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Qin Li

Publications and source records attributed to Qin Li.

At least 127 records · Page 7Linked to original sources
arXiv2023

Inference of interaction kernels in mean-field models of opinion dynamics

In models of opinion dynamics, many parameters -- either in the form of constants or in the form of functions -- play a critical role in describing, calibrating, and forecasting how opinions change with time. When examining a model of opinion dynamics, it is beneficial to infer its parameters using empirical data. In this paper, we study an example of such an inference problem. We consider a mean-field bounded-confidence model with an unknown interaction kernel between individuals. This interaction kernel encodes how individuals with different opinions interact and affect each other's opinions. Because it is often difficult to quantitatively measure opinions as empirical data from observations or experiments, we assume that the available data takes the form of partial observations of a cumulative distribution function of opinions. We prove that certain measurements guarantee a precise and unique inference of the interaction kernel and propose a numerical method to reconstruct an interaction kernel from a limited number of data points. Our numerical results suggest that the error of the inferred interaction kernel decays exponentially as we strategically enlarge the data set.

cs.SI↗
arXiv2023

Integrating LLM, EEG, and Eye-Tracking Biomarker Analysis for Word-Level Neural State Classification in Semantic Inference Reading Comprehension

With the recent proliferation of large language models (LLMs), such as Generative Pre-trained Transformers (GPT), there has been a significant shift in exploring human and machine comprehension of semantic language meaning. This shift calls for interdisciplinary research that bridges cognitive science and natural language processing (NLP). This pilot study aims to provide insights into individuals' neural states during a semantic relation reading-comprehension task. We propose jointly analyzing LLMs, eye-gaze, and electroencephalographic (EEG) data to study how the brain processes words with varying degrees of relevance to a keyword during reading. We also use a feature engineering approach to improve the fixation-related EEG data classification while participants read words with high versus low relevance to the keyword. The best validation accuracy in this word-level classification is over 60\% across 12 subjects. Words of high relevance to the inference keyword had significantly more eye fixations per word: 1.0584 compared to 0.6576 when excluding no-fixation words, and 1.5126 compared to 1.4026 when including them. This study represents the first attempt to classify brain states at a word level using LLM knowledge. It provides valuable insights into human cognitive abilities and the realm of Artificial General Intelligence (AGI), and offers guidance for developing potential reading-assisted technologies.

cs.CL↗
arXiv2023

Testing Lorentz symmetry with space-based gravitational-wave detectors

Lorentz symmetry (LS), one of the most fundamental physical symmetries, has been extensively studied in the context of quantum gravity and unification theories. Many of these theories predict a LS violation, which could arise from the discreteness of spacetime, or extra dimensions. Standard-model extension (SME) is an effective field theory to describe Lorentz violation whose effects can be explored using precision instruments such as atomic clocks and gravitational-wave (GW) detectors. Considering the pure-gravity sector and matter-gravity coupling sector in the SME, we studied the leading Lorentz-violating modifications to the time delay of light and the relativistic frequency shift of the clock in the space-based GW detectors. We found that the six data streams from the GW mission can construct various combinations of measurement signals, such as single-arm round-trip path, interference path, triangular round-trip path, etc. These measurements are sensitive to the different combinations of SME coefficients and provide novel linear combinations of SME coefficients different from previous studies. Based on the orbits of TianQin, LISA, and Taiji missions, we calculated the response of Lorentz-violating effects on the combinations of the measurement signal data streams. Our results allow us to estimate the sensitivities for SME coefficients: $10^{-6}$ for the gravity sector coefficient $\bar{s}^{TT}$, $10^{-6}$ for matter-gravity coupling coefficients $(\bar{a}^{(e+p)}_{\text{eff}})_{T}$ and $\bar{c}^{(e+p)}_{TT}$, and $10^{-5}$ for $(\bar{a}^{n}_{\text{eff}})_{T}$ and $\bar{c}^{n}_{TT}$.

gr-qc↗
arXiv2023

Solving the Wide-band Inverse Scattering Problem via Equivariant Neural Networks

This paper introduces a novel deep neural network architecture for solving the inverse scattering problem in frequency domain with wide-band data, by directly approximating the inverse map, thus avoiding the expensive optimization loop of classical methods. The architecture is motivated by the filtered back-projection formula in the full aperture regime and with homogeneous background, and it leverages the underlying equivariance of the problem and compressibility of the integral operator. This drastically reduces the number of training parameters, and therefore the computational and sample complexity of the method. In particular, we obtain an architecture whose number of parameters scale sub-linearly with respect to the dimension of the inputs, while its inference complexity scales super-linearly but with very small constants. We provide several numerical tests that show that the current approach results in better reconstruction than optimization-based techniques such as full-waveform inversion, but at a fraction of the cost while being competitive with state-of-the-art machine learning methods.

math.NA↗
arXiv2023

Kinetic chemotaxis tumbling kernel determined from macroscopic quantities

Chemotaxis is the physical phenomenon that bacteria adjust their motions according to chemical stimulus. A classical model for this phenomenon is a kinetic equation that describes the velocity jump process whose tumbling/transition kernel uniquely determines the effect of chemical stimulus on bacteria. The model has been shown to be an accurate model that matches with bacteria motion qualitatively. For a quantitative modeling, biophysicists and practitioners are also highly interested in determining the explicit value of the tumbling kernel. Due to the experimental limitations, measurements are typically macroscopic in nature. Do macroscopic quantities contain enough information to recover microscopic behavior? In this paper, we give a positive answer. We show that when given a special design of initial data, the population density, one specific macroscopic quantity as a function of time, contains sufficient information to recover the tumbling kernel and its associated damping coefficient. Moreover, we can read off the chemotaxis tumbling kernel using the values of population density directly from this specific experimental design. This theoretical result using kinetic theory sheds light on how practitioners may conduct experiments in laboratories.

math.AP↗
arXiv2023

Quantizable functions on Kähler manifolds and non-formal quantization

Applying the Fedosov connections constructed in our previous work, we find a (dense) subsheaf of smooth functions on a Kähler manifold $X$ which admits a non-formal deformation quantization. When $X$ is prequantizable and the Fedosov connection satisfies an integrality condition, we prove that this subsheaf of functions can be quantized to a sheaf of twisted differential operators (TDO), which is isomorphic to that associated to the prequantum line bundle. We also show that examples of such quantizable functions are given by images of quantum moment maps.

math.QA↗
arXiv2023

Towards Quantitative Evaluation of Crystal Structure Prediction Performance

Crystal structure prediction (CSP) is now increasingly used in the discovery of novel materials with applications in diverse industries. However, despite decades of developments, the problem is far from being solved. With the progress of deep learning, search algorithms, and surrogate energy models, there is a great opportunity for breakthroughs in this area. However, the evaluation of CSP algorithms primarily relies on manual structural and formation energy comparisons. The lack of a set of well-defined quantitative performance metrics for CSP algorithms make it difficult to evaluate the status of the field and identify the strengths and weaknesses of different CSP algorithms. Here, we analyze the quality evaluation issue in CSP and propose a set of quantitative structure similarity metrics, which when combined can be used to automatically determine the quality of the predicted crystal structures compared to the ground truths. Our CSP performance metrics can be then utilized to evaluate the large set of existing and emerging CSP algorithms, thereby alleviating the burden of manual inspection on a case-by-case basis. The related open-source code can be accessed freely at https://github.com/usccolumbia/CSPBenchMetrics

cond-mat.mtrl-sci↗
arXiv2023

MD-HIT: Machine learning for materials property prediction with dataset redundancy control

Materials datasets are usually featured by the existence of many redundant (highly similar) materials due to the tinkering material design practice over the history of materials research. For example, the materials project database has many perovskite cubic structure materials similar to SrTiO$_3$. This sample redundancy within the dataset makes the random splitting of machine learning model evaluation to fail so that the ML models tend to achieve over-estimated predictive performance which is misleading for the materials science community. This issue is well known in the field of bioinformatics for protein function prediction, in which a redundancy reduction procedure (CD-Hit) is always applied to reduce the sample redundancy by ensuring no pair of samples has a sequence similarity greater than a given threshold. This paper surveys the overestimated ML performance in the literature for both composition based and structure based material property prediction. We then propose a material dataset redundancy reduction algorithm called MD-HIT and evaluate it with several composition and structure based distance threshold sfor reducing data set sample redundancy. We show that with this control, the predicted performance tends to better reflect their true prediction capability. Our MD-hit code can be freely accessed at https://github.com/usccolumbia/MD-HIT

cond-mat.mtrl-sci↗
arXiv2023

AlphaCrystal: Contact map based crystal structure prediction using deep learning

Crystal structure prediction is one of the major unsolved problems in materials science. Traditionally, this problem is formulated as a global optimization problem for which global search algorithms are combined with first principle free energy calculations to predict the ground-state crystal structure given only a material composition or a chemical system. These ab initio algorithms usually cannot exploit a large amount of implicit physicochemical rules or geometric constraints (deep knowledge) of atom configurations embodied in a large number of known crystal structures. Inspired by the deep learning enabled breakthrough in protein structure prediction, herein we propose AlphaCrystal, a crystal structure prediction algorithm that combines a deep residual neural network model that learns deep knowledge to guide predicting the atomic contact map of a target crystal material followed by reconstructing its 3D crystal structure using genetic algorithms. Based on the experiments of a selected set of benchmark crystal materials, we show that our AlphaCrystal algorithm can predict structures close to the ground truth structures. It can also speed up the crystal structure prediction process by predicting and exploiting the predicted contact map so that it has the potential to handle relatively large systems. We believe that our deep learning based ab initio crystal structure prediction method that learns from existing material structures can be used to scale up current crystal structure prediction practice. To our knowledge, AlphaCrystal is the first neural network based algorithm for crystal structure contact map prediction and the first method for directly reconstructing crystal structures from materials composition, which can be further optimized by DFT calculations.

cond-mat.mtrl-sci↗
arXiv2023

Suppressing Instability in a Vlasov-Poisson System by an External Electric Field Through Constrained Optimization

Fusion energy offers the potential for the generation of clean, safe, and nearly inexhaustible energy. While notable progress has been made in recent years, significant challenges persist in achieving net energy gain. Improving plasma confinement and stability stands as a crucial task in this regard and requires optimization and control of the plasma system. In this work, we deploy a PDE-constrained optimization formulation that uses a kinetic description for plasma dynamics as the constraint. This is to optimize, over all possible controllable external electric fields, the stability of the plasma dynamics under the condition that the Vlasov--Poisson (VP) equation is satisfied. For computing the functional derivative with respect to the external field in the optimization updates, the adjoint equation is derived. Furthermore, in the discrete setting, where we employ the semi-Lagrangian method as the forward solver, we also explicitly formulate the corresponding adjoint solver and the gradient as the discrete analogy to the adjoint equation and the Frechet derivative. A distinct feature we observed of this constrained optimization is the complex landscape of the objective function and the existence of numerous local minima, largely due to the hyperbolic nature of the VP system. To overcome this issue, we utilize a gradient-accelerated genetic algorithm, leveraging the advantages of the genetic algorithm's exploration feature to cover a broader search of the solution space and the fast local convergence aided by the gradient information. We show that our algorithm obtains good electric fields that are able to maintain a prescribed profile in a beam shaping problem and uses nonlinear effects to suppress plasma instability in a two-stream configuration.

math.NA↗
arXiv2023

On optimal bases for multiscale PDEs and Bayesian homogenization

PDE solutions are numerically represented by basis functions. Classical methods employ pre-defined bases that encode minimum desired PDE properties, which naturally cause redundant computations. What are the best bases to numerically represent PDE solutions? From the analytical perspective, the Kolmogorov $n$-width is a popular criterion for selecting representative basis functions. From the Bayesian computation perspective, the concept of optimality selects the modes that, when known, minimize the variance of the conditional distribution of the rest of the solution. We show that these two definitions of optimality are equivalent. Numerically, both criteria reduce to solving a Singular Value Decomposition (SVD), a procedure that can be made numerically efficient through randomized sampling. We demonstrate computationally the effectiveness of the basis functions so obtained on several linear and nonlinear problems. In all cases, the optimal accuracy is achieved with a small set of basis functions.

math.NA↗
arXiv2023

Scintillation Minimization versus Intensity Maximization in Optimal Beams

In free-space optical communications and other applications, it is desirable to design optical beams that have reduced or even minimal scintillation. However, the optimization problem for minimizing scintillation is challenging, and few optimal solutions have been found. Here we investigate the general optimization problem of minimizing scintillation and formulate it as a convex optimization problem. An analytical solution is found and demonstrates that a beam that minimizes scintillation is incoherent light (i.e., spatially uncorrelated). Furthermore, numerical solutions show that beams minimizing scintillation give very low intensity at the receiver. To counteract this effect, we study a new convex cost function that balances both scintillation and intensity. We show through numerical experiments that the minimizers of this cost function reduce scintillation while preserving a significantly higher level of intensity at the receiver.

physics.optics↗
arXiv2023

Numerical investigations on interactions between 2D/3D conical shock wave and axisymmetric boundary layer at Ma=2.2

Numerical simulation and analysis are carried out on interactions between a 2D/3D conical shock wave and an axisymmetric boundary layer with reference to the experiment by Kussoy et al., in which the shock was generated by a 15-deg half-angle cone in a tube at 15-deg angle of attack (AOA). Based on the RANS equations and Menter's SST turbulence model, the present study uses the newly developed WENO3-PRM211 scheme and the PHengLEI CFD platform for the computations. First, computations are performed for the 3D interaction corresponding to the conditions of the experiment by Kussoy et al., and these are then extended to cases with AOA = 10-deg and 5-deg. For comparison, 2D axisymmetric counterparts of the 3D interactions are investigated for cones coaxial with the tube and having half-cone angles of 27.35-deg, 24.81-deg, and 20.96-deg. The shock wave structure, vortex structure, variable distributions, and wall separation topology of the interaction are computed. The results show that in 2D/3D interactions, a new Mach reflection-like event occurs and a Mach stem-like structure is generated above the front of the separation bubble, which differs from the model of Babinsky for 2D planar shock wave/boundary layer interaction. A new interaction model is established to describe this behavior. The relationship between the length of the circumferentially unseparated region in the tube and the AOA of the cone indicates the existence of a critical AOA at which the length is zero, and a prediction of this angle is obtained using an empirical fit, which is verified by computation. The occurrence of side overflow in the windward meridional plane is analyzed, and a quantitative knowledge is obtained. To elucidate the characteristics of the 3D interaction, the scale and structure of the vortex and the pressure and friction force distributions are presented and compared with those of the 2D interaction.

physics.flu-dyn↗
arXiv2023

Evaluation of wait time saving effectiveness of triage algorithms

In the past decade, Artificial Intelligence (AI) algorithms have made promising impacts to transform healthcare in all aspects. One application is to triage patients' radiological medical images based on the algorithm's binary outputs. Such AI-based prioritization software is known as computer-aided triage and notification (CADt). Their main benefit is to speed up radiological review of images with time-sensitive findings. However, as CADt devices become more common in clinical workflows, there is still a lack of quantitative methods to evaluate a device's effectiveness in saving patients' waiting times. In this paper, we present a mathematical framework based on queueing theory to calculate the average waiting time per patient image before and after a CADt device is used. We study four workflow models with multiple radiologists (servers) and priority classes for a range of AI diagnostic performance, radiologist's reading rates, and patient image (customer) arrival rates. Due to model complexity, an approximation method known as the Recursive Dimensionality Reduction technique is applied. We define a performance metric to measure the device's time-saving effectiveness. A software tool is developed to simulate clinical workflow of image review/interpretation, to verify theoretical results, and to provide confidence intervals of the performance metric we defined. It is shown quantitatively that a triage device is more effective in a busy, short-staffed setting, which is consistent with our clinical intuition and simulation results. Although this work is motivated by the need for evaluating CADt devices, the framework we present in this paper can be applied to any algorithm that prioritizes customers based on its binary outputs.

stat.AP↗
arXiv2023

Guaranteed lower eigenvalue bounds for Steklov operators using conforming finite element methods

For the eigenvalue problem of the Steklov differential operator, by following Liu's approach, an algorithm utilizing the conforming finite element method (FEM) is proposed to provide guaranteed lower bounds for the eigenvalues. The proposed method requires the a priori error estimation for FEM solution to nonhomogeneous Neumann problems, which is solved by constructing the hypercircle for the corresponding FEM spaces and boundary conditions. Numerical examples are also shown to confirm the efficiency of our proposed method.

math.NA↗
arXiv2023

Delegated variational quantum algorithms based on quantum homomorphic encryption

Variational quantum algorithms (VQAs) are considered as one of the most promising candidates for achieving quantum advantages on quantum devices in the noisy intermediate-scale quantum (NISQ) era. They have been developed for numerous applications such as image processing and solving linear systems of equations. The application of VQAs can be greatly enlarged if users with limited quantum capabilities can run them on remote powerful quantum computers. But the private data of clients may be leaked to quantum servers in such a quantum cloud model. To solve the problem, a novel quantum homomorphic encryption (QHE) scheme which is client-friendly and suitable for VQAs is constructed for quantum servers to calculate encrypted data. Then delegated VQAs are proposed based on the given QHE scheme, where the server can train the ansatz circuit using the client's data even without knowing the real input and the output of the client. Furthermore, a delegated variational quantum classifier to identify handwritten digit images is given as a specific example of delegated VQAs and simulated on the cloud platform of Original Quantum to show its feasibility.

quant-ph↗
arXiv2022

Spatial-temporal traffic modeling with a fusion graph reconstructed by tensor decomposition

Accurate spatial-temporal traffic flow forecasting is essential for helping traffic managers to take control measures and drivers to choose the optimal travel routes. Recently, graph convolutional networks (GCNs) have been widely used in traffic flow prediction owing to their powerful ability to capture spatial-temporal dependencies. The design of the spatial-temporal graph adjacency matrix is a key to the success of GCNs, and it is still an open question. This paper proposes reconstructing the binary adjacency matrix via tensor decomposition, and a traffic flow forecasting method is proposed. First, we reformulate the spatial-temporal fusion graph adjacency matrix into a three-way adjacency tensor. Then, we reconstructed the adjacency tensor via Tucker decomposition, wherein more informative and global spatial-temporal dependencies are encoded. Finally, a Spatial-temporal Synchronous Graph Convolutional module for localized spatial-temporal correlations learning and a Dilated Convolution module for global correlations learning are assembled to aggregate and learn the comprehensive spatial-temporal dependencies of the road network. Experimental results on four open-access datasets demonstrate that the proposed model outperforms state-of-the-art approaches in terms of the prediction performance and computational cost.

cs.LG↗
arXiv2022

Solar Flare Index Prediction Using SDO/HMI Vector Magnetic Data Products with Statistical and Machine Learning Methods

Solar flares, especially the M- and X-class flares, are often associated with coronal mass ejections (CMEs). They are the most important sources of space weather effects, that can severely impact the near-Earth environment. Thus it is essential to forecast flares (especially the M-and X-class ones) to mitigate their destructive and hazardous consequences. Here, we introduce several statistical and Machine Learning approaches to the prediction of the AR's Flare Index (FI) that quantifies the flare productivity of an AR by taking into account the numbers of different class flares within a certain time interval. Specifically, our sample includes 563 ARs appeared on solar disk from May 2010 to Dec 2017. The 25 magnetic parameters, provided by the Space-weather HMI Active Region Patches (SHARP) from Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO), characterize coronal magnetic energy stored in ARs by proxy and are used as the predictors. We investigate the relationship between these SHARP parameters and the FI of ARs with a machine-learning algorithm (spline regression) and the resampling method (Synthetic Minority Over-Sampling Technique for Regression with Gaussian Noise, short by SMOGN). Based on the established relationship, we are able to predict the value of FIs for a given AR within the next 1-day period. Compared with other 4 popular machine learning algorithms, our methods improve the accuracy of FI prediction, especially for large FI. In addition, we sort the importance of SHARP parameters by Borda Count method calculated from the ranks that are rendered by 9 different machine learning methods.

astro-ph.SR↗