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Researcher profile

Jia Guo

Jia Guo contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Computer Visioneess.IVeess.SYMachine Learningmath.OCSystems and Controlcond-mat.mtrl-scimath.DSQuantitative Methodscond-mat.str-elCryptography and Securityeess.ASmath.COmath.NAmath.PRMultimediaNumerical Analysisq-fin.MF

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Published work

26 published item(s)

preprint2026arXiv

A Proof-of-Concept Study of Multitask Learning for Cranial Synthetic CT Generation Across Heterogeneous MRI Field Strengths

Accurate synthesis of computed tomography (CT) images from magnetic resonance imaging (MRI) is clinically valuable for cranial applications such as attenuation correction, radiotherapy planning, and image-guided interventions. However, heterogeneity across MRI field strengths and acquisition protocols limits the generalizability of existing methods. In this study, we formulate cranial CT synthesis as a modular, structurally coupled problem and propose a deep learning framework to improve robustness across heterogeneous MRI conditions. The model is designed to adapt to variations in field strength and imaging protocols while preserving anatomical consistency. Experiments on multi-site datasets demonstrate improved performance and generalization compared with conventional approaches. The proposed method enables reliable CT synthesis across heterogeneous MRI settings, supporting broader clinical translation.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

ArcFace: Additive Angular Margin Loss for Deep Face Recognition

Recently, a popular line of research in face recognition is adopting margins in the well-established softmax loss function to maximize class separability. In this paper, we first introduce an Additive Angular Margin Loss (ArcFace), which not only has a clear geometric interpretation but also significantly enhances the discriminative power. Since ArcFace is susceptible to the massive label noise, we further propose sub-center ArcFace, in which each class contains $K$ sub-centers and training samples only need to be close to any of the $K$ positive sub-centers. Sub-center ArcFace encourages one dominant sub-class that contains the majority of clean faces and non-dominant sub-classes that include hard or noisy faces. Based on this self-propelled isolation, we boost the performance through automatically purifying raw web faces under massive real-world noise. Besides discriminative feature embedding, we also explore the inverse problem, mapping feature vectors to face images. Without training any additional generator or discriminator, the pre-trained ArcFace model can generate identity-preserved face images for both subjects inside and outside the training data only by using the network gradient and Batch Normalization (BN) priors. Extensive experiments demonstrate that ArcFace can enhance the discriminative feature embedding as well as strengthen the generative face synthesis.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Detecting Schizophrenia with 3D Structural Brain MRI Using Deep Learning

Schizophrenia is a chronic neuropsychiatric disorder that causes distinct structural alterations within the brain. We hypothesize that deep learning applied to a structural neuroimaging dataset could detect disease-related alteration and improve classification and diagnostic accuracy. We tested this hypothesis using a single, widely available, and conventional T1-weighted MRI scan, from which we extracted the 3D whole-brain structure using standard post-processing methods. A deep learning model was then developed, optimized, and evaluated on three open datasets with T1-weighted MRI scans of patients with schizophrenia. Our proposed model outperformed the benchmark model, which was also trained with structural MR images using a 3D CNN architecture. Our model is capable of almost perfectly (area under the ROC curve = 0.987) distinguishing schizophrenia patients from healthy controls on unseen structural MRI scans. Regional analysis localized subcortical regions and ventricles as the most predictive brain regions. Subcortical structures serve a pivotal role in cognitive, affective, and social functions in humans, and structural abnormalities of these regions have been associated with schizophrenia. Our finding corroborates that schizophrenia is associated with widespread alterations in subcortical brain structure and the subcortical structural information provides prominent features in diagnostic classification. Together, these results further demonstrate the potential of deep learning to improve schizophrenia diagnosis and identify its structural neuroimaging signatures from a single, standard T1-weighted brain MRI.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Kernel Methods for Regression in Continuous Time over Subsets and Manifolds

This paper derives error bounds for regression in continuous time over subsets of certain types of Riemannian manifolds.The regression problem is typically driven by a nonlinear evolution law taking values on the manifold, and it is cast as one of optimal estimation in a reproducing kernel Hilbert space (RKHS). A new notion of persistency of excitation (PE) is defined for the estimation problem over the manifold, and rates of convergence of the continuous time estimates are derived using the PE condition. We discuss and analyze two approximation methods of the exact regression solution. We then conclude the paper with some numerical simulations that illustrate the qualitative character of the computed function estimates. Numerical results from function estimates generated over a trajectory of the Lorenz system are presented. Additionally, we analyze an implementation of the two approximation methods using motion capture data.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Killing Two Birds with One Stone:Efficient and Robust Training of Face Recognition CNNs by Partial FC

Learning discriminative deep feature embeddings by using million-scale in-the-wild datasets and margin-based softmax loss is the current state-of-the-art approach for face recognition. However, the memory and computing cost of the Fully Connected (FC) layer linearly scales up to the number of identities in the training set. Besides, the large-scale training data inevitably suffers from inter-class conflict and long-tailed distribution. In this paper, we propose a sparsely updating variant of the FC layer, named Partial FC (PFC). In each iteration, positive class centers and a random subset of negative class centers are selected to compute the margin-based softmax loss. All class centers are still maintained throughout the whole training process, but only a subset is selected and updated in each iteration. Therefore, the computing requirement, the probability of inter-class conflict, and the frequency of passive update on tail class centers, are dramatically reduced. Extensive experiments across different training data and backbones (e.g. CNN and ViT) confirm the effectiveness, robustness and efficiency of the proposed PFC. The source code is available at \https://github.com/deepinsight/insightface/tree/master/recognition.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Koopman Methods for Estimation of Animal Motions over Unknown Submanifolds

This paper introduces a data-dependent approximation of the forward kinematics map for certain types of animal motion models. It is assumed that motions are supported on a low-dimensional, unknown configuration manifold $Q$ that is regularly embedded in high dimensional Euclidean space $X:=\mathbb{R}^d$. This paper introduces a method to estimate forward kinematics from the unknown configuration submanifold $Q$ to an $n$-dimensional Euclidean space $Y:=\mathbb{R}^n$ of observations. A known reproducing kernel Hilbert space (RKHS) is defined over the ambient space $X$ in terms of a known kernel function, and computations are performed using the known kernel defined on the ambient space $X$. Estimates are constructed using a certain data-dependent approximation of the Koopman operator defined in terms of the known kernel on $X$. However, the rate of convergence of approximations is studied in the space of restrictions to the unknown manifold $Q$. Strong rates of convergence are derived in terms of the fill distance of samples in the unknown configuration manifold, provided that a novel regularity result holds for the Koopman operator. Additionally, we show that the derived rates of convergence can be applied in some cases to estimates generated by the extended dynamic mode decomposition (EDMD) method. We illustrate characteristics of the estimates for simulated data as well as samples collected during motion capture experiments.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Multi-task Deep Learning for Cerebrovascular Disease Classification and MRI-to-PET Translation

Accurate quantification of cerebral blood flow (CBF) is essential for the diagnosis and assessment of cerebrovascular diseases such as Moyamoya, carotid stenosis, aneurysms, and stroke. Positron emission tomography (PET) is currently regarded as the gold standard for the measurement of CBF in the human brain. PET imaging, however, is not widely available because of its prohibitive costs, use of ionizing radiation, and logistical challenges, which require a co-localized cyclotron to deliver the 2 min half-life Oxygen-15 radioisotope. Magnetic resonance imaging (MRI), in contrast, is more readily available and does not involve ionizing radiation. In this study, we propose a multi-task learning framework for brain MRI-to-PET translation and disease diagnosis. The proposed framework comprises two prime networks: (1) an attention-based 3D encoder-decoder convolutional neural network (CNN) that synthesizes high-quality PET CBF maps from multi-contrast MRI images, and (2) a multi-scale 3D CNN that identifies the brain disease corresponding to the input MRI images. Our multi-task framework yields promising results on the task of MRI-to-PET translation, achieving an average structural similarity index (SSIM) of 0.94 and peak signal-to-noise ratio (PSNR) of 38dB on a cohort of 120 subjects. In addition, we show that integrating multiple MRI modalities can improve the clinical diagnosis of brain diseases.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Perspective Reconstruction of Human Faces by Joint Mesh and Landmark Regression

Even though 3D face reconstruction has achieved impressive progress, most orthogonal projection-based face reconstruction methods can not achieve accurate and consistent reconstruction results when the face is very close to the camera due to the distortion under the perspective projection. In this paper, we propose to simultaneously reconstruct 3D face mesh in the world space and predict 2D face landmarks on the image plane to address the problem of perspective 3D face reconstruction. Based on the predicted 3D vertices and 2D landmarks, the 6DoF (6 Degrees of Freedom) face pose can be easily estimated by the PnP solver to represent perspective projection. Our approach achieves 1st place on the leader-board of the ECCV 2022 WCPA challenge and our model is visually robust under different identities, expressions and poses. The training code and models are released to facilitate future research.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Physical realization of topological Roman surface by spin-induced ferroelectric polarization in cubic lattice

Topology, a mathematical concept in geometry, has become an ideal theoretical tool for describing topological states and phase transitions. Many topological concepts have found their physical entities in real or reciprocal spaces identified by topological/geometrical invariants, which are usually defined on orientable surfaces such as torus and sphere. It is natural to quest whether it is possible to find the physical realization of more intriguing non-orientable surfaces. Herein, we show that the set of spin-induced ferroelectric polarizations in cubic perovskite oxides AMn3Cr4O12 (A = La and Tb) resides on the topological Roman surface, a non-orientable two-dimensional manifold formed by sewing a Mobius strip edge to that of a disc. The induced polarization may travel in a loop along the non-orientable Mobius strip or orientable disc depending on how the spin evolves as controlled by external magnetic field. Experimentally, the periodicity of polarization can be the same or the twice of the rotating magnetic field, being well consistent with the orientability of disc and Mobius strip, respectively. This path dependent topological magnetoelectric effect presents a way to detect the global geometry of the surface and deepens our understanding of topology in both mathematics and physics

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

WT-MVSNet: Window-based Transformers for Multi-view Stereo

Recently, Transformers were shown to enhance the performance of multi-view stereo by enabling long-range feature interaction. In this work, we propose Window-based Transformers (WT) for local feature matching and global feature aggregation in multi-view stereo. We introduce a Window-based Epipolar Transformer (WET) which reduces matching redundancy by using epipolar constraints. Since point-to-line matching is sensitive to erroneous camera pose and calibration, we match windows near the epipolar lines. A second Shifted WT is employed for aggregating global information within cost volume. We present a novel Cost Transformer (CT) to replace 3D convolutions for cost volume regularization. In order to better constrain the estimated depth maps from multiple views, we further design a novel geometric consistency loss (Geo Loss) which punishes unreliable areas where multi-view consistency is not satisfied. Our WT multi-view stereo method (WT-MVSNet) achieves state-of-the-art performance across multiple datasets and ranks $1^{st}$ on Tanks and Temples benchmark.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Evolutionary Trigger Set Generation for DNN Black-Box Watermarking

The commercialization of deep learning creates a compelling need for intellectual property (IP) protection. Deep neural network (DNN) watermarking has been proposed as a promising tool to help model owners prove ownership and fight piracy. A popular approach of watermarking is to train a DNN to recognize images with certain \textit{trigger} patterns. In this paper, we propose a novel evolutionary algorithm-based method to generate and optimize trigger patterns. Our method brings a siginificant reduction in false positive rates, leading to compelling proof of ownership. At the same time, it maintains the robustness of the watermark against attacks. We compare our method with the prior art and demonstrate its effectiveness on popular models and datasets.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Monolithic integration of 940 nm AlGaAs distributed Bragg reflectors on bulk Ge substrates

High quality 940 nm Al$_x$Ga$_{1-x}$As n-type distributed Bragg reflectors (DBRs) were successfully monolithically grown on off-cut Ge (100) substrates. The Ge-DBRs have reflectivity spectra comparable to those grown on conventional bulk GaAs substrates and have smooth morphology, reasonable periodicity and uniformity. These results strongly support VCSEL growth and fabrication on more scalable bulk Ge substrates for large scale production of AlGaAs-based VCSELs.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

MusiCoder: A Universal Music-Acoustic Encoder Based on Transformers

Music annotation has always been one of the critical topics in the field of Music Information Retrieval (MIR). Traditional models use supervised learning for music annotation tasks. However, as supervised machine learning approaches increase in complexity, the increasing need for more annotated training data can often not be matched with available data. In this paper, a new self-supervised music acoustic representation learning approach named MusiCoder is proposed. Inspired by the success of BERT, MusiCoder builds upon the architecture of self-attention bidirectional transformers. Two pre-training objectives, including Contiguous Frames Masking (CFM) and Contiguous Channels Masking (CCM), are designed to adapt BERT-like masked reconstruction pre-training to continuous acoustic frame domain. The performance of MusiCoder is evaluated in two downstream music annotation tasks. The results show that MusiCoder outperforms the state-of-the-art models in both music genre classification and auto-tagging tasks. The effectiveness of MusiCoder indicates a great potential of a new self-supervised learning approach to understand music: first apply masked reconstruction tasks to pre-train a transformer-based model with massive unlabeled music acoustic data, and then finetune the model on specific downstream tasks with labeled data.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Reducing the Teacher-Student Gap via Spherical Knowledge Disitllation

Knowledge distillation aims at obtaining a compact and effective model by learning the mapping function from a much larger one. Due to the limited capacity of the student, the student would underfit the teacher. Therefore, student performance would unexpectedly drop when distilling from an oversized teacher, termed the capacity gap problem. We investigate this problem by study the gap of confidence between teacher and student. We find that the magnitude of confidence is not necessary for knowledge distillation and could harm the student performance if the student are forced to learn confidence. We propose Spherical Knowledge Distillation to eliminate this gap explicitly, which eases the underfitting problem. We find this novel knowledge representation can improve compact models with much larger teachers and is robust to temperature. We conducted experiments on both CIFAR100 and ImageNet, and achieve significant improvement. Specifically, we train ResNet18 to 73.0 accuracy, which is a substantial improvement over previous SOTA and is on par with resnet34 almost twice the student size. The implementation has been shared at https://github.com/forjiuzhou/Spherical-Knowledge-Distillation.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Approximations of the Reproducing Kernel Hilbert Space (RKHS) Embedding Method over Manifolds

The reproducing kernel Hilbert space (RKHS) embedding method is a recently introduced estimation approach that seeks to identify the unknown or uncertain function in the governing equations of a nonlinear set of ordinary differential equations (ODEs). While the original state estimate evolves in Euclidean space, the function estimate is constructed in an infinite-dimensional RKHS that must be approximated in practice. When a finite-dimensional approximation is constructed using a basis defined in terms of shifted kernel functions centered at the observations along a trajectory, the RKHS embedding method can be understood as a data-driven approach. This paper derives sufficient conditions that ensure that approximations of the unknown function converge in a Sobolev norm over a submanifold that supports the dynamics. Moreover, the rate of convergence for the finite-dimensional approximations is derived in terms of the fill distance of the samples in the embedded manifold. Numerical simulation of an example problem is carried out to illustrate the qualitative nature of convergence results derived in the paper.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Constructing Deep Neural Networks with a Priori Knowledge of Wireless Tasks

Deep neural networks (DNNs) have been employed for designing wireless systems in many aspects, say transceiver design, resource optimization, and information prediction. Existing works either use the fully-connected DNN or the DNNs with particular architectures developed in other domains. While generating labels for supervised learning and gathering training samples are time-consuming or cost-prohibitive, how to develop DNNs with wireless priors for reducing training complexity remains open. In this paper, we show that two kinds of permutation invariant properties widely existed in wireless tasks can be harnessed to reduce the number of model parameters and hence the sample and computational complexity for training. We find special architecture of DNNs whose input-output relationships satisfy the properties, called permutation invariant DNN (PINN), and augment the data with the properties. By learning the impact of the scale of a wireless system, the size of the constructed PINNs can flexibly adapt to the input data dimension. We take predictive resource allocation and interference coordination as examples to show how the PINNs can be employed for learning the optimal policy with unsupervised and supervised learning. Simulations results demonstrate a dramatic gain of the proposed PINNs in terms of reducing training complexity.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Continuity of Utility Maximization under Weak Convergence

In this paper we find tight sufficient conditions for the continuity of the value of the utility maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We also establish a weak convergence result for the terminal wealths of the optimal portfolios. Finally, we apply our results to the computation of the minimal expected shortfall (shortfall risk) in the Heston model by building an appropriate lattice approximation.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Darwin's Neural Network: AI-based Strategies for Rapid and Scalable Cell and Coronavirus Screening

Recent advances in the interdisciplinary scientific field of machine perception, computer vision, and biomedical engineering underpin a collection of machine learning algorithms with a remarkable ability to decipher the contents of microscope and nanoscope images. Machine learning algorithms are transforming the interpretation and analysis of microscope and nanoscope imaging data through use in conjunction with biological imaging modalities. These advances are enabling researchers to carry out real-time experiments that were previously thought to be computationally impossible. Here we adapt the theory of survival of the fittest in the field of computer vision and machine perception to introduce a new framework of multi-class instance segmentation deep learning, Darwin's Neural Network (DNN), to carry out morphometric analysis and classification of COVID19 and MERS-CoV collected in vivo and of multiple mammalian cell types in vitro.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Edge-fault-tolerant strong Menger edge connectivity of bubble-sort star graphs

The connectivity and edge connectivity of interconnection network determine the fault tolerance of the network. An interconnection network is usually viewed as a connected graph, where vertex corresponds processor and edge corresponds link between two distinct processors. Given a connected graph $G$ with vertex set $V(G)$ and edge set $E(G)$, if for any two distinct vertices $u,v\in V(G)$, there exist $\min\{d_G(u),d_G(v)\}$ edge-disjoint paths between $u$ and $v$, then $G$ is strongly Menger edge connected. Let $m$ be an integer with $m\geq1$. If $G-F_e$ remains strongly Menger edge connected for any $F_e\subseteq E(G)$ with $|F_e|\leq m$, then $G$ is $m$-edge-fault-tolerant strongly Menger edge connected. If $G-F_e$ is strongly Menger edge connected for any $F_e\subseteq E(G)$ with $|F_e|\leq m$ and $δ(G-F_e)\geq2$, then $G$ is $m$-conditional edge-fault-tolerant strongly Menger edge connected. In this paper, we consider the $n$-dimensional bubble-sort star graph $BS_n$. We show that $BS_n$ is $(2n-5)$-edge-fault-tolerant strongly Menger edge connected for $n\geq3$ and $(6n-17)$-conditional edge-fault-tolerant strongly Menger edge connected for $n\geq4$. Moreover, we give some examples to show that our results are optimal.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Intrinsic and Extrinsic Approximation of Koopman Operators over Manifolds

This paper derives rates of convergence of certain approximations of the Koopman operators that are associated with discrete, deterministic, continuous semiflows on a complete metric space $(X,d_X)$. Approximations are constructed in terms of reproducing kernel bases that are centered at samples taken along the system trajectory. It is proven that when the samples are dense in a certain type of smooth manifold $M\subseteq X$, the derived rates of convergence depend on the fill distance of samples along the trajectory in that manifold. Error bounds for projection-based and data-dependent approximations of the Koopman operator are derived in the paper. A discussion of how these bounds are realized in intrinsic and extrinsic approximation methods is given. Finally, a numerical example that illustrates qualitatively the convergence guarantees derived in the paper is given.

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preprint2020arXiv

Kernel Center Adaptation in the Reproducing Kernel Hilbert Space Embedding Method

The performance of adaptive estimators that employ embedding in reproducing kernel Hilbert spaces (RKHS) depends on the choice of the location of basis kernel centers. Parameter convergence and error approximation rates depend on where and how the kernel centers are distributed in the state-space. In this paper, we develop the theory that relates parameter convergence and approximation rates to the position of kernel centers. We develop criteria for choosing kernel centers in a specific class of systems - ones in which the state trajectory regularly visits the neighborhood of the positive limit set. Two algorithms, based on centroidal Voronoi tessellations and Kohonen self-organizing maps, are derived to choose kernel centers in the RKHS embedding method. Finally, we implement these methods on two practical examples and test their effectiveness.

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preprint2020arXiv

RKHS Embedding for Estimating Nonlinear Piezoelectric Systems

Nonlinearities in piezoelectric systems can arise from internal factors such as nonlinear constitutive laws or external factors like realizations of boundary conditions. It can be difficult or even impossible to derive detailed models from the first principles of all the sources of nonlinearity in a system. As a specific example, in traditional modeling techniques that use electric enthalpy density with higher-order terms, it can be problematic to choose which polynomial nonlinearities are essential. This paper introduces adaptive estimator techniques to estimate the nonlinearities that can arise in certain piezoelectric systems. Here an underlying assumption is that the nonlinearities can be modeled as functions in a reproducing kernel Hilbert space (RKHS). Unlike traditional modeling approaches, the approach discussed in this paper allows the development of models without knowledge of the precise form or structure of the nonlinearity. This approach can be viewed as a data-driven method to approximate the unknown nonlinear system. This paper introduces the theory behind the adaptive estimator and studies the effectiveness of this approach numerically for a class of nonlinear piezoelectric composite beams.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Segmentation with Residual Attention U-Net and an Edge-Enhancement Approach Preserves Cell Shape Features

The ability to extrapolate gene expression dynamics in living single cells requires robust cell segmentation, and one of the challenges is the amorphous or irregularly shaped cell boundaries. To address this issue, we modified the U-Net architecture to segment cells in fluorescence widefield microscopy images and quantitatively evaluated its performance. We also proposed a novel loss function approach that emphasizes the segmentation accuracy on cell boundaries and encourages shape feature preservation. With a 97% sensitivity, 93% specificity, 91% Jaccard similarity, and 95% Dice coefficient, our proposed method called Residual Attention U-Net with edge-enhancement surpassed the state-of-the-art U-Net in segmentation performance as evaluated by the traditional metrics. More remarkably, the same proposed candidate also performed the best in terms of the preservation of valuable shape features, namely area, eccentricity, major axis length, solidity and orientation. These improvements on shape feature preservation can serve as useful assets for downstream cell tracking and quantification of changes in cell statistics or features over time.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Substituting Gadolinium in Brain MRI Using DeepContrast

Cerebral blood volume (CBV) is a hemodynamic correlate of oxygen metabolism and reflects brain activity and function. High-resolution CBV maps can be generated using the steady-state gadolinium-enhanced MRI technique. Such a technique requires an intravenous injection of exogenous gadolinium based contrast agent (GBCA) and recent studies suggest that the GBCA can accumulate in the brain after frequent use. We hypothesize that endogenous sources of contrast might exist within the most conventional and commonly acquired structural MRI, potentially obviating the need for exogenous contrast. Here, we test this hypothesis by developing and optimizing a deep learning algorithm, which we call DeepContrast, in mice. We find that DeepContrast performs equally well as exogenous GBCA in mapping CBV of the normal brain tissue and enhancing glioblastoma. Together, these studies validate our hypothesis that a deep learning approach can potentially replace the need for GBCAs in brain MRI.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Sufficient Conditions for Parameter Convergence over Embedded Manifolds using Kernel Techniques

The persistence of excitation (PE) condition is sufficient to ensure parameter convergence in adaptive estimation problems. Recent results on adaptive estimation in reproducing kernel Hilbert spaces (RKHS) introduce PE conditions for RKHS. This paper presents sufficient conditions for PE for the particular class of uniformly embedded reproducing kernel Hilbert spaces (RKHS) defined over smooth Riemannian manifolds. This paper also studies the implications of the sufficient condition in the case when the RKHS is finite or infinite-dimensional. When the RKHS is finite-dimensional, the sufficient condition implies parameter convergence as in the conventional analysis. On the other hand, when the RKHS is infinite-dimensional, the same condition implies that the function estimate error is ultimately bounded by a constant that depends on the approximation error in the infinite-dimensional RKHS. We illustrate the effectiveness of the sufficient condition in a practical example.

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preprint2018arXiv

One-dimensional van der Waals heterostructures

Property by design is one appealing idea in material synthesis but hard to achieve in practice. A recent successful example is the demonstration of van der Waals (vdW) heterostructures,1-3 in which atomic layers are stacked on each other and different ingredients can be combined beyond symmetry and lattice matching. This concept, usually described as a nanoscale Lego blocks, allows to build sophisticated structures layer by layer. However, this concept has been so far limited in two dimensional (2D) materials. Here we show a class of new material where different layers are coaxially (instead of planarly) stacked. As the structure is in one dimensional (1D) form, we name it "1D vdW heterostructures". We demonstrate a 5 nm diameter nanotube consisting of three different materials: an inner conductive carbon nanotube (CNT), a middle insulating hexagonal boron nitride nanotube (BNNT) and an outside semiconducting MoS2 nanotube. As the technique is highly applicable to other materials in the current 2D libraries,4-6 we anticipate our strategy to be a starting point for discovering a class of new semiconducting nanotube materials. A plethora of function-designable 1D heterostructures will appear after the combination of CNTs, BNNTs and semiconducting nanotubes.

0 citations0 reviewsNo code linkedOpen access