arXiv subjects
Publications and source records attributed to Chunlei Liu.
The counting function for the numbers satisfying the Collatz conjecture is studied. A related exponential congruence equation is investigated, yielding a method to construct its solutions from free variables, and enabling us to find at least $x^{0.3227}$ Collatz numbers in the interval $[1,x]$. The historical record is 0.84.
Magnetic resonance imaging (MRI) exhibits rich and clinically useful endogenous contrast mechanisms, which can differentiate soft tissues and are sensitive to flow, diffusion, magnetic susceptibility, blood oxygenation level, and more. However, MRI sensitivity is ultimately constrained by Nuclear Magnetic Resonance (NMR) physics, and its spatiotemporal resolution is limited by SNR and spatial encoding. On the other hand, miniaturized implantable sensors offer highly localized physiological information, yet communication and localization can be challenging when multiple implants are present. This paper introduces the MRDust, an active ``contrast agent" that integrates active sensor implants with MRI, enabling the direct encoding of highly localized physiological data into MR images to augment the anatomical images. MRDust employs a micrometer-scale on-chip coil to actively modulate the local magnetic field, enabling MR signal amplitude and phase modulation for digital data transmission. Since MRI inherently captures the anatomical tissue structure, this method has the potential to enable simultaneous data communication, localization, and image registration with multiple implants. This paper presents the underlying physical principles, design tradeoffs, and design methodology for this approach. To validate the concept, a 900 $\times$ 990 $\mu$m$^2$ chip was designed using TSMC 28 nm technology, with an on-chip coil measuring 630 $\mu$m in diameter. The chip was tested with custom hardware in an MR750W GE3T MRI scanner. Successful voxel amplitude modulation is demonstrated with Spin-Echo Echo-Planar-Imaging (SE-EPI) sequence, achieving a contrast-to-noise ratio (CNR) of 25.58 with a power consumption of 130 $\mu$W.
Additive Fourier Transform is sdudied. A fast multiplication algorithm for polynomials over the binary field is given. The bit complexity of the algorithm is $O(n(log n)(\log\log n)^2)$.
Quantitative magnetic resonance imaging (qMRI) offers tissue-specific physical parameters with significant potential for neuroscience research and clinical practice. However, lengthy scan times for 3D multiparametric qMRI acquisition limit its clinical utility. Here, we propose SUMMIT, an innovative imaging methodology that includes data acquisition and an unsupervised reconstruction for simultaneous multiparametric qMRI. SUMMIT first encodes multiple important quantitative properties into highly undersampled k-space. It further leverages implicit neural representation incorporated with a dedicated physics model to reconstruct the desired multiparametric maps without needing external training datasets. SUMMIT delivers co-registered T1, T2, T2*, and quantitative susceptibility mapping. Extensive simulations and phantom imaging demonstrate SUMMIT's high accuracy. Additionally, the proposed unsupervised approach for qMRI reconstruction also introduces a novel zero-shot learning paradigm for multiparametric imaging applicable to various medical imaging modalities.
A new combinatorial game is given. It generalizes both Substraction and Nim. It is proved the computation of Nash equilibrium points in this new game is NP-hard.
Robotic assistance has broadened the capabilities of magnetic resonance imaging (MRI)-guided medical interventions, yet force-controlled actuators tailored for MRI environments remain limited. In this study, we present a novel MRI-compatible rotary series elastic actuator (SEA) module that employs velocity-sourced ultrasonic motors for force-controlled operation within MRI scanners. Unlike prior MRI-compatible SEA designs, our module uses a transmission force sensing SEA architecture, with four off-the-shelf compression springs placed between the gearbox and motor housings. To enable precise torque control, we develop a controller based on a disturbance observer, specifically designed for velocity-sourced motors. This controller improves torque regulation, even under varying external impedance, enhancing the actuator's suitability for MRI-guided medical interventions. Experimental validation confirms effective torque control in both 3 Tesla MRI and non-MRI settings, achieving a 5% settling time of 0.05 seconds and steady-state error within 2.5% of the actuator's maximum output torque. Notably, the controller maintains consistent performance across both low and high impedance conditions.
On a Goppa code whose structure polynomial has coefficients in the symbol field, the Frobenius acts. Its fixed codewords form a subcode. Deleting the naturally occurred redundance, we obtain a new code. It is proved that these new codes approach the Gilbert-Varshamov bound. It is also proved that these codes can be decoded within $O(n^2(\logn)^a)$ operations in the symbol field, which is usually much small than the location field, where $n$ is the codeword length, and $a$ a constant determined by the polynomial factorization algorithm.
Recent developments in single-cell omics technologies have enabled the quantification of molecular profiles in individual cells at an unparalleled resolution. Deep learning, a rapidly evolving sub-field of machine learning, has instilled a significant interest in single-cell omics research due to its remarkable success in analysing heterogeneous high-dimensional single-cell omics data. Nevertheless, the inherent multi-layer nonlinear architecture of deep learning models often makes them `black boxes' as the reasoning behind predictions is often unknown and not transparent to the user. This has stimulated an increasing body of research for addressing the lack of interpretability in deep learning models, especially in single-cell omics data analyses, where the identification and understanding of molecular regulators are crucial for interpreting model predictions and directing downstream experimental validations. In this work, we introduce the basics of single-cell omics technologies and the concept of interpretable deep learning. This is followed by a review of the recent interpretable deep learning models applied to various single-cell omics research. Lastly, we highlight the current limitations and discuss potential future directions. We anticipate this review to bring together the single-cell and machine learning research communities to foster future development and application of interpretable deep learning in single-cell omics research.
Parallel imaging is a commonly used technique to accelerate magnetic resonance imaging (MRI) data acquisition. Mathematically, parallel MRI reconstruction can be formulated as an inverse problem relating the sparsely sampled k-space measurements to the desired MRI image. Despite the success of many existing reconstruction algorithms, it remains a challenge to reliably reconstruct a high-quality image from highly reduced k-space measurements. Recently, implicit neural representation has emerged as a powerful paradigm to exploit the internal information and the physics of partially acquired data to generate the desired object. In this study, we introduced IMJENSE, a scan-specific implicit neural representation-based method for improving parallel MRI reconstruction. Specifically, the underlying MRI image and coil sensitivities were modeled as continuous functions of spatial coordinates, parameterized by neural networks and polynomials, respectively. The weights in the networks and coefficients in the polynomials were simultaneously learned directly from sparsely acquired k-space measurements, without fully sampled ground truth data for training. Benefiting from the powerful continuous representation and joint estimation of the MRI image and coil sensitivities, IMJENSE outperforms conventional image or k-space domain reconstruction algorithms. With extremely limited calibration data, IMJENSE is more stable than supervised calibrationless and calibration-based deep-learning methods. Results show that IMJENSE robustly reconstructs the images acquired at 5$\mathbf{\times}$ and 6$\mathbf{\times}$ accelerations with only 4 or 8 calibration lines in 2D Cartesian acquisitions, corresponding to 22.0% and 19.5% undersampling rates. The high-quality results and scanning specificity make the proposed method hold the potential for further accelerating the data acquisition of parallel MRI.
This article provides recommendations for implementing quantitative susceptibility mapping (QSM) for clinical brain research. It is a consensus of the ISMRM Electro-Magnetic Tissue Properties Study Group. While QSM technical development continues to advance rapidly, the current QSM methods have been demonstrated to be repeatable and reproducible for generating quantitative tissue magnetic susceptibility maps in the brain. However, the many QSM approaches available give rise to the need in the neuroimaging community for guidelines on implementation. This article describes relevant considerations and provides specific implementation recommendations for all steps in QSM data acquisition, processing, analysis, and presentation in scientific publications. We recommend that data be acquired using a monopolar 3D multi-echo GRE sequence, that phase images be saved and exported in DICOM format and unwrapped using an exact unwrapping approach. Multi-echo images should be combined before background removal, and a brain mask created using a brain extraction tool with the incorporation of phase-quality-based masking. Background fields should be removed within the brain mask using a technique based on SHARP or PDF, and the optimization approach to dipole inversion should be employed with a sparsity-based regularization. Susceptibility values should be measured relative to a specified reference, including the common reference region of whole brain as a region of interest in the analysis, and QSM results should be reported with - as a minimum - the acquisition and processing specifications listed in the last section of the article. These recommendations should facilitate clinical QSM research and lead to increased harmonization in data acquisition, analysis, and reporting.
Existing Binary Neural Networks (BNNs) mainly operate on local convolutions with binarization function. However, such simple bit operations lack the ability of modeling contextual dependencies, which is critical for learning discriminative deep representations in vision models. In this work, we tackle this issue by presenting new designs of binary neural modules, which enables BNNs to learn effective contextual dependencies. First, we propose a binary multi-layer perceptron (MLP) block as an alternative to binary convolution blocks to directly model contextual dependencies. Both short-range and long-range feature dependencies are modeled by binary MLPs, where the former provides local inductive bias and the latter breaks limited receptive field in binary convolutions. Second, to improve the robustness of binary models with contextual dependencies, we compute the contextual dynamic embeddings to determine the binarization thresholds in general binary convolutional blocks. Armed with our binary MLP blocks and improved binary convolution, we build the BNNs with explicit Contextual Dependency modeling, termed as BCDNet. On the standard ImageNet-1K classification benchmark, the BCDNet achieves 72.3% Top-1 accuracy and outperforms leading binary methods by a large margin. In particular, the proposed BCDNet exceeds the state-of-the-art ReActNet-A by 2.9% Top-1 accuracy with similar operations. Our code is available at https://github.com/Sense-GVT/BCDN
It is proven that there are infinitely prime pairs whose difference is no greater than 84. In proving that result, a new sieve weight is constructed. The new idea is to construct the largest sieve support which admits the use of the Bombieri-Vinogradov theorem.
Feature selection techniques are essential for high-dimensional data analysis. In the last two decades, their popularity has been fuelled by the increasing availability of high-throughput biomolecular data where high-dimensionality is a common data property. Recent advances in biotechnologies enable global profiling of various molecular and cellular features at single-cell resolution, resulting in large-scale datasets with increased complexity. These technological developments have led to a resurgence in feature selection research and application in the single-cell field. Here, we revisit feature selection techniques and summarise recent developments. We review their versatile application to a range of single-cell data types including those generated from traditional cytometry and imaging technologies and the latest array of single-cell omics technologies. We highlight some of the challenges and future directions on which feature selection could have a significant impact. Finally, we consider the scalability and make general recommendations on the utility of each type of feature selection method. We hope this review serves as a reference point to stimulate future research and application of feature selection in the single-cell era.
Quantitative susceptibility mapping (QSM) has demonstrated great potential in quantifying tissue susceptibility in various brain diseases. However, the intrinsic ill-posed inverse problem relating the tissue phase to the underlying susceptibility distribution affects the accuracy for quantifying tissue susceptibility. Recently, deep learning has shown promising results to improve accuracy by reducing the streaking artifacts. However, there exists a mismatch between the observed phase and the theoretical forward phase estimated by the susceptibility label. In this study, we proposed a model-based deep learning architecture that followed the STI (susceptibility tensor imaging) physical model, referred to as MoDL-QSM. Specifically, MoDL-QSM accounts for the relationship between STI-derived phase contrast induced by the susceptibility tensor terms (ki13,ki23,ki33) and the acquired single-orientation phase. The convolution neural networks are embedded into the physical model to learn a regularization term containing prior information. ki33 and phase induced by ki13 and ki23 terms were used as the labels for network training. Quantitative evaluation metrics (RSME, SSIM, and HFEN) were compared with recently developed deep learning QSM methods. The results showed that MoDL-QSM achieved superior performance, demonstrating its potential for future applications.
The $L$-function of exponential sums associated to the generic polynomial of degree $d$ in $n$ variables over a finite field of characteristic $p$ is studied. A polygon called the Frobenius polygon of the generic polynomial of degree $d$ in $n$ variables over a finite field of characteristic $p$ is defined. A $p$-adic Riemann hypothesis is formulated. It asserts that the Newton polygon of the $L$-function coincides with the Frobenius polygon when $p$ is large enough. This $p$-adic Riemann hypothesis is proved when $n=2$ and $p\equiv-1({\rm mod }\ d)$. In general, it is proved that the Newton polygon of the $L$-function lies above the Frobenius polygon with coincide endpoints when $p$ is large enough.
Training 1-bit deep convolutional neural networks (DCNNs) is one of the most challenging problems in computer vision, because it is much easier to get trapped into local minima than conventional DCNNs. The reason lies in that the binarized kernels and activations of 1-bit DCNNs cause a significant accuracy loss and training inefficiency. To address this problem, we propose Genetic Binary Convolutional Networks (GBCNs) to optimize 1-bit DCNNs, by introducing a new balanced Genetic Algorithm (BGA) to improve the representational ability in an end-to-end framework. The BGA method is proposed to modify the binary process of GBCNs to alleviate the local minima problem, which can significantly improve the performance of 1-bit DCNNs. We develop a new BGA module that is generic and flexible, and can be easily incorporated into existing DCNNs, such asWideResNets and ResNets. Extensive experiments on the object classification tasks (CIFAR, ImageNet) validate the effectiveness of the proposed method. To highlight, our method shows strong generalization on the object recognition task, i.e., face recognition, facial and person re-identification.
The rapidly decreasing computation and memory cost has recently driven the success of many applications in the field of deep learning. Practical applications of deep learning in resource-limited hardware, such as embedded devices and smart phones, however, remain challenging. For binary convolutional networks, the reason lies in the degraded representation caused by binarizing full-precision filters. To address this problem, we propose new circulant filters (CiFs) and a circulant binary convolution (CBConv) to enhance the capacity of binarized convolutional features via our circulant back propagation (CBP). The CiFs can be easily incorporated into existing deep convolutional neural networks (DCNNs), which leads to new Circulant Binary Convolutional Networks (CBCNs). Extensive experiments confirm that the performance gap between the 1-bit and full-precision DCNNs is minimized by increasing the filter diversity, which further increases the representational ability in our networks. Our experiments on ImageNet show that CBCNs achieve 61.4% top-1 accuracy with ResNet18. Compared to the state-of-the-art such as XNOR, CBCNs can achieve up to 10% higher top-1 accuracy with more powerful representational ability.
Small object tracking becomes an increasingly important task, which however has been largely unexplored in computer vision. The great challenges stem from the facts that: 1) small objects show extreme vague and variable appearances, and 2) they tend to be lost easier as compared to normal-sized ones due to the shaking of lens. In this paper, we propose a novel aggregation signature suitable for small object tracking, especially aiming for the challenge of sudden and large drift. We make three-fold contributions in this work. First, technically, we propose a new descriptor, named aggregation signature, based on saliency, able to represent highly distinctive features for small objects. Second, theoretically, we prove that the proposed signature matches the foreground object more accurately with a high probability. Third, experimentally, the aggregation signature achieves a high performance on multiple datasets, outperforming the state-of-the-art methods by large margins. Moreover, we contribute with two newly collected benchmark datasets, i.e., small90 and small112, for visually small object tracking. The datasets will be available in https://github.com/bczhangbczhang/.