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Abstract We study anN-player game where a pure action of each player is to select a nonnegative function on a Polish space supporting a finite diffuse measure, subject to a finite constraint on the integral of the function. This function is used to define the intensity of a Poisson point process on the Polish space. The processes are independent over the players, and the value to a player is the measure of the union of her open Voronoi cells in the superposition point process. Under randomized strategies, the process of points of a player is thus a Cox process, and the nature of competition between the players is akin to that in Hotelling competition games. We characterize when such a game admits Nash equilibria and prove that when a Nash equilibrium exists, it is unique and consists of pure strategies that are proportional in the same proportions as the total intensities. We give examples of such games where Nash equilibria do not exist. A better understanding of the criterion for the existence of Nash equilibria remains an intriguing open problem. 

Ising machines have recently been attracting attention due to their apparent ability to solve5 difficult combinatorial problems using analog operational principles. Oscillator Ising Machines6 (OIM) are especially attractive because they can be implemented easily as integrated circuits (ICs)7 in standard CMOS electronics. We explore the performance of OIM for decoding noisy Multi-User8 MIMO signals, a problem of considerable interest in modern telecommunications. Our results9 indicate that OIM-based decoding achieves error rates almost as good as the optimal Maximum10 Likelihood method, over a wide range of practical signal-to-noise (SNR) values. At high SNR11 values, OIM achieves ~20x fewer errors than LMMSE, a decoding method used widely in industry12 today. We also investigate the influence of parameter precision on decoding performance, finding13 that using 6 or more bits of precision largely retains OIM’s advantages across all SNR values. We14 estimate that straightforward CMOS OIM implementations can easily solve MU-MIMO decoding15 problems in under 10ns, more than 100x faster than current industrial requirements. We conclude16 that oscillator Ising machines can be effective for real-world applications, possibly serving as an17 important enabler for future telecommunication standards. Our results and data provide guidance18 for designing hardware OIM prototypes specialized for MU-MIMO decoding. 

Almost all practical systems rely heavily on physical parameters. As a result, parameter sensitivity, or the extent to which perturbations in parameter values affect the state of a system, is intrinsically connected to system design and optimization. We present TADsens, a method for computing the parameter sensitivities of an output of a differential algebraic equation (DAE) system. Specifically, we provide rigorous, insightful theory for adjoint sensitivity computation of DAEs, along with an efficient and numerically well-posed algorithm implemented in Berkeley MAPP. Our theory and implementation advances resolve longstanding issues that have impeded adoption of adjoint transient sensitivities in circuit simulators for over 5 decades. We present results and comparisons on two nonlinear analog circuits. TADsens is numerically well posed and accurate, and faster by a factor of 300 over direct sensitivity computation on a circuit with over 150 unknowns and 600 parameters.