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Published work

26 published item(s)

preprint2026arXiv

Unifying Sparse Attention with Hierarchical Memory for Scalable Long-Context LLM Serving

Long-context LLM serving is bottlenecked by the cost of attending over ever-growing KV caches. Dynamic sparse attention promises relief by accessing only a small, query-dependent subset of the KV state per decoding step and extending the KV storage to CPU memory. In practice, however, these algorithmic savings rarely translate into end-to-end system-level gains because sparse methods typically operate at different granularities and thus rely on ad hoc, per-algorithm implementations. At the same time, hierarchical KV storage introduces a new systems bottleneck: retrieving fine-grained, irregular KV subsets across the GPU-CPU boundary can easily erase the benefits of sparsity. We present SPIN, a sparse-attention-aware inference framework that co-designs the execution pipeline with hierarchical KV storage through three techniques: (1) a unified partition abstraction that maps different sparsity granularities onto a shared page-based KV substrate; (2) a locality-aware KV cache manager that dynamically sizes per-request HBM budgets and uses a GPU-friendly bucketed LRU policy to cut PCIe round-trips; and (3) a two-level hierarchical metadata layout sized to the active working set rather than the worst-case address space. Built on vLLM with three representative sparse attention algorithms, SPIN delivers 1.66-5.66x higher end-to-end throughput and 7-9x lower TTFT than vLLM, and reduces TPOT by up to 58% over the original sparse-attention implementations.

preprint2023arXiv

Attention-based Interactive Disentangling Network for Instance-level Emotional Voice Conversion

Emotional Voice Conversion aims to manipulate a speech according to a given emotion while preserving non-emotion components. Existing approaches cannot well express fine-grained emotional attributes. In this paper, we propose an Attention-based Interactive diseNtangling Network (AINN) that leverages instance-wise emotional knowledge for voice conversion. We introduce a two-stage pipeline to effectively train our network: Stage I utilizes inter-speech contrastive learning to model fine-grained emotion and intra-speech disentanglement learning to better separate emotion and content. In Stage II, we propose to regularize the conversion with a multi-view consistency mechanism. This technique helps us transfer fine-grained emotion and maintain speech content. Extensive experiments show that our AINN outperforms state-of-the-arts in both objective and subjective metrics.

preprint2023arXiv

Formation Tracking for a Multi-Auv System Based on an Adaptive Sliding Mode Method in the Water Flow Environment

In this paper, formation tracking for a multi-AUV system (MAS) using an improved adaptive sliding mode control method is studied in the Three Dimensional (3-D) underwater environment. Firstly, the kinematics model and the dynamic model of the AUVs are given as the Six Dimensions of Freedom (6-DOF) considered. Then, control law based on the mathematical model of the AUVs is proposed based on the improved sliding mode method. A second order sliding mode control method is adopted to eliminate the chatting phenomenon of the controller. Thirdly, considering the water flow in the underwater working environment of the AUVs, an adaptive module is added to the controller. With the adaptive approach, the finite disturbances caused by water flow could be handled with the controller. The proposed method achieves stability by substituting an adaptive continuous term for the switching term in the controller. At last, a robust sliding mode controller with continuous model predictive control strategy for the multi-AUV system is developed to achieve leader-follower formation tracking under the presence of bounded flow disturbances, and simulations are implemented to confirm the effectiveness of the proposed method.

preprint2022arXiv

Distill-VQ: Learning Retrieval Oriented Vector Quantization By Distilling Knowledge from Dense Embeddings

Vector quantization (VQ) based ANN indexes, such as Inverted File System (IVF) and Product Quantization (PQ), have been widely applied to embedding based document retrieval thanks to the competitive time and memory efficiency. Originally, VQ is learned to minimize the reconstruction loss, i.e., the distortions between the original dense embeddings and the reconstructed embeddings after quantization. Unfortunately, such an objective is inconsistent with the goal of selecting ground-truth documents for the input query, which may cause severe loss of retrieval quality. Recent works identify such a defect, and propose to minimize the retrieval loss through contrastive learning. However, these methods intensively rely on queries with ground-truth documents, whose performance is limited by the insufficiency of labeled data. In this paper, we propose Distill-VQ, which unifies the learning of IVF and PQ within a knowledge distillation framework. In Distill-VQ, the dense embeddings are leveraged as "teachers", which predict the query's relevance to the sampled documents. The VQ modules are treated as the "students", which are learned to reproduce the predicted relevance, such that the reconstructed embeddings may fully preserve the retrieval result of the dense embeddings. By doing so, Distill-VQ is able to derive substantial training signals from the massive unlabeled data, which significantly contributes to the retrieval quality. We perform comprehensive explorations for the optimal conduct of knowledge distillation, which may provide useful insights for the learning of VQ based ANN index. We also experimentally show that the labeled data is no longer a necessity for high-quality vector quantization, which indicates Distill-VQ's strong applicability in practice.

preprint2022arXiv

Fair Representation Learning through Implicit Path Alignment

We consider a fair representation learning perspective, where optimal predictors, on top of the data representation, are ensured to be invariant with respect to different sub-groups. Specifically, we formulate this intuition as a bi-level optimization, where the representation is learned in the outer-loop, and invariant optimal group predictors are updated in the inner-loop. Moreover, the proposed bi-level objective is demonstrated to fulfill the sufficiency rule, which is desirable in various practical scenarios but was not commonly studied in the fair learning. Besides, to avoid the high computational and memory cost of differentiating in the inner-loop of bi-level objective, we propose an implicit path alignment algorithm, which only relies on the solution of inner optimization and the implicit differentiation rather than the exact optimization path. We further analyze the error gap of the implicit approach and empirically validate the proposed method in both classification and regression settings. Experimental results show the consistently better trade-off in prediction performance and fairness measurement.

preprint2022arXiv

Optimization-Induced Graph Implicit Nonlinear Diffusion

Due to the over-smoothing issue, most existing graph neural networks can only capture limited dependencies with their inherently finite aggregation layers. To overcome this limitation, we propose a new kind of graph convolution, called Graph Implicit Nonlinear Diffusion (GIND), which implicitly has access to infinite hops of neighbors while adaptively aggregating features with nonlinear diffusion to prevent over-smoothing. Notably, we show that the learned representation can be formalized as the minimizer of an explicit convex optimization objective. With this property, we can theoretically characterize the equilibrium of our GIND from an optimization perspective. More interestingly, we can induce new structural variants by modifying the corresponding optimization objective. To be specific, we can embed prior properties to the equilibrium, as well as introducing skip connections to promote training stability. Extensive experiments show that GIND is good at capturing long-range dependencies, and performs well on both homophilic and heterophilic graphs with nonlinear diffusion. Moreover, we show that the optimization-induced variants of our models can boost the performance and improve training stability and efficiency as well. As a result, our GIND obtains significant improvements on both node-level and graph-level tasks.

preprint2022arXiv

Path Integral Method for Proportional Step and Proportional Double-Barrier Step Option Pricing

Path integral method in quantum mechanics provides a new thinking for barrier option pricing. For proportional step options, the option price changing process is similar to the one dimensional trapezoid potential barrier scattering problem in quantum mechanics; for double-barrier step options, the option price changing process is analogous to a particle moving in a finite symmetric square potential well. Using path integral method, the analytical expressions of pricing kernel and option price could be derived. Numerical results of option price as a function of underlying price, potential and exercise price are shown, which are consistent with the results given by mathematical method.

preprint2022arXiv

PolarStream: Streaming Lidar Object Detection and Segmentation with Polar Pillars

Recent works recognized lidars as an inherently streaming data source and showed that the end-to-end latency of lidar perception models can be reduced significantly by operating on wedge-shaped point cloud sectors rather then the full point cloud. However, due to use of cartesian coordinate systems these methods represent the sectors as rectangular regions, wasting memory and compute. In this work we propose using a polar coordinate system and make two key improvements on this design. First, we increase the spatial context by using multi-scale padding from neighboring sectors: preceding sector from the current scan and/or the following sector from the past scan. Second, we improve the core polar convolutional architecture by introducing feature undistortion and range stratified convolutions. Experimental results on the nuScenes dataset show significant improvements over other streaming based methods. We also achieve comparable results to existing non-streaming methods but with lower latencies. The code and pretrained models are available at \url{https://github.com/motional/polarstream}.

preprint2022arXiv

Proposal-free Lidar Panoptic Segmentation with Pillar-level Affinity

We propose a simple yet effective proposal-free architecture for lidar panoptic segmentation. We jointly optimize both semantic segmentation and class-agnostic instance classification in a single network using a pillar-based bird's-eye view representation. The instance classification head learns pairwise affinity between pillars to determine whether the pillars belong to the same instance or not. We further propose a local clustering algorithm to propagate instance ids by merging semantic segmentation and affinity predictions. Our experiments on nuScenes dataset show that our approach outperforms previous proposal-free methods and is comparable to proposal-based methods which requires extra annotation from object detection.

preprint2022arXiv

Results of the NeurIPS'21 Challenge on Billion-Scale Approximate Nearest Neighbor Search

Despite the broad range of algorithms for Approximate Nearest Neighbor Search, most empirical evaluations of algorithms have focused on smaller datasets, typically of 1 million points~\citep{Benchmark}. However, deploying recent advances in embedding based techniques for search, recommendation and ranking at scale require ANNS indices at billion, trillion or larger scale. Barring a few recent papers, there is limited consensus on which algorithms are effective at this scale vis-à-vis their hardware cost. This competition compares ANNS algorithms at billion-scale by hardware cost, accuracy and performance. We set up an open source evaluation framework and leaderboards for both standardized and specialized hardware. The competition involves three tracks. The standard hardware track T1 evaluates algorithms on an Azure VM with limited DRAM, often the bottleneck in serving billion-scale indices, where the embedding data can be hundreds of GigaBytes in size. It uses FAISS~\citep{Faiss17} as the baseline. The standard hardware track T2 additional allows inexpensive SSDs in addition to the limited DRAM and uses DiskANN~\citep{DiskANN19} as the baseline. The specialized hardware track T3 allows any hardware configuration, and again uses FAISS as the baseline. We compiled six diverse billion-scale datasets, four newly released for this competition, that span a variety of modalities, data types, dimensions, deep learning models, distance functions and sources. The outcome of the competition was ranked leaderboards of algorithms in each track based on recall at a query throughput threshold. Additionally, for track T3, separate leaderboards were created based on recall as well as cost-normalized and power-normalized query throughput.

preprint2021arXiv

On the $L^\infty$ stability of Prandtl expansions in Gevrey class

In this paper, we prove the $L^\infty\cap L^2$ stability of Prandtl expansions of shear flow type as $\big(U(y/\sqrtν),0\big)$ for the initial perturbation in the Gevrey class, where $U(y)$ is a monotone and concave function and $ν$ is the viscosity coefficient. To this end, we develop the direct resolvent estimate method for the linearized Orr-Sommerfeld operator instead of the Rayleigh-Airy iteration method introduced by Grenier, Guo and Nguyen.

preprint2021arXiv

Pareto-Frontier-aware Neural Architecture Generation for Diverse Budgets

Designing feasible and effective architectures under diverse computation budgets incurred by different applications/devices is essential for deploying deep models in practice. Existing methods often perform an independent architecture search for each target budget, which is very inefficient yet unnecessary. Moreover, the repeated independent search manner would inevitably ignore the common knowledge among different search processes and hamper the search performance. To address these issues, we seek to train a general architecture generator that automatically produces effective architectures for an arbitrary budget merely via model inference. To this end, we propose a Pareto-Frontier-aware Neural Architecture Generator (NAG) which takes an arbitrary budget as input and produces the Pareto optimal architecture for the target budget. We train NAG by learning the Pareto frontier (i.e., the set of Pareto optimal architectures) over model performance and computational cost (e.g., latency). Extensive experiments on three platforms (i.e., mobile, CPU, and GPU) show the superiority of the proposed method over existing NAS methods.

preprint2021arXiv

StrokeGAN: Reducing Mode Collapse in Chinese Font Generation via Stroke Encoding

The generation of stylish Chinese fonts is an important problem involved in many applications. Most of existing generation methods are based on the deep generative models, particularly, the generative adversarial networks (GAN) based models. However, these deep generative models may suffer from the mode collapse issue, which significantly degrades the diversity and quality of generated results. In this paper, we introduce a one-bit stroke encoding to capture the key mode information of Chinese characters and then incorporate it into CycleGAN, a popular deep generative model for Chinese font generation. As a result we propose an efficient method called StrokeGAN, mainly motivated by the observation that the stroke encoding contains amount of mode information of Chinese characters. In order to reconstruct the one-bit stroke encoding of the associated generated characters, we introduce a stroke-encoding reconstruction loss imposed on the discriminator. Equipped with such one-bit stroke encoding and stroke-encoding reconstruction loss, the mode collapse issue of CycleGAN can be significantly alleviated, with an improved preservation of strokes and diversity of generated characters. The effectiveness of StrokeGAN is demonstrated by a series of generation tasks over nine datasets with different fonts. The numerical results demonstrate that StrokeGAN generally outperforms the state-of-the-art methods in terms of content and recognition accuracies, as well as certain stroke error, and also generates more realistic characters.

preprint2021arXiv

Towards Accurate and Compact Architectures via Neural Architecture Transformer

Designing effective architectures is one of the key factors behind the success of deep neural networks. Existing deep architectures are either manually designed or automatically searched by some Neural Architecture Search (NAS) methods. However, even a well-designed/searched architecture may still contain many nonsignificant or redundant modules/operations. Thus, it is necessary to optimize the operations inside an architecture to improve the performance without introducing extra computational cost. To this end, we have proposed a Neural Architecture Transformer (NAT) method which casts the optimization problem into a Markov Decision Process (MDP) and seeks to replace the redundant operations with more efficient operations, such as skip or null connection. Note that NAT only considers a small number of possible transitions and thus comes with a limited search/transition space. As a result, such a small search space may hamper the performance of architecture optimization. To address this issue, we propose a Neural Architecture Transformer++ (NAT++) method which further enlarges the set of candidate transitions to improve the performance of architecture optimization. Specifically, we present a two-level transition rule to obtain valid transitions, i.e., allowing operations to have more efficient types (e.g., convolution->separable convolution) or smaller kernel sizes (e.g., 5x5->3x3). Note that different operations may have different valid transitions. We further propose a Binary-Masked Softmax (BMSoftmax) layer to omit the possible invalid transitions. Extensive experiments on several benchmark datasets show that the transformed architecture significantly outperforms both its original counterpart and the architectures optimized by existing methods.

preprint2020arXiv

A Thorough Comparison Study on Adversarial Attacks and Defenses for Common Thorax Disease Classification in Chest X-rays

Recently, deep neural networks (DNNs) have made great progress on automated diagnosis with chest X-rays images. However, DNNs are vulnerable to adversarial examples, which may cause misdiagnoses to patients when applying the DNN based methods in disease detection. Recently, there is few comprehensive studies exploring the influence of attack and defense methods on disease detection, especially for the multi-label classification problem. In this paper, we aim to review various adversarial attack and defense methods on chest X-rays. First, the motivations and the mathematical representations of attack and defense methods are introduced in details. Second, we evaluate the influence of several state-of-the-art attack and defense methods for common thorax disease classification in chest X-rays. We found that the attack and defense methods have poor performance with excessive iterations and large perturbations. To address this, we propose a new defense method that is robust to different degrees of perturbations. This study could provide new insights into methodological development for the community.

preprint2020arXiv

Attention-guided Context Feature Pyramid Network for Object Detection

For object detection, how to address the contradictory requirement between feature map resolution and receptive field on high-resolution inputs still remains an open question. In this paper, to tackle this issue, we build a novel architecture, called Attention-guided Context Feature Pyramid Network (AC-FPN), that exploits discriminative information from various large receptive fields via integrating attention-guided multi-path features. The model contains two modules. The first one is Context Extraction Module (CEM) that explores large contextual information from multiple receptive fields. As redundant contextual relations may mislead localization and recognition, we also design the second module named Attention-guided Module (AM), which can adaptively capture the salient dependencies over objects by using the attention mechanism. AM consists of two sub-modules, i.e., Context Attention Module (CxAM) and Content Attention Module (CnAM), which focus on capturing discriminative semantics and locating precise positions, respectively. Most importantly, our AC-FPN can be readily plugged into existing FPN-based models. Extensive experiments on object detection and instance segmentation show that existing models with our proposed CEM and AM significantly surpass their counterparts without them, and our model successfully obtains state-of-the-art results. We have released the source code at https://github.com/Caojunxu/AC-FPN.

preprint2020arXiv

Beyond $\mathcal{H}$-Divergence: Domain Adaptation Theory With Jensen-Shannon Divergence

We reveal the incoherence between the widely-adopted empirical domain adversarial training and its generally-assumed theoretical counterpart based on $\mathcal{H}$-divergence. Concretely, we find that $\mathcal{H}$-divergence is not equivalent to Jensen-Shannon divergence, the optimization objective in domain adversarial training. To this end, we establish a new theoretical framework by directly proving the upper and lower target risk bounds based on joint distributional Jensen-Shannon divergence. We further derive bi-directional upper bounds for marginal and conditional shifts. Our framework exhibits inherent flexibilities for different transfer learning problems, which is usable for various scenarios where $\mathcal{H}$-divergence-based theory fails to adapt. From an algorithmic perspective, our theory enables a generic guideline unifying principles of semantic conditional matching, feature marginal matching, and label marginal shift correction. We employ algorithms for each principle and empirically validate the benefits of our framework on real datasets.

preprint2020arXiv

Closed-loop Matters: Dual Regression Networks for Single Image Super-Resolution

Deep neural networks have exhibited promising performance in image super-resolution (SR) by learning a nonlinear mapping function from low-resolution (LR) images to high-resolution (HR) images. However, there are two underlying limitations to existing SR methods. First, learning the mapping function from LR to HR images is typically an ill-posed problem, because there exist infinite HR images that can be downsampled to the same LR image. As a result, the space of the possible functions can be extremely large, which makes it hard to find a good solution. Second, the paired LR-HR data may be unavailable in real-world applications and the underlying degradation method is often unknown. For such a more general case, existing SR models often incur the adaptation problem and yield poor performance. To address the above issues, we propose a dual regression scheme by introducing an additional constraint on LR data to reduce the space of the possible functions. Specifically, besides the mapping from LR to HR images, we learn an additional dual regression mapping estimates the down-sampling kernel and reconstruct LR images, which forms a closed-loop to provide additional supervision. More critically, since the dual regression process does not depend on HR images, we can directly learn from LR images. In this sense, we can easily adapt SR models to real-world data, e.g., raw video frames from YouTube. Extensive experiments with paired training data and unpaired real-world data demonstrate our superiority over existing methods.

preprint2020arXiv

DCANet: Learning Connected Attentions for Convolutional Neural Networks

While self-attention mechanism has shown promising results for many vision tasks, it only considers the current features at a time. We show that such a manner cannot take full advantage of the attention mechanism. In this paper, we present Deep Connected Attention Network (DCANet), a novel design that boosts attention modules in a CNN model without any modification of the internal structure. To achieve this, we interconnect adjacent attention blocks, making information flow among attention blocks possible. With DCANet, all attention blocks in a CNN model are trained jointly, which improves the ability of attention learning. Our DCANet is generic. It is not limited to a specific attention module or base network architecture. Experimental results on ImageNet and MS COCO benchmarks show that DCANet consistently outperforms the state-of-the-art attention modules with a minimal additional computational overhead in all test cases. All code and models are made publicly available.

preprint2020arXiv

Floquet engineering the Hofstadter butterfly in the square lattice and its effective Hamiltonian

In this paper, we use Floquet theory to theoretically study the effect of monochromatic circularly and linearly polarized light on the Hofstadter butterfly in the square lattice, which is induced by uniform perpendicular magnetic field. In the absence of laser, the butterfly has a fractal, self-similar structure particle-hole symmetry and reflection symmetry about magnetic flux $ϕ= 1/2$. These symmetries are preserved by the sub-lattice and the time-reversal symmetry, respectively. As the system is exposed to circularly polarized light, the original Hofsatdter butterfly in equilibrium is deformed by breaking both the particle-hole symmetry and the mirror symmetry, while the inversion symmetry about energy $E=0$ and magnetic flux $ϕ=1/2$ is preserved. Our study show that, the circularly polarized light break both the sub-lattice symmetry and the time-reversal symmetry. The inversion symmetry is preserved because the Hamiltonian at magnetic flux $ϕ$ and $1-ϕ$ is connected through the sub-lattice transformation. Focusing on the small flux region, we study the Landau level and the influence of circularly polarized light on the Landau level. On the contrary, the linearly polarized light deforms the original Hofstadter butterfly by breaking the rotational symmetry while preserving sub-lattice and the time-reversal symmetry. Further, we study the influence of the periodic drive on the Chern number of the lowest band in middle Floquet copy within the off-resonance regime. We found strong circularly polarized light will change the Chern number. For linearly polarized light, the Chern number will not change and the values stay independent of laser polarization direction. Our work highlights the generic features expected for the periodically driven Hofstadter problem on square lattice and provide the strategy to engineering the Hofstadter butterfly with laser.

preprint2020arXiv

Inertia and feedback parameters adaptive control of virtual synchronous generator

The virtual synchronous generator technology analogs the characteristics of the synchronous generator via the controller design. It improved the stability of the grid systems which include the new energy. At the same time, according to the adjustable characteristics of the virtual synchronous generator parameters, the parameter adaptive adjustment is used to improve the dynamic performance of the system. However, the traditional virtual synchronous generator adaptive control technology still has two drawbacks: on the one hand, the large-scale adjustment of the damping droop coefficient and the virtual moment of inertia requires the system having a high energy storage margin; On the other hand, there is a power overshoot phenomenon in the transient regulation process, which is disadvantageous to the power equipment. First, this paper provides a convenient adjustment method for improving the transient stability of the system, the system damping is adjusted by introducing the output speed feedback. Second, according to the transient power-angle characteristics of the system, a parameter adaptive control strategy is proposed, which shortens the transient adjustment time and ensures that the deviation of the system frequency in the transient adjustment process is within the allowable range, and improves the transient performance of the grid frequency adjustment, at the same time, the power overshoot is suppressed. Finally, the experimental results show that the proposed control strategy is superior to the existing adaptive control strategy.

preprint2020arXiv

Intelligent Home 3D: Automatic 3D-House Design from Linguistic Descriptions Only

Home design is a complex task that normally requires architects to finish with their professional skills and tools. It will be fascinating that if one can produce a house plan intuitively without knowing much knowledge about home design and experience of using complex designing tools, for example, via natural language. In this paper, we formulate it as a language conditioned visual content generation problem that is further divided into a floor plan generation and an interior texture (such as floor and wall) synthesis task. The only control signal of the generation process is the linguistic expression given by users that describe the house details. To this end, we propose a House Plan Generative Model (HPGM) that first translates the language input to a structural graph representation and then predicts the layout of rooms with a Graph Conditioned Layout Prediction Network (GC LPN) and generates the interior texture with a Language Conditioned Texture GAN (LCT-GAN). With some post-processing, the final product of this task is a 3D house model. To train and evaluate our model, we build the first Text-to-3D House Model dataset.

preprint2020arXiv

NAT: Neural Architecture Transformer for Accurate and Compact Architectures

Designing effective architectures is one of the key factors behind the success of deep neural networks. Existing deep architectures are either manually designed or automatically searched by some Neural Architecture Search (NAS) methods. However, even a well-searched architecture may still contain many non-significant or redundant modules or operations (e.g., convolution or pooling), which may not only incur substantial memory consumption and computation cost but also deteriorate the performance. Thus, it is necessary to optimize the operations inside an architecture to improve the performance without introducing extra computation cost. Unfortunately, such a constrained optimization problem is NP-hard. To make the problem feasible, we cast the optimization problem into a Markov decision process (MDP) and seek to learn a Neural Architecture Transformer (NAT) to replace the redundant operations with the more computationally efficient ones (e.g., skip connection or directly removing the connection). Based on MDP, we learn NAT by exploiting reinforcement learning to obtain the optimization policies w.r.t. different architectures. To verify the effectiveness of the proposed strategies, we apply NAT on both hand-crafted architectures and NAS based architectures. Extensive experiments on two benchmark datasets, i.e., CIFAR-10 and ImageNet, demonstrate that the transformed architecture by NAT significantly outperforms both its original form and those architectures optimized by existing methods.

preprint2020arXiv

Recurrence Quantification Analysis of Dynamic Brain Networks

Evidence suggests that brain network dynamics is a key determinant of brain function and dysfunction. Here we propose a new framework to assess the dynamics of brain networks based on recurrence analysis. Our framework uses recurrence plots and recurrence quantification analysis to characterize dynamic networks. For resting-state magnetoencephalographic dynamic functional networks (dFNs), we have found that functional networks recur more quickly in people with epilepsy than healthy controls. This suggests that recurrence of dFNs may be used as a biomarker of epilepsy. For stereo electroencephalography data, we have found that dFNs involved in epileptic seizures emerge before seizure onset, and recurrence analysis allows us to detect seizures. We further observe distinct dFNs before and after seizures, which may inform neurostimulation strategies to prevent seizures. Our framework can also be used for understanding dFNs in healthy brain function and in other neurological disorders besides epilepsy.

preprint2020arXiv

Transition threshold for the 3D Couette flow in a finite channel

In this paper, we study nonlinear stability of the 3D plane Couette flow $(y,0,0)$ at high Reynolds number ${Re}$ in a finite channel $\mathbb{T}\times [-1,1]\times \mathbb{T}$. It is well known that the plane Couette flow is linearly stable for any Reynolds number. However, it could become nonlinearly unstable and transition to turbulence for small but finite perturbations at high Reynolds number. This is so-called Sommerfeld paradox. One resolution of this paradox is to study the transition threshold problem, which is concerned with how much disturbance will lead to the instability of the flow and the dependence of disturbance on the Reynolds number. This work shows that if the initial velocity $v_0$ satisfies $\|v_0-(y,0,0)\|_{H^2}\le c_0{Re}^{-1}$ for some $c_0>0$ independent of $Re$, then the solution of the 3D Navier-Stokes equations is global in time and does not transition away from the Couette flow in the $L^\infty$ sense, and rapidly converges to a streak solution for $t\gg Re^{\frac 13}$ due to the mixing-enhanced dissipation effect. This result confirms the transition threshold conjecture proposed by Trefethen et al.(Science, 261(1993), 578-584). To this end, we develop the resolvent estimate method to establish the space-time estimates for the full linearized Navier-Stokes system around the flow $(V(t,y,z), 0,0)$, where $V(t,y,z)$ is a small perturbation(but independent of $Re$) of the Couette flow $y$.