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Berger-Joyal duality and traces I
Nicholas Cecil, Benjamin Cooper
https://arxiv.org/abs/2509.11423 https://arxiv.org/pdf/2509.11423

Berger-Joyal duality and traces I
We give a new proof that the opposite of Joyal's disk category $\mathcal{D}_n$ is Berger's wreath product category $Θ_n = Δ\wr\cdots\wrΔ$. Our techniques continue to apply when the simplex category $Δ$ is replaced by Connes' cyclic category $Λ$ and some other crossed simplicial groups.

Replaced article(s) found for cs.DS. https://arxiv.org/list/cs.DS/new
[1/1]:
- Upper and Lower Bounds on the Smoothed Complexity of the Simplex Method
Sophie Huiberts, Yin Tat Lee, Xinzhi Zhang

Geometric Analysis of Magnetic Labyrinthine Stripe Evolution via U-Net Segmentation
Vin\'icius Yu Okubo, Kotaro Shimizu, B. S. Shivaran, Gia-Wei Chern, Hae Yong Kim
https://arxiv.org/abs/2509.11485

Geometric Analysis of Magnetic Labyrinthine Stripe Evolution via U-Net Segmentation
Labyrinthine stripe patterns are common in many physical systems, yet their lack of long-range order makes quantitative characterization challenging. We investigate the evolution of such patterns in bismuth-doped yttrium iron garnet (Bi:YIG) films subjected to a magnetic field annealing protocol. A U-Net deep learning model, trained with synthetic degradations including additive white Gaussian and Simplex noise, enables robust segmentation of experimental magneto-optical images despite noise an…

Vandermonde Cells Through the Lens of Positive Geometry
Fatemeh Mohammadi, Sebastian Seemann
https://arxiv.org/abs/2510.11614 https://arxiv.org/pdf/2510.11…

Vandermonde Cells Through the Lens of Positive Geometry
We study the geometric and algebraic structure of Vandermonde cells, defined as images of the standard probability simplex under the Vandermonde map given by consecutive power sum polynomials. Motivated by their combinatorial equivalence to cyclic polytopes, which are well-known examples of positive geometries and tree amplituhedra, we investigate whether Vandermonde cells admit the structure of positive geometries. We derive explicit parametrizations and algebraic equations for their boundary …

Density estimation for compositional data using nonparametric mixtures
Jiajin Xie, Yong Wang, Eduardo Garc\'ia-Portugu\'es
https://arxiv.org/abs/2510.07608 https://

Density estimation for compositional data using nonparametric mixtures
Compositional data, representing proportions constrained to the simplex, arise in diverse fields such as geosciences, ecology, genomics, and microbiome research. Existing nonparametric density estimation methods often rely on transformations, which may induce substantial bias near the simplex boundary. We propose a nonparametric mixture-based framework for density estimation on compositions. Nonparametric Dirichlet mixtures are employed to naturally accommodate boundary values, thereby avoiding…

Simplex Frank-Wolfe: Linear Convergence and Its Numerical Efficiency for Convex Optimization over Polytopes
Haoning Wang, Houduo Qi, Liping Zhang
https://arxiv.org/abs/2509.24279

Simplex Frank-Wolfe: Linear Convergence and Its Numerical Efficiency for Convex Optimization over Polytopes
We investigate variants of the Frank-Wolfe (FW) algorithm for smoothing and strongly convex optimization over polyhedral sets, with the goal of designing algorithms that achieve linear convergence while minimizing per-iteration complexity as much as possible. Starting from the simple yet fundamental unit simplex, and based on geometrically intuitive motivations, we introduce a novel oracle called Simplex Linear Minimization Oracle (SLMO), which can be implemented with the same complexity as the…

Strategy Improvement, the Simplex Algorithm and Lopsidedness
Matthew Maat
https://arxiv.org/abs/2509.16075 https://arxiv.org/pdf/2509.16075

Strategy Improvement, the Simplex Algorithm and Lopsidedness
The strategy improvement algorithm for mean payoff games and parity games is a local improvement algorithm, just like the simplex algorithm for linear programs. Their similarity has turned out very useful: many lower bounds on running time for the simplex method have been created from lower bounds for strategy improvement. However, earlier connections between these algorithms required constructing an intermediate Markov decision process, which is not always possible. We prove a formal, direct c…

linrax: A JAX Compatible, Simplex Method Linear Program Solver
Brendan Gould, Akash Harapanahalli, Samuel Coogan
https://arxiv.org/abs/2509.19484 https://a…

linrax: A JAX Compatible, Simplex Method Linear Program Solver
We present linrax, the first simplex based linear program (LP) solver compatible with the JAX ecosystem. In many control algorithms, LPs are often automatically generated and frequently solved either offline or online in the control loop. This motivates the design of linrax, which is especially suited for compilation into a complex JAX-based pipeline as a subroutine. We discuss the challenges associated with implementing a general purpose LP solver under strict design requirements from JAX. Not…

Erf, the flagship implementation of the SimpleX Messaging Protocol uses version 17 but the last published specification only references v6, v7 and v9. How are we expected to implement compatible clients and servers?

The Use of the Simplex Architecture to Enhance Safety in Deep-Learning-Powered Autonomous Systems
Federico Nesti, Niko Salamini, Mauro Marinoni, Giorgio Maria Cicero, Gabriele Serra, Alessandro Biondi, Giorgio Buttazzo
https://arxiv.org/abs/2509.21014

The Use of the Simplex Architecture to Enhance Safety in Deep-Learning-Powered Autonomous Systems
Recently, the outstanding performance reached by neural networks in many tasks has led to their deployment in autonomous systems, such as robots and vehicles. However, neural networks are not yet trustworthy, being prone to different types of misbehavior, such as anomalous samples, distribution shifts, adversarial attacks, and other threats. Furthermore, frameworks for accelerating the inference of neural networks typically run on rich operating systems that are less predictable in terms of tim…