Dynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point

The most intriguing properties of non-Hermitian systems are found near the exceptional points (EPs) at which the Hamiltonian matrix becomes defective. Due to the complex topological structure of the energy Riemann surfaces close to an EP and the breakdown of the adiabatic theorem due to non-Hermiticity, the state evolution in non-Hermitian systems is much more complex than that in Hermitian systems. For example, recent experimental work [Doppler et al. Nature 537, 76 (2016)] demonstrated that dynamically encircling an EP can lead to chiral behaviors, i.e., encircling an EP in different directions results in different output states. Here, we propose a coupled ferromagnetic waveguide system that carries two EPs and design an experimental setup in which the trajectory of state evolution can be controlled in situ using a tunable external field, allowing us to dynamically encircle zero, one or even two EPs experimentally. The tunability allows us to control the trajectory of encircling in the parameter space, including the size of the encircling loop and the starting/end point. We discovered that whether or not the dynamics is chiral actually depends on the starting point of the loop. In particular, dynamically encircling an EP with a starting point in the parity-time-broken phase results in non-chiral behaviors such that the output state is the same no matter which direction the encircling takes. The proposed system is a useful platform to explore the topology of energy surfaces and the dynamics of state evolution in non-Hermitian systems and will likely find applications in mode switching controlled with external parameters.Comment: 15 pages, 11 figure

Performance of electronic dispersion compensator for 10Gb/s multimode fiber links

In high-speed optical links, electronic compensation circuits can be utilized to greatly improve the data transmission performance limited by fiber dispersion. In this paper, we develop a full link model, including multimode fibers, optical/electronics/optical components, clock-and-data recovery and electronic compensation circuits. The performance of various electronic compensation techniques, such as feed-forward equalizer and decision feedback equalizer for optical multimode fiber is investigated and numerically evaluated. Finally, a comparison of the performance of each compensation techniques and a proposal of optimal equalizer circuit implementation, achieving a 10-Gb/s transmission over 1-km standard multimode fiber are presented

Realizing bending waveguides with anisotropic epsilon-near-zero metamaterials

We study metamaterials with an anisotropic effective permittivity tensor in which one component is near zero. We find that such an anisotropic metamaterial can be used to control wave propagation and construct almost perfect bending waveguides with a high transmission rate (>95%). This interesting effect originates in the power flow redistribution by the surface waves on the input and output interfaces, which smoothly matches with the propagating modes inside the metamaterial waveguide. We also find that waves in such anisotropic epsilon-near-zero materials can be reflected by small-sized perfect magnetic conductor defects. Numerical calculations have been performed to confirm the above effects

PDE+: Enhancing Generalization via PDE with Adaptive Distributional Diffusion

The generalization of neural networks is a central challenge in machine learning, especially concerning the performance under distributions that differ from training ones. Current methods, mainly based on the data-driven paradigm such as data augmentation, adversarial training, and noise injection, may encounter limited generalization due to model non-smoothness. In this paper, we propose to investigate generalization from a Partial Differential Equation (PDE) perspective, aiming to enhance it directly through the underlying function of neural networks, rather than focusing on adjusting input data. Specifically, we first establish the connection between neural network generalization and the smoothness of the solution to a specific PDE, namely "transport equation". Building upon this, we propose a general framework that introduces adaptive distributional diffusion into transport equation to enhance the smoothness of its solution, thereby improving generalization. In the context of neural networks, we put this theoretical framework into practice as $\textbf{PDE+}$ ($\textbf{PDE}$ with $\textbf{A}$daptive $\textbf{D}$istributional $\textbf{D}$iffusion) which diffuses each sample into a distribution covering semantically similar inputs. This enables better coverage of potentially unobserved distributions in training, thus improving generalization beyond merely data-driven methods. The effectiveness of PDE+ is validated through extensive experimental settings, demonstrating its superior performance compared to SOTA methods.Comment: Accepted by Annual AAAI Conference on Artificial Intelligence (AAAI) 2024. Code is available at https://github.com/yuanyige/pde-ad

Ginsenoside Rb1 Preconditioning Enhances eNOS Expression and Attenuates Myocardial Ischemia/Reperfusion Injury in Diabetic Rats

Diabetes mellitus is associated with decreased NO bioavailability in the myocardium. Ginsenoside Rb1 has been shown to confer cardioprotection against ischemia reperfusion injury. The aim of this study was to investigate whether Ginsenoside Rb1 exerts cardioprotective effects during myocardial ischemia-reperfusion in diabetic rats and whether this effect is related to increase the production of NO via enhancing eNOS expression in the myocardium. The myocardial I/R injury were induced by occluding the left anterior descending artery for 30 min followed by 120 min reperfusion. An eNOS inhibitor L-NAME or Rb1 were respectively administered 25 min or 10 min before inducing ischemia. Ginsenoside Rb1 preconditioning reduced myocardial infarct size when compared with I/R group. Ginsenoside Rb1 induced myocardial protection was accompanied with increased eNOS expression and NO concentration and reduced plasma CK and LDH (P < 0.05). Moreover, the myocardial oxidative stress and tissue histological damage was attenuated by Ginsenoside Rb1 (P < 0.05). L-NAME abolished the protective effects of Ginsenoside Rb1. It is concluded that Ginsenoside Rb1 protects against myocardium ischemia/reperfusion injury in diabetic rat by enhancing the expression of eNOS and increasing the content of NO as well as inhibiting oxidative stress

Leveraging remotely sensed non-wall-to-wall data for wall-to-wall upscaling in forest inventory

Remote sensing (RS) has enhanced forest inventory with model-based inference, that is, a family of statistical procedures rigorously estimates the parameter of a variable of interest (VOI) for a spatial population, e.g., the mean or total of forest carbon for a study area. Upscaling in earth observation, alias to this estimation, aggregates VOI from a finer spatial resolution to a coarser one with reduced uncertainty, serving decision making for natural resource management at larger scales. However, conventional model-based estimation (CMB) confronts a major challenge: it only supports RS wall-to-wall data, meaning that remotely sensed data must be available in panorama and non-wall-to-wall but quality data such as lidar or even cloud-masked satellite imagery are not supported due to incomplete coverage, impeding precise upscaling with cutting-edge instruments or for large scale applications. Consequently, this study aims to develop and demonstrate the use and usefulness of RS nonwall-to-wall data for upscaling with Hierarchical model-based estimation (HMB) which incorporates a two-stage model for bridging RS non- and wall-to-wall data; and for optimizing cost-efficiency, to evaluate the effects of non-wall-to-wall sample size on upscaling precision. Three main conclusions are relevant: (1) the HMB is a variant of the CMB estimator through trading in the uncertainty of the second-stage model to enable estimation using RS non-wall-to-wall data; (2) a quality first-stage model is key to exerting the advantage of HMB relative to the CMB estimator; (3) the variance of the HMB estimator is dominated by the first-stage model variance component, indicating that increasing the sample size in the first-stage is effective for increasing the overall precision. Overall, the HMB estimator balances tradeoffs between cost, efficiency and flexibility when devising a model-based upscaling in earth observation