We show that a compact orientable 4-manifold M has a CR regular immersion into C3 if and only if both its first Pontryagin class and its Euler characteristic vanish, and has a CR regular embedding into C3 if and only if in addition the second Stiefel-Whitney class of M vanishes.
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48 results for “Class C3”
The paper extends a variance gamma model to quadratic functions, reducing arbitrage and computational costs.
problem Creating an arbitrage-free interpolation for option pricing models.
method Generalizing the local variance gamma model to a piecewise quadratic local variance function.
result The quadratic model results in an arbitrage-free interpolation of class C3, reducing knots and computational cost.
The paper examines Finsler metrics under Ricci flow and finds they are Einstein.
problem Understanding Finsler metrics under Ricci flow.
method Investigated C3-like Finsler metrics and proved they are Einstein.
result C3-like Finsler metrics are Einstein under Ricci flow.
C3 compresses images and videos with low complexity and high performance.
problem High complexity and low performance in neural compression models.
method Overfits a small model to each image or video separately, improving RD performance with low complexity.
result Matches the RD performance of state-of-the-art neural and video codecs with significantly lower decoding complexity.
Distributions of Monge type are a class of strongly regular bracket-generating distributions introduced by I. Anderson, Zh. Nie and P. Nurowski. Their symbol algebras prolong to simple graded Lie algebras, thus allowing one to associate a parabolic geometry to any given Monge distribution. This article is devoted to th…
We provide a uniform framework to study the exceptional homogeneous compact geometries of type C3. This framework is then used to show that these are simply connected, answering a question by Kramer and Lytchak, and to calculate the full automorphism groups.
Differentiable sorting and rank normalization are incompatible, with specific conditions for admissibility.
problem Incompatibility between differentiable sorting and rank normalization.
method Formalized admissibility through monotone invariance, batch independence, and rank-space stability conditions.
result Different gap-sensitive and batchwise relaxations of rank normalization violate the conditions for admissibility.
A classification of homogeneous compact Tits geometries of irreducible spherical type, with connected panels and admitting a compact flag-transitive automorphism group acting continuously on the geometry, has been obtained by Kramer and Lytchak (Homogeneous compact geometries, Transform. Groups 19 (2016), 43-58 and Err…
Revises Schwarzschild manifold rigidity proof for spin manifolds.
problem Rigidity of Schwarzschild manifold for spin manifolds.
method Spinorial proof approach.
result Generalizes and includes classical and recent black hole uniqueness theorems.
The paper studies Finsler spaces with semi-concurrent vector fields and their equivalence to Riemannian spaces.
problem Characterizing Finsler spaces with semi-concurrent vector fields.
method Analyzing various Finsler spaces and proving conditions for equivalence to Riemannian spaces.
result Various Finsler spaces (quasi--reducible, -like, -recurrent, -like) are equivalent to Riemannian spaces if they admit a semi-concurrent vector field.
Sharp gradient estimate for scalar curvature on 3-manifolds.
problem Control the rate of change of scalar curvature on 3-manifolds.
method Using a regularized distance function and Green's function, derive a sharp gradient estimate.
result Average of gradient of regularized distance is ≤ 1 on 3-manifolds with nonnegative scalar curvature.
Study finds almost contact structures in thermal QCD-like theories at intermediate coupling.
problem Understanding (Almost) Contact Structures in thermal QCD-like theories.
method Explicitly obtained (Almost) Contact Structures and SU(3) structures.
result Subspaces of C3S and AC3S are not mutually 'N-path connected' in the Infra-Red.
M/F-Theory as Mf-Theoryhep-th
New mathematical framework connects M-theory charges to stable homotopy groups.
problem Quantization of fluxes in M-theory and their mathematical representation.
method Establishing a correspondence between M-theory phenomena and stable homotopy theory concepts.
result Found a direct link between M-theory charges and stable homotopy groups.
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.
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…
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.
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.
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…
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.
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 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 …
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…
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.
This paper proposes a novel generic one-class feature learning method based on intra-class splitting. In one-class classification, feature learning is challenging, because only samples of one class are available during training. Hence, state-of-the-art methods require reference multi-class datasets to pretrain feature …
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.
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…
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.
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.
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…
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.
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…
New classes defined for manifold pseudogroups, linking to cohomology and bundle structures.
problem Characterizing pseudogroups of diffeomorphisms using characteristic classes.
method Defined Godbillon-Vey-Losik and first Chern-Losik classes via de Rham cohomology and frame bundles.
result Explicit expressions and geometric representations for the new classes.
Paper tackles many-class few-shot learning with class hierarchy, improving accuracy.
problem Many-class few-shot learning problem in practical applications.
method Leverages class hierarchy to train a coarse-to-fine classifier using memory-augmented hierarchical-classification network (MahiNet).
result MahiNet outperforms state-of-the-art models on MCFS problems in both supervised and meta-learning settings.
Solutions to Strominger system found for square of Kähler class.
problem Finding solutions to Strominger system with specific balanced classes.
method Deforming Calabi-Yau and Hermitian-Yang-Mills metrics.
result Classes that are squares of Kähler metrics admit solutions.
Continuous epimorphisms between certain mapping class groups are induced by homeomorphisms.
problem Understanding continuous epimorphisms between specific mapping class groups.
method Analyzing subgroups of mapping class groups of infinite-genus 2-manifolds with no planar ends.
result Continuous epimorphisms are induced by homeomorphisms for the specified subgroups.
We construct closed symplectic manifolds for which spherical classes generate arbitrarily large subspaces in 2-homology, such that the first Chern class and cohomology class of the symplectic form both vanish on all spherical classes. We construct both Kaehler and non-Kaehler examples, and show independence of the cond…
Proposes a method to improve class-conditional conformal prediction for many classes.
problem Weak guarantees for specific classes in classification problems.
method Clusters classes with similar conformal scores and performs conformal prediction at the cluster level.
result Clustered conformal typically outperforms existing methods in class-conditional coverage and set size metrics.
Two elements generate extended mapping class groups of certain surfaces.
problem Generating extended mapping class groups with specific elements.
method Analyzing finite order elements and isotopy classes of homeomorphisms.
result Extended mapping class groups of certain surfaces are generated by two elements of finite order.