arXiv subjects

Lan Gao

Publications and source records attributed to Lan Gao.

30 records · Page 2Linked to original sources

arXiv2024

An alkali-referenced vector spectrum analyzer for visible-light integrated photonics

Integrated photonics has reformed our information society by offering on-chip optical signal synthesis, processing and detection with reduced size, weight and power consumption. As such, it has been successfully established in the near-infrared (NIR) telecommunication bands. With the soaring demand in miniaturized systems for biosensing, quantum information and transportable atomic clocks, extensive endeavors have been stacked on translating integrated photonics into the visible spectrum, i.e. visible-light integrated photonics. Various innovative visible-light integrated devices have been demonstrated, such as lasers, frequency combs, and atom traps, highlighting the capacity and prospect to create chip-based optical atomic clocks that can make timing and frequency metrology ubiquitous. A pillar to the development of visible-light integrated photonics is characterization techniques featuring high frequency resolution and wide spectral coverage, which however remain elusive. Here, we demonstrate a vector spectrum analyzer (VSA) for visible-light integrated photonics, offering spectral bandwidth from 766 to 795 nm and frequency resolution of 415 kHz. The VSA is rooted on a widely chirping, high-power, narrow-linewidth, mode-hop-free laser around 780 nm, which is frequency-doubled from the near-infrared via an efficient, broadband CPLN waveguide. The VSA is further referenced to hyperfine structures of rubidium and potassium atoms, enabling 8.1 MHz frequency accuracy. We apply our VSA to showcase the characterization of loss, dispersion and phase response of passive integrated devices, as well as densely spaced spectra of mode-locked lasers. Combining operation in the NIR and visible spectra, our VSA allows characterization bandwidth exceeding an octave and can be an invaluable diagnostic tool for spectroscopy, nonlinear optical processing, imaging and quantum interfaces to atomic devices.

physics.optics↗

arXiv2024

Dynamic Contextual Pricing with Doubly Non-Parametric Random Utility Models

In the evolving landscape of digital commerce, adaptive dynamic pricing strategies are essential for gaining a competitive edge. This paper introduces novel {\em doubly nonparametric random utility models} that eschew traditional parametric assumptions used in estimating consumer demand's mean utility function and noise distribution. Existing nonparametric methods like multi-scale {\em Distributional Nearest Neighbors (DNN and TDNN)}, initially designed for offline regression, face challenges in dynamic online pricing due to design limitations, such as the indirect observability of utility-related variables and the absence of uniform convergence guarantees. We address these challenges with innovative population equations that facilitate nonparametric estimation within decision-making frameworks and establish new analytical results on the uniform convergence rates of DNN and TDNN, enhancing their applicability in dynamic environments. Our theoretical analysis confirms that the statistical learning rates for the mean utility function and noise distribution are minimax optimal. We also derive a regret bound that illustrates the critical interaction between model dimensionality and noise distribution smoothness, deepening our understanding of dynamic pricing under varied market conditions. These contributions offer substantial theoretical insights and practical tools for implementing effective, data-driven pricing strategies, advancing the theoretical framework of pricing models and providing robust methodologies for navigating the complexities of modern markets.

stat.ME↗

arXiv2024

ARK: Robust Knockoffs Inference with Coupling

We investigate the robustness of the model-X knockoffs framework with respect to the misspecified or estimated feature distribution. We achieve such a goal by theoretically studying the feature selection performance of a practically implemented knockoffs algorithm, which we name as the approximate knockoffs (ARK) procedure, under the measures of the false discovery rate (FDR) and $k$-familywise error rate ($k$-FWER). The approximate knockoffs procedure differs from the model-X knockoffs procedure only in that the former uses the misspecified or estimated feature distribution. A key technique in our theoretical analyses is to couple the approximate knockoffs procedure with the model-X knockoffs procedure so that random variables in these two procedures can be close in realizations. We prove that if such coupled model-X knockoffs procedure exists, the approximate knockoffs procedure can achieve the asymptotic FDR or $k$-FWER control at the target level. We showcase three specific constructions of such coupled model-X knockoff variables, verifying their existence and justifying the robustness of the model-X knockoffs framework. Additionally, we formally connect our concept of knockoff variable coupling to a type of Wasserstein distance.

stat.ME↗

arXiv2024

A chip-integrated comb-based microwave oscillator

Low-noise microwave oscillators are cornerstones for wireless communication, radar and clocks. Optical frequency combs have enabled photonic microwaves with unrivalled noise performance and bandwidth. Emerging interest is to generate microwaves using chip-based frequency combs, namely microcombs. Here, we demonstrate the first, fully integrated, microcomb-based, microwave oscillator chip. The chip, powered by a microelectronic circuit, leverages hybrid integration of a DFB laser, a nonlinear microresonator, and a high-speed photodetector. Each component represents the best of its own class, yet allows large-volume manufacturing with low cost in CMOS foundries. The hybrid chip outputs an ultralow-noise laser of 6.9 Hz linewidth, a microcomb of 10.7 GHz repetition rate, and a 10.7 GHz microwave of 6.3 mHz linewidth -- all three in one entity of 76 mm$^2$ size.The microwave phase noise reaches -75/-105/-130 dBc/Hz at 1/10/100 kHz Fourier offset frequency. Our results can reinvigorate our information society for communication, sensing, timing and precision measurement.

physics.optics↗

arXiv2023

Ion and Electron Acoustic Bursts during Anti-Parallel Magnetic Reconnection Driven by Lasers

Magnetic reconnection converts magnetic energy into thermal and kinetic energy in plasma. Among numerous candidate mechanisms, ion acoustic instabilities driven by the relative drift between ions and electrons, or equivalently electric current, have been suggested to play a critical role in dissipating magnetic energy in collisionless plasmas. However, their existence and effectiveness during reconnection have not been well understood due to ion Landau damping and difficulties in resolving the Debye length scale in the laboratory. Here we report a sudden onset of ion acoustic bursts measured by collective Thomson scattering in the exhaust of anti-parallel magnetically driven reconnection using high-power lasers. The ion acoustic bursts are followed by electron acoustic bursts with electron heating and bulk acceleration. We reproduce these observations with 1D and 2D particle-in-cell simulations in which electron outflow jet drives ion-acoustic instabilities, forming double layers. These layers induce electron two-stream instabilities that generate electron acoustic bursts and energize electrons. Our results demonstrate the importance of ion and electron acoustic dynamics during reconnection when ion Landau damping is ineffective, a condition applicable to a range of astrophysical plasmas including near-Earth space, stellar flares, and black hole accretion engines.

physics.plasm-ph↗

arXiv2023

Foundry manufacturing of tight-confinement, dispersion-engineered, ultralow-loss silicon nitride photonic integrated circuit

The foundry development of integrated photonics has revolutionized today's optical interconnect and datacenters. Over the last decade, we have witnessed the rising of silicon nitride (Si$_3$N$_4$) integrated photonics, which is currently transferring from laboratory research to foundry manufacturing. The development and transition are triggered by the ultimate need of low optical loss offered by Si$_3$N$_4$, which is beyond the reach of silicon and III-V semiconductors. Combined with modest Kerr nonlinearity, tight optical confinement and dispersion engineering, Si$_3$N$_4$ has today become the leading platform for linear and Kerr nonlinear photonics, and has enabled chip-scale lasers featuring ultralow noise on par with table-top fiber lasers. However, so far all the reported fabrication processes of tight-confinement, dispersion-engineered Si$_3$N$_4$ photonic integrated circuit (PIC) with optical loss down to few dB/m have only been developed on 4-inch or smaller wafers. Yet, to transfer these processes to established CMOS foundries that typically operate 6-inch or even larger wafers, challenges remain. In this work, we demonstrate the first foundry-standard fabrication process of Si$_3$N$_4$ PIC with only 2.6 dB/m loss, thickness above 800 nm, and near 100% fabrication yield on 6-inch wafers. Such thick and ultralow-loss Si$_3$N$_4$ PIC enables low-threshold generation of soliton frequency combs. Merging with advanced heterogeneous integration, active ultralow-loss Si$_3$N$_4$ integrated photonics could pave an avenue to addressing future demands in our increasingly information-driven society.

physics.optics↗

arXiv2022

Optimal Nonparametric Inference with Two-Scale Distributional Nearest Neighbors

The weighted nearest neighbors (WNN) estimator has been popularly used as a flexible and easy-to-implement nonparametric tool for mean regression estimation. The bagging technique is an elegant way to form WNN estimators with weights automatically generated to the nearest neighbors; we name the resulting estimator as the distributional nearest neighbors (DNN) for easy reference. Yet, there is a lack of distributional results for such estimator, limiting its application to statistical inference. Moreover, when the mean regression function has higher-order smoothness, DNN does not achieve the optimal nonparametric convergence rate, mainly because of the bias issue. In this work, we provide an in-depth technical analysis of the DNN, based on which we suggest a bias reduction approach for the DNN estimator by linearly combining two DNN estimators with different subsampling scales, resulting in the novel two-scale DNN (TDNN) estimator. The two-scale DNN estimator has an equivalent representation of WNN with weights admitting explicit forms and some being negative. We prove that, thanks to the use of negative weights, the two-scale DNN estimator enjoys the optimal nonparametric rate of convergence in estimating the regression function under the fourth-order smoothness condition. We further go beyond estimation and establish that the DNN and two-scale DNN are both asymptotically normal as the subsampling scales and sample size diverge to infinity. For the practical implementation, we also provide variance estimators and a distribution estimator using the jackknife and bootstrap techniques for the two-scale DNN. These estimators can be exploited for constructing valid confidence intervals for nonparametric inference of the regression function. The theoretical results and appealing finite-sample performance of the suggested two-scale DNN method are illustrated with several numerical examples.

stat.ML↗

arXiv2022

Compressing LSTM Networks by Matrix Product Operators

Long Short Term Memory(LSTM) models are the building blocks of many state-of-the-art natural language processing(NLP) and speech enhancement(SE) algorithms. However, there are a large number of parameters in an LSTM model. This usually consumes a large number of resources to train the LSTM model. Also, LSTM models suffer from computational inefficiency in the inference phase. Existing model compression methods (e.g., model pruning) can only discriminate based on the magnitude of model parameters, ignoring the issue of importance distribution based on the model information. Here we introduce the MPO decomposition, which describes the local correlation of quantum states in quantum many-body physics and is used to represent the large model parameter matrix in a neural network, which can compress the neural network by truncating the unimportant information in the weight matrix. In this paper, we propose a matrix product operator(MPO) based neural network architecture to replace the LSTM model. The effective representation of neural networks by MPO can effectively reduce the computational consumption of training LSTM models on the one hand, and speed up the computation in the inference phase of the model on the other hand. We compare the MPO-LSTM model-based compression model with the traditional LSTM model with pruning methods on sequence classification, sequence prediction, and speech enhancement tasks in our experiments. The experimental results show that our proposed neural network architecture based on the MPO approach significantly outperforms the pruning approach.

cs.NI↗

arXiv2022

Direct measurement of non-thermal electron acceleration from magnetically driven reconnection in a laboratory plasma

Magnetic reconnection is a ubiquitous astrophysical process that rapidly converts magnetic energy into some combination of plasma flow energy, thermal energy, and non-thermal energetic particles, including energetic electrons. Various reconnection acceleration mechanisms in different low-$β$ (plasma-to-magnetic pressure ratio) and collisionless environments have been proposed theoretically and studied numerically, including first- and second-order Fermi acceleration, betatron acceleration, parallel electric field acceleration along magnetic fields, and direct acceleration by the reconnection electric field. However, none of them have been heretofore confirmed experimentally, as the direct observation of non-thermal particle acceleration in laboratory experiments has been difficult due to short Debye lengths for \textit{in-situ} measurements and short mean free paths for \textit{ex-situ} measurements. Here we report the direct measurement of accelerated non-thermal electrons from low-$β$ magnetically driven reconnection in experiments using a laser-powered capacitor coil platform. We use kiloJoule lasers to drive parallel currents to reconnect MegaGauss-level magnetic fields in a quasi-axisymmetric geometry. The angular dependence of the measured electron energy spectrum and the resulting accelerated energies, supported by particle-in-cell simulations, indicate that the mechanism of direct electric field acceleration by the out-of-plane reconnection electric field is at work. Scaled energies using this mechanism show direct relevance to astrophysical observations. Our results therefore validate one of the proposed acceleration mechanisms by reconnection, and establish a new approach to study reconnection particle acceleration with laboratory experiments in relevant regimes.

physics.plasm-ph↗

arXiv2021

Refined Cramér Type Moderate Deviation Theorems for General Self-normalized Sums with Applications to Dependent Random Variables and Winsorized Mean

Let {(X_i,Y_i)}_{i=1}^n be a sequence of independent bivariate random vectors. In this paper, we establish a refined Cramér type moderate deviation theorem for the general self-normalized sum \sum_{i=1}^n X_i/(\sum_{i=1}^n Y_i^2)^{1/2}, which unifies and extends the classical Cramér (1938) theorem and the self-normalized Cramér type moderate deviation theorems by Jing, Shao and Wang (2003) as well as the further refined version by Wang (2011). The advantage of our result is evidenced through successful applications to weakly dependent random variables and self-normalized winsorized mean. Specifically, by applying our new framework on general self-normalized sum, we significantly improve Cramér type moderate deviation theorems for one-dependent random variables, geometrically β-mixing random variables and causal processes under geometrical moment contraction. As an additional application, we also derive the Cramér type moderate deviation theorems for self-normalized winsorized mean.

math.PR↗

arXiv2020

Asymptotic Distributions of High-Dimensional Distance Correlation Inference

Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null hypothesis of independence between the two random vectors when only the sample size or the dimensionality diverges. Yet its asymptotic null distribution for the more realistic setting when both sample size and dimensionality diverge in the full range remains largely underdeveloped. In this paper, we fill such a gap and develop central limit theorems and associated rates of convergence for a rescaled test statistic based on the bias-corrected distance correlation in high dimensions under some mild regularity conditions and the null hypothesis. Our new theoretical results reveal an interesting phenomenon of blessing of dimensionality for high-dimensional distance correlation inference in the sense that the accuracy of normal approximation can increase with dimensionality. Moreover, we provide a general theory on the power analysis under the alternative hypothesis of dependence, and further justify the capability of the rescaled distance correlation in capturing the pure nonlinear dependency under moderately high dimensionality for a certain type of alternative hypothesis. The theoretical results and finite-sample performance of the rescaled statistic are illustrated with several simulation examples and a blockchain application.

math.ST↗

arXiv2006

Novel Fabrication of Micromechanical Oscillators with Nanoscale Sensitivity at Room Temperature

We report on the design, fabrication, and implementation of ultrasensitive micromechanical oscillators. Our ultrathin single-crystal silicon cantilevers with integrated magnetic structures are the first of their kind: They are fabricated using a novel high-yield process in which magnetic film patterning and deposition are combined with cantilever fabrication. These novel devices have been developed for use as cantilever magnetometers and as force sensors in nuclear magnetic resonance force microscopy (MRFM). These two applications have achieved nanometer-scale resolution using the cantilevers described in this work. Current magnetic moment sensitivity achieved for the devices, when used as magnetometers, is 10^{-15} J/T at room temperature, which is more than a 1000 fold improvement in sensitivity, compared to conventional magnetometers. Current room temperature force sensitivity of MRFM cantilevers is ~10^{-16} N in a 1 Hz bandwidth, which is comparable to the room temperature sensitivities of similar devices of its type. Finite element modeling was used to improve design parameters, ensure that the devices meet experimental demands, and correlate mode shape with observed results. The photolithographic fabrication process was optimized, yielding an average of ~85% and alignment better than 1000 nm. Post-fabrication focused-ion-beam milling was used to further pattern the integrated magnetic structures when nanometer scale dimensions were required.

cond-mat.mes-hall↗