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pro vyhledávání: '"Crump P. A."'
We conjecture results about the moments of mixed derivatives of the Riemann zeta function, evaluated at the non-trivial zeros of the Riemann zeta function. We do this in two different ways, both giving us the same conjecture. In the first, we find as
Externí odkaz:
http://arxiv.org/abs/2406.08121
Autor:
Schloegel, Moritz, Bars, Nils, Schiller, Nico, Bernhard, Lukas, Scharnowski, Tobias, Crump, Addison, Ebrahim, Arash Ale, Bissantz, Nicolai, Muench, Marius, Holz, Thorsten
Fuzzing has proven to be a highly effective approach to uncover software bugs over the past decade. After AFL popularized the groundbreaking concept of lightweight coverage feedback, the field of fuzzing has seen a vast amount of scientific work prop
Externí odkaz:
http://arxiv.org/abs/2405.10220
A general theory for the intrinsic (Lorentzian) linewidth of photonic--crystal surface--emitting lasers (PCSELs) is presented. The effect of spontaneous emission is modeled by a classical Langevin force entering the equation for the slowly varying wa
Externí odkaz:
http://arxiv.org/abs/2402.11246
Autor:
Pearce-Crump, Edward
We derive the existence of a new type of neural network, called a compact matrix quantum group equivariant neural network, that learns from data that has an underlying quantum symmetry. We apply the Woronowicz formulation of Tannaka-Krein duality to
Externí odkaz:
http://arxiv.org/abs/2311.06358
Permutation equivariant neural networks are typically used to learn from data that lives on a graph. However, for any graph $G$ that has $n$ vertices, using the symmetric group $S_n$ as its group of symmetries does not take into account the relations
Externí odkaz:
http://arxiv.org/abs/2307.07810
Autor:
Tohfa, Hurum, Crump, Jack, Baker, Ethan, Hart, Luke, Grin, Daniel, Brosius, Madeline, Chluba, Jens
In some extensions of the standard model of particle physics, the values of the fundamental coupling constants vary in space and time. Some observations of quasars hint at time and spatial variation of the fine structure constant $\alpha$. Here, the
Externí odkaz:
http://arxiv.org/abs/2307.06768
Publikováno v:
Appl. Phys. Lett. 123, 134004 (2023)
In this work, we present a device consisting of two coupled transmon qubits, each of which are coupled to an independent high-overtone bulk acoustic wave resonator (HBAR). Both HBAR resonators support a plethora of acoustic modes, which can couple to
Externí odkaz:
http://arxiv.org/abs/2307.05544
Shanks conjectured that $\zeta ' (\rho)$, where $\rho$ ranges over non-trivial zeros of the Riemann zeta function, is real and positive in the mean. We present a history of this problem, including a generalisation to all higher-order derivatives $\ze
Externí odkaz:
http://arxiv.org/abs/2305.14253
Autor:
Pearce-Crump, Edward
The learnable, linear neural network layers between tensor power spaces of $\mathbb{R}^{n}$ that are equivariant to the orthogonal group, $O(n)$, the special orthogonal group, $SO(n)$, and the symplectic group, $Sp(n)$, were characterised in arXiv:22
Externí odkaz:
http://arxiv.org/abs/2304.14165
Autor:
Pearce-Crump, Edward
We present a novel application of category theory for deep learning. We show how category theory can be used to understand and work with the linear layer functions of group equivariant neural networks whose layers are some tensor power space of $\mat
Externí odkaz:
http://arxiv.org/abs/2304.14144