Surface modes (SM) are highly spatially localized modes existing at the core-cladding interface of photonic-bandgap hollow-core fiber (PBG-HCF). When coupling with SM, the air modes (AM) in the core would suffer a higher loss despite being spectrally
within the cladding photonic bandgap, and would be highly dispersive around the avoided crossing (anti-crossing) wavelength. In this paper, we numerically demonstrate that such avoided crossings can play an important role in the tuning of the temperature dependence of group delay of AM of PBG-HCF. At higher temperatures, both the thermal-optic effect and thermal expansion contribute to the redshift of avoided crossing wavelength, giving rise to a temperature dependence of the AM dispersion. Numerical simulations show that the redshift of avoided crossing can significantly tune the thermal coefficient of delay (TCD) of PBG-HCF from -400 ps/km/K to 400 ps/km/K, approximately -120 ppm/K to 120 ppm/K. In comparison with the known tuning mechanism by the thermal-induced redshift of photonic bandgap [Fokoua et al., Optica 4, 659, 2017], the tuning of TCD by SM coupling presents a much broader tuning range and higher efficiency. Our finding would provide a new route to design PBG-HCF for propagation time sensitive applications.
The group of diffeomorphisms commuting with an elliptic operator on a manifold is a compact Lie group under Compact-Open topology. In foliation theory, pseudogroup is introduced by Sacksteder. The pseudogroup of local transformations commuting with a
basic differential operator possesses the equicontinuity and the quasi-analyticity when conditions on operator are given. These properties serve to construct a transverse metric on the normal bundle under a good condition on operator. For this, the Average Method is applied as in the construction of basic connection on foliated bundles.
Completely randomized experiments have been the gold standard for drawing causal inference because they can balance all potential confounding on average. However, they can often suffer from unbalanced covariates for realized treatment assignments. Re
randomization, a design that rerandomizes the treatment assignment until a prespecified covariate balance criterion is met, has recently got attention due to its easy implementation, improved covariate balance and more efficient inference. Researchers have then suggested to use the assignments that minimize the covariate imbalance, namely the optimally balanced design. This has caused again the long-time controversy between two philosophies for designing experiments: randomization versus optimal and thus almost deterministic designs. Existing literature argued that rerandomization with overly balanced observed covariates can lead to highly imbalanced unobserved covariates, making it vulnerable to model misspecification. On the contrary, rerandomization with properly balanced covariates can provide robust inference for treatment effects while sacrificing some efficiency compared to the ideally optimal design. In this paper, we show it is possible that, by making the covariate imbalance diminishing at a proper rate as the sample size increases, rerandomization can achieve its ideally optimal precision that one can expect with perfectly balanced covariates while still maintaining its robustness. In particular, we provide the sufficient and necessary condition on the number of covariates for achieving the desired optimality. Our results rely on a more dedicated asymptotic analysis for rerandomization. The derived theory for rerandomization provides a deeper understanding of its large-sample property and can better guide its practical implementation. Furthermore, it also helps reconcile the controversy between randomized and optimal designs.
Motion prediction of vehicles is critical but challenging due to the uncertainties in complex environments and the limited visibility caused by occlusions and limited sensor ranges. In this paper, we study a new task, safety-aware motion prediction w
ith unseen vehicles for autonomous driving. Unlike the existing trajectory prediction task for seen vehicles, we aim at predicting an occupancy map that indicates the earliest time when each location can be occupied by either seen and unseen vehicles. The ability to predict unseen vehicles is critical for safety in autonomous driving. To tackle this challenging task, we propose a safety-aware deep learning model with three new loss functions to predict the earliest occupancy map. Experiments on the large-scale autonomous driving nuScenes dataset show that our proposed model significantly outperforms the state-of-the-art baselines on the safety-aware motion prediction task. To the best of our knowledge, our approach is the first one that can predict the existence of unseen vehicles in most cases. Project page at {url{https://github.com/xrenaa/Safety-Aware-Motion-Prediction}}.
We propose an imitation learning system for autonomous driving in urban traffic with interactions. We train a Behavioral Cloning~(BC) policy to imitate driving behavior collected from the real urban traffic, and apply the data aggregation algorithm t
o improve its performance iteratively. Applying data aggregation in this setting comes with two challenges. The first challenge is that it is expensive and dangerous to collect online rollout data in the real urban traffic. Creating similar traffic scenarios in simulator like CARLA for online rollout collection can also be difficult. Instead, we propose to create a weak simulator from the training dataset, in which all the surrounding vehicles follow the data trajectory provided by the dataset. We find that the collected online data in such a simulator can still be used to improve BC policys performance. The second challenge is the tedious and time-consuming process of human labelling process during online rollout. To solve this problem, we use an A$^*$ planner as a pseudo-expert to provide expert-like demonstration. We validate our proposed imitation learning system in the real urban traffic scenarios. The experimental results show that our system can significantly improve the performance of baseline BC policy.
The intracellular transport process plays an important role in delivering essential materials throughout branched geometries of neurons for their survival and function. Many neurodegenerative diseases have been associated with the disruption of trans
port. Therefore, it is essential to study how neurons control the transport process to localize materials to necessary locations. Here, we develop a novel optimization model to simulate the traffic regulation mechanism of material transport in complex geometries of neurons. The transport is controlled to avoid traffic jam of materials by minimizing a pre-defined objective function. The optimization subjects to a set of partial differential equation (PDE) constraints that describe the material transport process based on a macroscopic molecular-motor-assisted transport model of intracellular particles. The proposed PDE-constrained optimization model is solved in complex tree structures by using isogeometric analysis (IGA). Different simulation parameters are used to introduce traffic jams and study how neurons handle the transport issue. Specifically, we successfully model and explain the traffic jam caused by reduced number of microtubules (MTs) and MT swirls. In summary, our model effectively simulates the material transport process in healthy neurons and also explains the formation of a traffic jam in abnormal neurons. Our results demonstrate that both geometry and MT structure play important roles in achieving an optimal transport process in neuron.
We study infinite server queues driven by Cox processes in a fast oscillatory random environment. While exact performance analysis is difficult, we establish diffusion approximations to the (re-scaled) number-in-system process by proving functional c
entral limit theorems (FCLTs) using a stochastic homogenization framework. This framework permits the establishment of quenched and annealed limits in a unified manner. At the quantitative level, we identity two parameter regimes, termed subcritical and supercritical indicating the relative dominance between the two underlying stochasticities driving our system: the randomness in the arrival intensity and that in the serivce times. We show that while quenched FCLTs can only be established in the subcritical regime, annealed FCLTs can be proved in both cases. Furthermore, the limiting diffusions in the annealed FCLTs display qualitatively different diffusivity properties in the two regimes, even though the stochastic primitives are identical. In particular, when the service time distribution is heavy-tailed, the diffusion is sub- and super-diffusive in the sub- and super-critical cases. The results illustrate intricate interactions between the underlying driving forces of our system.
We numerically investigate turbulent Rayleigh-Benard convection within two immiscible fluid layers, aiming to understand how the layer thickness and fluid properties affect the heat transfer (characterized by the Nusselt number $Nu$) in two-layer sys
tems. Both two- and three-dimensional simulations are performed at fixed global Rayleigh number $Ra=10^8$, Prandtl number $Pr=4.38$, and Weber number $We=5$. We vary the relative thickness of the upper layer between $0.01 le alpha le 0.99$ and the thermal conductivity coefficient ratio of the two liquids between $0.1 le lambda_k le 10$. Two flow regimes are observed: In the first regime at $0.04lealphale0.96$, convective flows appear in both layers and $Nu$ is not sensitive to $alpha$. In the second regime at $alphale0.02$ or $alphage0.98$, convective flow only exists in the thicker layer, while the thinner one is dominated by pure conduction. In this regime, $Nu$ is sensitive to $alpha$. To predict $Nu$ in the system in which the two layers are separated by a unique interface, we apply the Grossmann-Lohse theory for both individual layers and impose heat flux conservation at the interface. Without introducing any free parameter, the predictions for $Nu$ and for the temperature at the interface well agree with our numerical results and previous experimental data.
We show that the principal algebraic actions of countably infinite groups associated to lopsided elements in the integral group ring satisfying some orderability condition are Bernoulli.
The effectiveness of shortcut/skip-connection has been widely verified, which inspires massive explorations on neural architecture design. This work attempts to find an effective way to design new network architectures. It is discovered that the main
difference between network architectures can be reflected in their recursion formulas. Based on this, a methodology is proposed to design novel network architectures from the perspective of mathematical formulas. Afterwards, a case study is provided to generate an improved architecture based on ResNet. Furthermore, the new architecture is compared with ResNet and then tested on ResNet-based networks. Massive experiments are conducted on CIFAR and ImageNet, which witnesses the significant performance improvements provided by the architecture.
