arXiv research

New risk-dependent centrality measures assess node importance in financial networks.

Unified approach to experimental design using interlacing polynomials.

We characterize those unions of embedded disjoint circles in the 2-sphere which can be the multiple point set of a generic immersion of the 2-sphere into 3-dimensional space in terms of the interlacement of the given circles. Our result is the one higher dimensional analogue of Rosenstiehl's characterization of words b…

New framework estimates eigenvalues of kernel matrices without full matrix construction.

Study eigenvector overlaps in large Gaussian matrices, simplifying for GOE.

A knot diagram has an associated looped interlacement graph, obtained from the intersection graph of the Gauss diagram by attaching loops to the vertices that correspond to negative crossings. This construction suggests an extension of the Kauffman bracket to an invariant of looped graphs, and an extension of Reidemeis…

Loops in surfaces and chord diagrams are studied with graph factorizations and grammars.

New concept of regular separation for ODEs leads to improved Hardy field results.

In earlier work we introduced the graph bracket polynomial of graphs with marked vertices, motivated by the fact that the Kauffman bracket of a link diagram D is determined by a looped, marked version of the interlacement graph associated to a directed Euler system of the universe graph of D. Here we extend the graph b…

DNA sequencing to identify genetic variants is becoming increasingly valuable in clinical settings. Assessment of variants in such sequencing data is commonly implemented through Bayesian heuristic algorithms. Machine learning has shown great promise in improving on these variant calls, but the input for these is still…

In this paper, we study distribution of the zeros of the Alexander polynomials of knots and links in S^3. We call a knot or link "real stable" (resp. "circular stable") if all the zeros of its Alexander polynomial are real (resp. unit complex). We give a general construction of real stable and circular stable knots and…

Gabai showed that the Whitehead manifold is the union of two submanifolds each of which is homeomorphic to $\mathbb R^3$ and whose intersection is again homeomorphic to $\mathbb R^3$. Using a family of generalizations of the Whitehead Link, we show that there are uncountably many contractible 3-manifolds with this doub…

Study surfaces with constant ratio of principal curvatures in Euclidean and isotropic geometries.

This paper establishes certain existence and classification results for solutions to $SU(n)$ Toda systems with three singular sources at 0, 1, and $\infty$. First, we determine the necessary conditions for such an $SU(n)$ Toda system to be related to an $n$th order hypergeometric equation. Then, we construct solutions …

We propose a model in which a spliced vector bundle (with an arbitrary number of gauge structures in the splice) possesses a geometry which do not split. The model employs connection 1-forms with values in a space-product of Lie algebras, and therefore interlaces the various gauge structures in a non-trivial manner. Sp…

The present paper is a review of the current state of Graph-Link Theory (graph-links are also closely related to homotopy classes of looped interlacement graphs), dealing with a generalisation of knots obtained by translating the Reidemeister moves for links into the language of intersection graphs of chord diagrams. I…

Paper proposes a robust framework for detecting multiple periodic components in time series.

Weaved helices form mechanically stable 3D structures.

Equation discovery method reconstructs model structure and parameters from data.

The paper examines circle graphs of Gauss diagrams and finds counterexamples to previous descriptions.

Solves Gursky-Streets equations for $σ_k$ Yamabe problem in dimensions $n \geq 2k$.

Let $D$ be an oriented classical or virtual link diagram with directed universe $\vec{U}$. Let $C$ denote a set of directed Euler circuits, one in each connected component of $U$. There is then an associated looped interlacement graph $L(D,C)$ whose construction involves very little geometric information about the way …

This work explains how tempering improves Bayesian neural networks by reducing the impact of data augmentation.

In this paper, we address the problem of synthesizing multi-parameter magnetic resonance imaging (mp-MRI) data, i.e. Apparent Diffusion Coefficients (ADC) and T2-weighted (T2w), containing clinically significant (CS) prostate cancer (PCa) via semi-supervised adversarial learning. Specifically, our synthesizer generates…

This paper protects rankings from differential privacy breaches.

The paper addresses privacy in rank aggregation using randomized responses.

This paper addresses the problem of rank aggregation, which aims to find a consensus ranking among multiple ranking inputs. Traditional rank aggregation methods are deterministic, and can be categorized into explicit and implicit methods depending on whether rank information is explicitly or implicitly utilized. Surpri…

We study the problem of rank aggregation: given a set of ranked lists, we want to form a consensus ranking. Furthermore, we consider the case of extreme lists: i.e., only the rank of the best or worst elements are known. We impute missing ranks by the average value and generalise Spearman's ρto extreme ranks. Our main …

Develops a method to infer partial rankings from sparse comparisons.

Research characterizes learnability of multilabel ranking problems.

This paper compares rank aggregation methods for partial label ranking.

The geometric approach [1312.1262] to iterated variations of local functionals -- e.g., of the (master-)action functional -- resulted in an extension of the deformation quantisation technique to the set-up of Poisson models of field theory [IHES/M/15/13]. It also allowed of a rigorous proof ([1312.1262],[1210.0726]) fo…

We study the problem of learning to rank from multiple information sources. Though multi-view learning and learning to rank have been studied extensively leading to a wide range of applications, multi-view learning to rank as a synergy of both topics has received little attention. The aim of the paper is to propose a c…

Study of WKB asymptotics of Stokes matrices and spectral curves, proving rhombus inequalities.

Paper tackles underranking in group-fair ranking systems, proving a trade-off and presenting an algorithm.

New ranking system balances fairness and user utility.

Introduces nondecreasing rank for matrices and tensors, developing methods and applications.

Analytic proof for minimal rank Sard conjecture.

Rank-one measurements limit feasible sets for low-rank PSD matrices.

Sparse reduced-rank regression selects variables and ranks via manifold optimization.

We consider the problem of statistical inference for ranking data, specifically rank aggregation, under the assumption that samples are incomplete in the sense of not comprising all choice alternatives. In contrast to most existing methods, we explicitly model the process of turning a full ranking into an incomplete on…

The paper tackles learning true rankings from noisy, incomplete data.

Paper introduces GAMs for interpretable learning-to-rank models.

Proposes tensor Q-rank for better tensor rank recovery in complex data.

Low-rank framework for task-specific LLM ranking from sparse comparisons.

New method solves nonsmooth low-rank matrix optimization problems efficiently.

New methods rank players using covariates and comparisons, outperforming existing algorithms.

This article reviews ranking problems and their solutions.