Proposes Causal k-Means Clustering to identify subgroup effects.
problem Identifying subgroup effects with heterogeneous treatment effects.
method Leverages k-means clustering to uncover unknown subgroup structure.
result Developed bias-corrected estimator with fast root-n rates and asymptotic normality.
Expands causal clustering framework with hierarchical and density-based methods.
problem Identifying heterogeneous treatment effects in unknown subgroup structure.
method Integrates hierarchical and density-based clustering algorithms into causal k-means clustering.
result Plug-in estimators for causal clustering are simple and readily implementable.
Improved linear regression for diverse data batches.
problem Learning from multiple heterogeneous data sources.
method Gradient-based algorithm for different input distributions.
result Significant reduction in the number of required batches and sample size.
ROME improves algorithmic fairness by learning latent group structure robustly.
problem Latent subgroup disparities and distribution shifts in machine learning models.
method ROME uses an Expectation-Maximization algorithm for linear models and a neural Mixture-of-Experts for nonlinear settings.
result ROME significantly improves fairness compared to standard methods while maintaining average performance.
Cluster analysis is an unsupervised learning strategy that can be employed to identify subgroups of observations in data sets of unknown structure. This strategy is particularly useful for analyzing high-dimensional data such as microarray gene expression data. Many clustering methods are available, but it is challengi…
Class I CR manifolds have initial G-structure a certain 4-dimensional subgroup of GL_3(C). Class II CR manifolds have initial G-structure a certain 10-dimensional subgroup of GL_4(C). Class III-1 CR manifolds have initial G-structure a certain 10-dimensional subgroup of GL_5(C). Class III-2 CR manifolds have initial G-…
Study of Hermitian structures on Lie groups with 2D commutator subgroups.
problem Classifying Hermitian structures on Lie groups with specific commutator subgroups.
method Explicit classification of Type I and Type II structures, computation of Bismut connections, and examples of Kahler structures.
result Classification of Kahler structures within Type I and Type II structures.
Completes results on complex braid group parabolic subgroups.
problem Proves properties of complex braid group parabolic subgroups.
method Uses Garside groupoid structure of B(G31) to extend results.
result Proves main theorems for B(G31) parabolic subgroups.
We describe classes of potential structures (covector fields) on Minkowski space that admit subgroups of the Poincaré group. We describe also seven classes of Maxwell spaces that admit subgroups of the Poincaré group.
Exponential growth of stable subgroups in Morse geodesics.
problem Growth rates of stable subgroups in complex groups.
method Theory of automatic structures on Morse geodesics.
result Exponential growth of stable subgroups is faster than their infinite index stable subgroups.
New combinatorial structures represent subgroups of surface groups, analogous to Stallings core graphs.
problem Representing subgroups of surface groups in a combinatorial way.
method Introducing core surfaces as 2-dimensional complexes made up of vertices, labeled edges, and 4g-gons.
result Core surfaces are compact when corresponding subgroups are finitely generated.
GAME improves matrix completion by considering subgroup-specific latent structures.
problem Heterogeneous data with overlapping categories, smoothing away subgroup-specific variation.
method Group-Aware Matrix Estimation (GAME) with overlapping nuclear-norm penalties.
result GAME outperforms global low-rank estimators in structured missingness regimes.
A new method improves AI fairness assessment by estimating performance across intersectional subgroups.
problem Limited evaluation of AI systems across intersectional subgroups due to small sample sizes.
method Structured regression approach to disaggregated evaluation.
result Our method yields more accurate performance estimates, especially for small subgroups.
We construct propose an anzatz for Spin(7) metrics as an R-bundle over closed G2 structures. These G2 structures are R3 bundles over 4-dimensional compact quaternion Kahler spaces. The inspiration for the anzatz metric comes from the Bryant-Salamon construction of G2 holonomy metrics and from the fact that the twistor …
The paper studies cohomologies of hypercomplex manifolds and their dimensions.
problem Understanding cohomologies and dimensions of invariant and anti-invariant subgroups.
method Proving a compact hypercomplex manifold is C∞-pure-and-full under certain conditions and studying dimensions of subgroups. result Characterization of hyperkähler with torsion metrics in terms of the dimension of the Jˉ-invariant subgroup. Unified algebraic framework for virtual braid structures with strong structural consequences.
problem Unified algebraic framework for virtual braid structures with various types of crossings.
method Introducing the universal virtual braid group UVn(c) and proving its properties. result Strong structural consequences including residual finiteness, linearity, and solvability of conjugacy problems.
New proof and description of commutator subgroups for free and surface groups.
problem Understanding commutator subgroups of free and surface groups.
method Geometric proof and representation-theoretic description.
result New free generating sets and structure descriptions for commutator subgroups.
Study C-Fuchsian subgroups of non-arithmetic lattices.
problem Understand structure and fundamental domains of C-Fuchsian subgroups. method General procedure to analyze structure and show fundamental domains lie on a complex geodesic.
result Fundamental domains of C-Fuchsian subgroups lie on a complex geodesic homeomorphic to the unit disk. The study classifies normal subgroups of mapping class groups of surfaces with Cantor subsets.
problem Understanding the structure of normal subgroups in mapping class groups of surfaces with specific subsets.
method Proves two structure theorems: purity and inertia, characterizing normal subgroups.
result Characterizes finite-type normal subgroups of mapping class groups of surfaces with Cantor subsets.
Suppose that all hyperbolic groups are residually finite. The following statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generated nilpotent subgroups, quasiconvex subgroups are separable; Geometrically finite subgroups of non-uniform lattices in rank one symmetric sp…
Proves finite measure implies product structure for certain discrete subgroups.
problem Classifying discrete subgroups with finite Bowen-Margulis-Sullivan measure.
method Product structure of leafwise measures and high entropy method.
result Proves virtually a product structure for certain subgroups.
No exact G₂-structures on compact Lie group quotients.
problem Existence of exact G₂-structures on compact quotients of Lie groups.
method Analyzing compact quotients of seven-dimensional Lie groups by co-compact discrete subgroups.
result Compact quotients of seven-dimensional Lie groups by co-compact discrete subgroups do not admit exact G₂-structures induced by left-invariant ones.
A square complex is a 2-complex formed by gluing squares together. This article is concerned with the fundamental group Γ of certain square complexes of nonpositive curvature, related to quaternion algebras. The abelian subgroup structure of Γ is studied in some detail.
Proposes a method to identify subgroup structure and estimate covariate effects for multivariate response data.
problem Identifying subgroup structure and estimating covariate effects in multivariate response data.
method Joint heterogeneity and reduced-rank learning framework using rank-constrained pairwise fusion penalization.
result Established the asymptotic properties of the estimators and proposed a predictive information criterion for rank selection.
Contact group retracts to unitary subgroup.
problem Understanding contact structures on 3-sphere.
method Proving deformation retraction to unitary subgroup.
result Group of contactomorphisms retracts to U(2).
Groups with specific properties have similar cubulations and coarse median structures.
problem Understanding the structure of certain groups through cubical coarsening.
method Analyzing right-angled Artin and Coxeter groups, focusing on automorphisms and cubulations.
result Automorphisms of specific groups preserve coarse median structures and have nice fixed subgroups.
For a compact almost complex 4-manifold (M,J), we study the subgroups HJ± of H2(M,R) consisting of cohomology classes representable by J-invariant, respectively, J-anti-invariant 2-forms. If b+=1, we show that for generic almost complex structures on M, the subgroup HJ− is trivial. …
Study of modular representations in homology of congruence subgroups.
problem Understanding modular representations in homology of congruence subgroups.
method Analysis of sequences of modular representations of symplectic and special linear groups over finite fields.
result Established periodic representation stability in the sense of Church--Farb.
Characterizes isolated compact subgroups in Lie groups.
problem Identifying isolated compact subgroups in Lie groups.
method Characterization based on intrinsic structure, irrelevant ambient group details.
result Characterization of isolated compact subgroups depends only on intrinsic structure.
A new GP framework for discovering unknown functions and hypergraph structure.
problem Discovering unknown functions and hypergraph structure in data.
method Interpretable Gaussian Process framework for Type 3 problems.
result Polynomial complexity for data-driven discovery of unknown functions and hypergraph structure.
Constructs flows on quotients of Lie groups for Anosov subgroups.
problem Understanding dynamics on quotients of Lie groups by Anosov subgroups.
method Utilizes geometric structures and Lie group theory to construct and analyze flows.
result Establishes that all refraction flows arise from this construction.
Inpatient care is a large share of total health care spending, making analysis of inpatient utilization patterns an important part of understanding what drives health care spending growth. Common features of inpatient utilization measures include zero inflation, over-dispersion, and skewness, all of which complicate st…
We develop the structure theory of full isometry groups of locally compact non-positively curved metric spaces. Amongst the discussed themes are de Rham decompositions, normal subgroup structure and characterising properties of symmetric spaces and Bruhat--Tits buildings. Applications to discrete groups and further dev…
BaCaDI discovers causal structures from unknown interventions.
problem Inferring causal structures from unknown interventions with limited data.
method Bayesian framework with gradient-based variational inference.
result BaCaDI outperforms related methods in identifying causal structures and intervention targets.
We develop a new criterion to tell if a group G has the maximal gap of 1/2 in stable commutator length (scl). For amalgamated free products G=A⋆CB we show that every element g in the commutator subgroup of G which does not conjugate into A or B satisfies scl(g)≥1/2, provided that C embed…
Proposes a tool to contrast global vs personalized models in clinical prediction.
problem Balancing global vs personalized models in clinical prediction.
method Localized regression approach using autoencoder for dimension reduction.
result Identification of patient subgroups where global models fall short.
Mahan Mitra (Mj) proved Cannon--Thurston maps exist for normal hyperbolic subgroups of a hyperbolic group. We prove that Cannon--Thurston maps do not exist for infinite normal hyperbolic subgroups of non-hyperbolic CAT(0) groups with isolated flats with respect to the visual boundaries. We also show Cannon--Thurston ma…
Study on subgroups' evolution in 3D Lie groups using mean curvature flow.
problem Existence of solutions to Mean Curvature Flow for 2D Lie subgroups in 3D Lie groups.
method Investigation of Lie groups with fixed left-invariant metrics, focusing on non-unimodular cases.
result Evolution of Lie subgroups is self-similar for abelian subgroups, but not for others.
Sparse GFA identifies disease factors in FTD subgroups.
problem Heterogeneity in neurological disorders hinders understanding and treatment.
method Sparse Group Factor Analysis (GFA) with regularised horseshoe priors.
result Identified latent disease factors differentially expressed in FTD subgroups.
The study explores congruence subgroups of braid groups and their quotients.
problem Understanding the structure of congruence subgroups of braid groups.
method Utilizing the integral Burau representation and results from integral matrices, the study examines quotients of these subgroups.
result Findings of quotients that are not isomorphic to symmetric groups.
Let K be a compact semi-simple Lie group. We classify K-invariant Kaehler structures on the space Kc/(P,P), where Kc is the complexification of K, P is a parabolic subgroup of Kc, and (P,P) the commutator subgroup. For each Kaehler structure, we study its moment map and associated pre-quantum line bundle for geometric …
Reduces field theories on principal bundles by a subgroup, deriving reduced equations.
problem Hamiltonian field theories on principal G-bundles with invariant densities.
method Lie-Poisson reduction using covariant bracket formulation.
result Derives reduced observables, brackets, and equations of motion for field theories.
New symmetric quandles constructed from group elements and subgroups.
problem Understanding the structure of symmetric quandles.
method Constructing symmetric quandles from specific group elements and subgroups.
result Every symmetric quandle is isomorphic to the disjoint union of constructed quandles.
The study examines discrete subgroups of PSL2 over non-archimedean fields.
problem Conditions for discrete subgroups of PSL2 over non-archimedean fields.
method Structure theorem for two-generator groups acting by isometries on a Λ-tree, practical algorithms.
result Necessary and sufficient conditions for discrete subgroups of PSL2 over non-archimedean fields.
We show that two knots have matching Vassiliev invariants of order less than n if and only if they are equivalent modulo the nth group of the lower central series of some pure braid group, thus characterizing Vassiliev's knot invariants in terms of the structure of the braid groups. We also prove some results about kno…
We partially describe equivariant Dirac and generalized complex structures on a homogeneous space G/K by giving equivalent data involving only the Lie algebra. We consider real semisimple adjoint orbits in any semisimple Lie algebra over R and real nilpotent orbits in sln(R). We give a complete …
The paper studies nilpotent structures in oriented neutral vector bundles and neutral hyperKähler structures.
problem Nilpotent structures in oriented neutral vector bundles and their relation to neutral hyperKähler structures.
method Defined H-nilpotent structures for Lie subgroups of SO(2n,2n) related to neutral hyperKähler structures. result Existence of complex and paracomplex structures forming neutral hyperKähler structures if and only if there exists an H-nilpotent structure. Study ramification in knot groups through finite covers and their quotients.
problem Understanding ramification in knot groups and their covers.
method Formalized ramification theory for knot groups, analyzed through finite quotients, profinite completions, and cohomology.
result Characterized ramification and inertia subgroups in knot groups and their covers.