arXiv subjects

Nan Wu

Publications and source records attributed to Nan Wu.

At least 109 records · Page 6Linked to original sources

arXiv2019

Deep Neural Networks Improve Radiologists' Performance in Breast Cancer Screening

We present a deep convolutional neural network for breast cancer screening exam classification, trained and evaluated on over 200,000 exams (over 1,000,000 images). Our network achieves an AUC of 0.895 in predicting whether there is a cancer in the breast, when tested on the screening population. We attribute the high accuracy of our model to a two-stage training procedure, which allows us to use a very high-capacity patch-level network to learn from pixel-level labels alongside a network learning from macroscopic breast-level labels. To validate our model, we conducted a reader study with 14 readers, each reading 720 screening mammogram exams, and find our model to be as accurate as experienced radiologists when presented with the same data. Finally, we show that a hybrid model, averaging probability of malignancy predicted by a radiologist with a prediction of our neural network, is more accurate than either of the two separately. To better understand our results, we conduct a thorough analysis of our network's performance on different subpopulations of the screening population, model design, training procedure, errors, and properties of its internal representations.

cs.LG↗

arXiv2019

Connecting Dots -- from Local Covariance to Empirical Intrinsic Geometry and Locally Linear Embedding

Local covariance structure under the manifold setup has been widely applied in the machine learning society. Based on the established theoretical results, we provide an extensive study of two relevant manifold learning algorithms, empirical intrinsic geometry (EIG) and the locally linear embedding (LLE) under the manifold setup. Particularly, we show that without an accurate dimension estimation, the geodesic distance estimation by EIG might be corrupted. Furthermore, we show that by taking the local covariance matrix into account, we can more accurately estimate the local geodesic distance. When understanding LLE based on the local covariance structure, its intimate relationship with the curvature suggests a variation of LLE depending on the "truncation scheme". We provide a theoretical analysis of the variation.

math.ST↗

arXiv2018

Network Modeling and Pathway Inference from Incomplete Data ("PathInf")

In this work, we developed a network inference method from incomplete data ("PathInf") , as massive and non-uniformly distributed missing values is a common challenge in practical problems. PathInf is a two-stages inference model. In the first stage, it applies a data summarization model based on maximum likelihood to deal with the massive distributed missing values by transforming the observation-wise items in the data into state matrix. In the second stage, transition pattern (i.e. pathway) among variables is inferred as a graph inference problem solved by greedy algorithm with constraints. The proposed method was validated and compared with the state-of-art Bayesian network method on the simulation data, and shown consistently superior performance. By applying the PathInf on the lymph vascular metastasis data, we obtained the holistic pathways of the lymph node metastasis with novel discoveries on the jumping metastasis among nodes that are physically apart. The discovery indicates the possible presence of sentinel node groups in the lung lymph nodes which have been previously speculated yet never found. The pathway map can also improve the current dissection examination protocol for better individualized treatment planning, for higher diagnostic accuracy and reducing the patients trauma.

stat.ML↗

arXiv2018

Entanglement Detection via Direct-Sum Majorization Uncertainty Relations

In this paper we investigate the relationship between direct-sum majorization formulation of uncertainty relations and entanglement, for the case of two and many observables. Our primary results are entanglement detection methods based on direct-sum majorization uncertainty relations. These nonlinear detectors provide a set of necessary conditions for detecting entanglement whose number grows with the dimension of the state being detected.

quant-ph↗

arXiv2018

Uncertainty Relations in the Presence of Quantum Memory for Mutually Unbiased Measurements

In [Berta 2014 Entanglement], uncertainty relations in the presence of quantum memory was formulated for mutually unbiased bases using conditional collision entropy. In this paper, we generalize their results to the mutually unbiased measurements. Our primary result is an equality between the amount of uncertainty for a set of measurements and the amount of entanglement of the measured state, both of which are quantified by the conditional collision entropy. Implications of this equality relation are discussed. We further show that similar equality relation can be obtained for generalized symmetric informationally complete measurements. We also derive an interesting equality for arbitrary orthogonal basis of the space of Hermitian, traceless operators.

quant-ph↗

arXiv2018

High-Resolution Breast Cancer Screening with Multi-View Deep Convolutional Neural Networks

Advances in deep learning for natural images have prompted a surge of interest in applying similar techniques to medical images. The majority of the initial attempts focused on replacing the input of a deep convolutional neural network with a medical image, which does not take into consideration the fundamental differences between these two types of images. Specifically, fine details are necessary for detection in medical images, unlike in natural images where coarse structures matter most. This difference makes it inadequate to use the existing network architectures developed for natural images, because they work on heavily downscaled images to reduce the memory requirements. This hides details necessary to make accurate predictions. Additionally, a single exam in medical imaging often comes with a set of views which must be fused in order to reach a correct conclusion. In our work, we propose to use a multi-view deep convolutional neural network that handles a set of high-resolution medical images. We evaluate it on large-scale mammography-based breast cancer screening (BI-RADS prediction) using 886,000 images. We focus on investigating the impact of the training set size and image size on the prediction accuracy. Our results highlight that performance increases with the size of training set, and that the best performance can only be achieved using the original resolution. In the reader study, performed on a random subset of the test set, we confirmed the efficacy of our model, which achieved performance comparable to a committee of radiologists when presented with the same data.

cs.CV↗

arXiv2018

Length of a shortest closed geodesic in manifolds of dimension four

In this paper, we show that for any closed 4-dimensional simply-connected Riemannian manifold $M$ with Ricci curvature $|Ric|\leq 3$, volume $vol(M)>v>0$, and diameter $diam(M)<D$, the length of a shortest closed geodesic is bounded by a function $F(v,D)$ which only depends on $v$ and $D$. The proofs of our result are based on a recent theorem of diffeomorphism finiteness of the manifolds satisfying the above conditions proven by J. Cheeger and A. Naber.

math.DG↗

arXiv2018

On existence of out-of-plane equilibrium points in restricted three-body problem with oblateness

We analyze in this paper the existence of the "out-of-plane" equilibrium points in the restricted three-body problem with oblateness. From the series expansion of the potential function of an oblate asteroid, we show analytically all equilibrium points locate on the orbital plane of primaries and how artificial equilibrium points may arise due to an inappropriate application of the potential function. Using the closed form of the potential of a triaxial ellipsoid, we analytically demonstrate that the gravitational acceleration in $z$-direction is always pointing toward the equatorial plane, thus it could not be balanced out at any value of $z\neq 0$ and the out-of-plane equilibrium points cannot exist. The out-of-plane equilibrium points appear only when additional acceleration other than the gravitation from primaries is taken into account. We suggest that special attention must be paid to the application of the spherical harmonics expansion of potential to find the equilibrium points, especially when these points may be very close to the celestial body.

astro-ph.EP↗

arXiv2017

An upper bound for the smallest area of a minimal surface in manifolds of dimension four

In this paper, we prove that for any closed 4-dimensional Riemannian manifold $M$ with trivial first homology group, if the Ricci curvature $|Ric|\leq3$, the diameter $diam(M)\leq D$ and the volume $vol(M)>v>0$, then the area of a smallest 2-dimensional stationary integral varifold in $M$ is bounded by F(v,D), for some function F that only depends on v and D. Our bound for the area is based on the estimation of the first homological filling function of $M$.

math.DG↗

arXiv2017

Cooperative Network Synchronization: Asymptotic Analysis

Accurate clock synchronization is required for collaborative operations among nodes across wireless networks. Compared with traditional layer-by-layer methods, cooperative network synchronization techniques lead to significant improvement in performance, efficiency, and robustness. This paper develops a framework for the performance analysis of cooperative network synchronization. We introduce the concepts of cooperative dilution intensity (CDI) and relative CDI to characterize the interaction between agents, which can be interpreted as properties of a random walk over the network. Our approach enables us to derive closed-form asymptotic expressions of performance limits, relating them to the quality of observations as well as network topology.

cs.IT↗

arXiv2017

Breast density classification with deep convolutional neural networks

Breast density classification is an essential part of breast cancer screening. Although a lot of prior work considered this problem as a task for learning algorithms, to our knowledge, all of them used small and not clinically realistic data both for training and evaluation of their models. In this work, we explore the limits of this task with a data set coming from over 200,000 breast cancer screening exams. We use this data to train and evaluate a strong convolutional neural network classifier. In a reader study, we find that our model can perform this task comparably to a human expert.

cs.CV↗

arXiv2017

Iterative Receivers for Downlink MIMO-SCMA: Message Passing and Distributed Cooperative Detection

The rapid development of the mobile communications requires ever higher spectral efficiency. The non-orthogonal multiple access (NOMA) has emerged as a promising technology to further increase the access efficiency of wireless networks. Amongst several NOMA schemes, the sparse code multiple access (SCMA) has been shown to be able to achieve better performance. In this paper, we consider a downlink MIMO-SCMA system over frequency selective fading channels. For optimal detection, the complexity increases exponentially with the product of the number of users, the number of antennas and the channel length. To tackle this challenge, we propose near optimal low-complexity iterative receivers based on factor graph. By introducing auxiliary variables, a stretched factor graph is constructed and a hybrid belief propagation (BP) and expectation propagation (EP) receiver, named as `Stretch-BP-EP', is proposed. Considering the convergence problem of BP algorithm on loopy factor graph, we convexify the Bethe free energy and propose a convergence-guaranteed BP-EP receiver, named as `Conv-BP-EP'. We further consider cooperative network and propose two distributed cooperative detection schemes to exploit the diversity gain, namely, belief consensus-based algorithm and Bregman alternative direction method of multipliers (ADMM)-based method. Simulation results verify the superior performance of the proposed Conv-BP-EP receiver compared with other methods. The two proposed distributed cooperative detection schemes can improve the bit error rate performance by exploiting the diversity gain. Moreover, Bregman ADMM method outperforms the belief consensus-based algorithm in noisy inter-user links.

cs.IT↗

arXiv2017

Think globally, fit locally under the Manifold Setup: Asymptotic Analysis of Locally Linear Embedding

Since its introduction in 2000, the locally linear embedding (LLE) has been widely applied in data science. We provide an asymptotical analysis of the LLE under the manifold setup. We show that for the general manifold, asymptotically we may not obtain the Laplace-Beltrami operator, and the result may depend on the non-uniform sampling, unless a correct regularization is chosen. We also derive the corresponding kernel function, which indicates that the LLE is not a Markov process. A comparison with the other commonly applied nonlinear algorithms, particularly the diffusion map, is provided, and its relationship with the locally linear regression is also discussed.

math.ST↗

arXiv2016

The Lackadaisical Quantum Walker is NOT Lazy at all

In this paper, we study the properties of lackadaisical quantum walks on a line. This model is first proposed in~\cite{wong2015grover} as a quantum analogue of lazy random walks where each vertex is attached $τ$ self-loops. We derive an analytic expression for the localization probability of the walker at the origin after infinite steps, and obtain the peak velocities of the walker. We also calculate rigorously the wave function of the walker starting from the origin and obtain a long time approximation for the entire probability density function. As an application of the density function, we prove that lackadaisical quantum walks spread ballistically for arbitrary $τ$, and give an analytic solution for the variance of the walker's probability distribution.

quant-ph↗

arXiv2016

Grover Walks on a Line with Absorbing Boundaries

In this paper, we study Grover walks on a line with one and two absorbing boundaries. In particular, we present some results for the absorbing probabilities both in a semi-finite and finite line. Analytical expressions for these absorbing probabilities are presented by using the combinatorial approach. These results are perfectly matched with numerical simulations. We show that the behavior of Grover walks on a line with absorbing boundaries is strikingly different from that of classical walks and that of Hadamard walks.

quant-ph↗

arXiv2016

A Real-Time and Energy-Efficient Implementation of Difference-of-Gaussian with Flexible Thin-Film Transistors

With many advantageous features, softness and better biocompatibility, flexible electronic devices have developed rapidly and increasingly attracted attention. Many currently applications with flexible devices are sensors and drivers, while there is nearly no utilization aiming at complex computation since flexible devices have lower electron mobility, simple structure and large process variation. In this paper, we proposed an innovative method that enabled flexible devices to implement real-time and energy-efficient Difference-of-Gaussian, which illustrated feasibility and potentials for them to achieve complicated real-time computation in future generation products.

cs.ET↗

arXiv2016

Cooperative Joint Localization and Clock Synchronization Based on Gaussian Message Passing in Asynchronous Wireless Networks

Localization and synchronization are very important in many wireless applications such as monitoring and vehicle tracking. Utilizing the same time of arrival (TOA) measurements for simultaneous localization and synchronization is challenging. In this paper, we present a factor graph (FG) representation of the joint localization and time synchronization problem based on TOA measurements, in which the non-line-of-sight measurements are also taken into consideration. On this FG, belief propagation (BP) message passing and variational message passing (VMP) are applied to derive two fully distributed cooperative algorithms with low computational requirements. Due to the nonlinearity in the observation function, it is intractable to compute the messages in closed form and most existing solutions rely on Monte Carlo methods, e.g., particle filtering. We linearize a specific nonlinear term in the expressions of messages, which enables us to use a Gaussian representation for all messages. Accordingly, only the mean and variance have to be updated and transmitted between neighboring nodes, which significantly reduces the communication overhead and computational complexity. A message passing schedule scheme is proposed to trade off between estimation performance and communication overhead. Simulation results show that the proposed algorithms perform very close to particle-based methods with much lower complexity especially in densely connected networks.

cs.IT↗

arXiv2015

TOA-based passive localization of multiple targets with inaccurate receivers based on belief propagation on factor graph

Location awareness is now becoming a vital requirement for many practical applications. In this paper, we consider passive localization of multiple targets with one transmitter and several receivers based on time of arrival (TOA) measurements. Existing studies assume that positions of receivers are perfectly known. However, in practice, receivers' positions might be inaccurate, which leads to localization error of targets. We propose factor graph (FG)-based belief propagation (BP) algorithms to locate the passive targets and improve the position accuracy of receivers simultaneously. Due to the nonlinearity of the likelihood function, messages on the FG cannot be derived in closed form. We propose both sample-based and parametric methods to solve this problem. In the sample-based BP algorithm, particle swarm optimization is employed to reduce the number of particles required to represent messages. In parametric BP algorithm, the nonlinear terms in messages are linearized, which results in closed-form Gaussian message passing on FG. The Bayesian Cramer-Rao bound (BCRB) for passive targets localization with uncertain receivers is derived to evaluate the performance of the proposed algorithms. Simulation results show that both the sample-based and parametric BP algorithms outperform the conventional method and attain the proposed BCRB. Receivers' positions can also be improved via the proposed BP algorithms. Although the parametric BP algorithm performs slightly worse than the sample-based BP method, it could be more attractive in practical applications due to the significantly lower computational complexity.

cs.IT↗