arXiv subjects

Cheng Zheng

Publications and source records attributed to Cheng Zheng.

At least 37 records · Page 2Linked to original sources

arXiv2023

Neural Lithography: Close the Design-to-Manufacturing Gap in Computational Optics with a 'Real2Sim' Learned Photolithography Simulator

We introduce neural lithography to address the 'design-to-manufacturing' gap in computational optics. Computational optics with large design degrees of freedom enable advanced functionalities and performance beyond traditional optics. However, the existing design approaches often overlook the numerical modeling of the manufacturing process, which can result in significant performance deviation between the design and the fabricated optics. To bridge this gap, we, for the first time, propose a fully differentiable design framework that integrates a pre-trained photolithography simulator into the model-based optical design loop. Leveraging a blend of physics-informed modeling and data-driven training using experimentally collected datasets, our photolithography simulator serves as a regularizer on fabrication feasibility during design, compensating for structure discrepancies introduced in the lithography process. We demonstrate the effectiveness of our approach through two typical tasks in computational optics, where we design and fabricate a holographic optical element (HOE) and a multi-level diffractive lens (MDL) using a two-photon lithography system, showcasing improved optical performance on the task-specific metrics.

physics.optics↗

arXiv2023

Learning to Read Analog Gauges from Synthetic Data

Manually reading and logging gauge data is time inefficient, and the effort increases according to the number of gauges available. We present a computer vision pipeline that automates the reading of analog gauges. We propose a two-stage CNN pipeline that identifies the key structural components of an analog gauge and outputs an angular reading. To facilitate the training of our approach, a synthetic dataset is generated thus obtaining a set of realistic analog gauges with their corresponding annotation. To validate our proposal, an additional real-world dataset was collected with 4.813 manually curated images. When compared against state-of-the-art methodologies, our method shows a significant improvement of 4.55 in the average error, which is a 52% relative improvement. The resources for this project will be made available at: https://github.com/fuankarion/automatic-gauge-reading.

cs.CV↗

arXiv2023

Quantification of follow-up time in oncology clinical trials with a time-to-event endpoint: Asking the right questions

For the analysis of a time-to-event endpoint in a single-arm or randomized clinical trial it is generally perceived that interpretation of a given estimate of the survival function, or the comparison between two groups, hinges on some quantification of the amount of follow-up. Typically, a median of some loosely defined quantity is reported. However, whatever median is reported, is typically not answering the question(s) trialists actually have in terms of follow-up quantification. In this paper, inspired by the estimand framework, we formulate a comprehensive list of relevant scientific questions that trialists have when reporting time-to-event data. We illustrate how these questions should be answered, and that reference to an unclearly defined follow-up quantity is not needed at all. In drug development, key decisions are made based on randomized controlled trials, and we therefore also discuss relevant scientific questions not only when looking at a time-to-event endpoint in one group, but also for comparisons. We find that different thinking about some of the relevant scientific questions around follow-up is required depending on whether a proportional hazards assumption can be made or other patterns of survival functions are anticipated, e.g. delayed separation, crossing survival functions, or the potential for cure. We conclude the paper with practical recommendations.

stat.ME↗

arXiv2023

A Simulation-free Group Sequential Design with Max-combo Tests in the Presence of Non-proportional Hazards

Non-proportional hazards (NPH) have been observed recently in many immuno-oncology clinical trials. Weighted log-rank tests (WLRT) with suitably chosen weights can be used to improve the power of detecting the difference of the two survival curves in the presence of NPH. However, it is not easy to choose a proper WLRT in practice when both robustness and efficiency are considered. A versatile maxcombo test was proposed to achieve the balance of robustness and efficiency and has received increasing attentions in both methodology development and application. However, survival trials often warrant interim analyses due to its high cost and long duration. The integration and application of maxcombo tests in interim analyses often require extensive simulation studies. In this paper, we propose a simulation-free approach for group sequential design with maxcombo test in survival trials. The simulation results support that the proposed approaches successfully control both the type I error rate and offer great accuracy and flexibility in estimating sample sizes, at the expense of light computation burden. Notably, our methods display a strong robustness towards various model misspecifications, and have been implemented in an R package for free access online.

stat.ME↗

arXiv2022

On the density of some sparse horocycles

Let $Γ$ be a non-uniform lattice in $\operatorname{PSL}(2,\mathbb R)$. In this note, we show that there exists a constant $γ_0>0$ such that for any $0<γ<γ_0$, any one-parametrer unipotent subgroup $\{u(t)\}_{t\in\mathbb R}$ and any $p\in\operatorname{PSL}(2,\mathbb R)/Γ$ which is not $u(t)$-periodic, the orbit $\{u(n^{1+γ})p:n\in\mathbb N\}$ is dense in $\operatorname{PSL}(2,\mathbb R)/Γ$. We also prove that there exists $N\in\mathbb N$ such that for the set $Ω(N)$ of $N$-almost primes, and for any $p\in\operatorname{PSL}(2,\mathbb R)/Γ$ which is not $u(t)$-periodic, the orbit $\{u(x)p:x\inΩ(N)\}$ is dense in $\operatorname{PSL}(2,\mathbb R)/Γ$.

math.DS↗

arXiv2022

A shrinking-target problem in the space of unimodular lattices in the three dimensional Euclidean space

In this paper, we study the shrinking-target problem with target at infinity induced by the injectivity radius function under the action of a regular diagonalizable flow on $\operatorname{SL}_3(\mathbb R)/\operatorname{SL}_3(\mathbb Z)$. In particular, we establish an explicit formula for the Hausdorff dimension of the subset of points $p$ whose orbit approaches the cusp infinitely often with a rate $γ\geq0$.

math.DS↗

arXiv2022

DEEP$^2$: Deep Learning Powered De-scattering with Excitation Patterning

Limited throughput is a key challenge in in-vivo deep-tissue imaging using nonlinear optical microscopy. Point scanning multiphoton microscopy, the current gold standard, is slow especially compared to the wide-field imaging modalities used for optically cleared or thin specimens. We recently introduced 'De-scattering with Excitation Patterning or DEEP', as a widefield alternative to point-scanning geometries. Using patterned multiphoton excitation, DEEP encodes spatial information inside tissue before scattering. However, to de-scatter at typical depths, hundreds of such patterned excitations are needed. In this work, we present DEEP$^2$, a deep learning based model, that can de-scatter images from just tens of patterned excitations instead of hundreds. Consequently, we improve DEEP's throughput by almost an order of magnitude. We demonstrate our method in multiple numerical and physical experiments including in-vivo cortical vasculature imaging up to four scattering lengths deep, in alive mice.

eess.IV↗

arXiv2022

FDR Controlled Multiple Testing for Union Null Hypotheses: A Knockoff-based Approach

False discovery rate (FDR) controlling procedures provide important statistical guarantees for the replicability in signal identification based on multiple hypotheses testing. In many fields of study, FDR controlling procedures are used in high-dimensional (HD) analyses to discover features that are truly associated with the outcome. In some recent applications, data on the same set of candidate features are independently collected in multiple different studies. For example, gene expression data are collected at different facilities and with different cohorts, to identify the genetic biomarkers of multiple types of cancers. These studies provide us opportunities to identify signals by considering information from different sources (with potential heterogeneity) jointly. This paper is about how to provide FDR control guarantees for the tests of union null hypotheses of conditional independence. We present a knockoff-based variable selection method (\textit{Simultaneous knockoffs}) to identify mutual signals from multiple independent data sets, providing exact FDR control guarantees under finite sample settings. This method can work with very general model settings and test statistics. We demonstrate the performance of this method with extensive numerical studies and two real data examples.

stat.ME↗

arXiv2022

Translates of S-arithmetic orbits and applications

We prove that certain sequences of periodic orbits of the diagonal group in the space of lattices equidistribute. As an application we obtain new information regarding the sequence of best approximations to certain vectors with algebraic coordinates. In order to prove these results we generalize the seminal work of Eskin Mozes and Shah about the equidistribution of translates of periodic measures from the real case to the S-arithmetic case.

math.DS↗

arXiv2022

Learning Scene Flow in 3D Point Clouds with Noisy Pseudo Labels

We propose a novel scene flow method that captures 3D motions from point clouds without relying on ground-truth scene flow annotations. Due to the irregularity and sparsity of point clouds, it is expensive and time-consuming to acquire ground-truth scene flow annotations. Some state-of-the-art approaches train scene flow networks in a self-supervised learning manner via approximating pseudo scene flow labels from point clouds. However, these methods fail to achieve the performance level of fully supervised methods, due to the limitations of point cloud such as sparsity and lacking color information. To provide an alternative, we propose a novel approach that utilizes monocular RGB images and point clouds to generate pseudo scene flow labels for training scene flow networks. Our pseudo label generation module infers pseudo scene labels for point clouds by jointly leveraging rich appearance information in monocular images and geometric information of point clouds. To further reduce the negative effect of noisy pseudo labels on the training, we propose a noisy-label-aware training scheme by exploiting the geometric relations of points. Experiment results show that our method not only outperforms state-of-the-art self-supervised approaches, but also outperforms some supervised approaches that use accurate ground-truth flows.

cs.CV↗

arXiv2022

SCTN: Sparse Convolution-Transformer Network for Scene Flow Estimation

We propose a novel scene flow estimation approach to capture and infer 3D motions from point clouds. Estimating 3D motions for point clouds is challenging, since a point cloud is unordered and its density is significantly non-uniform. Such unstructured data poses difficulties in matching corresponding points between point clouds, leading to inaccurate flow estimation. We propose a novel architecture named Sparse Convolution-Transformer Network (SCTN) that equips the sparse convolution with the transformer. Specifically, by leveraging the sparse convolution, SCTN transfers irregular point cloud into locally consistent flow features for estimating continuous and consistent motions within an object/local object part. We further propose to explicitly learn point relations using a point transformer module, different from exiting methods. We show that the learned relation-based contextual information is rich and helpful for matching corresponding points, benefiting scene flow estimation. In addition, a novel loss function is proposed to adaptively encourage flow consistency according to feature similarity. Extensive experiments demonstrate that our proposed approach achieves a new state of the art in scene flow estimation. Our approach achieves an error of 0.038 and 0.037 (EPE3D) on FlyingThings3D and KITTI Scene Flow respectively, which significantly outperforms previous methods by large margins.

cs.CV↗

arXiv2021

CoRGi: Content-Rich Graph Neural Networks with Attention

Graph representations of a target domain often project it to a set of entities (nodes) and their relations (edges). However, such projections often miss important and rich information. For example, in graph representations used in missing value imputation, items - represented as nodes - may contain rich textual information. However, when processing graphs with graph neural networks (GNN), such information is either ignored or summarized into a single vector representation used to initialize the GNN. Towards addressing this, we present CoRGi, a GNN that considers the rich data within nodes in the context of their neighbors. This is achieved by endowing CoRGi's message passing with a personalized attention mechanism over the content of each node. This way, CoRGi assigns user-item-specific attention scores with respect to the words that appear in an item's content. We evaluate CoRGi on two edge-value prediction tasks and show that CoRGi is better at making edge-value predictions over existing methods, especially on sparse regions of the graph.

cs.LG↗

arXiv2021

On High Dimensional Covariate Adjustment for Estimating Causal Effects in Randomized Trials with Survival Outcomes

The purpose of this work is to improve the efficiency in estimating the average causal effect (ACE) on the survival scale where right-censoring exists and high-dimensional covariate information is available. We propose new estimators using regularized survival regression and survival random forests (SRF) to make the adjustment for the high dimensional covariates to improve efficiency. We study the behavior of the adjusted estimator under mild assumptions and show theoretical guarantees that the proposed estimators are more efficient than the unadjusted ones asymptotically when using SRF for adjustment. In addition, these adjusted estimators are $\sqrt{n}$- consistent and asymptotically normally distributed. The finite sample behavior of our methods are studied by simulation, and the results are in agreement with the theoretical results. We also illustrate our methods by analyzing the real data from transplant research to identify the relative effectiveness of identical sibling donors compared to unrelated donors with the adjustment of cytogenetic abnormalities.

stat.ME↗

arXiv2021

Superconducting FeSe monolayer with milli-electron volt Fermi energy

Iron selenide (FeSe) is an iron-based superconductor which shows unique properties, including strongly anisotropic superconducting gap, paramagnetism in undoped compound and extremely small Fermi pocket size. In this work, we demonstrate that the sizes of electron and hole pockets in FeSe monolayer become much smaller than those in bulk. The Fermi energy is in the order of a few meV and can be fine-tuned by the thickness of graphene layers underneath. Despite the low carrier density, the FeSe monolayers grown on trilayer or multi-layer graphene are superconducting. The superconducting gap size is sensitive to the Fermi energy of the hole band. Remarkably, the FeSe monolayer provides the opportunity to study the physics in the crossover regime where the Fermi energy and superconducting gap are comparable to each other.

cond-mat.supr-con↗

arXiv2020

Nonsingular Block Graphs: An Open Problem

A block graph is a graph in which every block is a complete graph. Let $G$ be a block graph and let $A(G)$ be its (0,1)-adjacency matrix. Graph $G$ is called nonsingular (singular) if $A(G)$ is nonsingular (singular). An interesting open problem, proposed in 2013 by Bapat and Roy, is to characterize nonsingular block graphs. In this article, we present some classes of nonsingular and singular block graphs and related conjectures.

cs.DM↗

arXiv2019

On Data Enriched Logistic Regression

Biomedical researchers usually study the effects of certain exposures on disease risks among a well-defined population. To achieve this goal, the gold standard is to design a trial with an appropriate sample from that population. Due to the high cost of such trials, usually the sample size collected is limited and is not enough to accurately estimate some exposures' effect. In this paper, we discuss how to leverage the information from external `big data' (data with much larger sample size) to improve the estimation accuracy at the risk of introducing small bias. We proposed a family of weighted estimators to balance the bias increase and variance reduction when including the big data. We connect our proposed estimator to the established penalized regression estimators. We derive the optimal weights using both second order and higher order asymptotic expansions. Using extensive simulation studies, we showed that the improvement in terms of mean square error (MSE) for the regression coefficient can be substantial even with finite sample sizes and our weighted method outperformed the existing methods such as penalized regression and James Stein's approach. Also we provide theoretical guarantee that the proposed estimators will never lead to asymptotic MSE larger than the maximum likelihood estimator using small data only in general. We applied our proposed methods to the Asia Cohort Consortium China cohort data to estimate the relationships between age, BMI, smoking, alcohol use and mortality.

stat.AP↗

arXiv2019

A Shrinking Target Problem with Target at Infinity in Rank One Homogeneous Spaces

In this paper, we give a definition of Diophantine points of type $γ$ for $γ\geq0$ in a homogeneous space $G/Γ$, and compute the Hausdorff dimension of the subset of points which are not Diophantine of type $γ$ when $G$ is a semisimple Lie group of real rank one. We also deduce a Jarník-Besicovitch Theorem on Diophantine approximation in Heisenberg groups.

math.DS↗

arXiv2019

Nonsingular (Vertex-Weighted) Block Graphs

A graph $G$ is \emph{nonsingular (singular)} if its adjacency matrix $A(G)$ is nonsingular (singular). In this article, we consider the nonsingularity of block graphs, i.e., graphs in which every block is a clique. Extending the problem, we characterize nonsingular vertex-weighted block graphs in terms of reduced vertex-weighted graphs resulting after successive deletion and contraction of pendant blocks. Special cases where nonsingularity of block graphs may be directly determined are discussed.

cs.DM↗