKM actions on cohomogeneity one manifolds.
New approach for open ad hoc teamwork using graph-based policy learning.
problem Designing autonomous agents to collaborate with changing teams without prior coordination.
method Graph-based policy learning to adapt to dynamic team compositions.
result Successfully models the effects of other agents, leading to robust adaptation and superior performance.
We consider the orientation-preserving actions of finite groups G on pairs (S3,Γ), where Γ is a connected graph of genus g>1, embedded in S3. For each g we give the maximum order mg of such G acting on (S3,Γ) for all such Γ⊂S3. Indeed we will classify all graphs Γ⊂S3 which re…
CFRecs uses counterfactual reasoning to improve graph-based recommendations in real estate.
problem Improving model interpretability and actionable insights in graph-based recommender systems.
method A two-stage architecture combining GNN and Graph-VAE to propose minimal yet impactful changes in graph structure and node attributes.
result Demonstrates effectiveness in delivering actionable recommendations for home buyers and sellers.
Study homeomorphisms on fine curve graph of surfaces, revealing new types of dynamics.
problem Understanding dynamics of homeomorphisms on fine curve graphs of surfaces.
method Analyzing the action of homeomorphisms on the fine curve graph and relating to classical curve graphs.
result Homeomorphisms induce parabolic isometries, and all positive reals are realized as asymptotic translation lengths.
The study classifies and investigates translators invariant under hyperpolar actions on symmetric spaces.
problem Understanding translators invariant under hyperpolar actions on symmetric spaces.
method Classification and investigation of translators given by functions invariant under hyperpolar actions.
result Classification and investigation of translators in symmetric spaces under hyperpolar actions.
Characterizes ends and coends of graph pairs using quasi-median graphs.
problem Understanding the number of ends and coends in graph pairs.
method Characterizes ends and coends using quasi-median graphs.
result Characterizes ends and coends of graph pairs (G,H) in terms of quasi-median graphs. This is a survey on upper and lower bounds for finite group actions on bounded surfaces, 3-dimensional handlebodies and closed handles, handlebodies in arbitrary dimensions and finite graphs (the common feature of these objects is that all have free fundamental group).
The curve graph and related graphs are hyperbolic and have quasi-tree fibers.
problem Understanding the structure of the curve graph and related graphs.
method Analyzing a sequence of graphs with Lipschitz maps and proving hyperbolicity and quasi-tree properties.
result The graphs in the sequence are hyperbolic and have quasi-tree fibers, leading to bounds on asymptotic dimension and acylindrical actions.
We study when the mapping class group of an infinite-type surface S admits an action with unbounded orbits on a connected graph whose vertices are simple closed curves on S. We introduce a topological invariant for infinite-type surfaces that determines in many cases whether there is such an action. This allows us …
We show that the Gromov boundary of the free factor graph for the free group Fn with n>2 generators is the space of equivalence classes of minimal very small indecomposable projective Fn-trees without point stabilizer containing a free factor equipped with a quotient topology. Here two such trees are equivalent if the …
The paper studies actions on Bass-Serre trees and identifies new C∗-simple groups.
problem Investigating actions of fundamental groups on Bass-Serre trees and their C∗-algebraic properties. method Analyzing boundary actions of fundamental groups of graphs of groups on their Bass-Serre trees.
result Identification of new families of C∗-simple groups, including tubular groups and certain graphs of groups. A new benchmark task for evaluating policy learning in complex, high-dimensional action spaces.
problem Lack of a commonly accepted benchmark for evaluating policy learning in hierarchical tasks with high-dimensional action spaces.
method Proposed DinerDash Gym benchmark and Decomposed Policy Graph Modelling (DPGM) algorithm.
result DPGM achieves significant improvement over baselines and effectively injects domain knowledge.
New algorithm reduces bandit regret by graph domination number.
problem Adversarial multi-armed bandit with partial observations and switching costs.
method New algorithm with improved policy regret bounds.
result Regret depends only on the domination number of the feedback graph.
Neural Architecture Search (NAS) enabled the discovery of state-of-the-art architectures in many domains. However, the success of NAS depends on the definition of the search space. Current search spaces are defined as a static sequence of decisions and a set of available actions for each decision. Each possible sequenc…
Free finite group actions on non-positively curved 3-manifolds
problem Resolution of the remaining case of graph manifolds
method Proving the existence of a G-invariant NPC metric result Resolution of the remaining case of graph manifolds
We construct a graph TQFT for the minus flavor of Heegaard Floer homology. Our graph TQFT extends Ozsváth and Szabó's TQFT for closed and connected 3-manifolds, and allows for cobordisms with disconnected ends. As an application, we give an explicit formula for the chain homotopy type of the π1-action on Heegaard Fl…
Study of reinforcement learning with additional feedback observations.
problem Episodic reinforcement learning in Markov decision processes with feedback observations.
method Formalization of feedback graph, model-based algorithms leveraging feedback, regret bound analysis.
result Regret bound depends only on the size of the maximum acyclic subgraph of the feedback graph.
The paper shows how to find inaccessible hyperbolic actions in manifold groups.
problem Finding hyperbolic actions of 3-manifold groups that are inaccessible.
method Analyzing the partial order of cobounded actions on hyperbolic spaces.
result Proves the existence of finite covers with inaccessible fundamental groups.
The study examines groups acting loxodromically on hyperbolic graph products.
problem Understanding groups acting loxodromically on hyperbolic graph products.
method Examined groups acting on finite products of hyperbolic graphs, focusing on loxodromic elements.
result Strong structure theorems for groups in this subclass, excluding mapping class groups of genus at least 3 and certain automorphism groups.
Study on sample complexity for pure exploration in feedback graph settings.
problem Sample complexity of pure exploration in online learning with feedback graphs.
method Derive instance-specific lower bounds and present asymptotically optimal algorithm TaS-FG.
result TaS-FG is asymptotically optimal and efficient across different graph configurations.
The purpose of this paper is to establish an upper bound on the distance between two pants decompositions in the pants complex for a closed surface of genus g >= 2. This is done by use of graph theory. First distance is found in the pants graph modulo the action of the mapping class group, and then between pants decomp…
Improved bounds on acylindricity for right-angled Artin groups.
problem Bounding the acylindrical action of right-angled Artin groups on their extension graphs.
method Exploring lattice properties, studying prefixes of powers, and extending quasi-root uniqueness.
result Cardinality of r-quasi-stabilizer is bounded by a linear function of r. The aim of this paper is to give an upper bound for the dimension of a torus T which acts on a GKM manifold M effectively. In order to do that, we introduce a free abelian group of finite rank, denoted by A(Γ,α,∇), from an (abstract) (m,n)-type GKM graph (Γ,α,∇). Here, an (m,n)-type GKM …
The paper conjectures and proves fixed points for certain group actions on nonpositively curved spaces.
problem Actions by automorphisms of finitely generated groups on nonpositively curved complexes without fixed points.
method Use of Helly graphs and geodesic clique paths to prove ellipticity results.
result Finitely generated torsion groups cannot act without fixed points on nonpositively curved spaces.
We construct maps on hat Heegaard Floer homology for cobordisms decorated with graphs. The graph TQFT allows for cobordisms with disconnected ends. Our construction uses Juhász's sutured Floer TQFT. We compute the maps for several elementary graph cobordisms. As an application, we compute the action of the fundamental …
The action dimension of a discrete group G is the minimum dimension of contractible manifold that admits a proper G-action. We compute the action dimension of the direct limit of a simple complex of groups for several classes of examples including: 1) Artin groups, 2) graph products of groups, and 3) fundamental gr…
It is shown that for any action of a finitely presented group G on an R-tree, there is a decomposition of G as the fundamental group of a graph of groups related to this action. If the action of G on T is non-trivial, i.e. there is no global fixed point, then G has a non-trivial action on a simplcial R…
Improved RL for knowledge graph reasoning with entity types.
problem Challenges in path-based relational reasoning over knowledge graphs.
method Type-enhanced RL agent using GNN for neighborhood information.
result Outperforms state-of-the-art RL methods and discovers novel paths.