Tootfinder

Contributions to the Theory of Clifford-Cyclotomic Circuits
Linh Dinh (Dalhousie University), Neil J. Ross (Dalhousie University)
https://arxiv.org/abs/2508.14674 https://

Contributions to the Theory of Clifford-Cyclotomic Circuits
Let $n$ be a positive integer divisible by 8. The Clifford-cyclotomic gate set $\mathcal{G}_n$ consists of the Clifford gates, together with a $z$-rotation of order $n$. It is easy to show that, if a circuit over $\mathcal{G}_n$ represents a unitary matrix $U$, then the entries of $U$ must lie in $\mathcal{R}_n$, the smallest subring of $\mathbb{C}$ containing $1/2$ and $\mathrm{exp}(2πi/n)$. The converse implication, that every unitary $U$ with entries in $\mathcal{R}_n$ can be represented by…

FACT: the Features At Convergence Theorem for neural networks
Enric Boix-Adsera, Neil Mallinar, James B. Simon, Mikhail Belkin
https://arxiv.org/abs/2507.05644

FACT: the Features At Convergence Theorem for neural networks
A central challenge in deep learning theory is to understand how neural networks learn and represent features. To this end, we prove the Features at Convergence Theorem (FACT), which gives a self-consistency equation that neural network weights satisfy at convergence when trained with nonzero weight decay. For each weight matrix $W$, this equation relates the "feature matrix" $W^\top W$ to the set of input vectors passed into the matrix during forward propagation and the loss gradients passed t…

The CFT of Sen's Formulation of Chiral Gauge Fields
Chris Hull, Neil Lambert
https://arxiv.org/abs/2508.00199 https://arxiv.org/pdf/2508.00199

The CFT of Sen's Formulation of Chiral Gauge Fields
Sen's action for chiral bosons in 2 dimensions describes two chiral scalars, one of which couples to the physical metric and one of which couples to a flat metric. It has a generalisation in which the flat metric is replaced by an arbitrary second metric and so can be formulated on any curved world-sheet. When the two metrics are equal, the theory reduces to a $βγ$ system, giving a non-unitary $c=2$ conformal field theory. We argue that the relation between this and the theory of two chiral b…

Heat Transport and Dissipation in 2.5D Rotating Internally Heated and Cooled Convection
Tom Joshi-Hartley (University of Exeter), Matthew K. Browning (University of Exeter), Laura K. Currie (Durham University), Neil T. Lewis (University of Exeter), Benjamin P. Brown (University of Colorado at Boulder), Simon R. W. Lance (University of Exeter)
https:/…

Heat Transport and Dissipation in 2.5D Rotating Internally Heated and Cooled Convection
Models of astrophysical convection, such as mixing length theory, typically assume that the heat transport is independent of microphysical diffusivities. Such 'diffusion-free' behaviour is, however, not observed in numerical simulations employing standard fixed-flux or fixed-temperature boundary conditions, except possibly in extreme parameter regimes that are computationally expensive to achieve. Recent numerical and experimental work has suggested that internally heated and cooled convection …

A comparative study of the high-pressure structural stability of zirconolite materials for nuclear waste immobilisation
Daniel Errandonea, Robin Turnbull, Josu Sanchez-Martin, Robert Oliva, Alfonso Munoz, Silvana Radescu, Andres Mujica, Lewis Blackburn, Neil C. Hyatt, Catalin Popescu, Jordi Ibanez-Insa
https://arxiv.org/abs/2508.03786

A comparative study of the high-pressure structural stability of zirconolite materials for nuclear waste immobilisation
We present a comparative study of the high-pressure behaviours of the nuclear waste immobilisation materials zirconolite-2M, -4M, -3O, and -3T. The materials are studied under high-pressure conditions using synchrotron powder X-ray diffraction. For zirconolite-2M we also performed density-functional theory calculations. A new triclinic crystal structure (space group P-1), instead of the previously assigned monoclinic structure (space group C2/c) is proposed for zirconolite-2M. We named the tric…

The spectrum of global representations for families of bounded rank and VI-modules
Miguel Barrero, Tobias Barthel, Luca Pol, Neil Strickland, Jordan Williamson
https://arxiv.org/abs/2506.21525

The spectrum of global representations for families of bounded rank and VI-modules
A global representation is a compatible collection of representations of the outer automorphism groups of the finite groups belonging to a family $\mathscr{U}$. These arise in classical representation theory, in the study of representation stability, as well as in global homotopy theory. In this paper we begin a systematic study of the derived category $\mathsf{D}(\mathscr{U};k)$ of global representations over fields $k$ of characteristic zero, from the point-of-view of tensor-triangular geomet…

Quantising Chiral Bosons On Riemann Surfaces
Chris Hull, Neil Lambert
https://arxiv.org/abs/2508.02865 https://arxiv.org/pdf/2508.02865

Quantising Chiral Bosons On Riemann Surfaces
Sen's action in two dimensions governs a chiral boson coupled to a two-dimensional metric together with a second chiral boson that couples to a flat two-dimensional metric. This second scalar decouples from the physical degrees of freedom. The generalisation of this action to one in which the second chiral scalar couples to an arbitrary second metric is used to formulate the theory on an arbitrary two-dimensional manifold. We use this action with both metrics Riemannian (or complex) to formulat…