Study on homological Dehn functions of groups of type FP2.
problem Understanding the homological Dehn functions of groups of type FP2. method Proved foundational results, studied homological Dehn functions of Leary's groups, and provided methods to obtain groups with specific homological Dehn functions.
result Found groups of type FP2 with quartic homological Dehn function and unsolvable word problem. Paper explores hyperbolic groups with unique subgroup properties.
problem Creating examples of hyperbolic groups with specific subgroup finiteness properties.
method Develops new examples of subgroups of hyperbolic groups with various finiteness properties.
result Uncountably many groups of type FP2 with similar properties to subgroups of hyperbolic groups. New research shows uncountably many quasi-isometry classes of groups of type FP.
problem Identifying distinct quasi-isometry classes of groups of type FP. method Constructing uncountable families of groups and proving quasi-isometry classes.
result Uncountably many quasi-isometry classes of groups of type FP. We construct uncountably many discrete groups of type FP; in particular we construct groups of type FP that do not embed in any finitely presented group. We compute the ordinary, ℓ2- and compactly-supported cohomology of these groups. For each n≥4 we construct a closed aspherical n-manifold that admit…
Formanek and Procesi have demonstrated that Aut(F_n) is not linear for n >2. Their technique is to construct nonlinear groups of a special form, which we call FP-groups, and then to embed a special type of automorphism group, which we call a poison group, in Aut(F_n), from which they build an FP-group. We first prove t…
We determine when an arithmetic subgroup of a reductive group defined over a global function field is of type FP_\infty by comparing its large-scale geometry to the large-scale geometry of lattices in real semisimple Lie groups.
If S is a subgroup of a direct product of two limit groups, and S is of type FP(2) over the rationals, then S has a subgroup of finite index that is a direct product of at most two limit groups.
We study the asymptotic growth of homology groups and the cellular volume of classifying spaces as one passes to normal subgroups Gn<G of increasing finite index in a fixed finitely generated group G, assuming ⋂nGn=1. We focus in particular on finitely presented residually free groups, calculating thei…
If G1,...,Gn are limit groups and S⊂G1×...×Gn is of type $\FP_n(\mathbb Q)$ then S contains a subgroup of finite index that is itself a direct product of at most n limit groups. This settles a question of Sela.
Hougthon's groups H_n is a family of groups where each H_n consists of `translations at infinity' on n rays of discrete points emanating from the origin on the plane. Brown shows H_n has type FP_n-1 but not FP_n by constructing infinite dimensional cell complex on which H_n acts with certain conditions. We modify his i…
We introduce the class of perturbed right-angled Artin groups. These are constructed by gluing Bieri double groups into standard right-angled Artin groups. As a first application of this construction we obtain families of CAT(0) groups containing finitely presented subgroups which are not of type FP3, and h…
Not finitely presented group from CAT(0) cube complexes.
problem Identifying finitely presented groups.
method Developing techniques for proving non-simple connectedness of subcomplexes of CAT(0) cube complexes.
result Basilica Thompson group is not finitely presented.
The study generalizes cohomology results for hyperbolic groups.
problem Understanding cohomology of hyperbolic groups and their subgroups.
method Generalizing Gersten's theorem on ℓ∞-cohomology and applying it to hyperbolic groups. result Obtained hyperbolicity criteria for specific groups.
We exploit Zlil Sela's description of the structure of groups having the same elementary theory as free groups: they and their finitely generated subgroups form a prescribed subclass E of the hyperbolic limit groups. We prove that if G1,...,Gn are in E then a subgroup Γ⊂G1×...×Gn is of type $\…
L-CNNs approximate gauge actions, revealing fixed points with no lattice artifacts.
problem Approximating gauge actions with lattice artifacts.
method Lattice gauge-equivariant convolutional neural networks (L-CNNs).
result L-CNNs provide fixed point actions with no lattice artifacts.
The paper classifies PD_4-complexes based on their fundamental group properties.
problem Understanding the structure of PD_4-complexes based on their fundamental group properties.
method Analyzing the fundamental group and its modules to classify PD_4-complexes.
result The classification of PD_4-complexes based on their fundamental group properties.
Study presentations of groups that can be generalised over continuous open group monomorphisms.
problem Investigate presentations of groups that can be generalised over continuous open group monomorphisms.
method Systematic study of presentations with generalisation properties, focusing on right-angled Artin groups (RAAGs).
result Establish high connectivity properties for universal Salvetti-type complexes and novel examples of LC groups with prescribed compactness properties.
Let G be a Chevalley group scheme and B<=G a Borel subgroup scheme, both defined over Z. Let K be a global function field, S be a finite non-empty set of places over K, and O_S be the corresponding S-arithmetic ring. Then, the S-arithmetic group B(O_S) is of type F_{|S|-1} but not of type FP_{|S|}. Moreover one can der…
Surface Houghton groups are studied for their mapping class properties.
problem Understanding the mapping class properties of surface Houghton groups.
method Analyzing the asymptotic rigidity and monodromy homeomorphisms of fibered components.
result Surface Houghton groups are of type Fn−1 but not of type FPn. Develops a neural network approach to solve inverse stochastic problems from particle observations.
problem Inference of Fokker-Planck equation coefficients from sparse particle data.
method Physics-informed neural networks (PINNs) with Kullback-Leibler divergence loss.
result Simultaneous inference of Fokker-Planck equation and multi-dimensional PDF from few particle observations.
The study of PD3-pairs extends results for aspherical 3-manifolds.
problem Understanding PD3-pairs with aspherical ambient spaces. method Attaching 1-handles to PD3-pairs with aspherical ambient space and π1-injective boundary. result There are only finitely many PD3-pairs with a specific group property. Study of fixed points in large networks with random dependencies.
problem Systemic risk in large financial networks.
method Analysis of vector fixed point equations on random graphs, obtaining finite dimensional limits.
result Approximate solutions to random FP equations for large networks.
We study discrete group actions on coarse Poincare duality spaces, e.g. acyclic simplicial complexes which admit free cocompact group actions by Poincare duality groups. When G is an (n-1) dimensional duality group and X is a coarse Poincare duality space of formal dimension n, then a free simplicial action of G on X d…
This paper classifies quadratic form parameters over integers and computes their Witt groups.
problem Classifying quadratic form parameters over integers and computing their Witt groups.
method Study of quadratic forms and extended quadratic forms over the integers, defining and comparing different definitions of extended quadratic forms.
result Classification of all quadratic form parameters over the integers and computation of their Witt groups.
The paper defines a new condition for Finsler spaces and finds examples of spaces satisfying it.
problem Finding homogeneous Finsler spaces with specific curvature properties.
method Introducing the flag-wise positively curved condition, using Killing navigation, and developing new techniques.
result Most compact coset spaces cannot be endowed with positively curved homogeneous Finsler metrics, but some do satisfy the flag-wise positively curved condition.
New findings on group actions and stabilizers of infinite sets.
problem Understanding finiteness properties of stabilizers in group actions.
method Analyzing oligomorphic actions and permutational wreath products.
result Existence of finite subsets with non-FP∞ stabilizers. FP uses random projections to train networks without feedback, achieving comparable performance to backpropagation.
problem Training neural networks without feedback from downstream layers.
method Forward Projection (FP) method that uses randomised nonlinear projections and closed-form regression.
result FP achieves comparable generalisation to backpropagation methods with a single forward pass, offering significant speedup.
GGFPS improves model performance by sampling molecules more efficiently.
problem Improving model performance and reducing data costs in chemistry problems.
method Gradient-Guided Furthest Point Sampling (GGFPS) that leverages molecular force norms.
result GGFPS leads to superior data efficiency and model robustness compared to other sampling methods.
The study examines geodesic orbit Finsler spaces with non-negative flag curvature and (FP) condition, proving they are compact.
problem Characterizing geodesic orbit Finsler spaces with specific curvature conditions.
method Analyzes the interaction between geodesic orbit property and flag curvature conditions.
result Compactness of geodesic orbit Finsler spaces with non-negative flag curvature and (FP) condition.
The study shows higher incoherence in automorphism groups of free groups.
problem Understanding the finiteness properties of automorphism groups of free groups.
method Analyzing extensions of a finite-index subgroup of Aut(F_2) and using fiber maps.
result Upper bounds on the coherence of automorphism groups of free groups.
Model uses HS-FP framework for South African asset allocation.
problem Develops a flexible non-parametric asset allocation model for South African markets.
method Historical Simulation with Flexible Probabilities (HS-FP) framework, using relative entropy for distribution estimation.
result HS-FP model outperforms classic MVO and EW benchmarks in out-of-sample performance.
FP-UCB algorithm achieves bounded regret for finitely parameterized multi-armed bandits.
problem Finitely parameterized multi-armed bandits with unknown but known parameter set.
method FP-UCB algorithm using structural information about the parameter set.
result FP-UCB achieves bounded regret under structural condition, logarithmic otherwise.
New method improves feature selection by integrating stability paths.
problem Improving feature selection with tighter false positive control.
method Integrating stability paths to strengthen theoretical bounds on E(FP).
result Significantly more true positives with same E(FP) control.
Efficient algorithm for sparse PCA reduces data complexity.
problem Sparse PCA for high-dimensional data with non-convex optimization issues.
method Convex FPS formulation, gradient-based optimization, online learning extension.
result Explicit bounds on optimization error and statistical accuracy.
Scalable subspace clustering for high-dimensional data.
problem Finding clusters in non-disjoint subspaces and scaling to large data.
method Bottom-up strategy using FP-trees for frequent pattern mining.
result The proposed algorithm produces clusters with high accuracy and scales well to large data.
Paper analyzes Winograd convolution errors and proposes methods to reduce them.
problem Reduction of floating point error in Winograd convolution for deep neural networks.
method Analysis of worst case FP error, estimation of norm and conditioning, proposed evaluation orderings, sampling points selection, mixed-precision convolution, pairwise summation.
result Proposed methods significantly reduce FP error for a given block size, allowing larger block sizes and reduced computation.
New method learns diffusion transition density for Bayesian inference.
problem Bayesian inference on diffusions with inaccessible boundaries.
method Neural Galerkin framework to solve FP equation with Dirac mass.
result Approximates likelihood function for efficient posterior sampling.
The paper studies fibering properties of RACGs and random subcomplexes of buildings.
problem Higher virtual algebraic fibering properties of right-angled Coxeter groups.
method Generalization of Bestvina-Brady discrete Morse theory applied to Davis complex, combined with probabilistic arguments.
result Commutator subgroups of RACGs with certain finite building flag complexes admit epimorphisms to Z with strong topological finiteness properties.
A remarkable result of Gersten states that the class of hyperbolic groups of cohomological dimension 2 is closed under taking finitely presented (or more generally FP2) subgroups. We prove the analogous result for relatively hyperbolic groups of Bredon cohomological dimension 2 with respect to the family of para…
New activation networks improve model efficiency and performance.
problem Creating hardware-efficient deep learning models.
method Restructurable Activation Networks (RANs) with RAN-explicit and RAN-implicit methods.
result RANs achieve state-of-the-art results with improved hardware efficiency.
GAN-FP uses GANs to predict equipment failures from imbalanced data.
problem Accurately predicting equipment failures with limited data and high imbalance.
method GAN-FP employs two GAN networks to generate and classify imbalanced data, optimizing a weighted loss objective and a consistency GAN.
result GAN-FP outperforms traditional methods in imbalanced failure prediction.
New work shows FP potential monotonicity equals low-degree polynomial estimators limits.
problem Establishing a precise mathematical relationship between statistical physics and polynomial estimators limits.
method Analyzing Gaussian additive models (GAMs) to show FP potential monotonicity equals low-degree polynomial estimators limits.
result For a broad family of Gaussian additive models, the power of low-degree polynomials is equivalent to the monotonicity of the annealed FP potential.
New findings suggest weight maps from classifiers may not reliably indicate neural signals.
problem The reliability of interpreting weight maps from classifiers in neuroimaging studies.
method Used semi-simulated ECoG data to investigate signal-to-noise ratio and sparsity effects.
result Not all cases produce false positives and high-weight features are unlikely to be FP.
New invariant computed for Brieskorn homology spheres.
problem Computing an invariant for specific manifolds.
method Using Dijkgraaf--Witten invariants in topological K-theory.
result Computed invariant for Brieskorn homology spheres.
AI agent plays CSGO deathmatch with human-like style.
problem Lack of API for CSGO limits data for reinforcement learning.
method Behavioural cloning on large noisy and expert datasets.
result Matches human difficulty level in deathmatch mode.
This paper extends FP's method to complex hyperbolic branched covers to find Einstein metrics.
problem Finding Einstein metrics on non-locally symmetric manifolds.
method Generalized FP's construction to complex hyperbolic branched covers.
result Yields a negatively curved Einstein metric that asymptotically approaches GH's metric.
The presence of a sparse "truth" has been a constant assumption in the theoretical analysis of sparse PCA and is often implicit in its methodological development. This naturally raises questions about the properties of sparse PCA methods and how they depend on the assumption of sparsity. Under what conditions can the r…
In this paper we study the problem of approximation of the L2-topological invariants by their finite dimensional analogues. We obtain generalizations of the theorem of Lück, dealing with towers of finitely sheeted normal coverings. We prove approximation theorems, establishing relations between the homological invar…