arXiv subjects

Lei Cao

Publications and source records attributed to Lei Cao.

At least 91 records · Page 5Linked to original sources

arXiv2022

Parallel Fourier Ptychography reconstruction

Fourier ptychography has attracted a wide range of focus for its ability of large space-bandwidth-produce, and quantative phase measurement. It is a typical computational imaging technique which refers to optimizing both the imaging hardware and reconstruction algorithms simultaneously. The data redundancy and inverse problem algorithms are the sources of FPM's excellent performance. But at the same time, this large amount of data processing and complex algorithms also greatly reduce the imaging speed. In this article, we propose a parallel Fourier ptychography reconstruction framework consisting of three levels of parallel computing parts and implemented it with both central processing unit (CPU) and compute unified device architecture (CUDA) platform. In the conventional FPM reconstruction framework, the sample image is divided into multiple sub-regions for separately processing because the illumination angles for different subregions are varied for the same LED and different subregions contain different defocus distances due to the non-planar distribution or non-ideal posture of biological sample. We first build a parallel computing sub-framework in spatial domain based on the above-mentioned characteristics. And then, by utilizing the sequential characteristics of different spectrum regions to update, a parallel computing sub-framework in the spectrum domain is carried out in our scheme. The feasibility of the proposed parallel FPM reconstruction framework is verified with different experimental results acquired with the system we built.

eess.IV↗

arXiv2022

Fourier ptychography multi-parameter neural network with composite physical priori optimization

Fourier ptychography microscopy(FP) is a recently developed computational imaging approach for microscopic super-resolution imaging. By turning on each light-emitting-diode (LED) located on different position on the LED array sequentially and acquiring the corresponding images that contain different spatial frequency components, high spatial resolution and quantitative phase imaging can be achieved in the case of large field-of-view. Nevertheless, FPM has high requirements for the system construction and data acquisition processes, such as precise LEDs position, accurate focusing and appropriate exposure time, which brings many limitations to its practical applications. In this paper, inspired by artificial neural network, we propose a Fourier ptychography multi-parameter neural network (FPMN) with composite physical prior optimization. A hybrid parameter determination strategy combining physical imaging model and data-driven network training is proposed to recover the multi layers of the network corresponding to different physical parameters, including sample complex function, system pupil function, defocus distance, LED array position deviation and illumination intensity fluctuation, etc. Among these parameters, LED array position deviation is recovered based on the features of brightfield to darkfield transition low-resolution images while the others are recovered in the process of training of the neural network. The feasibility and effectiveness of FPMN are verified through simulations and actual experiments. Therefore FPMN can evidently reduce the requirement for practical applications of FPM.

physics.optics↗

arXiv2020

Building and Using Personal Knowledge Graph to Improve Suicidal Ideation Detection on Social Media

A large number of individuals are suffering from suicidal ideation in the world. There are a number of causes behind why an individual might suffer from suicidal ideation. As the most popular platform for self-expression, emotion release, and personal interaction, individuals may exhibit a number of symptoms of suicidal ideation on social media. Nevertheless, challenges from both data and knowledge aspects remain as obstacles, constraining the social media-based detection performance. Data implicitness and sparsity make it difficult to discover the inner true intentions of individuals based on their posts. Inspired by psychological studies, we build and unify a high-level suicide-oriented knowledge graph with deep neural networks for suicidal ideation detection on social media. We further design a two-layered attention mechanism to explicitly reason and establish key risk factors to individual's suicidal ideation. The performance study on microblog and Reddit shows that: 1) with the constructed personal knowledge graph, the social media-based suicidal ideation detection can achieve over 93% accuracy; and 2) among the six categories of personal factors, post, personality, and experience are the top-3 key indicators. Under these categories, posted text, stress level, stress duration, posted image, and ruminant thinking contribute to one's suicidal ideation detection.

cs.CL↗

arXiv2020

Hierarchical Graph Matching Network for Graph Similarity Computation

Graph edit distance / similarity is widely used in many tasks, such as graph similarity search, binary function analysis, and graph clustering. However, computing the exact graph edit distance (GED) or maximum common subgraph (MCS) between two graphs is known to be NP-hard. In this paper, we propose the hierarchical graph matching network (HGMN), which learns to compute graph similarity from data. HGMN is motivated by the observation that two similar graphs should also be similar when they are compressed into more compact graphs. HGMN utilizes multiple stages of hierarchical clustering to organize a graph into successively more compact graphs. At each stage, the earth mover distance (EMD) is adopted to obtain a one-to-one mapping between the nodes in two graphs (on which graph similarity is to be computed), and a correlation matrix is also derived from the embeddings of the nodes in the two graphs. The correlation matrices from all stages are used as input for a convolutional neural network (CNN), which is trained to predict graph similarity by minimizing the mean squared error (MSE). Experimental evaluation on 4 datasets in different domains and 4 performance metrics shows that HGMN consistently outperforms existing baselines in the accuracy of graph similarity approximation.

cs.DB↗

arXiv2020

Pattern-Avoiding (0,1)-Matrices

We investigate pattern-avoiding (0,1)-matrices as generalizations of pattern-avoiding permutations. Our emphasis is on 123-avoiding and 321-avoiding patterns for which we obtain exact results as to the maximum number of 1's such matrices can have. We also give algorithms when carried out in all possible ways, construct all of the pattern-avoiding matrices of these two types.

math.CO↗

arXiv2019

Centrosymmetric Stochastic Matrices

We consider the convex set $Γ_{m,n}$ of $m\times n$ stochastic matrices and the convex set $Γ_{m,n}^π\subset Γ_{m,n}$ of $m\times n$ centrosymmetric stochastic matrices (stochastic matrices that are symmetric under rotation by 180 degrees). For $Γ_{m,n}$, we demonstrate a Birkhoff theorem for its extreme points and create a basis from certain $(0,1)$-matrices. For $Γ_{m,n}^π$, we characterize its extreme points and create bases, whose construction depends on the parity of $m$, using our basis construction for stochastic matrices. For each of $Γ_{m,n}$ and $Γ_{m,n}^π$, we further characterize their extreme points in terms of their associated bipartite graphs, we discuss a graph parameter called the fill and compute it for the various basis elements, and we examine the number of vertices of the faces of these sets. We provide examples illustrating the results throughout.

math.CO↗

arXiv2019

Latent Suicide Risk Detection on Microblog via Suicide-Oriented Word Embeddings and Layered Attention

Despite detection of suicidal ideation on social media has made great progress in recent years, people's implicitly and anti-real contrarily expressed posts still remain as an obstacle, constraining the detectors to acquire higher satisfactory performance. Enlightened by the hidden "tree holes" phenomenon on microblog, where people at suicide risk tend to disclose their inner real feelings and thoughts to the microblog space whose authors have committed suicide, we explore the use of tree holes to enhance microblog-based suicide risk detection from the following two perspectives. (1) We build suicide-oriented word embeddings based on tree hole contents to strength the sensibility of suicide-related lexicons and context based on tree hole contents. (2) A two-layered attention mechanism is deployed to grasp intermittently changing points from individual's open blog streams, revealing one's inner emotional world more or less. Our experimental results show that with suicide-oriented word embeddings and attention, microblog-based suicide risk detection can achieve over 91\% accuracy. A large-scale well-labelled suicide data set is also reported in the paper.

cs.CL↗

arXiv2019

A short note on Multilevel Toeplitz Matrices

Chien, Liu, Nakazato, and Tam proved that all n by n classical Toeplitz matrices (one-level Toeplitz matrices) are unitarily similar to complex symmetric matrices via two types of unitary matrices and the type of the unitary matrices only depends on the parity of n. In this paper, we extend their result to multilevel Toeplitz matrices that any multilevel Toeplitz matrix is unitarily similar to a complex symmetric matrix. We provide a method to construct the unitary matrices that uniformly turn any multilevel Toeplitz matrix to a complex symmetric matrix by taking tensor products of these two types of unitary matrices for one-level Toeplitz matrices according to the parity of each level of the multilevel Toeplitz matrices. In addition, we introduce a class of complex symmetric matrices that are unitarily similar to some p-level Toeplitz matrices.

math.FA↗

arXiv2019

Domain Wall Solitons Arising in Classical Gauge Field Theories

Domain wall solitons are basic constructs realizing phase transitions in various field-theoretical models and are solutions to some nonlinear ordinary differential equations descending from the corresponding full sets of governing equations in higher dimensions. In this paper, we present a series of domain wall solitons arising in several classical gauge field theory models. In the context of the Abelian gauge field theory, we unveil the surprising result that the solutions may explicitly be constructed, which enriches our knowledge on integrability of the planar Liouville type equations in their one-dimensional limits. In the context of the non-Abelian gauge field theory, we obtain some existence theorems for domain wall solutions arising in the electroweak type theories by developing some methods of calculus of variations formulated as direct and constrained minimization problems over a weighted Sobolev space.

math-ph↗

arXiv2019

Determination of AdS Monopole Wall via Minimization

In this note we solve a minimization problem arising in a recent work of Bolognesi and Tong on the determination of an AdS monopole wall. We show that the problem has a unique solution. Although the solution cannot be obtained explicitly, we show that it may practically be constructed via a shooting method for which the correct shooting slope is unique. We also obtain some energy estimates which allow an asymptotic explicit determination of the monopole wall in a large coupling parameter limit.

hep-th↗

arXiv2018

Analysis and Design of Serially Concatenated LDGM Codes

In this paper, we first present the asymptotic performance of serially concatenated low-density generator-matrix (SCLDGM) codes for binary input additive white Gaussian noise channels using discretized density evolution (DDE). We then provide a necessary condition for the successful decoding of these codes. The error-floor analysis along with the lower bound formulas for both LDGM and SCLDGM codes are also provided and verified. We further show that by concatenating inner LDGM codes with a high-rate outer LDPC code instead of concatenating two LDGM codes as in SCLDGM codes, good codes without error floors can be constructed. Finally, with an efficient DDE-based optimization approach that utilizes the necessary condition for the successful decoding, we construct optimized SCLDGM codes that approach the Shannon limit. The improved performance of our optimized SCLDGM codes is demonstrated through both asymptotic and simulation results.

cs.IT↗

arXiv2018

DCSM Protocol for Content Transfer in Deep Space Network

To maximize file transfer from space vehicles to the Earth, we propose a new space-to-earth content transfer protocol that combines turbo codes, RaptorQ codes, real-time channel prediction, and dynamic code-rate selection. The protocol features a practical signal-to-noise ratio prediction model that facilitates periodic adjustment of the turbo encoder to achieve adaptive rate transmission. Our simulation results indicate that an increase of about 20% in file transfer rate is achievable using the proposed protocol.

eess.SP↗

arXiv2018

Partitions of the polytope of Doubly Substochastic Matrices

In this paper, we provide three different ways to partition the polytope of doubly substochastic matrices into subpolytopes via the prescribed row and column sums, the sum of all elements and the sub-defect respectively. Then we characterize the extreme points of each type of convex subpolytopes. The relations of the extreme points of the subpolytopes in the three partitions are also given.

math.CO↗

arXiv2018

A short note on doubly substochastic analog of Birkhoff's theorem

Let B be an n by n doubly substochastic matrix. We show that B can be written as a convex combination of no more than σ(B)+t subpermutation matrices, where σ(B) is the number of nonzero elements in B and t is the number of fully indecomposable components of B^{comp}, the minimal doubly stochastic completion of B obtained by a specific way.

math.CO↗

arXiv2017

On the maximum of the permanent of (I-A)

Let A be an n by n doubly substochastic matrix and denote σ(A) the sum of all elements of A. In this paper we give the upper bound of the permanent of (I-A) with respect to n and σ(A).

math.CO↗

arXiv2017

Real Zero Polynomials and A. Horn's Problem

A. Horn's problem concerns find two self adjoint matrices A, B, so that A, B, and A+B have prescribed spectrum. In this paper, we show how it connects to an interpolation problem for two variable real zero polynomials and a tracial moment problem. In addition, we outline an algorithm to construct a pair (A,B).

math.SP↗

arXiv2017

Symmetric, Hankel-symmetric, and Centrosymmetric Doubly Stochastic Matrices

We investigate convex polytopes of doubly stochastic matrices having special structures: symmetric, Hankel symmetric, centrosymmetric, and both symmetric and Hankel symmetric. We determine dimensions of these polytopes and classify their extreme points. We also determine a basis of the real vector spaces generated by permutation matrices with these special structures.

math.CO↗

arXiv2016

Partitions of Equiangular Tight Frames

We present a new efficient algorithm to construct partitions of a special class of equiangular tight frames (ETFs) that satisfy the operator norm bound established by a theorem of Marcus, Spielman, and Srivastava (MSS), which they proved as a corollary yields a positive solution to the Kadison-Singer problem. In particular, we prove that certain diagonal partitions of complex ETFs generated by recursive skew-symmetric conference matrices yield a refinement of the MSS bound. Moreover, we prove that all partitions of ETFs whose largest subset has cardinality three or less also satisfy the MSS bound.

math.FA↗