arXiv subjects

Sofia Lindqvist

Publications and source records attributed to Sofia Lindqvist.

8 recordsLinked to original sources

arXiv2025

The First WARA Robotics Mobile Manipulation Challenge -- Lessons Learned

The first WARA Robotics Mobile Manipulation Challenge, held in December 2024 at ABB Corporate Research in Västerås, Sweden, addressed the automation of task-intensive and repetitive manual labor in laboratory environments - specifically the transport and cleaning of glassware. Designed in collaboration with AstraZeneca, the challenge invited academic teams to develop autonomous robotic systems capable of navigating human-populated lab spaces and performing complex manipulation tasks, such as loading items into industrial dishwashers. This paper presents an overview of the challenge setup, its industrial motivation, and the four distinct approaches proposed by the participating teams. We summarize lessons learned from this edition and propose improvements in design to enable a more effective second iteration to take place in 2025. The initiative bridges an important gap in effective academia-industry collaboration within the domain of autonomous mobile manipulation systems by promoting the development and deployment of applied robotic solutions in real-world laboratory contexts.

cs.RO↗

arXiv2018

Rado's criterion over squares and higher powers

We establish partition regularity of the generalised Pythagorean equation in five or more variables. Furthermore, we show how Rado's characterisation of a partition regular equation remains valid over the set of positive $k$th powers, provided the equation has at least $(1+o(1))k\log k$ variables. We thus completely describe which diagonal forms are partition regular and which are not, given sufficiently many variables. In addition, we prove a supersaturated version of Rado's theorem for a linear equation restricted either to squares minus one or to logarithmically-smooth numbers.

math.NT↗

arXiv2018

Full Orbit Sequences in Affine Spaces via Fractional Jumps and Pseudorandom Number Generation

Let $n$ be a positive integer. In this paper we provide a general theory to produce full orbit sequences in the affine $n$-dimensional space over a finite field. For $n=1$ our construction covers the case of the Inversive Congruential Generators (ICG). In addition, for $n>1$ we show that the sequences produced using our construction are easier to compute than ICG sequences. Furthermore, we prove that they have the same discrepancy bounds as the ones constructed using the ICG.

math.NT↗

arXiv2017

Partition regularity of generalised Fermat equations

Let $α,β,γ\in\mathbb{N}$. We prove that given an $r$-colouring of $\mathbb{F}_p$ with $p$ prime, there are more than $c_{r,α,β,γ} p^2$ solutions to the equation $x^α+y^β=z^γ$ with all of $x,y,z$ of the same colour. Here $c_{r,α,β,γ}>0$ is some constant depending on the number of colours and the exponents in the equation. This is already a new result for $α=β=1$ and $γ=2$, that is to say for the equation $x+y=z^2$.

math.NT↗

arXiv2017

Weak approximation results for quadratic forms in four variables

Let $F$ be a quadratic form in four variables, let $m\in\mathbb{N}$ and let $\mathbf{k}\in \mathbb{Z}^4$. We count integer solutions to $F(\mathbf{x})=0$ with $\mathbf{x}\equiv \mathbf{k}\:\mathrm{mod}(m)$. One can compare this to the similar problem of counting solutions to $F(\mathbf{x})=0$ without the congruence condition. It turns out that adding the congruence condition sometimes gives a very different main term than the homogeneous case. In particular, there are examples where the number of primitive solutions to the problem is $0$, while the number of unrestricted solutions is nonzero.

math.NT↗

arXiv2016

Monochromatic solutions to $x + y = z^2$

Suppose that $\mathbb{N}$ is $2$-coloured. Then there are infinitely many monochromatic solutions to $x + y = z^2$. On the other hand, there is a $3$-colouring of $\mathbb{N}$ with only finitely many monochromatic solutions to this equation.

math.NT↗

arXiv2015

Large time step TVD schemes for hyperbolic conservation laws

Large time step explicit schemes in the form originally proposed by LeVeque have seen a significant revival in recent years. In this paper we consider a general framework of local 2k + 1 point schemes containing LeVeque's scheme (denoted as LTS-Godunov) as a member. A modified equation analysis allows us to interpret each numerical cell interface coefficient of the framework as a partial numerical viscosity coefficient. We identify the least and most diffusive TVD schemes in this framework. The most diffusive scheme is the 2k + 1-point Lax-Friedrichs scheme (LTS-LxF). The least diffusive scheme is the Large Time Step scheme of LeVeque based on Roe upwinding (LTS-Roe). Herein, we prove a generalization of Harten's lemma: all partial numerical viscosity coefficients of any local unconditionally TVD scheme are bounded by the values of the corresponding coefficients of the LTS-Roe and LTS-LxF schemes. We discuss the nature of entropy violations associated with the LTS-Roe scheme, in particular we extend the notion of transonic rarefactions to the LTS framework. We provide explicit inequalities relating the numerical viscosities of LTS-Roe and LTS-Godunov across such generalized transonic rarefactions, and discuss numerical entropy fixes. Finally, we propose a one-parameter family of Large Time Step TVD schemes spanning the entire range of the admissible total numerical viscosity. Extensions to nonlinear systems are obtained through the Roe linearization. The 1D Burgers equation and the Euler system are used as numerical illustrations.

math.NA↗

arXiv2015

Moments of random multiplicative functions and truncated characteristic polynomials

We give an asymptotic formula for the $2k$th moment of a sum of multiplicative Steinhaus variables. This was recently computed independently by Harper, Nikeghbali and Radziwiłł. We also compute the $2k$th moment of a truncated characteristic polynomial of a unitary matrix. This provides an asymptotic equivalence with the moments of Steinhaus variables. Similar results for multiplicative Rademacher variables are given.

math.NT↗