arXiv research

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

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

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

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…

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.

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

New surgeries on knots preserve contact structures.

Enhances contrastive learning for better representation learning on wild images.

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…

Paper develops tighter risk certificates for contrastive learning models.

Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods are reminiscent of the well-known word2vec embedding algorithm: leveraging availability of pairs of semantically "similar" data points and "n…

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

In this paper the geometry of normal metric contact pair manifolds is studied under the flatness of conformal, concircular and quasi-conformal curvature tensors. It is proved that a conformal flat normal metric contact pair manifold is an Einstein manifold with a negative scalar curvature and has positive sectional cur…

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.

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 …

Novel unsupervised feature selection method using multi-step Markov transition probability.

Link prediction requires predicting which new links are likely to appear in a graph. Being able to predict unseen links with good accuracy has important applications in several domains such as social media, security, transportation, and recommendation systems. A common approach is to use features based on the common ne…

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…

Proves accuracy guarantees for self-supervised learning with correlated positive pairs.

Area under the receiver operating characteristics curve (AUC) is an important metric for a wide range of signal processing and machine learning problems, and scalable methods for optimizing AUC have recently been proposed. However, handling very large datasets remains an open challenge for this problem. This paper prop…

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…

A new method for PU learning improves classification error on CIFAR-10.

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…

We demonstrate how a 3-manifold, a Heegaard diagram, and a group presentation can each be interpreted as a pair of signed permutations in the symmetric group $S_d.$ We demonstrate the power of permutation data in programming and discuss an algorithm we have developed that takes the permutation data as input and determi…

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 …

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

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…

This paper proposes an inexpensive way to learn an effective dissimilarity function to be used for $k$-nearest neighbor ($k$-NN) classification. Unlike Mahalanobis metric learning methods that map both query (unlabeled) objects and labeled objects to new coordinates by a single transformation, our method learns a trans…

Up to symmetries, the orbits of three equal masses under an inverse cube force with zero angular momentum and constant moment of inertia can be reparametrized as the geodesics of a complete, negatively curved metric on a pair of pants. The ends of the pants represent binary collisions. Here we will examine the visibili…

Proposes Contrastive Clustering for improved clustering performance.

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

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

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.

New method identifies causal relationships using proxy variables in the presence of unmeasured confounders.

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.