arXiv research

New model accounts for scale variation and noise in pairwise comparisons.

Differentiable sorting and rank normalization are incompatible, with specific conditions for admissibility.

Let $\A$ be a line arrangement in the complex projective plane $\PP^2$. Denote by $M$ its complement and by $\M$ the set of points in $\A$ with multiplicity at least 3. A rank one local system $\mathcal{L}$ on $M$ is admissible if roughly speaking the dimension of the cohomology groups $H^m(M,\mathcal{L})$ can be compu…

New method calibrates reference distributions for bounded support.

Investigates metric degeneracies on symplectic leaves using a generalized gradient flow.

Four geometries govern sequential and distribution-free inference.

Given a rank 2 hermitian bundle over a 3-manifold that is non-trivial admissible in the sense of Floer, one defines its Casson invariant as half the signed count of its projectively flat connections, suitably perturbed. We show that the 2-divisibility of this integer invariant is controlled in part by a formula involvi…

Stability in homology of moduli spaces of admissible covers.

The study describes special real manifolds and invariant admissible cubics in Vinberg cones.

Proposes causal modeling for intersectional fairness in rankings.

The paper contains a short review of techniques examining regional wealth inequalities based on recently published research work but is also presenting unpublished features. The data pertains to Italy (IT), over the period 2007-2011: the number of cities in regions, the number of inhabitants in cities and in regions, a…

We show the existence of isometric (or Ford) fundamental regions for a large class of subgroups of the isometry group of any rank one Riemannian symmetric space of noncompact type. The proof does not use the classification of symmetric spaces. All hitherto known existence results of isometric fundamental regions and do…

Conventional Learning-to-Rank (LTR) methods optimize the utility of the rankings to the users, but they are oblivious to their impact on the ranked items. However, there has been a growing understanding that the latter is important to consider for a wide range of ranking applications (e.g. online marketplaces, job plac…

Art historians and archaeologists have long grappled with the regional classification of ancient Near Eastern ivory carvings. Based on the visual similarity of sculptures, individuals within these fields have proposed object assemblages linked to hypothesized regional production centers. Using quantitative rather than …

New method classifies special Vinberg cones of rank 4.

Low-rank matrix regression refers to the instances of recovering a low-rank matrix based on specially designed measurements and the corresponding noisy outcomes. In the last decade, numerous statistical methodologies have been developed for efficiently recovering the unknown low-rank matrices. However, in some applicat…

Deep ReLU networks with extra parameters have mostly good loss landscapes.

Let $Γ$ be a relatively hyperbolic group and let $μ$ be an admissible symmetric finitely supported probability measure on $Γ$. We extend Floyd-Ancona type inequalities up to the spectral radius of $μ$. We then show that when the parabolic subgroups are virtually abelian, the Martin boundary of the induced random walk o…

The goal of tensor completion is to fill in missing entries of a partially known tensor (possibly including some noise) under a low-rank constraint. This may be formulated as a least-squares problem. The set of tensors of a given multilinear rank is known to admit a Riemannian manifold structure, thus methods of Rieman…

The paper proves Mabuchi solitons and constants on Fano admissible manifolds.

Paper provides criteria to detect non-admissible quandles via coloring.

Study describes severe dengue ICU patients in Brazil, 2012-2024.

Inferring the functional specificity of brain regions from functional Magnetic Resonance Images (fMRI) data is a challenging statistical problem. While the General Linear Model (GLM) remains the standard approach for brain mapping, supervised learning techniques (a.k.a.} decoding) have proven to be useful to capture mu…

The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but non-linear and non-convex constraint. The main results of this paper are significan…

A Lie-admissible algebra gives by anticommutativity a Lie algebra. In this work we study remarkable classes of Lie-admissible algebras such as Vinberg, PreLie algebras. We compute the corresponding binary quadratic operads and study their Koszul duality. Considering Lie algebras as Lie-admissible algebras we can define…

We study algebraic varieties of ReLU networks to understand their representable functions.

Wide neural networks learn features under $μ$P, identifying weights and decomposing support.

We propose a general theory for studying the \xl{landscape} of nonconvex \xl{optimization} with underlying symmetric structures \tz{for a class of machine learning problems (e.g., low-rank matrix factorization, phase retrieval, and deep linear neural networks)}. In specific, we characterize the locations of stationary …

Investigates admissible metrics on compact Kähler varieties and their stability.

New examples show deletion type admissible pairs can be rigid under rational saturation.

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

In a recent work of Ayaka Shimizu$^{[5]}$, she defined an operation named region crossing change on link diagrams, and showed that region crossing change is an unknotting operation for knot diagrams. In this paper, we prove that region crossing change on a 2-component link diagram is an unknotting operation if and only…

The paper proves Liouville rigidity for Hessian equations, characterizing geometric conditions for constant solutions.

Paper develops inference methods for low-rank tensors without debiasing.

This paper proposes a new method to compress CNNs for medical image analysis, improving efficiency and accuracy.

Study on complexity of random polynomials with deterministic spikes, identifying phase transitions.

This paper ranks Latin American countries based on AI potential.

Given a hyperbolic surface, the set of all closed geodesics whose length is minimal form a graph on the surface, in fact a so-called fat graph, which we call the systolic graph. We study which fat graphs are systolic graphs for some surface (we call these admissible). There is a natural necessary condition on such grap…

Study on pre-Lie structures for semisimple Lie algebras over C.

Statistical tests for fairness in admissions data reveal hidden patterns.

Model predicts wound and episode-level readmission risk and time to re-admit.

The choice of admissible trading strategies in mathematical modelling of financial markets is a delicate issue, going back to Harrison and Kreps (1979). In the context of optimal portfolio selection with expected utility preferences this question has been a focus of considerable attention over the last twenty years. We…

Introduces admissible skein modules for non-semisimple categories.

Classifies rank-one submanifolds in Euclidean space.

We propose a novel non-parametric adaptive anomaly detection algorithm for high dimensional data based on rank-SVM. Data points are first ranked based on scores derived from nearest neighbor graphs on n-point nominal data. We then train a rank-SVM using this ranked data. A test-point is declared as an anomaly at alpha-…

The purpose of this paper is to extend the Donaldson-Corlette theorem to the case of vector bundles over cell complexes. We define the notion of a vector bundle and a Higgs bundle over a complex, and describe the associated Betti, de Rham and Higgs moduli spaces. The main theorem is that the $SL(r, \mathbb{C})$ charact…

We conduct large-scale studies on `human attention' in Visual Question Answering (VQA) to understand where humans choose to look to answer questions about images. We design and test multiple game-inspired novel attention-annotation interfaces that require the subject to sharpen regions of a blurred image to answer a qu…

The paper characterizes curves in pseudo-Galilean 4-space.