Tootfinder

Fixed Points of Meir-Keeler and Leader Contractions with bounded orbits in b-Metric Spaces
Hassan Khandani
https://arxiv.org/abs/2506.09074 https://…

Fixed Points of Meir-Keeler and Leader Contractions with bounded orbits in b-Metric Spaces
We establish fixed-point theorems for Meir-Keeler-type contractions in b-metric spaces. While Lu et al. demonstrated via an explicit counterexample that classical Meir-Keeler contractions may fail to admit fixed points in this setting, we prove that a natural strengthening of the conditions yields existence results. Specifically, we show that every non-expansive Leader contraction with bounded orbits in a b-metric space possesses a fixed point. To contextualize our findings, we present a hier…

Scalable Counting of Minimal Trap Spaces and Fixed Points in Boolean Networks
Mohimenul Kabir, Van-Giang Trinh, Samuel Pastva, Kuldeep S Meel
https://arxiv.org/abs/2506.06013

Scalable Counting of Minimal Trap Spaces and Fixed Points in Boolean Networks
Boolean Networks (BNs) serve as a fundamental modeling framework for capturing complex dynamical systems across various domains, including systems biology, computational logic, and artificial intelligence. A crucial property of BNs is the presence of trap spaces -- subspaces of the state space that, once entered, cannot be exited. Minimal trap spaces, in particular, play a significant role in analyzing the long-term behavior of BNs, making their efficient enumeration and counting essential. The…

Stochastic Krasnosel skii-Mann Iterations in Banach Spaces with Bregman Distances
Saeed Hashemi Sababe, Ehsan Lotfali Ghasab
https://arxiv.org/abs/2506.08031

Stochastic Krasnosel skii-Mann Iterations in Banach Spaces with Bregman Distances
We propose a generalization of the stochastic Krasnoselskil-Mann $(SKM)$ algorithm to reflexive Banach spaces endowed with Bregman distances. Under standard martingale-difference noise assumptions in the dual space and mild conditions on the distance-generating function, we establish almost-sure convergence to a fixed point and derive non-asymptotic residual bounds that depend on the uniform convexity modulus of the generating function. Extensions to adaptive Bregman geometries and robust noise…

Effective positivity of Hodge bundles and applications
Giulio Codogni, Zsolt Patakfalvi, Luca Tasin
https://arxiv.org/abs/2506.10515 https://

Effective positivity of Hodge bundles and applications
We show boundedness results that are from different areas of algebraic geometry, but they are closely connected mathematically. The technical starting point is bounding the integer $q>0$ for which the $q$-th Hodge bundles becomes (semi-)positive for families of stable varieties. We then draw many consequences, among which: 1.) a lower bound for the Chow-Mumford volumes of fibrations of fixed dimension and klt general fiber; 2.) a lower bound on the Chow-Moumford volume of moduli spaces of stabl…

Latent geometry emerging from network-driven processes
Andrea Filippo Beretta, Davide Zanchetta, Sebastiano Bontorin, Manlio De Domenico
https://arxiv.org/abs/2506.09616

Latent geometry emerging from network-driven processes
Understanding network functionality requires integrating structure and dynamics, and emergent latent geometry induced by network-driven processes captures the low-dimensional spaces governing this interplay. Here, we focus on generative-model-based approaches, distinguishing two reconstruction classes: fixed-time methods, which infer geometry at specific temporal scales (e.g., equilibrium), and multi-scale methods, which integrate dynamics across near- and far-from-equilibrium scales. Over the …

Invertible Complex Measures on Euclidean Spaces
David Berger, Alexander Lindner
https://arxiv.org/abs/2506.09012 https://arxiv.org/pd…

Invertible Complex Measures on Euclidean Spaces
In 1971 Taylor characterised all complex measures on $\mathbb{R}$ that are invertible with respect to convolution as those which can be written in the form $δ_γ\ast σ^{\ast m} \ast \exp(ν)$ for some $γ\in \mathbb{R}$, some complex measure $ν$, some $m\in \mathbb{Z}$ and a given fixed invertible finite signed measure $σ$ (which has characteristic function $\mathbb{R} \ni z \mapsto (1+i z)/(1-i z)$). We extend Taylor's result to complex measures on $\mathbb{R}^n$. Somewhat surprisingly, th…

This https://arxiv.org/abs/2502.07606 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csGT_…

Algorithmic Aspects of Strategic Trading
Algorithmic trading in modern financial markets is widely acknowledged to exhibit strategic, game-theoretic behaviors whose complexity can be difficult to model. A recent series of papers (Chriss, 2024b,c,a, 2025) has made progress in the setting of trading for position building. Here parties wish to buy or sell a fixed number of shares in a fixed time period in the presence of both temporary and permanent market impact, resulting in exponentially large strategy spaces. While these papers prima…

This https://arxiv.org/abs/2208.00889 has been replaced.
link: https://scholar.google.com/scholar?q=a

Gromov-Witten/Hurwitz wall-crossing
For a target variety $X$ and a nodal curve $C$, we introduce a one-parameter stability condition, termed $ε$-admissibility, for maps from nodal curves to $X\times C$. If $X$ is a point, $ε$-admissibility interpolates between moduli spaces of stable maps to $C$ relative to some fixed points and moduli spaces of admissible covers with arbitrary ramifications over the same fixed points and simple ramifications elsewhere on $C$. Using Zhou's entangled tails, we prove wall-crossing formulas relati…

This https://arxiv.org/abs/2503.21224 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Efficient Learning for Entropy-Regularized Markov Decision Processes via Multilevel Monte Carlo
Designing efficient learning algorithms with complexity guarantees for Markov decision processes (MDPs) with large or continuous state and action spaces remains a fundamental challenge. We address this challenge for entropy-regularized MDPs with Polish state and action spaces, assuming access to a generative model of the environment. We propose a novel family of multilevel Monte Carlo (MLMC) algorithms that integrate fixed-point iteration with MLMC techniques and a generic stochastic approximat…

Code-based $[3,1]$-avoiders in finite affine spaces $\mathrm{AG}(n,2)$
Benedek Kov\'acs
https://arxiv.org/abs/2505.24072 https://…

Code-based $[3,1]$-avoiders in finite affine spaces $\mathrm{AG}(n,2)$
The author, together with Nagy, studied the following problem on unavoidable intersections of given size in binary affine spaces. Given an $m$-element set $S\subseteq \mathbb{F}_2^n$, is there guaranteed to be a $[k,t]$-flat, that is, a $k$-dimensional affine subspace of $\mathbb{F}_2^n$ containing exactly $t$ points of $S$? Such problems can be viewed as generalizations of the cap set problem over the binary field. They conjectured that for every fixed pair $(k,t)$ with $k\ge 1$ and $0\le t\le…