Tootfinder

today in "draw the rest of the fucking owl"

Nuclear fusion plasma fuelling with ice pellets using a neuromorphic controller
L. L. T. C. Jansen, E. Petri, M. van Berkel, W. P. M. H. Heemels
https://arxiv.org/abs/2509.02147

Nuclear fusion plasma fuelling with ice pellets using a neuromorphic controller
In reactor-grade tokamaks, pellet injection is the best candidate for core plasma fuelling. However, density control schemes that can handle the hybrid nature of this type of fuelling, i.e., the discrete impact of the pellets on the continuously evolving plasma density, are lacking. This paper proposes a neuromorphic controller, inspired by the integrate-and-fire neuronal model, to address this problem. The overall system is modelled as a hybrid system, and we analyse the proposed controller in…

Call for evidence:
"Following an initial evidence session in Parliament on the role of the UK’s refinery industry in the energy transition, the Committee is launching a new inquiry and call for evidence on the future of UK oil and gas.
"Data from the oil and gas industry shows that it directly supports around 26,000 jobs across the UK and indirectly supports 95,000 more."
Managing the future of UK oil and gas - Committees - UK Parliament

Listen to me get croakier and huskier through this episode as I talk about the surprisingly helpful benefits of "acting as if"
In your podcast app any minute now :)
https://www.overcomecompulsivehoarding.co.uk/podcast-ep-202-ac…

Podcast ep 202: "Acting as if" for hoarding disorder
In this episode, I talk about the idea of "acting as if" - taking action before you fully believe you can, and using that to chip away at compulsive hoarding behaviours. I share stories from my own life, including how channelling others’ confidence helped me move through paralysing shyness, and how small steps can help shift thinking around possessions and habits. It’s all about behaving your way to progress, even when your feelings haven’t caught up yet. Listen in to find out more, inclu…

Morse sequences on stacks and flooding sequences
Gilles Bertrand
https://arxiv.org/abs/2509.01384 https://arxiv.org/pdf/2509.01384

Morse sequences on stacks and flooding sequences
This paper builds upon the framework of \emph{Morse sequences}, a simple and effective approach to discrete Morse theory. A Morse sequence on a simplicial complex consists of a sequence of nested subcomplexes generated by expansions and fillings-two operations originally introduced by Whitehead. Expansions preserve homotopy, while fillings introduce critical simplexes that capture essential topological features. We extend the notion of Morse sequences to \emph{stacks}, which are monotonic funct…

Homotopy lifting, asymptotic homomorphisms, and traces
Tatiana Shulman
https://arxiv.org/abs/2508.00125 https://arxiv.org/pdf/2508.00125

Homotopy lifting, asymptotic homomorphisms, and traces
The following homotopy lifting theorem is proved: Let $ϕ, ψ: B \to D/I$ be homotopic $\ast$-homomorphisms and suppose $ψ$ lifts to a (discrete) asymptotic homomorphism. Then $ϕ$ lifts to a (discrete) asymptotic homomorphism. Moreover the whole homotopy lifts. We also prove a cp version of this theorem and a version where $ϕ$ is replaced by an asymptotic homomorphism. We obtain a lifting characterization of several important properties of C*-algebras and use them together with the lifting t…

Falling stars: a fall-decorated rational shuffle theorem
Alessandro Iraci, Roberto Pagaria, Giovanni Paolini
https://arxiv.org/abs/2508.20935 https://arxiv…

Falling stars: a fall-decorated rational shuffle theorem
In this paper, we formulate a rational analog of the fall Delta theorem and the Delta square conjecture. We find a new dinv statistic on fall-decorated paths on a $(m+k) \times (n+k)$ rectangle that simultaneously extends the previously known dinv statistics on decorated square objects and non-decorated rectangular objects. We prove a symmetric function formula for the $q,t$-generating function of fall-decorated rectangular Dyck paths as a skewing operator applied to $e_{m,n+km}$ and, condi…

Random burning of the Euclidean lattice
Guillaume Blanc, Alice Contat
https://arxiv.org/abs/2509.02562 https://arxiv.org/pdf/2509.02562

Random burning of the Euclidean lattice
The burning number of a graph is the minimal number of steps that are needed to burn all of its vertices, with the following burning procedure: at each step, one can choose a point to set on fire, and the fire propagates constantly at unit speed along the edges of the graph. In this paper, we consider two natural random burning procedures in the discrete Euclidean torus $\mathbb{T}_n^d$, in which the points that we set on fire at each step are random variables. Our main result deals with the ca…

An improved Copson inequality
Bikram Das, Atanu Manna
https://arxiv.org/abs/2508.00388 https://arxiv.org/pdf/2508.00388

An improved Copson inequality
In this paper, we prove that the discrete Copson inequality (E.T. Copson, \emph{Notes on a series of positive terms}, J. London Math. Soc., 2 (1927), 49-51) of one-dimension in general cases admits an improvement. In fact we study the improvement of the following Copson's inequality \begin{align*} &\displaystyle\sum_{n=1}^{\infty}\frac{Q_{n}^α|A_n-A_{n-1}|^{2}}{q_{n}}\geq\frac{(α-1)^2}{4}\displaystyle\sum_{n=1}^{\infty} \frac{q_{n}}{Q_{n}^{2-α}}|A_{n}|^{2}, \end{align*}wh…

On three classes of logarithmic integrals
Necdet Bat{\i}r, Nandan Sai Dasireddy
https://arxiv.org/abs/2510.00870 https://arxiv.org/pdf/2510.00870

On three classes of logarithmic integrals
In this paper, we evaluate the following families of definite integrals in closed form and we show that they are expressible only in terms of the dilogarithm function and the inverse tangent integral, and elementary functions. \begin{equation*} \int_{0}^{1}\frac{\log\big(x^m+1\big)}{x+1}\thinspace{\rm d}x \quad \mbox{and}\quad \int_{0}^{1}\frac{\log\big(x^m+1\big)}{x^2+1}\thinspace{\rm d}x, \end{equation*} where $m$ is a positive odd integer. When $m$ is a positive even integer, these integrals…