Infinite verbal width for certain groups like hyperbolic and mapping class groups.
problem Verbal width of acylindrically hyperbolic groups.
method Analyzing properties of acylindrically hyperbolic groups.
result Infinite verbal width for these groups.
New flag-no-square 4-manifolds discovered with unique triangulations.
problem Identifying 4-manifolds with specific triangulation properties.
method Introduced star-connected-sum operation to preserve flag-no-square property; derived new constructions.
result Found non-aspherical flag-no-square 4-manifolds, answering a question by Przytycki and Swiatkowski.
The paper proves rigidity for cocycles from higher rank lattices to Out(FN).
problem Proving rigidity for cocycles from higher rank lattices to Out(FN).
method Geometric tool: barycenter map.
result Every Borel cocycle is cohomologous to a cocycle with finite image.
We prove that the mapping torus group $\FN \rtimes_α \Z$ of any automorphism α of a free group $\FN$ of finite rank n≥2 is weakly hyperbolic relative to the canonical (up to conjugation) family H(α) of subgroups of $\FN$ which consists of (and contains representatives of all) conjugacy classes that …
Study uses ML to predict cancer patient mortality from FN onset.
problem Predicting mortality in cancer patients with FN to improve survival.
method Multi-domain machine learning models using HCUP data.
result Clinical diagnoses have highest predictive power for FN mortality.
We define lines of minima in the thick part of Outer space for the free group Fn with n>2 generators. We show that these lines of minima are contracting for the Lipschitz metric. Every fully irreducible outer automorphism of Fn defines such a line a minima. Now let G be a subgroup of the outer automorphism group of Fn …
The outer automorphism group Out(F_2g) of a free group on 2g generators naturally contains the mapping class group of a punctured surface as a subgroup. We define a subsurface projection of the sphere complex of the connected sum of n copies of S^1 x S^2 into the arc complex of the surface and use this to show that thi…
We relate ergodic-theoretic properties of a very small tree or lamination to the behavior of folding and unfolding paths in Outer space that approximate it, and we obtain a criterion for unique ergodicity in both cases. Our main result is that non-unique ergodicity gives rise to a transverse decomposition of the foldin…
We study very small trees from the point of view of reducing systems of free factors, which are analogues of reducing systems of curves for a surface lamination; a non-trivial, proper free factor $F \leq \FN$ reduces T if and only if F acts on some subtree of T with dense orbits. We characterize those trees, call…
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 …
A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general construction of many actions of groups on quasi-trees. The groups we can handle include non-elementary (relatively) hyperbolic groups, rank 1 CAT(0) groups, mapping class groups and Out(Fn). As an application, we show that mapping clas…
ESE-FN improves elderly activity recognition accuracy.
problem Recognizing individual actions and human-object interactions in elderly activities.
method Exploits multi-modal features from RGB videos and skeleton sequences using ESE attentions and a new Multi-modal Loss.
result ESE-FN achieves best accuracy on ETRI-Activity3D dataset.
Layer normalization improves federated learning with skewed labels.
problem Label skewness in federated learning datasets.
method Identified feature normalization as key mechanism; applied to latent features before classifier.
result Normalization accelerates global training and improves convergence under extreme label shift.
New optimization method improves AUC for binary classification and changepoint detection.
problem Non-convex AUC and sub-optimal points in ROC curves.
method AUM (Area Under Min(FP, FN)) surrogate loss function based on sorting and summing ROC curve points.
result AUM minimization learning algorithm improves AUC and speeds up compared to previous methods.
In this paper, we study local solutions F=(F1,..,Fn) of a general functional equation of the form F1(U1(x,y))+....+Fn(Un(x,y))=0. A such equation will be called an ``abelian functional equation'' (Afe). We will restrict ourselves to the case when the inner functions Ui's are real rational functions. First we prove that…
The paper studies deformations of submanifolds using a new algebraic structure.
problem Deformations of submanifolds in geometric contexts.
method Introduces strongly homotopy Lie algebras to govern deformations of submanifolds.
result Deformations of submanifolds form an analytic variety under certain assumptions.
We prove that a monomorphic functor F:Comp→Comp with finite supports is epimorphic, continuous, and its maximal ∅-modification F∘ preserves intersections. This implies that a monomorphic functor F:Comp→Comp of finite degree degF≤n preserves (finite-dimensional) compact ANR's if the spac…
It is known from work by H. Abels and P. Abramenko that for a classical Fq-group G of rank n the arithemetic lattice G(Fq[t]) of Fq[t]-rational points is of type Fn-1 provided that q is large enough. We show that the statement is true without any assumption on q and for any isotropic, absolutely almost simple group G d…
Enhances stability ranges for Torelli and congruence subgroup homologies.
problem Improving stability ranges for specific subgroup homologies.
method Analyzes H2(Torelli subgroup of Aut(Fn)'s), H2(Torelli subgroup of mapping class groups), and Hk(congruence subgroups of GL_n(R)'s).
result Improved central stability ranges for various subgroup homologies.
We extend the characterization of the integrability of an almost complex structure J on differentiable manifolds via the vanishing of the Frölicher-Nijenhuis bracket [J,J]FN to an analogous characterization of torsion-free G2-structures and torsion-free Spin(7)-structures. We also explain the Fernández-Gray…
Study of groups and their quasi-isometrically embedded subgroups.
problem Understanding the structure and properties of groups and their subgroups.
method Abstracting the notion of A/QI triples and using methods from geometric group theory.
result Stability of quasi-isometrically embedded subgroups in finitely generated groups.
We propose a hierarchy for approximate inference based on the Dobrushin, Lanford, Ruelle (DLR) equations. This hierarchy includes existing algorithms, such as belief propagation, and also motivates novel algorithms such as factorized neighbors (FN) algorithms and variants of mean field (MF) algorithms. In particular, w…
Study geometric properties and spectral estimates on warped products.
problem Investigate Ricci curvature and spectral estimates in warped products.
method Establish integral inequalities and sufficient conditions for geometric properties.
result Sufficient conditions for intersection of warped products with totally geodesic hypersurfaces.
FinCausal 2020 task detects financial document causality.
problem Detect causal relationships in financial documents.
method Binary classification and relation extraction tasks.
result 16 teams participated, 13 submitted system descriptions.
We start by studying the distribution of (cyclically reduced) elements of the free groups Fn with respect to their abelianization (or equivalently, their integer homology class. We derive an explicit generating function, and a limiting distribution, by means of certain results (of independent interest) on Chebyshev pol…
This is the first in a series of papers studying w-knotted objects (w-knots, w-braids, w-tangles, etc.), which make a class of knotted objects which is {w}ider but {w}eaker than their usual counterparts. The group of w-braids was studied (as "{w}elded braids") by Fenn-Rimanyi-Rourke and was shown to be isomorphic to th…
Lectures detail field theory dynamics and exact WKB analysis.
problem Understanding quantum field theories with four supercharges.
method Combining WKB analysis with 2D quantum field theories.
result Partition function characterizes non-perturbative dynamics.
Smart Close-out Netting aims to automate close-out netting processes.
problem Inefficiencies in close-out netting processes for financial institutions.
method Standardisation and automation of legal and regulatory processes using a data-driven framework and controlled natural language.
result Standardisation and automation can improve close-out netting processes for prudentially regulated financial institutions.
Quasi-geodesics in Out(F_n) are not always geodesics, with backtracking in free factors.
problem Characterizing quasi-geodesics in Out(F_n) and their properties.
method Analysis of various paths in Out(F_n) and construction of counterexamples.
result Quasi-geodesics in Out(F_n) can backtrack in free factors, unlike in mapping class groups.
Out(FN) is boundary amenable, solving related conjectures.
problem Proving boundary amenability of Out(FN) and related groups. method Analyzing properties of Out(FN) and related groups. result Out(FN) and related groups are boundary amenable, satisfying Novikov conjecture. Optimizes Lasso hyperparameters using leave-one-out CV.
problem Finding optimal hyperparameters for Lasso regression.
method Develops an algorithm to compute exact or approximate leave-one-out CV.
result Algorithm finds optimal hyperparameters for Lasso.
We show that there is no uniform upper bound on |Out(Aut(A))| when A ranges over all right-angled Artin groups. This is in contrast with the cases where A is free or free abelian: for all n, Dyer-Formanek and Bridson-Vogtmann showed that Out(Aut(F_n)) = 1, while Hua-Reiner showed |Out(Aut(Z^n)| = |Out(GL(n,Z))| < 5. We…
Train track automata for fully irreducible elements in Out(F_r).
problem Understanding fully irreducible elements in Out(F_r).
method Describing train track automata and geodesics in Outer Space.
result Geodesics in Culler-Vogtmann Outer Space for fully irreducible elements.
Agghoo averages hold-out learning rules for theoretical and practical risk minimization.
problem Theoretical and practical risk minimization for various learning problems.
method Averaging hold-out learning rules.
result Agghoo performs at worst like hold-out for convex risks and classification with 0-1 risk.
Simple methods combine statistical tests for out-of-distribution detection.
problem Detecting data points not following the training distribution.
method Combining classical parametric tests (Rao's score test) and a typicality test.
result Combining Fisher's method of test statistics improves out-of-distribution detection accuracy.
New theorem on subgroup dynamics of Out(F_N).
problem Understanding subgroups of Out(F_N).
method Analogous to Ivanov's and Handel-Mosher's theorems.
result Subgroups either contain atoroidal elements or fix conjugacy classes.
The paper proposes a method to improve neural network confidence for out-of-distribution detection.
problem Improving neural networks' ability to recognize when predictions are incorrect.
method A method of learning confidence estimates for neural networks that produces interpretable outputs.
result The proposed method outperforms existing techniques in out-of-distribution detection.
Generates confident out-of-distribution samples to improve classifier robustness.
problem Overconfidence in deep learning models on out-of-distribution inputs.
method Uses a GAN to generate out-of-distribution samples that the classifier is confident on, maximizing entropy.
result Shows effectiveness on handwritten characters and natural images datasets.
A companion result of the the Tits alternative for Out(Fn) is proved: Every solvable subgroup of Out(Fn) is finitely generated and virtually abelian.
Torelli subgroup rigidity in Out(F_N) proven for N≥4.
problem Proving rigidity of Torelli subgroup in Out(F_N).
method Injective homomorphisms and conjugation analysis.
result Every injective homomorphism from Torelli subgroup to Out(F_N) is conjugate to inclusion.
Method enhances anomaly detection using contrastive learning and out-of-distribution data.
problem Improving anomaly detection in datasets with limited out-of-distribution data.
method Proposes a contrastive learning method that incorporates out-of-distribution data to enhance anomaly detection performance.
result The method significantly improves anomaly detection performance, even with limited out-of-distribution data.
New proof confirms subgroup commensurators for N≥3.
problem Understanding commensurators of subgroups of Out(F_N).
method New proof of Farb-Handel theorem, generalizations, sufficient conditions.
result Abstract commensurators of certain subgroups are isomorphic to Out(F_N).
The study revisits inaccuracies in time series averaging under dynamic time warping.
problem Inaccuracies in time series averaging under dynamic time warping.
method Analysis of existing correctness-criterion and introduction of drift-outs, showing their insufficiency and inconclusiveness.
result Sample means as global minimizers of a Fréchet function never drift out, and the adjusted drift-out is a test for coherence.
Adapts GAN-based robustness training to live traffic data.
problem Improving classifier robustness to out-of-distribution samples in real-world traffic.
method Adaptive regularization technique based on maximum predictive probability score.
result Significantly improved detection of out-of-distribution samples without degrading in-distribution performance.
New framework infers causal shifts in event sequences under out-of-domain interventions.
problem Inferring causal relationships in event sequences without considering out-of-domain interventions.
method Proposes a new causal framework to define ATE, designs an unbiased ATE estimator, and uses a Transformer-based neural network model.
result Demonstrates superior performance in ATE estimation and goodness-of-fit under out-of-domain-augmented point processes.
FRODO method rejects out-of-distribution chest x-ray images with high accuracy.
problem Rejecting out-of-distribution samples in medical image analysis.
method Uses feature activations and Mahalanobis distance to measure distribution mismatch.
result Achieves an AUC score of 0.99 in classifying chest x-ray images as in or out of distribution.
Free group automorphisms group rigidity proven.
problem Proving rigidity of Out(F_N).
method Measure equivalence rigidity, new canonical splittings.
result Superrigidity of Out(F_N).
The paper proves limit theorems for graph embeddings out-of-sample.
problem Proving limit theorems for graph embeddings out-of-sample.
method Least-squares and maximum-likelihood objectives for adjacency and Laplacian spectral embeddings.
result Out-of-sample extensions based on these objectives obey central limit theorems and concentration inequalities.