arXiv research

Pedagogical approaches help interpret embedding models in knowledge bases.

The article describes Horn(p,q) with integer p and q.

Study of Horn's problem in PU(n,1) for n≥1.

We answer Question 6.12 in the paper "Monoids in the mapping class group" written by Etnyre and Van Horn-Morris.

Lifted Relational Neural Networks (LRNNs) describe relational domains using weighted first-order rules which act as templates for constructing feed-forward neural networks. While previous work has shown that using LRNNs can lead to state-of-the-art results in various ILP tasks, these results depended on hand-crafted ru…

Study on heat equation and eigenfunctions on RCD spaces, proving unique continuation.

The paper studies connectivity of Schur-Horn map images in real Grassmannians.

In this paper we discuss the index problem for geometric differential operators (Spin-Dirac operator, Gauß-Bonnet operator, Signature operator) on manifolds with metric horns. On singular manifolds these operators in general do not have unique closed extensions. But there always exist two extremal extensions $D_{min}$ …

We prove that the indices of fibered-cusp and $d$-Dirac operators on a spin manifold with fibered boundary coincide if the associated family of Dirac operators on the fibers of the boundary is invertible. This answers a question raised by Piazza. Under this invertibility assumption, our method yields an index formula f…

Study inequalities for singular values of rectangular matrices.

Proves positive mass theorem for AF spin manifolds with conical singularities.

The paper proves convexity results for a specific type of Lie groups.

We present a large family of knots for which the Rasmussen s-invariants of arbitrary satellites do not detect sliceness. This answers a question of Hedden. The proof hinges on work of Kronheimer-Mrowka and Cochran-Harvey-Horn.

We study Question 7.9 in the paper "Monoids in the mapping class group" by Etnyre and Van Horn-Morris; whether a symmetric mapping class admitting a positive factorization is a lift of a quasi-positive braid. We answer affirmatively for mapping classes satisfying certain cyclic conditions.

Let V be a compact real analytic surface with isolated singularities embedded in $R^N$, and assume its smooth part is equipped with a Riemannian metric that is induced from some analytic Riemannian metric on $R^N$. We prove: 1. Each point of V has a neighborhood which is quasi-isometric (naturally and 'almost isometric…

It is shown that 3D part of a spherically symmetric solution in conformal Weyl gravity interacting with Maxwell electrodynamics is a Yamabe flow as well. The Yamabe flow describes the transition from a horn of an initial wormhole to a 3D Euclidean space both filled with a radial electric field. It is supposed that such…

In this paper we show that to each planar line arrangement defined over the real numbers, for which no two lines are parallel, one can write down a corresponding relation on Dehn twists that can be read off from the combinatorics and relative locations of intersections. This leads to an alternate proof of Wajnryb's gen…

New method shows some 3D shapes can't be filled in certain ways.

We propose a conceptual design for a quantum blockchain. Our method involves encoding the blockchain into a temporal GHZ (Greenberger-Horne-Zeilinger) state of photons that do not simultaneously coexist. It is shown that the entanglement in time, as opposed to an entanglement in space, provides the crucial quantum adva…

The bipolar filtration of Cochran, Harvey and Horn presents a framework of the study of deeper structures in the smooth concordance group of topologically slice knots. We show that the graded quotient of the bipolar filtration of topologically slice knots has infinite rank at each stage greater than one. To detect nont…

Study shows bounds on symplectic fillings for spinal open book decompositions.

In the present paper we describe compatible open books for the fibre connected sum along binding components of open books, as well as for the fibre connected sum along multi-sections of open books. As an application the first description provides simple ways of constructing open books supporting all tight contact struc…

By recent results of Baker--Etnyre--Van Horn-Morris, a rational open book decomposition defines a compatible contact structure. We show that the Heegaard Floer contact invariant of such a contact structure can be computed in terms of the knot Floer homology of its (rationally null-homologous) binding. We then use this …

mfEGRA uses active learning to efficiently locate failure boundaries in reliability analysis.

We extend the Heegaard Floer homological definition of spectral order for closed contact 3-manifolds due to Kutluhan, Matić, Van Horn-Morris, and Wand to contact 3-manifolds with convex boundary. We show that the order of a codimension zero contact submanifold bounds the order of the ambient manifold from above. As the…

This is a technical paper, which is a continuation of math.DG/0211159. Here we construct Ricci flow with surgeries and verify most of the assertions, made in section 13 of that e-print; the exceptions are (1) the statement that manifolds that can collapse with local lower bound on sectional curvature are graph manifold…

On a compact oriented surface of genus $g$ with $n\geq 1$ boundary components, $δ_1, δ_2,\ldots, δ_n$, we consider positive factorizations of the boundary multitwist $t_{δ_1} t_{δ_2} \cdots t_{δ_n}$, where $t_{δ_i}$ is the positive Dehn twist about the boundary $δ_i$. We prove that for $g\geq 3$, the boundary multitwis…

We study the structure of the exteriors of gropes and Whitney towers in dimension 4, focusing on their fundamental groups. In particular we introduce a notion of unknottedness of gropes and Whitney towers in the 4-sphere. We prove that various modifications of gropes and Whitney towers preserve the unknottedness and do…

Researchers found a canonical form for pairs of Hermitian and antilinear operators.

Continuing our previous work (arXiv:1509.07981v1), we derive another global gradient estimate for positive functions, particularly for positive solutions to the heat equation on finite or locally finite graphs. In general, the gradient estimate in the present paper is independent of our previous one. As applications, i…

Classification of fillings for a specific type of contact surgery on the Hopf link.

Generalizes cohomology ring result for combinatorial line arrangements.

Quantum states in 4-manifolds linked to hyperbolic geometry.

A two-dimensional open book (S,h) determines a closed, oriented three-manifold Y(S,h) and a contact structure C(S,h) on Y(S,h). The contact structure C(S,h) is Stein fillable if h is positive, i.e. h can be written as a product of right-handed Dehn twists. Work of Wendl implies that when S has genus zero the converse s…

The bipolar filtration introduced by T. Cochran, S. Harvey, and P. Horn is a framework for the study of smooth concordance of topologically slice knots and links. It is known that there are topologically slice 1-bipolar knots which are not 2-bipolar. For knots, this is the highest known level at which the filtration do…

We derive a gradient estimate for positive functions, in particular for positive solutions to the heat equation, on finite or locally finite graphs. Unlike the well known Li-Yau estimate, which is based on the maximum principle, our estimate follows from the graph structure of the gradient form and the Laplacian operat…

Machine learning classifies IoT noise in smart cities.

New derivation shows how a three-factor learning rule is derived from Oja's rule.

DeepCTRL integrates rules into deep learning models, allowing flexible control at inference.

New methods prune unpromising rules from KGs, improving scalability and runtime.

Subcartesian spaces follow Leibniz' rule, simplifying differential calculus.

In this study, we give the relationships between the conical curvatures of ruled surfaces drawn by the unit vectors of the ruling, central normal and central tangent of a regular ruled surface in the Euclidean -space. We obtain the differential equations characterizing slant ruled surfaces and if the reference ruled su…

New framework learns interpretable rule ensembles without sacrificing accuracy.

R2N learns interpretable rules and literals from numerical features.

Study ruled surfaces with finite multiplicity, focusing on their curves and singularities.

Paper classifies ruled surfaces in Lorentz-Minkowski space for a specific flow.

In this study, we define some new types of ruled surfaces called slant ruled surfaces. We give some characterizations for a regular ruled surface to be a slant ruled surface in Euclidean 3- space. We show that if the slant ruled surface is developable then the striction curve is a general helix or a slant helix accordi…

In this paper we use fuzzy systems theory to convert the technical trading rules commonly used by stock practitioners into excess demand functions which are then used to drive the price dynamics. The technical trading rules are recorded in natural languages where fuzzy words and vague expressions abound. In Part I of t…