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Existing phase optimization methods in reconfigurable intelligent surfaces (RISs) face significant challenges in achieving flexible beam synthesis, especially for directional beam suppression. This paper introduces a Max-min criterion incorporating non-linear constraints, utilizing optimization techniques to enable multi-beam enhancement and suppression via transmissive RISs. A realistic model grounded in geometrical optics is first presented to characterize the input/output behavior of transmissive RIS, effectively linking explicit beam-forming operations with practical implementation. Subsequently, a highly efficient bisection-based algorithm for constrained Max-min optimization involving quadratic forms is developed, utilizing an auxiliary variable and Moreau envelope to iteratively reach the optimal solution. This approach demonstrates excellent extensibility and is applicable to a wide range of constrained Max-min problems. Numerical simulations validate the proposed methods, confirming that the framework enables beam enhancement or suppression at designated spatial positions.

In this article, the non-Hermitian characteristics of three-dimensional PT-symmetric coupled electronic resonators are theoretically analyzed. First, the concept of non-Hermitian PT symmetry is illustrated in the context of electronics using a pair of coupled electronic resonators. Two typical configurations of parallel-coupled PT-symmetric electronic trimers are then analyzed. The results indicate that, for the planar configuration, the system can exhibit two phase transitions as the coupling coefficient or gain-loss parameter changes, different from the linear configuration. By comparing system equations based on coupled-mode theory and circuit theory, it is shown that high dimensionality alone is not a sufficient condition for the existence of a higher-order exceptional point; an approximation condition is also required. A modified exceptional point is proposed, and the approximation conditions for the mean deviation $D$ for the real part of the three eigenfrequencies, satisfying $D \leq 1\%$ and $D \leq 0.1\%$, are discussed, respectively. The theoretical results presented in this paper not only reveal the unique non-Hermitian characteristics of high-dimensional PT-symmetric electronic systems but also offer theoretical support for wireless power transmission and wireless sensing technologies.

A primary challenge in wireless power transfer (WPT) systems is to achieve efficient and stable power transmission without complex control strategies when load conditions change dynamically. Addressing this issue, we propose a third-order pseudo-Hermitian WPT system whose output characteristics exhibit a stable frequency and constant power. The frequency selection mechanism and energy efficiency of the nonlinear WPT system based on pseudo-Hermitian under the coupling mode theory approximation are analyzed. Theoretical analysis indicates that under certain coupling coefficients and load conditions, the proposed system can achieve frequency adaptation in a stable frequency mode without the need to change the circuit frequency. When the load changes dynamically, the stability of the power output is maintained using a proportional integral (PI) control strategy that only collects the voltage and current at the transmitting end, eliminating the need for wireless communication circuits with feedback from the receiving side. Experimental results demonstrate that the proposed design scheme can achieve constant power transmission when load conditions change, maintaining stable and relatively high transmission efficiency. The proposed scheme exhibits benefits in practical applications since no communication is required.

Parity-time symmetry is a fundamental concept in non-Hermitian physics that has recently gained attention for its potential in engineering advanced electronic systems and achieving robust wireless power transfer even in the presence of disturbances, through the incorporation of nonlinearity. However, the current parity-time-symmetric scheme falls short of achieving the theoretical maximum efficiency of wireless power transfer and faces challenges when applied to non-resistive loads. In this study, we propose a theoretical framework and provide experimental evidence demonstrating that asymmetric resonance, based on dispersive gain, can greatly enhance the efficiency of wireless power transfer beyond the limits of symmetric approaches. By leveraging the gain spectrum interleaving resulting from dispersion, we observe a mode switching phenomenon in asymmetric systems similar to the symmetry-breaking effect. This phenomenon reshapes the distribution of resonance energy and enables more efficient wireless power transfer compared to conventional methods. Our findings open up new possibilities for harnessing dispersion effects in various domains such as electronics, microwaves, and optics. This work represents a significant step towards exploiting dispersion as a means to optimize wireless power transfer and lays the foundation for future advancements in these fields.

The existing methods for Reconfigurable Intelligent Surface (RIS) beamforming in wireless communication are typically limited to uniform phase quantization. However, in real world applications, the phase and bit resolution of RIS units are often non-uniform due to practical requirements and engineering challenges. To fill this research gap, we formulate an optimization problem for discrete non-uniform phase configuration in RIS assisted multiple-input single-output (MISO) communications. Subsequently, a partition-and-traversal (PAT) algorithm is proposed to solve that, achieving the global optimal solution. The efficacy and superiority of the PAT algorithm are validated through numerical simulations, and the impact of non-uniform phase quantization on system performance is analyzed.

This paper investigates a general discrete $\ell_p$-norm maximization problem, with the power enhancement at steering directions through reconfigurable intelligent surfaces (RISs) as an instance. We propose a mathematically concise iterative framework composed of alternating inner product maximizations, well-suited for addressing $\ell_1$- and $\ell_2$-norm maximizations with either discrete or continuous uni-modular variable constraints. The iteration is proven to be monotonically non-decreasing. Moreover, this framework exhibits a distinctive capability to mitigate performance degradation due to discrete quantization, establishing it as the first post-rounding lifting approach applicable to any algorithm intended for the continuous solution. Additionally, as an integral component of the alternating iterations framework, we present a divide-and-sort (DaS) method to tackle the discrete inner product maximization problem. In the realm of $\ell_\infty$-norm maximization with discrete uni-modular constraints, the DaS ensures the identification of the global optimum with polynomial search complexity. We validate the effectiveness of the alternating inner product maximization framework in beamforming through RISs using both numerical experiments and field trials on prototypes. The results demonstrate that the proposed approach achieves higher power enhancement and outperforms other competitors. Finally, we show that discrete phase configurations with moderate quantization bits (e.g., 4-bit) exhibit comparable performance to continuous configurations in terms of power gains.

Learning feature interaction is the critical backbone to building recommender systems. In web-scale applications, learning feature interaction is extremely challenging due to the sparse and large input feature space; meanwhile, manually crafting effective feature interactions is infeasible because of the exponential solution space. We propose to leverage a Transformer-based architecture with attention layers to automatically capture feature interactions. Transformer architectures have witnessed great success in many domains, such as natural language processing and computer vision. However, there has not been much adoption of Transformer architecture for feature interaction modeling in industry. We aim at closing the gap. We identify two key challenges for applying the vanilla Transformer architecture to web-scale recommender systems: (1) Transformer architecture fails to capture the heterogeneous feature interactions in the self-attention layer; (2) The serving latency of Transformer architecture might be too high to be deployed in web-scale recommender systems. We first propose a heterogeneous self-attention layer, which is a simple yet effective modification to the self-attention layer in Transformer, to take into account the heterogeneity of feature interactions. We then introduce \textsc{Hiformer} (\textbf{H}eterogeneous \textbf{I}nteraction Trans\textbf{former}) to further improve the model expressiveness. With low-rank approximation and model pruning, \hiformer enjoys fast inference for online deployment. Extensive offline experiment results corroborates the effectiveness and efficiency of the \textsc{Hiformer} model. We have successfully deployed the \textsc{Hiformer} model to a real world large scale App ranking model at Google Play, with significant improvement in key engagement metrics (up to +2.66\%).

A fair beam allocation framework through reconfigurable intelligent surfaces (RISs) is proposed, incorporating the Max-min criterion. This framework focuses on designing explicit beamforming functionalities through optimization. Firstly, realistic models, grounded in geometrical optics, are introduced to characterize the input/output behaviors of RISs, effectively bridging the gap between the requirements on explicit beamforming operations and their practical implementations. Then, a highly efficient algorithm is developed for Max-min optimizations involving quadratic forms. Leveraging the Moreau-Yosida approximation, we successfully reformulate the original problem and propose iterations to attain the optimal solution. A comprehensive analysis of the algorithm's convergence is provided. Importantly, this approach exhibits excellent extensibility, making it readily applicable to address a broader class of Max-min optimization problems. Finally, numerical and prototype experiments are conducted to validate the effectiveness of the framework. With the proposed beam allocation framework and algorithm, we clarify that several crucial redistribution functionalities of RISs, such as explicit beam-splitting, fair beam allocation, and wide-beam generation, can be effectively implemented. These explicit beamforming functionalities have not been thoroughly examined previously.

Exceptional points (EP) in non-Hermitian systems have been widely investigated due to their enhanced sensitivity in comparison to standard systems. In this letter, we report the observation of higher-order pseudo-Hermitian degeneracies in an electronic platform comprised of three inductively coupled gain-loss-loss LC resonators. Theoretical analysis demonstrates that the proposed system can realize third-order EP with asymmetric coupling between adjacent inductors and an arbitrary scaling factor between two loss resonators. When capacitive perturbation is introduced on the middle resonator, the perturbed eigenfrequencies follow a cube-root dependence on the perturbation parameter; in this case, the sensitivity is significantly greater than conventional wireless readout methods. Our work enriches the explorations of higher-order EP on electronic platforms and provides a new degree of design freedom for the non-Hermitian-EP-enhanced wireless sensing system.

High-performance interrogation of inductor-capacitor (LC) microsensor has been a long-standing challenge due to the limited size of the sensor. Parity-time (PT) symmetry, an intriguing concept originated from quantum physics, has been utilized to improve the spectral resolution and sensitivity of the conventional readout circuit, while the PT symmetry condition has to be satisfied. In this work, a sandwich-type wireless capacitance readout mechanism based on perturbed PT-symmetric electronic trimer without manual tuning of the reader circuit is proposed. Theoretical eigenvalue analysis by solving the system equations shows that the system exhibits single real mode in weak coupling regime whose eigenfrequency changes in response to the capacitance of the neutral resonator. Furthermore, the proposed readout system exhibits wider readout capacitance range compared to standard PT-symmetry-based system while retaining higher Q-factor compared to conventional readout method, which has been validated with the experimental prototype based on printed circuit board. Our work not only enriches the underlying theory of non-Hermitian physics, but also shows potential applications in scenarios where longer interrogation distance is required, such as implanted medical devices, parameter detection in harsh environment, etc., Comment: 9 pages, 10 figures

Non-radiative wireless power transfer (WPT) technology has made considerable progress with the application of the parity-time (PT) symmetry concept. In this letter, we extend the standard second-order PT-symmetric Hamiltonian to high-order symmetric tridiagonal pseudo-Hermitian Hamiltonian, relaxing the limitation of multi-source/multi-load system based on non-Hermitian physics. We proposed a three-mode pseudo-Hermitian dual-transmitter-single-receiver circuit and demonstrate that robust efficiency and stable frequency WPT can be achieved even though PT-symmetry is not satisfied as usual. In addition, no active tuning is required when the coupling coefficient between the intermediate transmitter and the receiver is changed. Moreover, the proposed system has an open frequency band gap with an abrupt frequency change at the phase transition point, which is expected to advance wireless sensing technologies.

In this article, we report a vector-network-analyzer-free and real-time LC wireless capacitance readout system based on perturbed nonlinear parity-time (PT) symmetry. The system is composed of two inductively coupled reader-sensor parallel RLC resonators with gain and loss respectively. By searching for the real mode that requires the minimum saturation gain, the steady-state frequency evolution as a function of the sensor capacitance perturbation is analytically deduced. The proposed system can work in different modes by setting different perturbation point. In particular, at the exceptional point of PT symmetry, the system exhibits high sensitivity. Experimental demonstrations revealed the viability of the proposed readout mechanism by measuring the steady-state frequency of the reader resonator in response to the change of trimmer capacitor on the sensor side. Our findings could impact many emerging applications such as implantable medical device for health monitoring, parameter detection in harsh environment and sealed food packages, etc.