arXiv research

The study investigates the impact of negative examples in contrastive learning.

This paper shows how optimizing with hard negative examples improves image retrieval.

New method learns from either positive or negative feedback alone.

The Wu-Yau theorem is verified for negative curvature, and new examples of Kähler-Einstein metrics are found.

Computational approaches to transcription factor binding site identification have been actively researched for the past decade. Negative examples have long been utilized in de novo motif discovery and have been shown useful in transcription factor binding site search as well. However, understanding of the roles of nega…

Novel neural likelihood ratio estimation for negative data in particle physics.

Motivated by applications in protein function prediction, we consider a challenging supervised classification setting in which positive labels are scarce and there are no explicit negative labels. The learning algorithm must thus select which unlabeled examples to use as negative training points, possibly ending up wit…

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…

Paper proposes a new loss function for PU learning without negative examples.

We give examples of pinched negatively curved manifolds for which the Ricci flow does not converge smoothly.

The paper proposes methods to estimate positive examples and learn classifiers from mixed data.

Classifies Einstein metrics on R^4 with Heisenberg symmetry, finding incomplete Ricci-flat metrics and two complete negative-curvature examples.

We give examples of harmonic maps between negatively curved manifolds with special properties. These negatively curved manifolds do not have the homotopy type of a locally symmetric space.

It was asked by J.Birman, Williams, and L.Rudolph whether nontrivial Lorentz knots have always positive signature. Lorentz knots are examples of positive braids (in our convention they have all crossings negative so they are negative links). It was shown by L.Rudolph that positive braids have positive signature (if the…

This paper proves equivalences of portfolio optimization problems with negative expectile and omega ratio. We derive subgradients for the negative expectile as a function of the portfolio from a known dual representation of expectile and general theory about subgradients of risk measures. We also give an elementary der…

Every negative amphichiral knot is rationally slice.

It is proved that a compact Kahler manifold whose Ricci tensor has two distinct, constant, non-negative eigenvalues is locally the product of two Kahler-Einstein manifolds. A stronger result is established for the case of Kahler surfaces. Irreducible Kahler manifolds with two distinct, constant eigenvalues of the Ricci…

New Einstein metrics found from para-Sasaki-like Riemannian manifolds.

Uniform negative immersions prove coherence of one-relator groups.

We give a geometric obstruction to the non-negativity of the sectional curvature in the total spaces of certain Riemannian submersions with totally geodesic fibers; applications of this obstruction to several examples are given.

We provide in this note two relevant examples of Lagrangian cobordisms. The first one gives an example of two exact Lagrangian submanifolds which cannot be composed in an exact fashion. The second one is an example of an exact Lagrangian cobordism on which all primitive of the Liouville form is not constant on the nega…

A simplicial complex is called negatively curved if all its simplices are isometric to simplices in hyperbolic space, and it satisfies Gromov's Link Condition. We prove that, subject to certain conditions, a compact graph of spaces whose vertex spaces are negatively curved 2-complexes, and whose edge spaces are points …

Generative replay improves continual learning by using generated data as negative examples.

Noisy PN learning is the problem of binary classification when training examples may be mislabeled (flipped) uniformly with noise rate rho1 for positive examples and rho0 for negative examples. We propose Rank Pruning (RP) to solve noisy PN learning and the open problem of estimating the noise rates, i.e. the fraction …

New Bochner technique for foliations with non-negative Ricci curvature.

New infinite families of twisted torus knots found.

An updated version with a few corrections.

CR Paneitz operator on non-embeddable tori has infinitely many negative eigenvalues

Hass and Scott's example of a 4-valent graph on the 3-punctured sphere that cannot be realized by geodesics in any metric of negative curvature is generalized to impossible configurations filling surfaces of genus $n$ with $k$ punctures for any $n$ and $k$.

In contrast to the homogeneous case, we show that there are compact cohomogeneity one manifolds, that do not support invariant metrics of non-negative sectional curvature. In fact we exhibit infinite families of such manifolds including the exotic Kervaire spheres. Such examples exist for any codimension of the singula…

Paper examines floating exercise boundaries for American options in time-inhomogeneous models.

New unsupervised method selects hard negative samples for contrastive learning.

Ricci flow deforms metrics with positive curvature to include negative curvature.

Until a couple of years ago, the only known examples of Lie groups admitting left-invariant metrics with negative Ricci curvature were either solvable or semisimple. We use a general construction from a previous article of the second named author to produce a great amount of examples with compact Levy factor. Given a c…

The paper introduces negative controls to evaluate causal discovery algorithms, improving their reliability.

Unified framework for word embedding models using noise examples.

Topological obstructions to admissibility in $σ_k$-Loewner--Nirenberg problem

Detection of protein-protein interactions (PPIs) plays a vital role in molecular biology. Particularly, infections are caused by the interactions of host and pathogen proteins. It is important to identify host-pathogen interactions (HPIs) to discover new drugs to counter infectious diseases. Conventional wet lab PPI pr…

In this paper we prove that for all $n=4k-2$, $k\ge2$ there exists closed $n$-dimensional Riemannian manifolds $M$ with negative sectional curvature that do not have the homotopy type of a locally symmetric space, such that $π_{1}(\mathcal{T}^{<0}(M))$ is non-trivial. $\mathcal{T}^{<0}(M)$ denotes the Teichmüller space…

We give examples of harmonic cellular maps between negatively curved manifolds which are not diffeomorphisms but are homotopic to diffeomorphisms.

We study minimal hypersurfaces in manifolds of non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay at infinity. By comparison with capped spherical cones, we identify a precise borderline for the Ricci curvature decay. Above this value, no complete area-minimizing hypersurfaces exist. Be…

The study proves Lieb-Thirring inequalities on hyperbolic manifolds.

We give conceptual proofs of some well known results concerning compact non-positively curved locally symmetric spaces. We discuss vanishing and non-vanishing of Pontrjagin numbers and Euler characteristics for these locally symmetric spaces. We also establish vanishing results for Stiefel-Whitney numbers of (finite co…

We construct new homogeneous Einstein spaces with negative Ricci curvature in two ways: First, we give a method for classifying and constructing a class of rank one Einstein solvmanifolds whose derived algebras are two-step nilpotent. As an application, we describe an explicit continuous family of ten-dimensional Einst…

The optimal dividend problem by De Finetti (1957) has been recently generalized to the spectrally negative Lévy model where the implementation of optimal strategies draws upon the computation of scale functions and their derivatives. This paper proposes a phase-type fitting approximation of the optimal strategy. We con…

Let $N$ be a smooth manifold that is homeomorphic but not diffeomorphic to a closed hyperbolic manifold $M$. In this paper, we study the extent to which $N$ admits as much symmetry as $M$. Our main results are examples of $N$ that exhibit two extremes of behavior. On the one hand, we find $N$ with maximal symmetry, i.e…

Study properties of solutions with singularities in the negative cone.

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 …