arXiv subjects

Jie Sun

Publications and source records attributed to Jie Sun.

At least 109 records · Page 6Linked to original sources

arXiv2020

A variable metric mini-batch proximal stochastic recursive gradient algorithm with diagonal Barzilai-Borwein stepsize

Variable metric proximal gradient methods with different metric selections have been widely used in composite optimization. Combining the Barzilai-Borwein (BB) method with a diagonal selection strategy for the metric, the diagonal BB stepsize can keep low per-step computation cost as the scalar BB stepsize and better capture the local geometry of the problem. In this paper, we propose a variable metric mini-batch proximal stochastic recursive gradient algorithm VM-mSRGBB, which updates the metric using a new diagonal BB stepsize. The linear convergence of VM-mSRGBB is established for strongly convex, non-strongly convex and convex functions. Numerical experiments on standard data sets show that VM-mSRGBB is better than or comparable to some variance reduced stochastic gradient methods with best-tuned scalar stepsizes or BB stepsizes. Furthermore, the performance of VM-mSRGBB is superior to some advanced mini-batch proximal stochastic gradient methods.

math.OC↗

arXiv2020

Risk Minimization, Regret Minimization and Progressive Hedging Algorithms

This paper begins with a study on the dual representations of risk and regret measures and their impact on modeling multistage decision making under uncertainty. A relationship between risk envelopes and regret envelopes is established by using the Lagrangian duality theory. Such a relationship opens a door to a decomposition scheme, called progressive hedging, for solving multistage risk minimization and regret minimization problems. In particular, the classical progressive hedging algorithm is modified in order to handle a new class of linkage constraints that arises from reformulations and other applications of risk and regret minimization problems. Numerical results are provided to show the efficiency of the progressive hedging algorithms.

q-fin.MF↗

arXiv2020

RODE-Net: Learning Ordinary Differential Equations with Randomness from Data

Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge. Extracting the governing equations from data with less prior knowledge remains a great challenge. In this paper, we propose a deep neural network, called RODE-Net, to tackle such challenge by fitting a symbolic expression of the differential equation and the distribution of parameters simultaneously. To train the RODE-Net, we first estimate the parameters of the unknown RODE using the symbolic networks \cite{long2019pde} by solving a set of deterministic inverse problems based on the measured data, and use a generative adversarial network (GAN) to estimate the true distribution of the RODE's parameters. Then, we use the trained GAN as a regularization to further improve the estimation of the ODE's parameters. The two steps are operated alternatively. Numerical results show that the proposed RODE-Net can well estimate the distribution of model parameters using simulated data and can make reliable predictions. It is worth noting that, GAN serves as a data driven regularization in RODE-Net and is more effective than the $\ell_1$ based regularization that is often used in system identifications.

math.NA↗

arXiv2020

Data-Driven Learning of Boolean Networks and Functions by Optimal Causation Entropy Principle (BoCSE)

Boolean functions and networks are commonly used in the modeling and analysis of complex biological systems, and this paradigm is highly relevant in other important areas in data science and decision making, such as in the medical field and in the finance industry. Automated learning of a Boolean network and Boolean functions, from data, is a challenging task due in part to the large number of unknowns (including both the structure of the network and the functions) to be estimated, for which a brute force approach would be exponentially complex. In this paper we develop a new information theoretic methodology that we show to be significantly more efficient than previous approaches. Building on the recently developed optimal causation entropy principle (oCSE), that we proved can correctly infer networks distinguishing between direct versus indirect connections, we develop here an efficient algorithm that furthermore infers a Boolean network (including both its structure and function) based on data observed from the evolving states at nodes. We call this new inference method, Boolean optimal causation entropy (BoCSE), which we will show that our method is both computationally efficient and also resilient to noise. Furthermore, it allows for selection of a set of features that best explains the process, a statement that can be described as a networked Boolean function reduced order model. We highlight our method to the feature selection in several real-world examples: (1) diagnosis of urinary diseases, (2) Cardiac SPECT diagnosis, (3) informative positions in the game Tic-Tac-Toe, and (4) risk causality analysis of loans in default status. Our proposed method is effective and efficient in all examples.

cs.AI↗

arXiv2020

Bright solitons in a spin-tensor-momentum-coupled Bose-Einstein condensate

Synthetic spin-tensor-momentum coupling has recently been proposed to realize in atomic Bose-Einstein condensates. Here we study bright solitons in Bose-Einstein condensates with spin-tensor-momentum coupling and spin-orbit coupling. The properties and dynamics of spin-tensor-momentum-coupled and spin-orbit-coupled bright solitons are identified to be different. We contribute the difference to the different symmetries.

cond-mat.quant-gas↗

arXiv2019

How Entropic Regression Beats the Outliers Problem in Nonlinear System Identification

In this work, we developed a nonlinear System Identification (SID) method that we called Entropic Regression. Our method adopts an information-theoretic measure for the data-driven discovery of the underlying dynamics. Our method shows robustness toward noise and outliers and it outperforms many of the current state-of-the-art methods. Moreover, the method of Entropic Regression overcomes many of the major limitations of the current methods such as sloppy parameters, diverse scale, and SID in high dimensional systems such as complex networks. The use of information-theoretic measures in entropic regression poses unique advantages, due to the Asymptotic Equipartition Property (AEP) of probability distributions, that outliers and other low-occurrence events are conveniently and intrinsically de-emphasized as not-typical, by definition. We provide a numerical comparison with the current state-of-the-art methods in sparse regression, and we apply the methods to different chaotic systems such as the Lorenz System, the Kuramoto-Sivashinsky equations, and the Double Well Potential.

eess.SP↗

arXiv2019

Graphene-assisted preparation of large-scale single crystal Ag(111) nanoparticle arrays

Surface plasmon resonance of metal nanostructures has broad application prospects in the fields of photocatalysis, optical sensing, biomarkers and surface-enhanced Raman scattering. This paper reports a graphene-assisted method for preparing large-scale single crystal Ag(111) nanoparticle arrays based on ion implantation technique. By surface periodic treatment and annealing of the implanted sample, regularly arranged Ag nanoparticles can be prepared on the sample surface. A new application for graphene is proposed, that is, as a perfect barrier layer to prevent metal atoms from evaporating or diffusing. All the Ag NPs show (111) crystal orientation. Besides, the Ag atoms are covered by graphene immediately when they precipitate from the substrate, which can prevent them from being oxidized. On the basis of this structure, as one of the applications of metal SPR, we measured the Raman enhancement effect, and found that the G peak of the Raman spectrum of graphene achieved about 20 times enhancement.

physics.app-ph↗

arXiv2019

Automated Artery Localization and Vessel Wall Segmentation of Magnetic Resonance Vessel Wall Images using Tracklet Refinement and Polar Conversion

Quantitative analysis of vessel wall structures by automated vessel wall segmentation provides useful imaging biomarkers in evaluating atherosclerotic lesions and plaque progression time-efficiently. To quantify vessel wall features, drawing lumen and outer wall contours of the artery of interest is required. To alleviate manual labor in contour drawing, some computer-assisted tools exist, but manual preprocessing steps, such as region of interest identification and boundary initialization are needed. In addition, the prior knowledge of the ring shape of vessel wall is not taken into consideration in designing the segmentation method. In this work, trained on manual vessel wall contours, a fully automated artery localization and vessel wall segmentation system is proposed. A tracklet refinement algorithm is used to robustly identify the centerlines of arteries of interest from a neural network localization architecture. Image patches are extracted from the centerlines and segmented in a polar coordinate system to use 3D information and to overcome problems such as contour discontinuity and interference from neighboring vessels. From a carotid artery dataset with 116 subjects (3406 slices) and a popliteal artery dataset with 5 subjects (289 slices), the proposed system is shown to robustly identify the artery of interest and segment the vessel wall. The proposed system demonstrates better performance on the carotid dataset with a Dice similarity coefficient of 0.824, compared with traditional vessel wall segmentation methods, Dice of 0.576, and traditional convolutional neural network approaches, Dice of 0.747. This vessel wall segmentation system will facilitate research on atherosclerosis and assist radiologists in image review.

eess.IV↗

arXiv2019

Synchronization of Network-Coupled Oscillators with Uncertain Dynamics

Synchronization of network-coupled dynamical units is important to a variety of natural and engineered processes including circadian rhythms, cardiac function, neural processing, and power grids. Despite this ubiquity, it remains poorly understood how complex network structures and heterogeneous local dynamics combine to either promote or inhibit synchronization. Moreover, for most real-world applications it is impossible to obtain the exact specifications of the system, and there is a lack of theory for how uncertainty affects synchronization. We address this open problem by studying the Synchrony Alignment Function (SAF), which is an objective measure for the synchronization properties of a network of heterogeneous oscillators with given natural frequencies. We extend the SAF framework to analyze network-coupled oscillators with heterogeneous natural frequencies that are drawn as a multivariate random vector. Using probability theory for quadratic forms, we obtain expressions for the expectation and variance of the SAF for given network structures. We conclude with numerical experiments that illustrate how the incorporation of uncertainty yields a more robust theoretical framework for enhancing synchronization, and we provide new perspectives for why synchronization is generically promoted by network properties including degree-frequency correlations, link directedness, and link weight delocalization.

nlin.AO↗

arXiv2019

A Novel Euler's Elastica based Segmentation Approach for Noisy Images via using the Progressive Hedging Algorithm

Euler's Elastica based unsupervised segmentation models have strong capability of completing the missing boundaries for existing objects in a clean image, but they are not working well for noisy images. This paper aims to establish a Euler's Elastica based approach that properly deals with random noises to improve the segmentation performance for noisy images. We solve the corresponding optimization problem via using the progressive hedging algorithm (PHA) with a step length suggested by the alternating direction method of multipliers (ADMM). Technically, all the simplified convex versions of the subproblems derived from the major framework of PHA can be obtained by using the curvature weighted approach and the convex relaxation method. Then an alternating optimization strategy is applied with the merits of using some powerful accelerating techniques including the fast Fourier transform (FFT) and generalized soft threshold formulas. Extensive experiments have been conducted on both synthetic and real images, which validated some significant gains of the proposed segmentation models and demonstrated the advantages of the developed algorithm.

cs.CV↗

arXiv2019

An electrochemical thermal transistor

The ability to actively regulate heat flow at the nanoscale could be a game changer for applications in thermal management and energy harvesting. Such a breakthrough could also enable the control of heat flow using thermal circuits, in a manner analogous to electronic circuits. Here we demonstrate switchable thermal transistors with an order of magnitude thermal on/off ratio, based on reversible electrochemical lithium intercalation in MoS2 thin films. We use spatially-resolved time-domain thermoreflectance to map the lithium ion distribution during device operation, and atomic force microscopy to show that the lithiated state correlates with increased thickness and surface roughness. First principles calculations reveal that the thermal conductance modulation is due to phonon scattering by lithium rattler modes, c-axis strain, and stacking disorder. This study lays the foundation for electrochemically-driven nanoscale thermal regulators, and establishes thermal metrology as a useful probe of spatio-temporal intercalant dynamics in nanomaterials.

physics.app-ph↗

arXiv2019

Quantum Differential Cryptanalysis

In this paper, we propose a quantum version of the differential cryptanalysis which offers a quadratic speedup over the existing classical one and show the quantum circuit implementing it. The quantum differential cryptanalysis is based on the quantum minimum/maximum-finding algorithm, where the values to be compared and filtered are obtained by calling the quantum counting algorithm. Any cipher which is vulnerable to the classical differential cryptanalysis based on counting procedures can be cracked more quickly under this quantum differential attack.

quant-ph↗

arXiv2018

Node Diversification in Complex Networks by Decentralized Coloring

We develop a decentralized coloring approach to diversify the nodes in a complex network. The key is the introduction of a local conflict index that measures the color conflicts arising at each node which can be efficiently computed using only local information. We demonstrate via both synthetic and real-world networks that the proposed approach significantly outperforms random coloring as measured by the size of the largest color-induced connected component. Interestingly, for scale-free networks further improvement of diversity can be achieved by tuning a degree-biasing weighting parameter in the local conflict index.

cs.SI↗

arXiv2018

Spectral operators of matrices: semismoothness and characterizations of the generalized Jacobian

Spectral operators of matrices proposed recently in [C. Ding, D.F. Sun, J. Sun, and K.C. Toh, Math. Program. {\bf 168}, 509--531 (2018)] are a class of matrix valued functions, which map matrices to matrices by applying a vector-to-vector function to all eigenvalues/singular values of the underlying matrices. Spectral operators play a crucial role in the study of various applications involving matrices such as matrix optimization problems (MOPs) {that include semidefinite programming as one of the most important example classes}. In this paper, we will study more fundamental first- and second-order properties of spectral operators, including the Lipschitz continuity, $ρ$-order B(ouligand)-differentiability ($0<ρ\le 1$), $ρ$-order G-semismoothness ($0<ρ\le 1$), and characterization of generalized Jacobians.

math.OC↗

arXiv2018

Bayesian Optical Flow with Uncertainty Quantification

Optical flow refers to the visual motion observed between two consecutive images. Since the degree of freedom is typically much larger than the constraints imposed by the image observations, the straightforward formulation of optical flow as an inverse problem is ill-posed. Standard approaches to determine optical flow rely on formulating and solving an optimization problem that contains both a data fidelity term and a regularization term, the latter effectively resolves the otherwise ill-posedness of the inverse problem. In this work, we depart from the deterministic formalism, and instead treat optical flow as a statistical inverse problem. We discuss how a classical optical flow solution can be interpreted as a point estimate in this more general framework. The statistical approach, whose "solution" is a distribution of flow fields, which we refer to as Bayesian optical flow, allows not only "point" estimates (e.g., the computation of average flow field), but also statistical estimates (e.g., quantification of uncertainty) that are beyond any standard method for optical flow. As application, we benchmark Bayesian optical flow together with uncertainty quantification using several types of prescribed ground-truth flow fields and images.

stat.ML↗

arXiv2018

A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs

With the help of a logarithmic barrier augmented Lagrangian function, we can obtain closed-form solutions of slack variables of logarithmic-barrier problems of nonlinear programs. As a result, a two-parameter primal-dual nonlinear system is proposed, which corresponds to the Karush-Kuhn-Tucker point and the infeasible stationary point of nonlinear programs, respectively, as one of two parameters vanishes. Based on this distinctive system, we present a primal-dual interior-point method capable of rapidly detecting infeasibility of nonlinear programs. The method generates interior-point iterates without truncation of the step. It is proved that our method converges to a Karush-Kuhn-Tucker point of the original problem as the barrier parameter tends to zero. Otherwise, the scaling parameter tends to zero, and the method converges to either an infeasible stationary point or a singular stationary point of the original problem. Moreover, our method has the capability to rapidly detect the infeasibility of the problem. Under suitable conditions, not only the method can be superlinearly or quadratically convergent to the Karush-Kuhn-Tucker point as the original problem is feasible, but also it can be superlinearly or quadratically convergent to the infeasible stationary point when a problem is infeasible. Preliminary numerical results show that the method is efficient in solving some simple but hard problems and some standard test problems from the CUTE collection, where the superlinear convergence is demonstrated when we solve two infeasible problems and one well-posed feasible counterexample presented in the literature.

math.OC↗

arXiv2018

Anatomy of Leadership in Collective Behaviour

Understanding the mechanics behind the coordinated movement of mobile animal groups (collective motion) provides key insights into their biology and ecology, while also yielding algorithms for bio-inspired technologies and autonomous systems. It is becoming increasingly clear that many mobile animal groups are composed of heterogeneous individuals with differential levels and types of influence over group behaviors. The ability to infer this differential influence, or leadership, is critical to understanding group functioning in these collective animal systems. Due to the broad interpretation of leadership, many different measures and mathematical tools are used to describe and infer "leadership", e.g., position, causality, influence, information flow. But a key question remains: which, if any, of these concepts actually describes leadership? We argue that instead of asserting a single definition or notion of leadership, the complex interaction rules and dynamics typical of a group implies that leadership itself is not merely a binary classification (leader or follower), but rather, a complex combination of many different components. In this paper we develop an anatomy of leadership, identify several principle components and provide a general mathematical framework for discussing leadership. With the intricacies of this taxonomy in mind we present a set of leadership-oriented toy models that should be used as a proving ground for leadership inference methods going forward. We believe this multifaceted approach to leadership will enable a broader understanding of leadership and its inference from data in mobile animal groups and beyond.

cs.MA↗

arXiv2018

Geometric k-nearest neighbor estimation of entropy and mutual information

Nonparametric estimation of mutual information is used in a wide range of scientific problems to quantify dependence between variables. The k-nearest neighbor (knn) methods are consistent, and therefore expected to work well for large sample size. These methods use geometrically regular local volume elements. This practice allows maximum localization of the volume elements, but can also induce a bias due to a poor description of the local geometry of the underlying probability measure. We introduce a new class of knn estimators that we call geometric knn estimators (g-knn), which use more complex local volume elements to better model the local geometry of the probability measures. As an example of this class of estimators, we develop a g-knn estimator of entropy and mutual information based on elliptical volume elements, capturing the local stretching and compression common to a wide range of dynamical systems attractors. A series of numerical examples in which the thickness of the underlying distribution and the sample sizes are varied suggest that local geometry is a source of problems for knn methods such as the Kraskov-Stögbauer-Grassberger (KSG) estimator when local geometric effects cannot be removed by global preprocessing of the data. The g-knn method performs well despite the manipulation of the local geometry. In addition, the examples suggest that the g-knn estimators can be of particular relevance to applications in which the system is large, but data size is limited.

math.ST↗