arXiv research

Study asymptotics of one part monotone Hurwitz numbers in high genus.

Knot Floer homology detects ribbon concordance.

We show several results comparing sharp eigenvalue bounds for the first Steklov eigenvalue on surfaces under change of the topology. Among others, we obtain strict monotonicity in the genus. Combined with results of the second named author \cite{petrides_2} this implies the existence of free boundary minimal immersions…

Constructs families of monotone Lagrangians in Brieskorn-Pham hypersurfaces.

Certain classes of 3-manifolds, following Thurston, give rise to a 'skinning map', a self-map of the Teichmüller space of the boundary. This paper examines the skinning map of a 3-manifold M, a genus-2 handlebody with two rank-1 cusps. We exploit an orientation-reversing isometry of M to conclude that the skinning map …

The paper constructs families of high genus CMC surfaces in the 3-sphere.

A virtual $n$-string $α$ is a collection of $n$ oriented smooth generic loops on a surface $M$. A stabilization of $α$ is a surgery that results in attaching a handle to $M$ along disks avoiding $α$, and the inverse operation is a destabilization of $α$. We consider virtual $n$-strings up to virtual homotopy, i.e., seq…

This is a revised version of our short note [arxiv.math.DG/0403065] where we discuss the monotonicity of the eigen-values of the Laplacian operator to the Ricci-Hamilton flow on a compact or a complete non-compact Riemannian manifold. We show that the eigenvalue of the Lapacian operator on a compact domain associated w…

The paper addresses monotonicity in machine learning models for fairness and accountability.

The paper tackles non-monotonic learning performance and proposes algorithms to make models more monotone.

Probit Monotone BART estimates binary outcomes using monotonic functions.

Monotone neural networks can approximate and interpolate functions efficiently.

Improves k-NN for monotonic data with robustness against noise.

Study examines explainable machine learning for monotonic models, finding Integrated gradients better for strong monotonicity.

Formula proves monotonicity for anisotropic minimal hypersurfaces.

The paper develops algorithms to restore monotonicity in non-monotone functions.

New example of manifolds with monotonic heat kernels found.

Proposes a Bayesian nonparametric model for monotonic functions.

Nonnegative matrix factorization (NMF) factorizes a non-negative matrix into product of two non-negative matrices, namely a signal matrix and a mixing matrix. NMF suffers from the scale and ordering ambiguities. Often, the source signals can be monotonous in nature. For example, in source separation problem, the source…

In [S. Basu, A. Gabrielov, N. Vorobjov, Semi-monotone sets. arXiv:1004.5047v2 (2011)] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals, and having connected intersections with all translated coordinate cones in R^n. In this paper we develop this theory further by d…

COMET learns monotonic neural networks by incorporating counterexamples.

Monotonic differentiable sorting networks improve upon previous methods.

We prove three new monotonicity formulas for manifolds with a lower Ricci curvature bound and show that they are connected to rate of convergence to tangent cones. In fact, we show that the derivative of each of these three monotone quantities is bounded from below in terms of the Gromov-Hausdorff distance to the neare…

Proves monotonicity of parabolic frequency on all manifolds without curvature assumptions.

Paper introduces algorithms for explaining monotonic classifiers.

Develops monotone tree-based GAMI models using XGBoost.

The paper evaluates the importance of monotonicity in AI fairness across various fields.

We introduce large scale analogues of topological monotone and light maps, which we call coarsely monotone and coarsely light maps respectively. We show that these two classes of maps constitute a factorization system on the coarse category. We also show how coarsely monotone maps arise from a reflection in a similar w…

Study on biharmonic map heat flow with monotonicity formula.

A local monotonicity formula for the Yang-Mills-Higgs flow on $G$-bundles over $\mathbb{R}^{n}$ ($n>4$) is proved. It is shown that the monotone quantity coïncides on certain self-similar solutions with that appearing in existing non-local monotonicity formulæ for the Yang-Mills and Yang-Mills-Higgs flows.

This paper benchmarks monotone-constrained models for credit PD across datasets and finds constraints are mostly costless.

Study on pairwise counter-monotonicity, a type of negative dependence.

This paper introduces a novel monotone curve estimation framework based on convex duality.

Classical Hurwitz numbers count branched covers of the Riemann sphere with prescribed ramification data, or equivalently, factorisations in the symmetric group with prescribed cycle structure data. Monotone Hurwitz numbers restrict the enumeration by imposing a further monotonicity condition on such factorisations. In …

This is the first part of an article in two parts, which builds the foundation of a Floer-theoretic invariant, (I_F). (See math.DG/0505013 for part II). The Floer homology can be trivial in many variants of the Floer theory; it is therefore interesting to consider more refined invariants of the Floer complex. We consid…

Study derives new equation for reserves in non-monotone information scenarios.

Study on MMV in jump-diffusion models resolves MV's non-monotonicity issues.

In this paper we generalize the monotonicity formulas of [C] for manifolds with nonnegative Ricci curvature. Monotone quantities play a key role in analysis and geometry; see, e.g., [A], [CM1] and [GL] for applications of monotonicity to uniqueness. Among the applications here is that level sets of Green's function on …

The paper investigates quantitative rigidity using Colding's monotonicity formulas for Ricci curvature.

We propose learning deep models that are monotonic with respect to a user-specified set of inputs by alternating layers of linear embeddings, ensembles of lattices, and calibrators (piecewise linear functions), with appropriate constraints for monotonicity, and jointly training the resulting network. We implement the l…

Investigates polar tangential angles of curves and their monotonicity.

We propose an algorithm for a family of optimization problems where the objective can be decomposed as a sum of functions with monotonicity properties. The motivating problem is optimization of hyperparameters of machine learning algorithms, where we argue that the objective, validation error, can be decomposed as mono…

The problem of existence of arbitrage free and monotone CDO term structure models is studied. Conditions for positivity and monotonicity of the corresponding Heath-Jarrow-Morton-Musiela equation for the $x$-forward rates with the use of the Milian type result are formulated. Two state spaces are taken into account - of…

New models ensure monotonicity in preference learning, improving accuracy especially with limited data.

In this paper, we introduce a monotonicity formula for the mean curvature flow. We also apply this monotonicity formula to study the asymptotic behavior of eternal solutions.

The study finds monotonic properties of harmonic functions on 3-manifolds with a flat end.

We investigate monotonicity properties of $p$-harmonic vector bundle-valued $k$-forms by studying the energy-momentum tensor associated with such a form. As a consequence, we obtain a unified proof of the monotonicity formulæ for $p$-harmonic maps and Yang-Mills connections, proving a monotonicity formula for $p$-Yang-…

Under certain topological assumptions, we show that two monotone Lagrangian submanifolds embedded in the standard symplectic vector space with the same monotonicity constant cannot link one another and that, individually, their smooth knot type is determined entirely by the homotopy theoretic data which classifies the …