Tootfinder

Das #VACCELERATE Freiwilligenregister sucht Teilnehmende für eine klinische Studie zu einem noch nicht zugelassenen Medikament für die Behandlung von #Herpes.

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- Stability of simplex slicing
Serhii Myroshnychenko, Colin Tang, Kateryna Tatarko, Tomasz Tkocz

Fundamental Limits of Learning High-dimensional Simplices in Noisy Regimes
Seyed Amir Hossein Saberi, Amir Najafi, Abolfazl Motahari, Babak H. khalaj
https://arxiv.org/abs/2506.10101

Fundamental Limits of Learning High-dimensional Simplices in Noisy Regimes
In this paper, we establish sample complexity bounds for learning high-dimensional simplices in $\mathbb{R}^K$ from noisy data. Specifically, we consider $n$ i.i.d. samples uniformly drawn from an unknown simplex in $\mathbb{R}^K$, each corrupted by additive Gaussian noise of unknown variance. We prove an algorithm exists that, with high probability, outputs a simplex within $\ell_2$ or total variation (TV) distance at most $\varepsilon$ from the true simplex, provided $n \ge (K^2/\varepsilon^2…

On a class of toric manifolds arising from simplicial complexes
Ivan Limonchenko, Marinko Timotijevi\'c, Rade \v{Z}ivaljevi\'c
https://arxiv.org/abs/2506.13547

On a class of toric manifolds arising from simplicial complexes
Given an arbitrary abstract simplicial complex $K$ on $[m]:=\{1,2,\ldots,m\}$, different from the simplex $Δ_{[m]}$ with $m$ vertices, we introduce and study a canonical $(2m-2)$-dimensional toric manifold $X_K$, associated to the canonical $(m-1)$-dimensional complete regular fan $Σ_K$. This construction yields an infinite family of toric manifolds that are not quasitoric and provides a topological proof of the Dehn-Sommerville relations for the associated Bier sphere $\mathrm{Bier}(K)$. Fin…

On the minimum number of non-monochromatic simplices for Sperner labelings of a regular triangulation
L. \'A. Calvo, S. Merch\'an, D. Raboso, J. Rodrigo, J. S. Rodr\'iguez
https://arxiv.org/abs/2506.05581

On the minimum number of non-monochromatic simplices for Sperner labelings of a regular triangulation
Attending to an open problem in the literature stated by Mirzakhani and Vondrák, we give a lower bound of the number of non-monochromatic simplices for Sperner labelings of the vertices of a triangulation of a given $ k$-simplex with vertices of integer coordinates. This triangulation maximizes the number of simplices over all the triangulations of the $ k$-simplex with vertices of integer coordinates.

Dirichlet kernel density estimation for strongly mixing sequences on the simplex
Hanen Daayeb, Salah Khardani, Fr\'ed\'eric Ouimet
https://arxiv.org/abs/2506.08816

Dirichlet kernel density estimation for strongly mixing sequences on the simplex
This paper investigates the theoretical properties of Dirichlet kernel density estimators for compositional data supported on simplices, for the first time addressing scenarios involving time-dependent observations characterized by strong mixing conditions. We establish rigorous results for the asymptotic normality and mean squared error of these estimators, extending previous findings from the independent and identically distributed (iid) context to the more general setting of strongly mixing …

Interacting Geodesics on Discrete Manifolds
Oliver Knill
https://arxiv.org/abs/2506.12054 https://arxiv.org/pdf/2506.12054

Interacting Geodesics on Discrete Manifolds
We define an evolution of multiple particles on a discrete manifold $G$. Each particle alone moves on geodesics and particles can interact if they are on the same facet. They move deterministically and reversibly on the frame bundle $P$ of the abstract simplicial complex $G$. Particles are signed and each is represented by a totally ordered maximal simplex $p \in P$ in $G$. The motion of divisors on $P$ also defines a time dependent reversible deformation of space.

Information Geometry on the $\ell^2$-Simplex via the $q$-Root Transform
Levin Maier
https://arxiv.org/abs/2506.00485 https://arxiv.or…

Information Geometry on the $\ell^2$-Simplex via the $q$-Root Transform
In this paper, we introduce \emph{$\ell^p$-information geometry}, an infinite dimensional framework that shares key features with the geometry of the space of probability densities \( \mathrm{Dens}(M) \) on a closed manifold, while also incorporating aspects of measure-valued information geometry. We define the \emph{$\ell^2$-probability simplex} with a noncanonical differentiable structure induced via the \emph{$q$-root transform} from an open subset of the $\ell^p$-sphere. This structure rend…

On combinatorial aspects of fat Delta
Sti\'ephen Pradal
https://arxiv.org/abs/2506.01717 https://arxiv.org/pdf/2506.01717

On combinatorial aspects of fat Delta
The category fat Delta, introduced by J. Kock, is a modification of the simplex category where the degeneracies behave weakly. The objective of this note is to provide tools for working with fat Delta. In particular, we identify three types of morphisms: degenerated, standard and vertical faces, and establish six relations between these classes. We then show that fat Delta is generated by these morphisms and relations.

Repelling curvature via $\epsilon-$repelling Laplacian on positive connected signed graphs
Yong Lin, Shi Wan
https://arxiv.org/abs/2506.10492 https://

Repelling curvature via $ε-$repelling Laplacian on positive connected signed graphs
The paper defines a positive semidefinite operator called $ε-$repelling Laplacian on a positive connected signed graph where $ε$ is an arbitrary positive number less than a constant $ε_0$ related to the graph's consensus problem. Then we investigate the upper bound of the second smallest eigenvalue of $ε-$repelling Laplacian. Besides, we use the pseudoinverse of $ε-$repelling Laplacian to construct a simplex as well as $ε-$repelling cost whose square root turns out to be a distance among …

Sperner's colorings of hypergraphs arising from edgewise triangulations
Du\v{s}ko Joji\'c, Ognjen Papaz
https://arxiv.org/abs/2506.07201 https://…

Sperner's colorings of hypergraphs arising from edgewise triangulations
We investigate Sperner's labelings of $H^π_{k,q}$, the hypergraph whose hyperedges are facets of the edgewise triangulation of a $(k-1)$-simplex defined by a permutation $π\in \mathbb{S}_{k-1}$. Mirzakhani and Vondr\' ak showed that the greedy coloring of $H^{\mathrm{Id}}_{k,q}$ produces the maximal number of monochromatic hyperedges. The line graph of $H_{k,q}^π$ is built from the copies of the graph $G_π$ that represents which subsets of consecutive numbers of $[k-1]$ are contiguous in $�…

This https://arxiv.org/abs/2501.00671 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sylvester's problem for beta-type distributions
Consider $d+2$ i.i.d. random points $X_1,\ldots, X_{d+2}$ in $\mathbb R^d$. In this note, we compute the probability that their convex hull is a simplex focusing on three specific distributional settings: (i) the distribution of $X_1$ is multivariate standard normal; (ii) the density of $X_1$ is proportional to $(1-\|x\|^2)^β$ on the unit ball (the beta distribution); (iii) the density of $X_1$ is proportional to $(1+\|x\|^2)^{-β}$ (the beta prime distribution). In the Gau…

This https://arxiv.org/abs/2304.07859 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Affine Isoperimetric Inequalities for Higher-Order Projection and Centroid Bodies
In 1970, Schneider introduced the $m$th order difference body of a convex body, and also established the $m$th-order Rogers-Shephard inequality. In this paper, we extend this idea to the projection body, centroid body, and radial mean bodies, as well as prove the associated inequalities (analogues of Zhang's projection inequality, Petty's projection inequality, the Busemann-Petty centroid inequality and Busemann's random simplex inequality). We also establish a new proof of Schneider's $m$th-or…

Self-adjoint operators in Z-stable C$^*$-algebras with prescribed spectral data
Andrew S. Toms, Hao Wan
https://arxiv.org/abs/2505.22448 https://

Self-adjoint operators in Z-stable C$^*$-algebras with prescribed spectral data
We consider the variety of spectral measures that are induced by quasitraces on the spectrum of a self-adjoint operator in a simple separable unital and Z-stable C$^*$-algebra. This amounts to a continuous map from the simplex of quasitraces of the C$^*$-algebra into regular Borel probability measures on the spectrum of the operator under consideration. In the case of a connected spectrum this data determines the unitary equivalence class of the operator, and may be reduced to to the case of an…

Vietoris--Rips Shadow for Euclidean Graph Reconstruction
Rafal Komendarczyk, Sushovan Majhi, Atish Mitra
https://arxiv.org/abs/2506.01603 https://

Vietoris--Rips Shadow for Euclidean Graph Reconstruction
The shadow of an abstract simplicial complex $K$ with vertices in $\mathbb R^N$ is a subset of $\mathbb R^N$ defined as the union of the convex hulls of simplices of $K$. The Vietoris--Rips complex of a metric space $(S,d)$ at scale $β$ is an abstract simplicial complex whose each $k$-simplex corresponds to $(k+1)$ points of $S$ within diameter $β$. In case $S\subset\mathbb R^2$ and $d(a,b)=\|a-b\|$ standard Euclidean, the natural shadow projection of the Vietoris--Rips is already p…

There is only one Farey map
Giovanni Panti
https://arxiv.org/abs/2506.02984 https://arxiv.org/pdf/2506.02984

There is only one Farey map
Let A_0, A_1 be nonnegative matrices in GL(n+1,Z) such that the subsimplexes A_0[Delta], A_1[Delta] split the standard unit n-dimensional simplex Delta in two. We prove that, for every n=1,2,... and up to the natural action of the symmetric group by conjugation, there are precisely three choices for the pair (A_0, A_1) such that the resulting projective Iterated Function System is topologically contractive. In equivalent terms, in every dimension there exist precisely three continued fraction a…

Quasi-symmetry and geometric marginal homogeneity: A simplicial approach to square contingency tables
Keita Nakamura, Tomoyuki Nakagawa, Kouji Tahata
https://arxiv.org/abs/2506.02474

Quasi-symmetry and geometric marginal homogeneity: A simplicial approach to square contingency tables
Square contingency tables are traditionally analyzed with a focus on the symmetric structure of the corresponding probability tables. We view probability tables as elements of a simplex equipped with the Aitchison geometry. This perspective allows us to present a novel approach to analyzing symmetric structure using a compositionally coherent framework. We present a geometric interpretation of quasi-symmetry as an e-flat subspace and introduce a new concept called geometric marginal homogeneity…

This https://arxiv.org/abs/2407.01353 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Isotropic constants and regular polytopes
We discuss first-order optimality conditions for the isotropic constant and combine them with RS-movements to obtain structural information about polytopal maximizers. Strengthening a result by Rademacher, it is shown that a polytopal local maximizer with a simplicial vertex must be a simplex. A similar statement is shown for a centrally symmetric local maximizer with a simplicial vertex: it has to be a cross-polytope. Moreover, we show that a zonotope that maximizes the isotropic constant and …