arXiv research

This paper studies properties of weak reducing pairs in critical Heegaard splittings.

Reduces weak reducing pairs to spheres in 3-sphere Heegaard surfaces.

In this article, we prove that a tunnel number two knot induces a critical Heegaard splitting in its exterior if there are two weak reducing pairs such that each weak reducing pair contains the cocore disk of each tunnel. Moreover, we prove that a connected sum of two 2-bridge knots or more generally that of two $(1,1)…

Reduces connectivity problem for genus-4 Heegaard surface in 3-sphere.

Let $K$ be an unknot in $8$-bridge position in the $3$-sphere. We give an example of a pair of weak reducing disks $D_1$ and $D_2$ for $K$ such that both disks obtained from $D_i$ ($i = 1, 2$) by a surgery along any outermost disk in $D_{3-i}$, cut off by an outermost arc of $D_i \cap D_{3-i}$ in $D_{3-i}$, are not wea…

Let $M$ be an orientable, irreducible $3$-manifold and $(\mathcal{V},\mathcal{W};F)$ a weakly reducible, unstabilized Heegaard splitting of $M$ of genus at least three. In this article, we define an equivalent relation $\sim$ on the set of the generalized Heegaard splittings obtained by weak reductions and find special…

Weak dual pairs defined in Dirac-Jacobi geometry, proving equivalence and leaf correspondence theorems.

Investigates how diversification preferences relate to risk attitudes.

W2S FT often outperforms weak teachers due to low intrinsic dimensionality.

Learning disentangled representations that correspond to factors of variation in real-world data is critical to interpretable and human-controllable machine learning. Recently, concerns about the viability of learning disentangled representations in a purely unsupervised manner has spurred a shift toward the incorporat…

SIMPLE-RC method tests group membership profiles in large networks with weak signals.

We show that the complex of weak reducing disks for the unknot in $3$-bridge position is contractible.

We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs of Lagrangian subspaces in continuously varying Banach spaces. We derive basic …

Let $M$ be a compact orientable irreducible 3-manifold and $H$ be an unstabilized genus three Heegaard splitting of $M$. In this article, we will define a simplicial complex of weak reducing pairs for $H$ and find several properties of this complex. Using this method, we will prove that an unstabilized Heegaard splitti…

Unified approach for multicalibration in weakly supervised learning.

Study counts sub-chord diagrams to classify spherical curves.

Construct algorithms for Frobenius manifolds and residue pairings on Calabi-Yau varieties.

New proof for weak mixing in polygonal billiards.

Let $M$ be an orientable, irreducible $3$-manifold admitting a weakly reducible genus three Heegaard splitting as a minimal genus Heegaard splitting. In this article, we prove that if $[f]$, $[g]\in Mod(M)$ give the same correspondence between two isotopy classes of generalized Heegaard splittings consisting of two Hee…

Let (W,S) be a finite rank Coxeter system with W infinite. We prove that the limit weak order on the blocks of infinite reduced words of W is encoded by the topology of the Tits boundary of the Davis complex X of W. We consider many special cases, including W word hyperbolic, and X with isolated flats. We establish tha…

Paper proves non-compact inaudibility of symmetry and commutativity.

New method learns useful disentangled representations from weakly labeled data.

Mitigates bias in weakly supervised datasets.

Using crossed homomorphisms, we show that the category of weak representations (resp. admissible representations) of Lie-Rinehart algebras (resp. Leibniz pairs) is a left module category over the monoidal category of representations of Lie algebras. In particular, the corresponding bifunctor of monoidal categories is e…

Control data constructed for smooth weak deformation retraction of stratified spaces.

Pairwise "same-cluster" queries are one of the most widely used forms of supervision in semi-supervised clustering. However, it is impractical to ask human oracles to answer every query correctly. In this paper, we study the influence of allowing "not-sure" answers from a weak oracle and propose an effective algorithm …

New heat flow for harmonic maps avoids singularities but not bubbles.

Study the geometry of weak para-f-structures and subclasses.

The paper studies limits of flows on Kähler surfaces, proving convergence to solutions of equations.

We study the spectral properties of a large class of compact flat Riemannian manifolds of dimension 4, namely, those whose corresponding Bieberbach groups have the canonical lattice as translation lattice. By using the explicit expression of the heat trace of the Laplacian acting on $p$-forms, we determine all $p$-isos…

Solves pair trading problem using consumption-investment theory.

The paper proves conditions for the Abundance conjecture in minimal projective klt pairs.

Paper develops equivariant basic cohomology for Lie groupoids.

Research on the multi-armed bandit problem has studied the trade-off of exploration and exploitation in depth. However, there are numerous applications where the cardinal absolute-valued feedback model (e.g. ratings from one to five) is not suitable. This has motivated the formulation of the duelling bandits problem, w…

We study the time dependent cross correlations of stock returns, i.e. we measure the correlation as the function of the time shift between pairs of stock return time series using tick-by-tick data. We find a weak but significant effect showing that in many cases the maximum correlation is at nonzero time shift indicati…

We show that every co--orientable taut foliation F of an orientable, atoroidal 3-manifold admits a transverse essential lamination. If this transverse lamination is a foliation G, the pair F,G are the unstable and stable foliation respectively of an Anosov flow. Otherwise, F admits a pair of transverse very full genuin…

Study uses weak transport for non-convex costs in fixed-income markets.

We study weakened $f$-structures on manifolds, generalizing classical results.

Constructs non-isometric iso-length-spectral surfaces.

Recently, researches related to unsupervised disentanglement learning with deep generative models have gained substantial popularity. However, without introducing supervision, there is no guarantee that the factors of interest can be successfully recovered. Motivated by a real-world problem, we propose a setting where …

The paper establishes general results in Lorentzian optimal transport theory.

Benchmark evaluates financial misinformation detection models, revealing weaknesses without external context.

Given a matched pair of Lie groups, we show that the tangent bundle of the matched pair group is isomorphic to the matched pair of the tangent groups. We thus obtain the Euler-Lagrange equations on the trivialized matched pair of tangent groups, as well as the Euler-Poincaré equations on the matched pair of Lie algebra…

Proves finitely generated associated graded rings for valuations on log Fano pairs.

The problem of prescribing conformally the scalar curvature of a closed Riemannian manifold as a given Morse function reduces to solving an elliptic partial differential equation with critical Sobolev exponent. Two ways of attacking this problem consist in subcritical approximations or negative pseudo gradient flows. W…

We define an n-plectic structure as a commutative and torsionless Lie Rinehart pair, together with a distinguished cocycle from its Chevalley-Eilenberg complex. This 'n-plectic cocycle' gives rise to an extension of the Chevalley-Eilenberg complex by so called symplectic tensors. The cohomology of this extension genera…

We consider a continuous curve of self-adjoint Fredholm extensions of a curve of closed symmetric operators with fixed minimal domain $D_m$ and fixed {\it intermediate} domain $D_W$. Our main example is a family of symmetric generalized operators of Dirac type on a compact manifold with boundary with varying well-posed…

Avoids noncompact hypersurfaces from touching in evolving flows.