We obtain a combinatorial formula for the Miller-Morita-Mumford classes for the mapping class group of punctured surfaces and prove Witten's conjecture that they are proportional to the dual to the Witten cycles. The proportionality constant is shown to be exactly as conjectured by Arbarello and Cornalba [J. Alg. Geom.…
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48 results for “Miller--Morita--Mumford classes”
Study K3 manifold bundles proving Miller--Morita--Mumford classes non-zero.
problem Proving non-zero characteristic classes for K3 manifold bundles.
method Two methods: Franke's stable cohomology result and Miller--Morita--Mumford classes.
result Proves non-zero characteristic classes for certain bundles.
Kappa classes on KSBA spacesmath.AG
Defines kappa classes on KSBA spaces, generalizing classes on curves.
problem Generalizing Miller-Morita-Mumford classes to KSBA stable varieties and pairs.
method Defining kappa classes on KSBA moduli spaces and computing them in specific cases.
result Computed kappa classes on Campedelli surfaces, including finding the Chow ring of a specific GIT quotient.
We prove vanishing results for the generalized Miller-Morita-Mumford classes of some smooth bundles whose fiber is a closed manifold that supports a nonpositively curved Riemannian metric. We also find, under some extra conditions, that the vertical tangent bundle is topologically rigid.
Tautological classes, or generalised Miller-Morita-Mumford classes, are basic characteristic classes of smooth fibre bundles, and have recently been used to describe the rational cohomology of classifying spaces of diffeomorphism groups for several types of manifolds. We show that rationally tautological classes depend…
Study characteristic classes for manifold bundles, focusing on fiber families.
problem Understanding characteristic classes for families of bundles.
method Construction of relative Sullivan models and explicit cocycle representatives for characteristic classes.
result Tools for computing the rational cohomology ring of and subring of generalized Miller-Morita-Mumford classes.
Using certain Thom spectra appearing in the study of cobordism categories, we show that the odd half of the Miller-Morita-Mumford classes on the mappping class group of a surface with negative Euler characteristic vanish in integral cohomology when restricted to the handlebody subgroup. This is a special case of a more…
This paper attempts to investigate the space of various characteristic classes for smooth manifold bundles with local system on the total space inducing a finite holonomy covering. These classes are known as twisted higher torsion classes. We will give a system of axioms that we require these cohomology classes to sati…
New configuration space integrals show nontrivial formal smooth structures on 4-manifold bundles.
problem Disproving the 4-dimensional Smale conjecture by constructing nontrivial bundles.
method Defining new configuration space integrals relying on formal smooth structures.
result Discovering a generalized Miller-Morita-Mumford class obstructing formal smooth structures.
Diagonalizes tautological classes of definite 4-manifolds.
problem Diagonalizing tautological classes of definite 4-manifolds.
method Families version of Bauer-Furuta cohomotopy refinement of Seiberg-Witten theory.
result Completely determined tautological rings of and .
Characteristic classes of oriented vector bundles can be identified with cohomology classes of the disjoint union of classifying spaces BSO_n of special orthogonal groups SO_n with n=0,1,... A characteristic class is stable if it extends to a cohomology class of a homotopy colimit BSO of classifying spaces BSO_n. Simil…
We study smooth bundles over surfaces with highly connected almost parallelizable fiber of even dimension, providing necessary conditions for a manifold to be bordant to the total space of such a bundle and showing that, in most cases, these conditions are also sufficient. Using this, we determine the characteristi…
We revisit three results due to Morita expressing certain natural integral cohomology classes on the universal family of Riemann surfaces C_g, coming from the parallel symplectic form on the universal jacobian, in terms of the Miller-Morita-Mumford classes e and e_1. Our discussion will be on the level of the natural 2…
A singular point of a smooth map F: M -> N of manifolds is a point in M at which the rank of the differential dF is less than the minimum of dimensions of M and N. The classical invariant of the set S of singular points of F of a given type is defined by taking the fundamental class [\bar{S}]\in H_*(M) of the closure o…
Torelli groups' homology is finitely generated in stable range.
problem Whether the homology groups of Torelli subgroups are finitely generated in stable range.
method Using unipotency condition and Tavgen's theorem.
result Homology groups are finitely generated in stable range.
Classifies manifolds with dense conjugacy classes in their mapping class groups.
problem Classifying manifolds based on conjugacy classes in their mapping class groups.
method Analyzing connected orientable 2-manifolds and their mapping class groups.
result Mapping class groups of certain manifolds have dense conjugacy classes.
Generic pseudo-Anosov mapping classes in mapping class groups.
problem Understanding the prevalence of pseudo-Anosov mapping classes.
method Proving genericity with respect to specific notions of genericity.
result Pseudo-Anosov mapping classes are generic in mapping class groups.
This paper tackles worst-class error rate in classification tasks.
problem Minimizing worst-class error rate in classification tasks, especially in medical image classification.
method Designing a boosting approach to bound the worst-class error rate using Deep Neural Networks (DNNs).
result The proposed boosting approach lowers worst-class test error rates while avoiding overfitting.
New method learns multi-class from single-class data with confidences.
problem Learning multi-class from single-class data without additional data.
method Empirical risk minimization framework for multi-class classification.
result Method achieves Bayes-consistency with noisy confidences.
Paper constructs a cohomology class related to McDuff's secondary class, proving it transgresses to the Euler class of foliated sphere bundles.
problem Finding higher-dimensional analogs of the Calabi invariant and its transgression to the Euler class.
method Constructing a cohomology class of volume-preserving diffeomorphisms and proving transgression to the Euler class of foliated sphere bundles.
result The cohomology class transgresses to the Euler class of foliated sphere bundles.
One of the earliest conjectures in computational learning theory-the Sample Compression conjecture-asserts that concept classes (equivalently set systems) admit compression schemes of size linear in their VC dimension. To-date this statement is known to be true for maximum classes---those that possess maximum cardinali…
A new method learns features for one-class classification using intra-class splitting.
problem Challenges in one-class classification due to limited normal class samples.
method Intra-class splitting and joint training of typical and atypical samples with loss functions.
result The method outperforms other models in one-class classification tasks.
The paper proves inequalities for orbifold second Chern classes in Fujiki's class.
problem Inequalities for orbifold second Chern classes of compact normal analytic varieties.
method Generic nefness theorems for tangent and cotangent sheaves, and an orbifold Bogomolov--Gieseker inequality for mixed polarizations.
result Semipositivity of the orbifold second Chern class for varieties with nef anti-canonical divisor.
Study on characteristic classes for foliation deformations.
problem Characterizing and understanding characteristic classes for foliation deformations.
method Introduced a differential graded algebra (DGA) to recover Bott vanishing and formulae, and discussed properties of its cohomology.
result Discovered new classes that cannot be described by existing classes like Godbillon--Vey and Fuks--Lodder--Kotschick.
The hyperelliptic mapping class group has been studied in various contexts within topology and algebraic geometry. What makes this study tractable is that there is a surjective map from the hyperelliptic mapping class group to a mapping class group of a punctured sphere. The more general family of superelliptic mapping…
CILF learns adaptive embeddings for class-incremental learning with novel class detection and model update.
problem Handling unknown classes and model update in streaming data with new classes.
method CILF uses decoupled prototype based loss for intra-class and inter-class structure improvement, and a learnable curriculum clustering operator for adaptive embedding.
result CILF effectively detects multiple novel classes and mitigates embedding confusion, while updating the model without catastrophic forgetting.
A new method identifies class-specific covariates in multi-class prediction tasks.
problem Identifying covariates specifically associated with one or more outcome classes in multi-class prediction tasks.
method Introducing multi forests (MuFs) with multi-way and binary splits to measure class-associated discriminatory ability.
result The multi-class VIM specifically ranks class-associated covariates highly, unlike conventional VIMs.
In this paper we give explicit formulas of differential characteristic classes of principal -bundles with connections and prove their expected properties. In particular, we obtain explicit formulas for differential Chern classes, differential Pontryagin classes and differential Euler class. Furthermore, we show that…
Paper shows Euler class vanishes in certain subgroup of mapping class group.
problem Vanishing of the Euler class in power subgroups of mapping class group.
method Used Dahmani's result to show triviality of Euler class.
result Euler class vanishes in power subgroup of mapping class group.
Paper shows mapping classes are largely determined by their finite quotient actions.
problem Understanding the equivalence of mapping classes based on their finite quotient actions.
method Analyzes procongruent conjugacy classes and their dependence on finite quotients.
result Procongruent conjugacy classes are largely determined by their finite quotient actions.
Study of conjugacy classes in infinite-type surfaces' mapping class groups.
problem Characterizing conjugacy classes in infinite-type surfaces' mapping class groups.
method Model-theoretic methods developed by Kechris, Rosendal, and Truss.
result Detailed classification of conjugacy classes in mapping class groups of infinite-type surfaces.
The paper classifies dense conjugacy classes in mapping class groups of locally finite graphs.
problem Identifying which mapping class groups have dense conjugacy classes.
method Developed flux homomorphisms and combinatorial criteria for stability.
result A complete classification for self-similar locally finite graphs and a criterion for stability.
We present a simple generative framework for learning to predict previously unseen classes, based on estimating class-attribute-gated class-conditional distributions. We model each class-conditional distribution as an exponential family distribution and the parameters of the distribution of each seen/unseen class are d…
We give a complete description of conjugacy classes of finite subgroups of the mapping class group of the sphere with r marked points. As a corollary we obtain a description of conjugacy classes of maximal finite subgroups of the hyperelliptic mapping class group. In particular, we prove that for a fixed genus g there …
SWRLDA improves LDA for multi-class classification with edge classes.
problem LDA's vulnerability to edge classes causing biased mean and large distances.
method Self-weighted robust LDA with l21-norm distance criterion.
result SWRLDA outperforms other methods on synthetic and real-world datasets.
For a local Lie group M we define odd order cohomology classes. The first class is an obstruction to globalizability of the local Lie group. The third class coincides with Godbillon-Vey class in a particular case. These classes are secondary as they emerge when curvature vanishes.
CP-GAN generates images selectively conditioned on class specificity, capturing between-class relationships.
problem Generating images selectively conditioned on class specificity in class-overlapping data.
method Proposed Classifier's Posterior GAN (CP-GAN) that redesigns generator input and objective function for class-overlapping data.
result Demonstrated effectiveness of CP-GAN using both controlled and real-world class-overlapping data.
This research sets limits on how complex multi-class learning problems can be.
problem Understanding the complexity of multi-class classification problems.
method Established upper bounds on Natarajan dimensions for specific function classes.
result Upper bounds on Natarajan dimensions for multi-class decision trees, random forests, and neural networks.
Infinitely many unique ways to generate a surface's mapping class group.
problem Identifying unique ways to generate mapping class groups.
method Analyzing Nielsen equivalence classes of two-element generators.
result There are infinitely many unique ways to generate a surface's mapping class group.
Single Class Universum-SVM uses additional data to improve single class learning.
problem Improving single class learning with limited positive data.
method Proposes Single Class Universum-SVM, incorporating additional data with different distribution.
result Empirical comparisons show the utility of the proposed approach.
Study rigid classes on hyperkahler manifolds, showing general ones are rigid.
problem Characterize rigid classes on compact hyperkahler manifolds.
method Analyze eigenvectors of hyperbolic automorphisms and use BBF form.
result General parabolic classes on hyperkahler manifolds are rigid.
By analyzing how the Borel regulator classes vanish on various groups related to , we define three series of secondary characteristic classes for subgroups of automorphism groups of free groups. The first case is the -automorphism groups and we show that our classes coincide with…
The paper analyzes how well classes are separated in neural network feature space.
problem Understanding class separability in neural network feature space.
method Theoretical analysis of intra-class and inter-class distances in feature space.
result A lower bound for the probability of inter-class distance being greater than intra-class distance as a function of loss value.
DRAGON improves learning for rare classes in unbalanced datasets using class descriptions.
problem Learning rare classes in unbalanced datasets with deep models.
method DRAGON is a late-fusion architecture that corrects bias towards frequent classes and fuses class-descriptions to improve tail-class accuracy.
result DRAGON outperforms state-of-the-art models on new benchmarks for long-tail learning with class descriptors.
Gen1S learns novel classes with 1-shot data using residual space and generative models.
problem Learning new classes with limited data in a growing dataset.
method Mapping embeddings to a residual space, using generative models to learn multi-modal distribution, and applying it as a structural prior.
result Consistent improvement over state-of-the-art methods in recognizing novel classes.
A new active learning method for one-class classification using two classifiers.
problem Reducing manual labeling efforts in one-class classification.
method Uses two one-class classifiers for active learning, proposing new query strategies.
result Improved results compared to existing methods on various datasets.
Distribution networks model novel classes in open set learning.
problem Modeling novel classes in open set learning.
method Distribution networks map samples to a latent space where known and novel classes' distributions are jointly learned.
result Distribution networks accurately detect and model novel classes for subsequent classification.
We study types of mapping classes which arise as a product of a given mapping class and powers of certain pure mapping classes. We derive an explicit constant depending only on a surface such that almost all above pure mapping classes give rise to pseudo-Anosov type whenever their powers are larger than the constant. F…