Tootfinder

Flagged LLT polynomials, nonsymmetric plethysm, and nonsymmetric Macdonald polynomials
Jonah Blasiak, Mark Haiman, Jennifer Morse, Anna Pun, George H. Seelinger
https://arxiv.org/abs/2506.09015

Flagged LLT polynomials, nonsymmetric plethysm, and nonsymmetric Macdonald polynomials
The plethystic transformation $f[X] \mapsto f[X/(1-t)]$ and LLT polynomials are central to the theory of symmetric Macdonald polynomials. In this work, we introduce and study nonsymmetric flagged LLT polynomials. We show that these admit both an algebraic and a combinatorial description, that they Weyl symmetrize to the usual symmetric LLT polynomials, and we conjecture that they expand positively in terms of Demazure atoms. Additionally, we construct a nonsymmetric plethysm operator $Π_{t,x}$…

Just scrolling through the "Tree Preservation Orders" MHCLG has published geo-data for.
https://www.planning.data.gov.uk/dataset/tree

Re4MPC: Reactive Nonlinear MPC for Multi-model Motion Planning via Deep Reinforcement Learning
Ne\c{s}et \"Unver Akmandor, Sarvesh Prajapati, Mark Zolotas, Ta\c{s}k{\i}n Pad{\i}r
https://arxiv.org/abs/2506.08344

Re4MPC: Reactive Nonlinear MPC for Multi-model Motion Planning via Deep Reinforcement Learning
Traditional motion planning methods for robots with many degrees-of-freedom, such as mobile manipulators, are often computationally prohibitive for real-world settings. In this paper, we propose a novel multi-model motion planning pipeline, termed Re4MPC, which computes trajectories using Nonlinear Model Predictive Control (NMPC). Re4MPC generates trajectories in a computationally efficient manner by reactively selecting the model, cost, and constraints of the NMPC problem depending on the comp…

Critical points of random polynomials and finite free cumulants
Octavio Arizmendi, Andrew Campbell, Katsunori Fujie
https://arxiv.org/abs/2506.08910 https:…

Critical points of random polynomials and finite free cumulants
A result of Hoskins and Steinerberger [Int. Math. Res. Not., (13):9784-9809, 2022] states that repeatedly differentiating a random polynomials with independent and identically distributed mean zero and variance one roots will result, after an appropriate rescaling, in a Hermite polynomial. We use the theory of finite free probability to extend this result in two natural directions: (1) We prove central limit theorems for the fluctuations around these deterministic limits for the polynomials and…

Exploring Noncommutative Polynomial Equation Methods for Discrete-Time Quaternionic Control
Michael Sebek
https://arxiv.org/abs/2506.08034 https://

Exploring Noncommutative Polynomial Equation Methods for Discrete-Time Quaternionic Control
We present new polynomial-based methods for discrete-time quaternionic systems, highlighting how noncommutative multiplication modifies classical control approaches. Defining quaternionic polynomials via a backward-shift operator, we examine left and right fraction representations of transfer functions, showing that right zeros correspond to similarity classes of quaternionic matrix right eigenvalues. We then propose a feedback design procedure that generalizes pole placement to quaternions - a…

Characteristic polynomials of semimatroids and their connections to matroids, hyperplane arrangements and graph colorings
Fu Houshan
https://arxiv.org/abs/2506.07071

Characteristic polynomials of semimatroids and their connections to matroids, hyperplane arrangements and graph colorings
We primarily investigate the properties of characteristic polynomials of semimatroids. In particular, we provide a combinatorial interpretation of their coefficients, generalizing the Whitney's Broken Circuit Theorem. We also prove that the unsigned coefficients of the characteristic polynomial form a unimodal and log-concave sequence, extending the Rota-Heron-Welsh Conjecture to semimatroids. Furthermore, we present convolution identities for the multiplicative characteristic and Tutte polynom…

PhyBlock: A Progressive Benchmark for Physical Understanding and Planning via 3D Block Assembly
Liang Ma, Jiajun Wen, Min Lin, Rongtao Xu, Xiwen Liang, Bingqian Lin, Jun Ma, Yongxin Wang, Ziming Wei, Haokun Lin, Mingfei Han, Meng Cao, Bokui Chen, Ivan Laptev, Xiaodan Liang
https://arxiv.org/abs/2506.08708

PhyBlock: A Progressive Benchmark for Physical Understanding and Planning via 3D Block Assembly
While vision-language models (VLMs) have demonstrated promising capabilities in reasoning and planning for embodied agents, their ability to comprehend physical phenomena, particularly within structured 3D environments, remains severely limited. To close this gap, we introduce PhyBlock, a progressive benchmark designed to assess VLMs on physical understanding and planning through robotic 3D block assembly tasks. PhyBlock integrates a novel four-level cognitive hierarchy assembly task alongside …

Introducing a vertex polynomial invariant for embedded graphs
Qi Yan, Qingying Deng, Metrose Metsidik
https://arxiv.org/abs/2506.07522 https://

Introducing a vertex polynomial invariant for embedded graphs
The ribbon group action extends geometric duality and Petrie duality by defining two embedded graphs as twisted duals precisely when they lie within the same orbit under this group action. Twisted duality yields numerous novel properties of fundamental graph polynomials. In this paper, we resolve a problem raised by Ellis-Monaghan and Moffatt [Trans. Amer. Math. Soc. 364 (2012), 1529--1569] for vertex counts by introducing the vertex polynomial: a generating function quantifying vertex distribu…

Deep Reinforcement Learning-Based Motion Planning and PDE Control for Flexible Manipulators
Amir Hossein Barjini, Seyed Adel Alizadeh Kolagar, Sadeq Yaqubi, Jouni Mattila
https://arxiv.org/abs/2506.08639

Deep Reinforcement Learning-Based Motion Planning and PDE Control for Flexible Manipulators
This article presents a motion planning and control framework for flexible robotic manipulators, integrating deep reinforcement learning (DRL) with a nonlinear partial differential equation (PDE) controller. Unlike conventional approaches that focus solely on control, we demonstrate that the desired trajectory significantly influences endpoint vibrations. To address this, a DRL motion planner, trained using the soft actor-critic (SAC) algorithm, generates optimized trajectories that inherently …

Attention-based Learning for 3D Informative Path Planning
Rui Zhao, Xingjian Zhang, Yuhong Cao, Yizhuo Wang, Guillaume Sartoretti
https://arxiv.org/abs/2506.08434

Attention-based Learning for 3D Informative Path Planning
In this work, we propose an attention-based deep reinforcement learning approach to address the adaptive informative path planning (IPP) problem in 3D space, where an aerial robot equipped with a downward-facing sensor must dynamically adjust its 3D position to balance sensing footprint and accuracy, and finally obtain a high-quality belief of an underlying field of interest over a given domain (e.g., presence of specific plants, hazardous gas, geological structures, etc.). In adaptive IPP task…