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Fully relativistic particle-in-cell (PIC) simulations are crucial for advancing our knowledge of plasma physics. Modern supercomputers based on graphics processing units (GPUs) offer the potential to perform PIC simulations of unprecedented scale, but require robust and feature-rich codes that can fully leverage their computational resources. In this work, this demand is addressed by adding GPU acceleration to the PIC code Osiris. An overview of the algorithm, which features a CUDA extension to the underlying Fortran architecture, is given. Detailed performance benchmarks for thermal plasmas are presented, which demonstrate excellent weak scaling on NERSC's Perlmutter supercomputer and high levels of absolute performance. The robustness of the code to model a variety of physical systems is demonstrated via simulations of Weibel filamentation and laser-wakefield acceleration run with dynamic load balancing. Finally, measurements and analysis of energy consumption are provided that indicate that the GPU algorithm is up to ${\sim }$
14 times faster and $\sim$
7 times more energy efficient than the optimized CPU algorithm on a node-to-node basis. The described development addresses the PIC simulation community's computational demands both by contributing a robust and performant GPU-accelerated PIC code and by providing insight into efficient use of GPU hardware.
We present a new explicit formula for the determinant that contains superexponentially fewer terms than the usual Leibniz formula. As an immediate corollary of our formula, we show that the tensor rank of the 
$n \times n$ determinant tensor is no larger than the 
$n$-th Bell number, which is much smaller than the previously best-known upper bounds when 
$n \geq 4$. Over fields of non-zero characteristic we obtain even tighter upper bounds, and we also slightly improve the known lower bounds. In particular, we show that the 
$4 \times 4$ determinant over 
${\mathbb{F}}_2$ has tensor rank exactly equal to 
$12$. Our results also improve upon the best-known upper bound for the Waring rank of the determinant when 
$n \geq 17$, and lead to a new family of axis-aligned polytopes that tile 
${\mathbb{R}}^n$.
