Study ping-pong dynamics in hyperbolic-like groups with non-simple points.
problem Investigate the ping-pong dynamics of hyperbolic-like groups.
method Explicitly provide a proper ping-pong partition for any pair of non-cyclic point stabilizers.
result Existence of a proper ping-pong partition for any pair of non-cyclic point stabilizers.
Groups without non-trivial finite normal subgroups have a strong ping pong property.
problem Proving a strong ping pong property for acylindrically hyperbolic groups.
method Proving the Pnaive property for groups with no non-trivial finite normal subgroups. result Groups satisfying the condition have a strong ping pong property.
Study estimates gaps in semigroup products, proving embedding properties.
problem Estimating singular value gaps in semigroup products.
method Lower estimates for singular value gaps of free products of semigroups in ping-pong position.
result Groups generated by semigroups in ping-pong position are quasi-isometrically embedded.
New groups discovered with unique properties in a specific space.
problem Finding new discrete subgroups with special properties in a mathematical space.
method Proved by showing groups play ping-pong on cones, related to crooked surfaces.
result Infinite family of discrete subgroups with remarkable properties in Sp4(R). Geometric group theory explores groups through their geometric properties.
problem Understanding groups via geometric properties.
method Cayley and Schreier graphs, ping-pong lemma, quasi-isometries, growth of groups, hyperbolicity.
result Gromov's theorem on groups of polynomial growth and amenability.
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.
Algorithm determines discrete, free subgroups of SL2 over non-archimedean fields.
problem Identifying discrete, free subgroups of SL2 over non-archimedean fields.
method Ping Pong Lemma applied to Bruhat-Tits tree action.
result Algorithm determines if subgroup is discrete and free of rank two.
The study examines subgroups of torus mapping class group generated by Dehn twists powers.
problem Characterizing subgroups generated by powers of Dehn twists.
method Using the ping pong lemma and geometric intersection numbers.
result Subgroups can be free groups, direct products, or have specific ranks.
We prove that if φ,ψ∈Out(FN) are hyperbolic iwips (irreducible with irreducible powers) such that <φ,ψ>≤Out(FN) is not virtually cyclic then some high powers of φ and ψ generate a free subgroup of rank two, all of whose nontrivial elements are again hyperbolic iwips. Being a hyperbolic iwip element of $…
The paper proves a quantitative Tits alternative for negatively pinched manifolds.
problem Proving a quantitative version of the Tits alternative for negatively pinched manifolds.
method Analyzing discrete isometry subgroups generated by two non-elliptic isometries.
result A free subgroup of rank 2 is found in the isometry subgroup, which is convex-cocompact when one of the generators is hyperbolic.
Local-to-global principle for Morse actions on symmetric spaces.
problem Recognizing Morse actions on symmetric spaces.
method Equivariant Morse quasiisometric embeddings of trees into symmetric spaces.
result Algorithmic recognizability of Morse actions and construction of Morse Schottky subgroups.
Researchers discover all affinely homogeneous models for surfaces in 4D space.
problem Identifying all affinely homogeneous models for surfaces in 4D space.
method Improved power series method of equivalence, capturing invariants at the origin, creating branches, and infinitesimalizing calculations.
result Find several inequivalent terminal branches yielding each to some nonempty moduli space of homogeneous models.
This note removes technical assumptions and characterizes relatively dominated representations.
problem Geometrically finiteness and Anosov conditions in higher-rank settings.
method Characterization using eigenvalue gaps and limit maps.
result Relatively dominated representations are characterized using eigenvalue gaps and limit maps.
New algebra pong algebra computed for knot Floer homology.
problem Computing A-infinity structure on knot Floer homology.
method Introduced differential graded algebra, pong algebra.
result Computed A-infinity structure on pong algebra's homology.
We study the geometry and dynamics of discrete infinite covolume subgroups of higher rank semisimple Lie groups. We introduce and prove the equivalence of several conditions, capturing "rank one behavior'' of discrete subgroups of higher rank Lie groups. They are direct generalizations of rank one equivalents to convex…
Study matches two noisy point clouds with geometric transformations and relabeling.
problem Matching two noisy point clouds with orthogonal transformations and relabeling.
method Information-theoretic results and Ping-Pong algorithm for computational alignment.
result The Ping-Pong algorithm retrieves the planted signal after one step.
Deep RL learns to play Pong from frames alone.
problem Scaling up RL problems leads to computational bottlenecks.
method End-to-end DRL approach using ANN and Policy Gradients.
result Successfully learned to play Pong from frames.
Study weightings from singular Lie filtrations.
problem Generalize constructions for singular Lie filtrations.
method Study weightings arising from singular Lie filtrations.
result Generalizes constructions for (regular) Lie filtrations.
VIPER learns verifiable decision tree policies from deep reinforcement learning.
problem Ensuring safety of learned reinforcement learning policies.
method VIPER combines model compression and imitation learning to train decision tree policies.
result VIPER learns decision tree policies that are provably robust and stable.
Improved DRL performance with novel pre-training method.
problem Data inefficiency in DRL algorithms.
method Jointly pre-training with supervised, autoencoder, and value losses.
result Significantly improved learning performance in Atari games.
We prove that the cotangent of a double Lie groupoid S has itself a double groupoid structure with sides the duals of associated Lie algebroids, and double base the dual of the Lie algebroid of the core of S. Using this, we prove a result outlined by Weinstein in 1988, that the side groupoids of a general symplectic do…
Defines new two-variable elliptic genera for manifolds and derives modular forms.
problem Develops new elliptic genera for manifolds.
method Introduces and defines new two-variable elliptic genera for manifolds and derives their properties.
result Derives modular forms from the elliptic genera.
The paper models and deforms A-infinity structures for bordered knot algebras.
problem Understanding A-infinity structures for bordered knot algebras.
method Combinatorial model and weighted deformation of A-infinity structures.
result Explicit combinatorial model for bordered knot algebras' A-infinity structure.
Defines Wodzicki residue using groupoids and fibered distributions.
problem Defining and understanding the Wodzicki residue in noncommutative geometry.
method Using groupoid language and filtered manifolds, defining the residue and showing its properties.
result The groupoidal residue is a trace on pseudodifferential operators and matches the usual residue in certain cases.
Paper presents certified defenses against adversarial patch attacks.
problem Certified defenses against adversarial patch attacks are needed.
method Proposes the first certified defense and faster training methods.
result Demonstrates robustness transfer across different patch shapes.
WMPG reduces policy gradient variance using world models.
problem Reducing variance in policy gradient estimates.
method Trains a world model online to estimate policy gradients and uses imagined trajectories as a baseline.
result WMPG achieves better sample efficiency compared to AC and MAC.
Proposes a new neural network architecture inspired by biology to improve learning and information flow.
problem Improving artificial neural networks to match biological neuron properties like multidirectional propagation and probabilistic modeling.
method Extends KAN approach with joint distribution neurons that can propagate values and distributions, including variance and higher-order moments.
result Proposed architecture can predict and propagate distributions, including expected values and variances.
We define an abstract notion of double Lie algebroid, which includes as particular cases: (1) the double Lie algebroid of a double Lie groupoid in the sense of the author, such as the iterated tangent bundle of an ordinary manifold, and various iterated tangent/cotangent constructions in symplectic and Poisson geometry…
Inspired by recent works of Zang Liu, Alan Weinstein and Ping Xu, we introduce the notions of CC algebroids and non asymmetric Courant algebroids and study these structures. It is shown that CC algebroids of rank greater than 3 are the same as Courant algebroids up to a constant factor, though the definition of CC alge…
Market manipulation is a strategy used by traders to alter the price of financial securities. One type of manipulation is based on the process of buying or selling assets by using several trading strategies, among them spoofing is a popular strategy and is considered illegal by market regulators. Some promising tools h…
The paper introduces MDP homomorphic networks for faster reinforcement learning.
problem Current reinforcement learning approaches do not exploit symmetries in the joint state-action space.
method Equivariant neural networks with group-structured symmetries (reflections, rotations).
result MDP homomorphic networks converge faster than unstructured baselines on various tasks.
Paper introduces a technique to simplify RNN policies for better understanding and analysis.
problem Difficulty in explaining and analyzing RNN policies due to continuous-valued memory vectors and observation features.
method Quantized Bottleneck Insertion technique to learn finite representations of RNN vectors and features.
result Finite representations of RNN policies can be as small as 3 discrete memory states and 10 observations, improving interpretability.
Scalable web crawling using noisy change-indicating signals.
problem Optimizing web page freshness with limited bandwidth and noisy side information.
method Proposes a scalable crawling algorithm that uses noisy side information optimally.
result Achieves constant total rate of crawling without spikes in bandwidth usage.
Improved off-policy reinforcement learning by discounting and soft normalization.
problem Divergence issues in off-policy reinforcement learning.
method Introducing a discount factor and a soft normalization penalty into COP-TD.
result Discounted COP-TD is better behaved both theoretically and empirically.
Proposes tunable GMM kernels for classification tasks.
problem Lack of competitive performance of GMM kernels compared to tree methods on deep learning datasets.
method Introduces tunable GMM kernels with added parameters and combines basic kernels for improved performance.
result Tunable GMM kernels can produce good results for various classification tasks.
Researchers use FIR filters to predict COVID-19 infections and recoveries.
problem Predicting the spread of COVID-19 without a vaccine.
method Modified numerical method using FIR filters and ridge regression.
result Modified algorithm yields better approximation errors.
Paper introduces a simulator-free approach to reinforcement learning policy distillation.
problem Learning multiplicity of cases corresponding to a given action in reinforcement learning.
method Generative adversarial approach to find multiple exemplars for each output class.
result Improves over state-of-the-art on data-free learning of student networks.
Measures intrinsic dimension of neural network landscapes.
problem Quantifying the difficulty of machine learning problems.
method Train networks in randomly oriented subspaces of varying dimensions.
result Intrinsic dimensions are often smaller than expected.
Teichmuller solved the type problem for Riemann surfaces.
problem Deciding if a Riemann surface is conformally equivalent to the complex plane or unit disc.
method Using line complexes and quasiconformal mappings, Teichmuller proved equivalence of surfaces with the same ramification measure.
result A simply connected Riemann surface is hyperbolic if sufficiently ramified.
Groups with Property (T) have fiber products with Property (T).
problem When does the fiber product of groups with Property (T) have Property (T)?
method Analyzing fiber products of groups with Property (T).
result Fiber products of groups with Property (T) also have Property (T).
New findings on asymptotic property C in infinite dimensional spaces.
problem Understanding infinite dimensional spaces with infinite asymptotic dimension.
method Showed preservation of asymptotic property C in infinite products and introduced hyperbolic property C.
result Infinite products and restricted direct products of countable groups with finite asymptotic dimension have asymptotic property C.
We prove recognition theorems for codimension one manifold factors of dimension n≥4. In particular, we formalize topographical methods and introduce three ribbons properties: the crinkled ribbons property, the twisted crinkled ribbons property, and the fuzzy ribbons property. We show that X×R i…
The study shows that several properties are not profinite invariants.
problem Determining which properties are profinite invariants.
method Combining Rips constructions and iterated group-theoretic Dehn filling on hyperbolic virtually special groups.
result Several properties (stable commutator length, quasimorphisms, property NL, property FW∞, property FA, and non-abelian free subgroups) are not profinite invariants. We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note …
New complexity notion connects finite decomposition and asymptotic property C.
problem Understanding and connecting different properties in metric spaces.
method Introducing finite APC-decomposition complexity and proving its implications.
result Finite APC-decomposition complexity implies property A for metric spaces.
Abstract: Formalizes metric spaces with coarse properties, generalizing finite decomposition complexity.
problem Understanding metric spaces with coarse properties.
method Formalizing and generalizing finite decomposition complexity.
result Determines sufficient conditions for metric spaces to satisfy Property A.
Extended Tetrahedral Property to non-Euclidean spaces.
problem Prove Tetrahedral Property in non-Euclidean spaces.
method Extend Tetrahedral Property to less restrictive definition and prove its properties.
result Generalized Tetrahedral Property retains original properties and leads to convergence results.
Investigates stability properties of Haezendonck-Goovaerts premium principles in Orlicz spaces.
problem Stability properties of Haezendonck-Goovaerts premium principles in various Orlicz spaces.
method Analysis of stability properties including Fatou and Lebesgue properties, and continuity with respect to Φ-weak convergence. result Haezendonck-Goovaerts principles satisfy the Fatou property and Lebesgue property under certain conditions.