arXiv subjects

Teng Zhang

Publications and source records attributed to Teng Zhang.

At least 181 records · Page 10Linked to original sources

arXiv2019

Tightness of the semidefinite relaxation for orthogonal trace-sum maximization

This paper studies an optimization problem on the sum of traces of matrix quadratic forms on $m$ orthogonal matrices, which can be considered as a generalization of the synchronization of rotations. While the problem is nonconvex, the paper shows that its semidefinite programming relaxation can solve the original nonconvex problems exactly, under an additive noise model with small noise in the order of $O(-m^{1/4})$, where $m$ is the number of orthogonal matrices. This result can be considered as a generalization of existing results on phase synchronization.

math.OC↗

arXiv2019

Harnessing energy landscape exploration to control the buckling of cylindrical shells

The complexity and unpredictability of postbuckling responses in even simple thin shells have raised great challenges to emerging technologies exploiting buckling transitions. Here we comprehensively survey the buckling landscapes to show the full complexity of the stable buckling states and the transition mechanisms between each of them. This is achieved by combining a simple and versatile triangulated lattice model for modelling the shell morphologies with efficient high-dimensional free-energy minimisation and transition path finding algorithms. We show how the simple free energy landscapes of short, lightly compressed cylinders become vastly more complex at high compressive strains or aspect ratios. We then exploit these landscapes to introduce an effective method for targeted design - landscape biasing. This is used to inform thickness modifications enabling landscape redesign, and the development of structures which are highly resistant to lateral perturbations. Our methods are general, and can be extended to studying postbuckling responses of other geometries.

cond-mat.mtrl-sci↗

arXiv2019

To What Extent Does Downsampling, Compression, and Data Scarcity Impact Renal Image Analysis?

The condition of the Glomeruli, or filter sacks, in renal Direct Immunofluorescence (DIF) specimens is a critical indicator for diagnosing kidney diseases. A digital pathology system which digitizes a glass histology slide into a Whole Slide Image (WSI) and then automatically detects and zooms in on the glomeruli with a higher magnification objective will be extremely helpful for pathologists. In this paper, using glomerulus detection as the study case, we provide analysis and observations on several important issues to help with the development of Computer Aided Diagnostic (CAD) systems to process WSIs. Large image resolution, large file size, and data scarcity are always challenging to deal with. To this end, we first examine image downsampling rates in terms of their effect on detection accuracy. Second, we examine the impact of image compression. Third, we examine the relationship between the size of the training set and detection accuracy. To understand the above issues, experiments are performed on the state-of-the-art detectors: Faster R-CNN, R-FCN, Mask R-CNN and SSD. Critical findings are observed: (1) The best balance between detection accuracy, detection speed and file size is achieved at 8 times downsampling captured with a $40\times$ objective; (2) compression which reduces the file size dramatically, does not necessarily have an adverse effect on overall accuracy; (3) reducing the amount of training data to some extents causes a drop in precision but has a negligible impact on the recall; (4) in most cases, Faster R-CNN achieves the best accuracy in the glomerulus detection task. We show that the image file size of $40\times$ WSI images can be reduced by a factor of over 6000 with negligible loss of glomerulus detection accuracy.

cs.CV↗

arXiv2019

An Algorithm for Graph-Fused Lasso Based on Graph Decomposition

This work proposes a new algorithm for solving the graph-fused lasso (GFL), a method for parameter estimation that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. The proposed method applies the alternating direction method of multipliers (ADMM) algorithm and is based on the decomposition of the objective function into two components. While ADMM has been widely used in this problem, existing works such as network lasso decompose the objective function into the loss function component and the total variation penalty component. In comparison, this work proposes to decompose the objective function into two components, where one component is the loss function plus part of the total variation penalty, and the other component is the remaining total variation penalty. Compared with the network lasso algorithm, this method has a smaller computational cost per iteration and converges faster in most simulations numerically.

math.OC↗

arXiv2019

Deep inspection: an electrical distribution pole parts study via deep neural networks

Electrical distribution poles are important assets in electricity supply. These poles need to be maintained in good condition to ensure they protect community safety, maintain reliability of supply, and meet legislative obligations. However, maintaining such a large volumes of assets is an expensive and challenging task. To address this, recent approaches utilise imagery data captured from helicopter and/or drone inspections. Whilst reducing the cost for manual inspection, manual analysis on each image is still required. As such, several image-based automated inspection systems have been proposed. In this paper, we target two major challenges: tiny object detection and extremely imbalanced datasets, which currently hinder the wide deployment of the automatic inspection. We propose a novel two-stage zoom-in detection method to gradually focus on the object of interest. To address the imbalanced dataset problem, we propose the resampling as well as reweighting schemes to iteratively adapt the model to the large intra-class variation of major class and balance the contributions to the loss from each class. Finally, we integrate these components together and devise a novel automatic inspection framework. Extensive experiments demonstrate that our proposed approaches are effective and can boost the performance compared to the baseline methods.

cs.CV↗

arXiv2019

Deep Instance-Level Hard Negative Mining Model for Histopathology Images

Histopathology image analysis can be considered as a Multiple instance learning (MIL) problem, where the whole slide histopathology image (WSI) is regarded as a bag of instances (i.e, patches) and the task is to predict a single class label to the WSI. However, in many real-life applications such as computational pathology, discovering the key instances that trigger the bag label is of great interest because it provides reasons for the decision made by the system. In this paper, we propose a deep convolutional neural network (CNN) model that addresses the primary task of a bag classification on a WSI and also learns to identify the response of each instance to provide interpretable results to the final prediction. We incorporate the attention mechanism into the proposed model to operate the transformation of instances and learn attention weights to allow us to find key patches. To perform a balanced training, we introduce adaptive weighing in each training bag to explicitly adjust the weight distribution in order to concentrate more on the contribution of hard samples. Based on the learned attention weights, we further develop a solution to boost the classification performance by generating the bags with hard negative instances. We conduct extensive experiments on colon and breast cancer histopathology data and show that our framework achieves state-of-the-art performance.

cs.CV↗

arXiv2019

CORAL8: Concurrent Object Regression for Area Localization in Medical Image Panels

This work tackles the problem of generating a medical report for multi-image panels. We apply our solution to the Renal Direct Immunofluorescence (RDIF) assay which requires a pathologist to generate a report based on observations across the eight different WSI in concert with existing clinical features. To this end, we propose a novel attention-based multi-modal generative recurrent neural network (RNN) architecture capable of dynamically sampling image data concurrently across the RDIF panel. The proposed methodology incorporates text from the clinical notes of the requesting physician to regulate the output of the network to align with the overall clinical context. In addition, we found the importance of regularizing the attention weights for word generation processes. This is because the system can ignore the attention mechanism by assigning equal weights for all members. Thus, we propose two regularizations which force the system to utilize the attention mechanism. Experiments on our novel collection of RDIF WSIs provided by a large clinical laboratory demonstrate that our framework offers significant improvements over existing methods.

cs.CV↗

arXiv2019

Non-uniform Curvature and Anisotropic Deformation Control Wrinkling Patterns on Tori

We investigate wrinkling patterns in a tri-layer torus consisting of an expanding thin outer layer, an intermediate soft layer and an inner core with a tunable shear modulus, inspired by pattern formation in developmental biologies, such as follicle pattern formation during the development of chicken embryos. We show from large-scale finite element simulations that hexagonal wrinkling patterns form for stiff cores whereas stripe wrinkling patterns develop for soft cores. Hexagons and stripes co-exist to form hybrid patterns for cores with intermediate stiffness. The governing mechanism for the pattern transition is that the stiffness of the inner core controls the degree to which the major radius of the torus expands this has a greater effect on deformation in the long direction as compared to the short direction of the torus. This anisotropic deformation alters stress states in the outer layer which change from biaxial (preferred hexagons) to uniaxial (preferred stripes) compression as the core stiffness is reduced. As the outer layer continues to expand, stripe and hexagon patterns will evolve into Zigzag and segmented labyrinth, respectively. Stripe wrinkles are observed to initiate at the inner surface of the torus while hexagon wrinkles start from the outer surface as a result of curvature-dependent stresses in the torus. We further discuss the effects of elasticities and geometries of the torus on the wrinkling patterns.

cond-mat.soft↗

arXiv2019

Tuning Water Slip Behavior in Nanochannels using Self-Assembled Monolayers

Water slip at solid surfaces is important for a wide range of micro/nano-fluidic applications. While it is known that water slip behavior depends on surface functionalization, how it impacts the molecular level dynamics and mass transport at the interface is still not thoroughly understood. In this paper, we use nonequilibrium molecular dynamics simulations to investigate the slip behavior of water confined between gold surfaces functionalized by self-assembled monolayer (SAM) molecules with different polar functional groups. We observe a positive-to-negative slip transition from hydrophobic to hydrophilic SAM functionalizations, which is found related to the stronger interfacial interaction between water molecules and more hydrophilic SAM molecules. The stronger interaction increases the surface friction and local viscosity, making water slip more difficult. More hydrophilic functionalization also slows down the interfacial water relaxation and leads to more pronounced water trapping inside the SAM layer, which both impede water slip. The results from this work will provide useful insights to the understanding of the water slip at functionalized surfaces and design guidelines for various applications.

physics.app-ph↗

arXiv2019

A Well-Tempered Landscape for Non-convex Robust Subspace Recovery

We present a mathematical analysis of a non-convex energy landscape for robust subspace recovery. We prove that an underlying subspace is the only stationary point and local minimizer in a specified neighborhood under a deterministic condition on a dataset. If the deterministic condition is satisfied, we further show that a geodesic gradient descent method over the Grassmannian manifold can exactly recover the underlying subspace when the method is properly initialized. Proper initialization by principal component analysis is guaranteed with a simple deterministic condition. Under slightly stronger assumptions, the gradient descent method with a piecewise constant step-size scheme achieves linear convergence. The practicality of the deterministic condition is demonstrated on some statistical models of data, and the method achieves almost state-of-the-art recovery guarantees on the Haystack Model for different regimes of sample size and ambient dimension. In particular, when the ambient dimension is fixed and the sample size is large enough, we show that our gradient method can exactly recover the underlying subspace for any fixed fraction of outliers (less than 1).

cs.LG↗

arXiv2019

Element-wise estimation error of a total variation regularized estimator for change point detection

This work studies the total variation regularized $\ell_2$ estimator (fused lasso) in the setting of a change point detection problem. Compared with existing works that focus on the sum of squared estimation errors, we give bound on the element-wise estimation error. Our bound is nearly optimal in the sense that the sum of squared error matches the best existing result, up to a logarithmic factor. This analysis of the element-wise estimation error allows a screening method that can approximately detect all the change points. We also generalize this method to the muitivariate setting, i.e., to the problem of group fused lasso.

math.ST↗

arXiv2018

Phase Retrieval by Alternating Minimization with Random Initialization

We consider a phase retrieval problem, where the goal is to reconstruct a $n$-dimensional complex vector from its phaseless scalar products with $m$ sensing vectors, independently sampled from complex normal distributions. We show that, with a random initialization, the classical algorithm of alternating minimization succeeds with high probability as $n,m\rightarrow\infty$ when ${m}/{\log^3m}\geq Mn^{3/2}\log^{1/2}n$ for some $M>0$. This is a step toward proving the conjecture in \cite{Waldspurger2016}, which conjectures that the algorithm succeeds when $m=O(n)$. The analysis depends on an approach that enables the decoupling of the dependency between the algorithmic iterates and the sensing vectors.

math.ST↗

arXiv2018

Buckling without bending: a new paradigm in morphogenesis

A curious feature of organ and organoid morphogenesis is that in certain cases, spatial oscillations in the thickness of the growing "film" are out-of-phase with the deformation of the slower-growing "substrate," while in other cases, the oscillations are in-phase. The former cannot be explained by elastic bilayer instability, and contradict the notion that there is a universal mechanism by which brains, intestines, teeth, and other organs develop surface wrinkles and folds. Inspired by the microstructure of the embryonic cerebellum, we develop a new model of 2d morphogenesis in which system-spanning elastic fibers endow the organ with a preferred radius, while a separate fiber network resides in the otherwise fluid-like film at the outer edge of the organ and resists thickness gradients thereof. The tendency of the film to uniformly thicken or thin is described via a "growth potential". Several features of cerebellum, +blebbistatin organoid, and retinal fovea morphogenesis, including out-of-phase behavior and a film thickness amplitude that is comparable to the radius amplitude, are readily explained by our simple analytical model, as may be an observed scale-invariance in the number of folds in the cerebellum. We also study a nonlinear variant of the model, propose further biological and bio-inspired applications, and address how our model is and is not unique to the developing nervous system.

physics.bio-ph↗

arXiv2018

A note on the non-commutative arithmetic-geometric mean inequality

This note proves the following inequality: if $n=3k$ for some positive integer $k$, then for any $n$ positive definite matrices $A_1,A_2,\cdots,A_n$, \begin{equation} \frac{1}{n^3}\Big\|\sum_{j_1,j_2,j_3=1}^{n}A_{j_1}A_{j_2}A_{j_3}\Big\| \geq \frac{(n-3)!}{n!} \Big\|\sum_{\substack{j_1,j_2,j_3=1,\\\text{$j_1$, $j_2$, $j_3$ all distinct}}}^{n}A_{j_1}A_{j_2}A_{j_3}\Big\|, \end{equation} where $\|\cdot\|$ represents the operator norm. This inequality is a special case of a recent conjecture by Recht and Ré.

math.SP↗

arXiv2018

Phase retrieval using alternating minimization in a batch setting

This paper considers the problem of phase retrieval, where the goal is to recover a signal $z\in C^n$ from the observations $y_i=|a_i^* z|$, $i=1,2,\cdots,m$. While many algorithms have been proposed, the alternating minimization algorithm has been one of the most commonly used methods, and it is very simple to implement. Current work has proved that when the observation vectors $\{a_i\}_{i=1}^m$ are sampled from a complex Gaussian distribution $N(0, I)$, it recovers the underlying signal with a good initialization when $m=O(n)$, or with random initialization when $m=O(n^2)$, and it conjectured that random initialization succeeds with $m=O(n)$. This work proposes a modified alternating minimization method in a batch setting, and proves that when $m=O(n\log^{3}n)$, the proposed algorithm with random initialization recovers the underlying signal with high probability. The proof is based on the observation that after each iteration of alternating minimization, with high probability, the angle between the estimated signal and the underlying signal is reduced.

math.OC↗

arXiv2018

Exact Camera Location Recovery by Least Unsquared Deviations

We establish exact recovery for the Least Unsquared Deviations (LUD) algorithm of Ozyesil and Singer. More precisely, we show that for sufficiently many cameras with given corrupted pairwise directions, where both camera locations and pairwise directions are generated by a special probabilistic model, the LUD algorithm exactly recovers the camera locations with high probability. A similar exact recovery guarantee was established for the ShapeFit algorithm by Hand, Lee and Voroninski, but with typically less corruption.

cs.CV↗

arXiv2018

Deriving a lattice model for neo-Hookean solids from finite element methods

Lattice models are popular methods for simulating deformation of solids by discretizing continuum structures into spring networks. Despite the simplicity and efficiency, most lattice models only rigorously converge to continuum models for lattices with regular shapes. Here, we derive a lattice model for neo-Hookean solids directly from finite element methods (FEM). The proposed lattice model can handle complicated geometries and tune the material compressibility without significantly increasing the complexity of the model. Distinct lattices are required for irregular structures, where the lattice spring stiffness can be pre-calculated with the aid of FEM shape functions. Multibody interactions are incorporated to describe the volumetric deformation. We validate the lattice model with benchmark tests using FEM. The simplicity and adoptability of the proposed lattice model open possibilities to develop novel numerical platforms for simulating multiphysics and multiscale problems via integrating it with other modeling techniques.

cond-mat.soft↗

arXiv2018

Efficient Signal Inclusion With Genomic Applications

This paper addresses the challenge of efficiently capturing a high proportion of true signals for subsequent data analyses when sample sizes are relatively limited with respect to data dimension. We propose the signal missing rate as a new measure for false negative control to account for the variability of false negative proportion. Novel data-adaptive procedures are developed to control signal missing rate without incurring many unnecessary false positives under dependence. We justify the efficiency and adaptivity of the proposed methods via theory and simulation. The proposed methods are applied to GWAS on human height to effectively remove irrelevant SNPs while retaining a high proportion of relevant SNPs for subsequent polygenic analysis.

stat.ME↗