Tootfinder

This https://arxiv.org/abs/2309.15943 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Scalable Multi-Robot Collaboration with Large Language Models: Centralized or Decentralized Systems?
A flurry of recent work has demonstrated that pre-trained large language models (LLMs) can be effective task planners for a variety of single-robot tasks. The planning performance of LLMs is significantly improved via prompting techniques, such as in-context learning or re-prompting with state feedback, placing new importance on the token budget for the context window. An under-explored but natural next direction is to investigate LLMs as multi-robot task planners. However, long-horizon, hetero…

A Semi-orthogonal Sequence in the Derived Category of the Hilbert Scheme of Three Points
Erik Nikolov
https://arxiv.org/abs/2404.12851 https://

A Semi-orthogonal Sequence in the Derived Category of the Hilbert Scheme of Three Points
For a smooth projective variety $X$ of dimension $d \geq 5$ over an algebraically closed field $k$ of characteristic zero, it is shown in this paper that the bounded derived category of the Hilbert scheme of three points $X^{[3]}$ admits a semi-orthogonal sequence of length $\binom{d-3}{2}$. Each subcategory in this sequence is equivalent to the derived category of $X$ and realized as the image of a Fourier-Mukai transform along a Grassmannian bundle $\mathbb{G}$ over $X$ parametrizing planar s…

This https://arxiv.org/abs/2401.08528 has been replaced.
link: https://scholar.google.com/scholar?q=a

Pebbling number of polymers
Let $G=(V,E)$ be a simple graph. A function $f:V\rightarrow \mathbb{N}\cup \{0\}$ is called a configuration of pebbles on the vertices of $G$ and the quantity $\vert f\vert=\sum_{u\in V}f(u)$ is called the weight of $f$ which is just the total number of pebbles assigned to vertices. A pebbling step from a vertex $u$ to one of its neighbors $v$ reduces $f(u)$ by two and increases $f(v)$ by one. A pebbling configuration $f$ is said to be solvable if for every vertex $ v $, there exists a sequence…

Bending Energy-Driven Cooperative Patterning of 2D Colloids in Elastic 2D Fluids
Weiyue XinDepartment of Chemical Engineering, University of Massachusetts, Maria M. SantoreDepartment of Polymer Science and Engineering, University of Massachusetts
https://arxiv.org/abs/2402.15068

Bending Energy-Driven Cooperative Patterning of 2D Colloids in Elastic 2D Fluids
Suspensions of colloidal microplates in contoured 2D elastic fluids sheets are dominated by the bending mechanics and shear rigidity of the plates and the contrasting in-plane shear flow of the 2D fluid. Using the phase separated phospholipid membranes of individual giant unilamellar vesicles as models of contoured 2D suspensions, where solid domains act as colloids in a fluid membrane, we explore bending elasticity-driven assembly. The plate-shaped domains are varied between 1-10 μm in diamet…

This https://arxiv.org/abs/2308.07399 has been replaced.
initial toot: https://mastoxiv.page/@ar…

Bayesian inference of vorticity in unbounded flow from limited pressure measurements
We study the instantaneous inference of an unbounded planar flow from sparse noisy pressure measurements. The true flow field comprises one or more regularized point vortices of various strength and size. We interpret the true flow's measurements with a vortex estimator, also consisting of regularized vortices, and attempt to infer the positions and strengths of this estimator assuming little prior knowledge. The problem often has several possible solutions, many due to a variety of symmetries.…

This https://arxiv.org/abs/2310.06198 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Motion Memory: Leveraging Past Experiences to Accelerate Future Motion Planning
When facing a new motion-planning problem, most motion planners solve it from scratch, e.g., via sampling and exploration or starting optimization from a straight-line path. However, most motion planners have to experience a variety of planning problems throughout their lifetimes, which are yet to be leveraged for future planning. In this paper, we present a simple but efficient method called Motion Memory, which allows different motion planners to accelerate future planning using past experien…

Axial, Planar-Diagonal, Body-Diagonal Fields on the Cubic-Spin Spin Glass in d=3: A Plethora of Ordered Phases under Finite Fields
E. Can Artun, Deniz Sarman, A. Nihat Berker
https://arxiv.org/abs/2404.11701

Axial, Planar-Diagonal, Body-Diagonal Fields on the Cubic-Spin Spin Glass in d=3: A Plethora of Ordered Phases under Finite Fields
A nematic phase, previously seen in the d=3 classical Heisenberg spin-glass system, occurs in the n-component cubic-spin spin-glass system, between the low-temperature spin-glass phase and the high-temperature disordered phase, for number of spin components n>=3, in spatial dimension d=3, thus constituting a liquid-crystal phase in a dirty (quenched-disordered) magnet. Furthermore, under application of a variety of uniform magnetic fields, a veritable plethora of phases are found. Under uniform…

This https://arxiv.org/abs/2209.12873 has been replaced.
link: https://scholar.google.com/scholar?q=a

Emergence of new optical resonances in single-layer transition metal dichalcogenides with atomic-size phase patterns
Atomic-scale control of light-matter interactions represent the ultimate frontier for many applications in photonics and quantum technology. Two-dimensional semiconductors, including transition metal dichalcogenides, are a promising platform to achieve such control due to the combination of an atomically thin geometry and convenient photophysical properties. Here, we demonstrate that a variety of durable polymorphic structures can be combined to generate additional optical resonances beyond the…

Solving Functional Equations Dear to W.T. Tutte using the Naive (yet fullly rigorous!) Guess And Check Method
Shalosh B. Ekhad, Doron Zeilberger
https://arxiv.org/abs/2403.07009 <…

Solving Functional Equations Dear to W.T. Tutte using the Naive (yet fullly rigorous!) Guess And Check Method
In his seminal paper ``A census of planar triangulations", published in 1962, the iconic graph theorist (and code-breaker), W.T. Tutte, spent a few pages to prove that a certain bi-variate generating function that enumerates triangulations, satisfies a certain functional equation. He then used his genius to actually solve it, giving closed-form solutions to the enumerating sequences. While the first part, of deriving the functional equation, still needs human ingenuity, the second part, of solv…

Radial amplitude equations for fully localised planar patterns
Dan J. Hill, David J. B. Lloyd
https://arxiv.org/abs/2403.02949 https://

Radial amplitude equations for fully localised planar patterns
Isolated patches of spatially oscillating pattern have been found to emerge near a pattern-forming instability in a wide variety of experiments and mathematical models. However, there is currently no mathematical theory to explain this emergence or characterise the structure of these patches. We provide a method for formally deriving radial amplitude equations to planar patterns via non-autonomous multiple-scale analysis and convolutional sums of products of Bessel functions. Our novel approach…