A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New concept of coarse medians for higher rank symmetric spaces.
Unique median structures found in hyperbolic spaces.
Groups with specific properties have similar cubulations and coarse median structures.
The paper studies automorphisms of RAAGs and RACGs, proving properties of their fixed subgroups.
Study of automorphisms and splittings of special groups, showing infinite groups under certain conditions.
Study on connectivity and geometry of random Coxeter groups.
Generators found for automorphisms of special groups.
We show that many graphs naturally associated to a connected, compact, orientable surface are hierarchically hyperbolic spaces in the sense of Behrstock, Hagen and Sisto. They also automatically have the coarse median property defined by Bowditch. Consequences for such graphs include a distance formula analogous to Mas…
Hierarchically hyperbolic spaces (HHSs) are a large class of spaces that provide a unified framework for studying the mapping class group, right-angled Artin and Coxeter groups, and many 3--manifold groups. We investigate strongly quasiconvex subsets in this class and characterize them in terms of their contracting pro…
We construct compactifications for median spaces with compact intervals, generalising Roller boundaries of cube complexes. Examples of median spaces with compact intervals include all finite rank median spaces and all proper median spaces of infinite rank. Our methods also work for general median algebra…
Study on median algebra structures on Euclidean spaces and manifolds with local CAT(0) cubulation.
We prove a geometric model for HHS hierarchies as CAT(0) cube complexes.
We prove a version of the Tits alternative for groups acting on complete, finite rank median spaces. This shows that group actions on finite rank median spaces are much more restricted than actions on general median spaces. Along the way, we extend to median spaces the Caprace-Sageev machinery and part of Hagen's theor…
We show that uniform lattices of isometries of products of real hyperbolic spaces act properly discontinuously and cocompactly on a median space. For lattices in products of at least two factors, this is the strongest degree of compatibility possible with the median geometry. Our theorem is also relevant for potential …
Convex cores found for group actions on median spaces.
We introduce and begin to explore the mean and median of finite sets of shapes represented as integral currents. The median can be computed efficiently in practice, and we focus most of our theoretical and computational attention on medians. We consider questions on the existence and regularity of medians. While the me…
This paper is a short summary of our recent work on the medians and means of probability measures in Riemannian manifolds. Firstly, the existence and uniqueness results of local medians are given. In order to compute medians in practical cases, we propose a subgradient algorithm and prove its convergence. After that, F…
A method for estimating the median of gradients in stochastic optimization.
This paper introduces online algorithms to estimate robust geometric median in large data streams.
The study finds that maximizing median returns is the only viable strategy in portfolio selection.
New graph properties inherited by Frechet mean and median.
The consistency of Fréchet medians is proved for probability measures in proper metric spaces. In the context of Riemannian manifolds, assuming that the probability measure has more than a half mass lying in a convex ball and verifies some concentration conditions, the positions of its Fréchet medians are estimated. It…
In high dimensions, the mean and geometric median are nearly identical.
New subspace prototype flag median improves clustering on noisy data.
Study semi-coarse spaces' homotopy and homology, extending coarse geometry.
Improved median of means estimator with tighter bounds.
Empirical median performs well in estimating location with varying scales.
This article is devoted to the problem of predicting the value taken by a random permutation , describing the preferences of an individual over a set of numbered items say, based on the observation of an input/explanatory r.v. e.g. characteristics of the individual), when error is measured…
We define a notion of free product for coarse spaces that generalizes the corresponding notion of a free product for groups. We show that free products preserve coarse properties such as coarse property C, finite coarse decomposition complexity, and coarse property A. We also give an upper bound estimate on the dimensi…
Defines coarse cohomology of space complements, proving new duality results.
Study growth rates of automorphisms of special groups.
New estimator for symmetric kernel expectations, robust to missing data.
For every strong coarse homology theory we construct a coarse assembly map as a natural transformation between coarse homology theories. We provide various conditions implying that this assembly map is an equivalence. These results generalize known results for the analytic coarse assembly map for K-homology to general …
Median-of-means sampling outperforms mean-of-means for large sample sizes in numerical integration.
Upper bound for Hausdorff distance between hyperbolic space and its medianization.
In this article, we introduce the notion of a functor on coarse spaces being coarsely excisive- a coarse analogue of the notion of a functor on topological spaces being excisive. Further, taking cones, a coarsely excisive functor yields a topologically excisive functor, and for coarse topological spaces there is an ass…
Paper proposes a novel method to improve matrix completion with median loss for large datasets.
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…
Interprets coarse symbol and index classes for Callias type operators.
The coarse category was established by Roe to distill the salient features of the large-scale approach to metric spaces and groups that was started by Gromov. In this paper, we use the language of coarse spaces to define coarse versions of asymptotic property C and decomposition complexity. We prove that coarse propert…
Evolutionary algorithms (EAs) are a sort of nature-inspired metaheuristics, which have wide applications in various practical optimization problems. In these problems, objective evaluations are usually inaccurate, because noise is almost inevitable in real world, and it is a crucial issue to weaken the negative effect …
We show that coarse property C is preserved by finite coarse direct products. We also show that the coarse analog of Dydak's countable asymptotic dimension is equivalent to the coarse version of straight finite decomposition complexity and is therefore preserved by direct products.
In this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse structures. We introduce (in a geometric way) coarse homotopy groups. The main result is that the coarse homotopy groups of cone of a compa…
We introduce a new variant of the coarse Baum-Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum-Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that are known to be counterexamples to the coarse Baum-Connes conjecture. In particula…
Marine buoys aid in the battle against Illegal, Unreported and Unregulated (IUU) fishing by detecting fishing vessels in their vicinity. Marine buoys, however, may be disrupted by natural causes and buoy vandalism. In this paper, we formulate marine buoy placement as a clustering problem, and propose dropout k-means an…
In kernel methods, the median heuristic has been widely used as a way of setting the bandwidth of RBF kernels. While its empirical performances make it a safe choice under many circumstances, there is little theoretical understanding of why this is the case. Our aim in this paper is to advance our understanding of the …
Study shows Roller compactification's median graph has limited asymptotic dimension.
Extends graph factor system to quasi-median graphs.