Tootfinder

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…

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?

Complexity Analysis of the Regular Simplicial Search Method with Reflection and Shrinking Steps for Derivative-Free Optimization
Liyuan Cao, Wei Hu, Jinxin Wang
https://arxiv.org/abs/2508.16561

Complexity Analysis of the Regular Simplicial Search Method with Reflection and Shrinking Steps for Derivative-Free Optimization
Simplex-type methods, such as the well-known Nelder-Mead algorithm, are widely used in derivative-free optimization (DFO), particularly in practice. Despite their popularity, the theoretical understanding of their convergence properties has been limited, and until very recently essentially no worst-case complexity bounds were available. Recently, Cao et al. provided a sharp error bound for linear interpolation and extrapolation and derived a worst-case complexity result for a basic simplex-type…

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…

The Geometry of Constrained Optimization: Constrained Gradient Flows via Reparameterization: A-Stable Implicit Schemes, KKT from Stationarity, and Geometry-Respecting Algorithms
Valentin Leplat
https://arxiv.org/abs/2508.18764

The Geometry of Constrained Optimization: Constrained Gradient Flows via Reparameterization: A-Stable Implicit Schemes, KKT from Stationarity, and Geometry-Respecting Algorithms
Gradient-flow (GF) viewpoints unify and illuminate optimization algorithms. Yet most GF analyses focus on unconstrained settings. We develop a geometry-respecting framework for constrained problems by (i) reparameterizing feasible sets with maps whose Jacobians vanish on the boundary (orthant/box) or are rank \(n{-}1\) (simplex), (ii) deriving flows in the parameter space which induce feasible primal dynamics, (iii) discretizing with A-stable implicit schemes solvable by robust inner loops (Mod…

Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- A unified worst case for classical simplex and policy iteration pivot rules
Yann Disser, Nils Mosis

The distribution of calibrated likelihood functions on the probability-likelihood Aitchison simplex
Paul-Gauthier No\'e, Andreas Nautsch, Driss Matrouf, Pierre-Michel Bousquet, Jean-Fran\c{c}ois Bonastre
https://arxiv.org/abs/2509.03365

The distribution of calibrated likelihood functions on the probability-likelihood Aitchison simplex
While calibration of probabilistic predictions has been widely studied, this paper rather addresses calibration of likelihood functions. This has been discussed, especially in biometrics, in cases with only two exhaustive and mutually exclusive hypotheses (classes) where likelihood functions can be written as log-likelihood-ratios (LLRs). After defining calibration for LLRs and its connection with the concept of weight-of-evidence, we present the idempotence property and its associated constrai…

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.

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…

A Structure-Preserving Rational Integrator for the Replicator Dynamics on the Probability Simplex
Mario Pezzella
https://arxiv.org/abs/2507.22609 https://a…

A Structure-Preserving Rational Integrator for the Replicator Dynamics on the Probability Simplex
In this work, we introduce a quadratically convergent and dynamically consistent integrator specifically designed for the replicator dynamics. The proposed scheme combines a two-stage rational approximation with a normalization step to ensure confinement to the probability simplex and unconditional preservation of non-negativity, invariant sets and equilibria. A rigorous convergence analysis is provided to establish the scheme's second-order accuracy, and an embedded auxiliary method is devised…

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 …

Generalization of Ceva theorem
Wojciech Wdowski
https://arxiv.org/abs/2508.11853 https://arxiv.org/pdf/2508.11853…

Generalization of Ceva theorem
In this paper, we present a novel generalization of the classical Ceva theorem to arbitrarily dimensional simplexes. Our approach allows cevians to have any dimension (smaller than the dimension of the base simplex). Consequently, our result unifies other generalizations of the Ceva theorem obtained in recent years.

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…

Hausdorff Dimension of Sets of Generic Points for Non-statistical Dynamical Systems
Douglas Coates, Katrin Gelfert
https://arxiv.org/abs/2509.00241 https://

Hausdorff Dimension of Sets of Generic Points for Non-statistical Dynamical Systems
We consider one dimensional maps with several neutral fixed points that do not admit any physical measures. We show that there is simplex of measures so that every measure in this simplex has a basin which has full Hausdorff dimension.

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…

One-weight codes in the sum-rank metric
Usman Mushrraf, Ferdinando Zullo
https://arxiv.org/abs/2508.04262 https://arxiv.org/pdf/2508.04262

One-weight codes in the sum-rank metric
One-weight codes, in which all nonzero codewords share the same weight, form a highly structured class of linear codes with deep connections to finite geometry. While their classification is well understood in the Hamming and rank metrics - being equivalent to (direct sums of) simplex codes - the sum-rank metric presents a far more intricate landscape. In this work, we explore the geometry of one-weight sum-rank metric codes, focusing on three distinct classes. First, we introduce and classify …

Optimal Thresholds for Monotone Non-Boolean Functions
Saba Lepsveridze, Allen Lin
https://arxiv.org/abs/2509.07246 https://arxiv.org/pdf/2509.07246

Optimal Thresholds for Monotone Non-Boolean Functions
Let $[q] = \{0,1,\ldots,q-1\}$, let $Δ[q]$ denote the simplex of probability measures on $[q]$, and let $λ$ denote the Lebesgue measure. We prove that for any symmetric monotone function $f \colon[q]^n \to [q]$ and any $a \in [q]$ we have \begin{equation*} λ(\{μ\in Δ[q]\;\vert\;\mathbf{Pr}_{x\simμ^{\otimes n}}[f(x)=a] \in (\varepsilon,1-\varepsilon)\}) = O(1/\log n)\textrm{.} \end{equation*} We also show that this bound is tight. This improves Kalai and Mossel's previous bound of $O…

Epsilon-Minimax Solutions of Statistical Decision Problems
Andr\'es Aradillas Fern\'andez, Jos\'e Blanchet, Jos\'e Luis Montiel Olea, Chen Qiu, J\"org Stoye, Lezhi Tan
https://arxiv.org/abs/2509.08107

Epsilon-Minimax Solutions of Statistical Decision Problems
A decision rule is epsilon-minimax if it is minimax up to an additive factor epsilon. We present an algorithm for provably obtaining epsilon-minimax solutions of statistical decision problems. We are interested in problems where the statistician chooses randomly among I decision rules. The minimax solution of these problems admits a convex programming representation over the (I-1)-simplex. Our suggested algorithm is a well-known mirror subgradient descent routine, designed to approximately solv…

Light S-wave pentaquarks on the light front
Fangcheng He, Edward Shuryak, Wan Wu, Ismail Zahed
https://arxiv.org/abs/2510.02076 https://arxiv.org/pdf/2510.…

Light S-wave pentaquarks on the light front
We construct an explicit basis set for pentaquark states on a regular 4-simplex, that diagonalizes the Hamiltonian for light pentaquarks with confinement on the light front (LF). The ensuing eigenstates are free of the center of mass motion and satisfy exact Dirichlet boundary conditions. Hyperfine interactions in the form of color-spin or flavor-spin are shown to lift the degeneracy of the 16 pentastates, with a spectrum that compares fairly with some of the empirical nucleon excited states. T…

Replaced article(s) found for math.CO. https://arxiv.org/list/math.CO/new
[1/1]:
- Simplex faces of order and chain polytopes
Aki Mori
https://

A trace pairing and Elliott invariant for groupoid homology
Robin Deeley, Rufus Willett
https://arxiv.org/abs/2509.03759 https://arxiv.org/pdf/2509.03759…

A trace pairing and Elliott invariant for groupoid homology
For an étale groupoid, we define a pairing between the Crainic-Moerdijk groupoid homology and the simplex of invariant Borel probability measures on the base space. The main novelty here is that the groupoid need not have totally disconnected base space, and thus the pairing can give more refined information than the measures of clopen subsets of the base space. Our principal motivation is $C^*$-algebra theory. The Elliott invariant of a $C^*$-algebra is defined in terms of $K$-theory and tr…

Soil Texture Prediction with Bayesian Generalized Additive Models for Spatial Compositional Data
Joaqu\'in Mart\'inez-Minaya, Lore Zumeta-Olaskoaga, Dae-Jin Lee
https://arxiv.org/abs/2508.07708

Soil Texture Prediction with Bayesian Generalized Additive Models for Spatial Compositional Data
Compositional data (CoDa) plays an important role in many fields such as ecology, geology, or biology. The most widely used modeling approaches are based on the Dirichlet and the logistic-normal formulation under Aitchison geometry. Recent developments in the mathematical field on the simplex geometry allow to express the regression model in terms of coordinates and estimate its coefficients. Once the model is projected in the real space, we can employ a multivariate Gaussian regression to deal…

Stochastic Bandits for Crowdsourcing and Multi-Platform Autobidding
Fran\c{c}ois Bachoc, Nicol\`o Cesa-Bianchi, Tommaso Cesari, Roberto Colomboni
https://arxiv.org/abs/2508.05844

Stochastic Bandits for Crowdsourcing and Multi-Platform Autobidding
Motivated by applications in crowdsourcing, where a fixed sum of money is split among $K$ workers, and autobidding, where a fixed budget is used to bid in $K$ simultaneous auctions, we define a stochastic bandit model where arms belong to the $K$-dimensional probability simplex and represent the fraction of budget allocated to each task/auction. The reward in each round is the sum of $K$ stochastic rewards, where each of these rewards is unlocked with a probability that varies with the fraction…

Short circuit walks in fixed dimension
Alexander E. Black, Christian N\"obel, Raphael Steiner
https://arxiv.org/abs/2510.01916 https://arxiv.org/pdf/2…

Short circuit walks in fixed dimension
Circuit augmentation schemes are a family of combinatorial algorithms for linear programming that generalize the simplex method. To solve the linear program, they construct a so-called monotone circuit walk: They start at an initial vertex of the feasible region and traverse a discrete sequence of points on the boundary, while moving along certain allowed directions (circuits) and improving the objective function at each step until reaching an optimum. Since the existence of short circuit walks…

A note concerning frames and geometric inequalities
Jeff Ledford, Kevin Rivera-Ayala, Emma Schroeder
https://arxiv.org/abs/2509.05611 https://arxiv.org/pdf…

A note concerning frames and geometric inequalities
One may associate several frames to a given polytope, such as its collection of vertices, edges, or facet normal vectors. In this note, we use these frames to generate geometric inequalities for the simplex in $\mathbb{R}^d$ and polytopes with $d+2$ vertices in dimension 2 and 3.

Extendability of $1$-decomposable complexes
Rhea Ghosal, Melody Han, Benjamin Keller, Scarlett Kerr, Justin Liu, SuHo Oh, Ryan Tang, Chloe Weng
https://arxiv.org/abs/2508.04555 …

Extendability of $1$-decomposable complexes
A well-known conjecture of Simon (1994) states that any pure $d$-dimensional shellable complex on $n$ vertices can be extended to $Δ_{n-1}^{(d)}$, the $d$-skeleton of the $(n-1)$-dimensional simplex, by attaching one facet at a time while maintaining shellability. The notion of $k$-decomposability for simplicial complexes, which generalizes shellability, was introduced by Provan and Billera (1980). Coleman, Dochtermann, Geist, and Oh (2022) showed that any pure $d$-dimensional $0$-decomposab…

Interpretable dimension reduction for compositional data
Junyoung Park, Cheolwoo Park, Jeongyoun Ahn
https://arxiv.org/abs/2509.05563 https://arxiv.org/pdf…

Interpretable dimension reduction for compositional data
High-dimensional compositional data, such as those from human microbiome studies, pose unique statistical challenges due to the simplex constraint and excess zeros. While dimension reduction is indispensable for analyzing such data, conventional approaches often rely on log-ratio transformations that compromise interpretability and distort the data through ad hoc zero replacements. We introduce a novel framework for interpretable dimension reduction of compositional data that avoids extra trans…

A Relaxation Approach to Synthetic Control
Chengwang Liao, Zhentao Shi, Yapeng Zheng
https://arxiv.org/abs/2508.01793 https://arxiv.org/pdf/2508.01793

A Relaxation Approach to Synthetic Control
The synthetic control method (SCM) is widely used for constructing the counterfactual of a treated unit based on data from control units in a donor pool. Allowing the donor pool contains more control units than time periods, we propose a novel machine learning algorithm, named SCM-relaxation, for counterfactual prediction. Our relaxation approach minimizes an information-theoretic measure of the weights subject to a set of relaxed linear inequality constraints in addition to the simplex constra…

Monotone Paths on Acyclic 3-Regular Graphs
Fran\c{c}ois Cl\'ement, Dan Guyer
https://arxiv.org/abs/2508.02108 https://arxiv.org/pdf/2508.02108

Monotone Paths on Acyclic 3-Regular Graphs
Motivated by trying to understand the behavior of the simplex method, Athanasiadis, De Loera and Zhang provided upper and lower bounds on the number of the monotone paths on 3-polytopes. For simple 3-polytopes with $2n$ vertices, they showed that the number of monotone paths is bounded above by $(1+φ)^n$, with $φ$ being the golden ratio. We improve the result and show that for a larger family of graphs the number is bounded above by $c \cdot 1.6779^n$ for some universal constant $c$. Meanwhil…

Domination numbers and homotopy in certain ternary graphs
Taehyun Eom, Jinha Kim, Minki Kim
https://arxiv.org/abs/2508.00699 https://arxiv.org/pdf/2508.006…

Domination numbers and homotopy in certain ternary graphs
A ternary graph is a graph with no induced cycles of length $0$ modulo $3$. It was recently shown that, if the independence complex of a ternary graph is not contractible, then it is homotopy equivalent to a sphere. When a ternary graph also does not contain induced cycles of length $1$ modulo $3$, we prove that the dimension of the sphere is equal to the dimension of a minimum maximal simplex of the independence complex, or equivalently, to the value obtained by subtracting $1$ from the indepe…

Repulsive mixtures via the sparsity-inducing partition prior
Alexander Mozdzen, Timothy Wertz, Maria De Iorio, Andrea Cremaschi, Gregor Kastner, Johan Eriksson
https://arxiv.org/abs/2509.25860

Repulsive mixtures via the sparsity-inducing partition prior
We introduce a novel prior distribution for modelling the weights in mixture models based on a generalisation of the Dirichlet distribution, the Selberg Dirichlet distribution. This distribution contains a repulsive term, which naturally penalises values that lie close to each other on the simplex, thus encouraging few dominating clusters. The repulsive behaviour induces additional sparsity on the number of components. We refer to this construction as sparsity-inducing partition (SIP) prior. By…

Volumes of Regular Hyperbolic Simplices
Zakhar Kabluchko, Philipp Schange
https://arxiv.org/abs/2508.20450 https://arxiv.org/pdf/2508.20450

Volumes of Regular Hyperbolic Simplices
We derive an explicit formula for the volume of a regular simplex in the hyperbolic space of any dimension.