arXiv research

A new method improves graph node embeddings by considering both nearby and distant node similarities.

GP-ND avoids obstacles in trajectory planning using Gaussian Process regression.

Paper explains contrastive learning using cosine similarity and proposes mitigations for batch size effects.

Study disproves a generalized numerical criterion for certain pairs.

We generalize the Schouten calculus of multivector fields to commutative Lie Rinehart pairs and define a non negatively graded Lie oo-algebra on their exterior power.

We prove that a pair (X, D) with X Fano and D a smooth anti-canonical divisor is K-unstable for negative angles, and K-semistable for zero angle.

A fast $k$-NN classifier without negative pairs.

New surgeries on knots preserve contact structures.

Let $M$ be a closed orientable Riemannian surface. Consider an SO(3)-connection $A$ and a Higgs field $Φ:M\to so(3)$. The pair $(A,Φ)$ naturally induces a cocycle over the geodesic flow of $M$. We classify (up to gauge transformations) cohomologically trivial pairs $(A,Φ)$ with finite Fourier series in terms of a suita…

In this paper, we study the boundary behavior of the negatively curved Kähler-Einstein metric attached to a log canonical pair $(X,D)$ such that $K_X+D$ is ample. In the case where $X$ is smooth and $D$ has simple normal crossings support (but possibly negative coefficients), we provide a very precise estimate on the p…

Improved KG completion on large datasets using entity-relation pair occurrences.

Protein-protein interaction (PPI) prediction is an important problem in machine learning and computational biology. However, there is no data set for training or evaluation purposes, where all the instances are accurately labeled. Instead, what is available are instances of positive class (with possibly noisy labels) a…

The paper studies Kähler-Einstein metrics with singularities and their limits.

Let (X,D) be a klt pair. Assuming either K_X+D big or -(K_X+D) ample, and that the coefficients of D are greater than 1/2, we show that the Kähler-Einstein metric attached to (X,D) -whenever it exists- has cone singularities along D on the log-smooth locus of the pair intersected with the ample locus of K_X+D (in the n…

Study shows how lengths of geodesic arcs determine linking number of Legendrian knots.

The paper finds virtual knots with specific unknotting indices.

Predicts unseen links in graphs using motifs of 3-5 nodes.

The paper examines flatness conditions on normal metric contact pairs and proves properties of Einstein manifolds.

In this paper, complement-equivalent arithmetic Zariski pairs will be exhibited answering in the negative a question by Eyral-Oka on these curves and their groups. A complement-equivalent arithmetic Zariski pair is a pair of complex projective plane curves having Galois-conjugate equations in some number field whose co…

We introduce a model for Hermitian holormorphic Deligne cohomology on a projective algebraic manifold which allows to incorporate singular hermitian structures along a normal crossing divisor. In the case of a projective curve, the cup-product in cohomology is shown to correspond to a generalization of the Deligne pair…

A parameter-free statistical model is used to study multiplicity signatures for coherent production of charged-pairs of parabosons of order p=2 in comparison with those arising in the case of ordinary bosons, p=1. Two non-negative real parameters arise because "ab" and "ba" are fundamentally distinct pair operators of …

Model learns image-word associations from captions using contrastive learning.

We discuss a correspondence between certain contact pairs on the one hand, and certain locally conformally symplectic forms on the other. In particular, we characterize these structures through suspensions of contactomorphisms. If the contact pair is endowed with a normal metric, then the corresponding lcs form is loca…

K. Grove, L. Verdiani, B. Wilking and W. Ziller gave the first examples of cohomogeneity one manifolds which do not carry invariant metrics with non-negative sectional curvatures. In this paper we generalize their results to a larger family. We also classified all class one representations for a pair (G;H) with G/H som…

Given a compact orientable surface of negative Euler characteristic, there exists a natural pairing between the Teichmueuller space of the surface and the set of homotopy classes of simple loops and arcs. The length pairing sends a hyperbolic metric and a homotopy class of a simple loop or arc to the length of geodesic…

A new SSL method using whitening of latent-space features.

To what extent does the eigenvalue spectrum of the Laplace-Beltrami operator on a compact Riemannian manifold determine the geometry of the manifold? We give examples of isospectral manifolds with different local geometry including continuous families of isospectral negatively curved manifolds with boundary as well as …

Our earlier twisted-face-pairing construction showed how to modify an arbitrary orientation-reversing face-pairing on a faceted 3-ball in a mechanical way so that the quotient is automatically a closed, orientable 3-manifold. The modifications were, in fact, parametrized by a finite set of positive integers, arbitraril…

Enhances contrastive learning for better representation learning on wild images.

Examining orbits ending in binary collisions for three equal masses under an inverse cube force.

A novel GNN architecture improves link prediction by combining positive and negative samples.

Abstract result on correlations of pairs in exponentially growing discrete subsets.

Paper proposes a fast, learning-rate free method for optimizing AUC.

In this paper we develop a complete theory of factorization for isometries of hyperbolic 4-space. Of special interest is the case where a pair of isometries is linked, that is, when a pair of isometries can be expressed each as compositions of two involutions, one of which is common to both isometries. Here we develop …

We extend the geometric study of the Wasserstein space W(X) of a simply connected, negatively curved metric space X by investigating which pairs of boundary points can be linked by a geodesic, when X is a tree.

We introduce a geometric evolution equation for 3-manifolds with sectional curvature of one sign which is in some sense dual to the Ricci flow. On a closed 3-manifold with negative sectional curvature, we establish short time existence and a pair of monotonicity formulas for solutions to the flow. One of these formulas…

This paper uses cointegration to identify profitable pair-trading strategies for Indian stocks.

Extends conformal prediction to contrastive learning for better coverage of positive samples.

Let P(S) be the space of convex projective structures on a surface S with negative Euler characteristic. Goldman and Bonahon-Dreyer constructed two different sets of global coordinates for P(S), both associated to a pair of pants decomposition of the surface S. The article explicitly describes the coordinate change bet…

Tests assess if predictions are prudent by comparing observations and predictions.

Contrastive learning performance doesn't degrade with more negative samples.

New proof shows surfaces can have identical length spectra but not simple ones.

In this paper, we prove that (1) For any integers $n\geq 1$ and $g\geq 2$, there is a closed 3-manifold $M_{g}^{n}$ which admits a distance $n$ Heegaard splitting of genus $g$ except that the pair of $(g, n)$ is $(2, 1)$. Furthermore, $M_{g}^{n}$ can be chosen to be hyperbolic except that the pair of $(g, n)$ is $(3, 1…

Proposes a new loss function to avoid treating missing information as positive or negative feedback.

New method learns from either positive or negative feedback alone.

A pair of distinct free homotopy classes of closed curves in an orientable surface $F$ with negative Euler characteristic is said to be length equivalent if for any hyperbolic structure on $F$, the length of the geodesic representative of one class is equal to the length of the geodesic representative of the other clas…

We answer Mark Kacs famous question - can one hear the shape of a drum - in the negative for orbifolds that are spherical space forms. This is done by extending the techniques developed by A. Ikeda on Lens Spaces to the orbifold setting. Several results are proved to show that with certain restrictions on the dimension…

New insights into negative sampling for graph representation learning.