arXiv research

Functorial properties of knot invariants under specific concordances.

We demonstrate how to combinatorially calculate the EH-class of a compatible contact structure in the sutured Floer homology group of a balanced sutured three manifold which is associated to an abstract partial open book decomposition. As an application we show that every contact three manifold (closed or with convex b…

The paper shows non-balanced condition for a specific metric.

This work optimizes DNN inference for energy-harvesting devices by compressing and selectively executing neural network exits.

Study Kähler-Einstein manifolds with holomorphic isometries into blow-ups of complex spaces.

Paper develops a distributed power control method for large energy harvesting networks using deep reinforcement learning.

In the limit $\hbar\to 0$, we analyze a class of Schrödinger operators $H_\hbar = \hbar^2 L + \hbar W + V\cdot \mathrm{id}$ acting on sections of a vector bundle $\mathcal{Eh}$ over a Riemannian manifold $M$ where $L$ is a Laplace type operator, $W$ is an endomorphism field and the potential energy $V$ has a non-degene…

Insurance and annuity products covering several lives require the modelling of the joint distribution of future lifetimes. In the interest of simplifying calculations, it is common in practice to assume that the future lifetimes among a group of people are independent. However, extensive research over the past decades …

We prove the equivalence of the invariants EH(L) and LOSS-(L) for oriented Legendrian knots L in the 3-sphere equipped with the standard contact structure, partially extending a previous result by Stipsicz and Vertesi. In the course of the proof we relate the sutured Floer homology groups associated with a knot complem…

We consider compact homogeneous spaces G/H of positive Euler characteristic endowed with an invariant almost complex structure J and the canonical action θof the maximal torus T ^{k} on G/H. We obtain explicit formula for the cobordism class of such manifold through the weights of the action θat the identity fixed poin…

Energy-efficient DL inference for IoT devices reduces power consumption and improves performance.

We define the action of the homology group $H_1(M,\partial M)$ on the sutured Floer homology $SFH(M,γ)$. It turns out that the contact invariant $EH(M,γ,ξ)$ is usually sent to zero by this action. This fact allows us to refine an earlier result proved by Ghiggini and the author. As a corollary, we classify knots in $#^…

New algorithm explores reinforcement learning with noisy data.

A compact Riemannian homogeneous space $G/H$, with a bi--invariant orthogonal decomposition $\mathfrak{g}=\mathfrak{h}+\mathfrak{m}$ is called positively curved for commuting pairs, if the sectional curvature vanishes for any tangent plane in $T_{eH}(G/H)$ spanned by a linearly independent commuting pair in $\mathfrak{…

Iterative method finds Hermitian-Einstein metrics on stable bundles.

The study explores Legendrian invariants and half Giroux torsion in contact structures.

UCB-TQL learns from multiple tasks with shared dynamics and adapts to task-specific variations.

Classifies manifolds with dense conjugacy classes in their mapping class groups.

Generic pseudo-Anosov mapping classes in mapping class groups.

This paper tackles worst-class error rate in classification tasks.

New method learns multi-class from single-class data with confidences.

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…

Paper constructs a cohomology class related to McDuff's secondary class, proving it transgresses to the Euler class of foliated sphere bundles.

A new method learns features for one-class classification using intra-class splitting.

The paper proves inequalities for orbifold second Chern classes in Fujiki's class.

Study on characteristic classes for foliation deformations.

New classes generalize Chern classes in supergeometry.

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.

A new method identifies class-specific covariates in multi-class prediction tasks.

In this paper we give explicit formulas of differential characteristic classes of principal $G$-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.

Paper shows mapping classes are largely determined by their finite quotient actions.

Study of conjugacy classes in infinite-type surfaces' mapping class groups.

The paper classifies dense conjugacy classes in mapping class groups of locally finite graphs.

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.

A simple framework predicts unseen classes using exponential family distributions.

CP-GAN generates images selectively conditioned on class specificity, capturing between-class relationships.

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 research sets limits on how complex multi-class learning problems can be.

Infinitely many unique ways to generate a surface's mapping class group.

Single Class Universum-SVM uses additional data to improve single class learning.

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…

The paper shows Euler classes for homeomorphisms of Seifert fibered 3-manifolds are unbounded.

Study rigid classes on hyperkahler manifolds, showing general ones are rigid.

Defines kappa classes on KSBA spaces, generalizing classes on curves.

The paper analyzes how well classes are separated in neural network feature space.