Algorithm computes Čech cohomology of decomposition spaces.
problem Computing Čech cohomology of decomposition spaces.
method Algorithmic approach to compute Čech cohomology.
result Algorithm provides a presentation for Čech cohomology.
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48 results for “malnormal collection”
Proves existence of certain subgroups in hyperbolic groups.
problem Existence of weakly malnormal quasiconvex subgroups in hyperbolic groups.
method Proof of existence in nonelementary hyperbolic groups.
result Existence of weakly malnormal, virtually free, quasiconvex subgroups in hyperbolic groups.
New space of currents defined for nonabelian free groups and malnormal subgroups.
problem Understanding growth under iteration of outer automorphisms of nonabelian free groups.
method Introducing a new topological space of currents relative to a malnormal subgroup system.
result Currents associated with elements not in conjugates of are dense in the space of currents relative to .
New trilinear form invariant for hyperbolic or malnormal knots.
problem Invariants for hyperbolic or malnormal knots.
method Introduce a trilinear form as a topological invariant.
result Trilinear form equals the pairing of the (twisted) triple cup product and the fundamental relative 3-class.
We give an alternate proof of Wise's Malnormal Special Quotient Theorem (MSQT), avoiding cubical small cancellation theory. We also show how to deduce Wise's Quasiconvex Hierarchy Theorem from the MSQT and theorems of Hsu--Wise and Haglund--Wise.
Complex captures group properties, invariant under quasi-isometry.
problem Classical properties of subgroups in a group pair.
method Introduces coset intersection complex to study group properties.
result Quasi-isometry invariance of coset intersection complex.
New hierarchy for a special group type.
problem Classifying relatively hyperbolic virtually special groups.
method Constructing a new virtual quasiconvex hierarchy.
result Generalized Malnormal Special Quotient Theorem.
The aim of the current paper is to explore the implications on the group of the non-vanishing of the cohomology in degree one of one of its representation , given some mixing conditions on . In one direction, harmonic cocycles are used to show that the FC-centre should be finite (for mildly mixing unitary rep…
The paper proves that relative Dehn functions are invariant under quasi-isometry.
problem Invariance of relative Dehn functions under quasi-isometry.
method Proof of quasi-isometry invariance of relative Dehn functions.
result Relative Dehn functions are invariant under quasi-isometry.
We introduce the notion of controlled Floyd separation between geodesic rays starting at the identity in a finitely generated group G. Two such geodesic rays are said to be Floyd separated with respect to quasigeodesics if the (Floyd) length of c-quasigeodesics (for fixed but arbitrary c) joining points on the geodesic…
Counterexamples to Wise's theorem found using triangle groups and Ramanujan graphs.
problem A stronger form of Wise's theorem does not hold.
method Generalized triangle groups and Ramanujan graphs.
result A desired stronger form of Wise's malnormal special quotient theorem does not hold.
Splittings and C-complexesmath.GR
The intersection pattern of the translates of the limit set of a quasi-convex subgroup of a hyperbolic group can be coded in a natural incidence graph, which suggests connections with the splittings of the ambient group. A similar incidence graph exists for any subgroup of a group. We show that the disconnectedness of …
Study abelian subgroups in 3-manifolds, linking to splitting properties.
problem Separation of abelian peripheral subgroups under conjugacy and malnormality.
method Examining acylindrical splittings of 3-manifold groups.
result Existence of acylindrical splittings related to abelian subgroups.
New insights into the structure of blown-up corona of hyperbolic groups.
problem Understanding the structure of blown-up corona of relatively hyperbolic groups.
method Equivariant compactification and cohomological dimension analysis.
result Blown-up corona of a relatively hyperbolic group is contractible and homeomorphic to the Gromov boundary.
For any finitely generated, non-elementary, torsion-free group that is hyperbolic relative to , we show that there exists a group containing such that is hyperbolic relative to and is not relatively quasiconvex in . This generalizes a result of I. Kapovich for hyperbo…
The Farrell-Jones Conjecture holds for groups acting acylindrically on trees.
problem Verifying the Farrell-Jones Conjecture for groups acting on trees.
method Analyzing acylindrical actions on simplicial trees and using the Farrell-Jones Conjecture.
result The Farrell-Jones Conjecture holds for groups acting acylindrically on trees.
Explicit bounds on group size for certain geometric actions.
problem Bounding group size in geometric actions with bounded entropy.
method Proving an explicit function F(k, E) for groups with k-acylindrical splittings.
result Groups with bounded entropy have a finite size bound.
Graphically discrete groups have strong rigidity properties.
problem Understanding the rigidity of group actions on graphs.
method Introducing graphical discreteness and proving rigidity properties.
result Free products of graphically discrete groups are action rigid.
Characterizes strongly quasiconvex subsets in hierarchically hyperbolic spaces.
problem Understanding the structure of strongly quasiconvex subsets in HHSs.
method Characterization through contracting properties, relative divergence, and hierarchical structure.
result Proves characterization of hyperbolically embedded subgroups in hierarchically hyperbolic groups.
We study automorphisms of a relatively hyperbolic group G. When G is one-ended, we describe Out(G) using a preferred JSJ tree over subgroups that are virtually cyclic or parabolic. In particular, when G is toral relatively hyperbolic, Out(G) is virtually built out of mapping class groups and subgroups of GL_n(Z) fixing…
Study collective pricing and hedging with admissible risk exchanges forming a finitely generated convex cone.
problem Collective pricing and hedging with exchanges forming a finitely generated convex cone.
method Extend collective First Fundamental Theorem of Asset Pricing and pricing-hedging duality.
result No collective arbitrage implies the closedness of the aggregate feasibility cone.
Measures collectivity in financial covariances and correlations to reveal trends and precursors.
problem Capturing collective motion in financial markets to predict trends and precursors.
method Measures collectivity using the largest eigenvalue and average sector collectivity.
result Identifies collective signals around major financial events and captures trends in covariances and correlations.
Evaluating the Effect of Credit Collection Policy on Portfolio Quality of Micro-Finance Bankq-fin.PM
Study finds strict collection policies improve portfolio quality of microfinance banks.
problem Improving portfolio quality of microfinance banks through better credit collection policies.
method Multi-stage sampling, regression analysis, descriptive statistics.
result Collection policy has a higher effect on portfolio quality.
Generative model predicts NFT collection transactions based on early history.
problem Predict future transactions of newly minted NFT collections.
method Unsupervised learning to extract contexts, then generate future transactions.
result Projected market value of new NFT collections.
The paper extends collective arbitrage concepts to multi-agent markets with cooperation.
problem Understanding collective market completeness and pricing in multi-agent systems.
method Develops new techniques and theorems to establish collective pricing-hedging duality and collective replication.
result Established a Second Fundamental Theorem of Asset Pricing in cooperative multi-agent settings.
Study shows cooperation can reduce investment risk and price gaps.
problem Investment risk and price gaps in cooperative markets.
method Introduced Collective Arbitrage and Collective Super-replication, established asset pricing theorems.
result Reduction of price intervals through collective super-replication.
Researchers identify graph components for unicellular collections.
problem Understanding connected components of surgery graph for unicellular collections.
method Group-theoretic approach involving mapping class group action.
result Connected components enumerated by a homological invariant.
Active data collection improves convergence rates in operator learning.
problem Improving convergence rates in operator learning with linear target and stochastic input.
method Active data collection strategies with mean-zero stochastic process and continuous covariance kernels.
result Achieves arbitrarily fast error convergence rates with eigenvalue decay of covariance kernels.
A universal collection of 4 invariants improves neural network accuracy for molecular dynamics.
problem Improving accuracy of neural networks in molecular dynamics.
method Developed a universal collection of 4 smooth scalar invariants on M(3) x M(3) and evaluated their effectiveness in a PONITA neural network architecture.
result Using a universal collection of invariants significantly improves neural network accuracy.
This study examines how learning algorithms affect collective action in machine learning.
problem The impact of collective action on machine learning is limited when not considering the choice of learning algorithms.
method Focuses on distributionally robust optimization and stochastic gradient descent, analyzing their effects on collective success.
result The choice of learning algorithm significantly impacts the effective size and success of a collective in machine learning.
This review explores the use of machine learning in discovering collective variables for biomolecular dynamics.
problem Understanding the conformational dynamics and molecular recognition in biomolecules.
method Statistical analysis of high-dimensional spatiotemporal data generated from molecular dynamics simulations.
result Machine learning algorithms can be used to discover abstract collective variables that describe biomolecular dynamics.
CUDC collects diverse data for offline RL by predicting future states.
problem Challenges in collecting task-agnostic data for offline RL.
method Adaptive temporal distances for curiosity-driven data collection.
result CUDC outperforms existing unsupervised methods in offline RL tasks.
Collectives can manipulate learning platforms by coordinated data submission, requiring strategic assessments and algorithms.
problem Collectives can influence learning platforms by altering data, posing risks and requiring strategic planning.
method Developed a theoretical and algorithmic framework to understand and mitigate collective manipulation of learning platforms.
result Demonstrated the need for strategic assessments and implementable coordination algorithms to prevent collective manipulation.
Post-ADC inference corrects bias in statistical inference after active data collection.
problem Bias in inference after active data collection.
method Post-ADC inference framework that corrects bias from both ADC process and data-driven target construction.
result Valid inference for data collected by SMBO methods like GP-UCB and TPE.
Study shows small groups can influence machine learning algorithms.
problem How small groups can influence machine learning algorithms deployed on digital platforms.
method Proposed a theoretical model and conducted experiments on a large-scale language model.
result Small groups can exert significant control over machine learning algorithms.
Comparing the collective behavior of banking industryphysics.soc-ph
The study examines collective behavior in banking sectors across mature and emerging markets.
problem Understanding collective behavior in banking sectors across different market types.
method Applied Random Matrix Theory (RMT) to analyze the banking sectors of 4 world stock markets.
result Mature markets exhibit higher collective behavior compared to emerging markets.
Optimal online data collection for semiparametric inference reduces regret.
problem Sequential data collection decisions for efficient estimation under budget constraints.
method Online Moment Selection framework; Explore-then-Commit and Explore-then-Greedy policies.
result Online data collection policies achieve zero regret relative to an oracle policy.
Survey on data collection challenges in machine learning.
problem Data scarcity and need for labeled data in machine learning.
method Comprehensive study of data acquisition, labeling, and improvement techniques.
result Identification of research challenges in data collection.
We address the collective matrix completion problem of jointly recovering a collection of matrices with shared structure from partial (and potentially noisy) observations. To ensure well--posedness of the problem, we impose a joint low rank structure, wherein each component matrix is low rank and the latent space of th…
Efficient method detects point and collective anomalies in data sequences.
problem Efficiently identifying anomalies in data sequences, especially collective anomalies.
method CAPA: a computationally efficient approach for detecting collective and point anomalies.
result CAPA is consistent at detecting collective anomalies and has close to linear computational cost.
Proposes online debiasing to correct bias in adaptive data collection for high-dimensional linear regression.
problem Bias in adaptive data collection for high-dimensional linear regression.
method Online debiasing procedure for LASSO and other estimators.
result Optimal debiasing of LASSO estimator in specific sparsity regime.
Classifies collective motions in biological networks using graph dynamic mode decomposition.
problem Classifying complex collective motions in biological networks based on transient and complexly changing network properties.
method Data-driven spectral analysis (graph dynamic mode decomposition) to extract dynamical properties.
result Contextual node information and physical properties are crucial for classifying collective motions.
Recognizes collective sheep movement activities online.
problem Recognizing collective animal movement activities.
method Discriminative framework for tracking flock positions and velocities online.
result Good accuracy in learning skewed collective activities.
New algorithm for collective Gaussian hidden Markov models inference.
problem Inference of collective Gaussian hidden Markov models from aggregate data.
method Collective Gaussian forward-backward algorithm, extending Sinkhorn belief propagation.
result Convergence guarantee and applicability to single individual Kalman filter.
New algorithms reduce costly feature collection in bandits.
problem Costly feature collection in contextual bandits.
method Proposes algorithms avoiding unnecessary feature collection.
result Strong regret guarantees maintained with reduced feature collection.
We determine the extent to which the collection of -Euler-Satake characteristics classify closed 2-orbifolds. In particular, we show that the closed, connected, effective, orientable 2-orbifolds are classified by the collection of -Euler-Satake characteristics corresponding to free or free abelian and are not…
Adapting policy learning for data collected from evolving systems.
problem Challenges in learning optimal policies from adaptively collected data.
method Proposes an algorithm based on generalized augmented inverse propensity weighted (AIPW) estimators to control worst-case estimation variance.
result Achieves minimax rate optimal regret guarantees even with diminishing exploration.
Improved disability insurance model with collective health claims.
problem Enhance disability insurance model with collective health claims.
method Expand classic semi-Markov model with collective health claims, solve many-body problem using mean-field approach.
result Mean-field approach simplifies complex model into a transparent pricing method.