arXiv subjects

Min Tang

Publications and source records attributed to Min Tang.

At least 91 records · Page 5Linked to original sources

arXiv2021

On kinetic and macroscopic models for the stripe formation in engineered bacterial populations

We study the well-posedness of the biological models with AHL-dependent cell mobility on engineered Escherichia coli populations. For the kinetic model proposed by Xue-Xue-Tang recently, the local existence for large initial data is proved first. Furthermore, the positivity and local conservation laws for density $ρ(t,x,z)$ and nutrient $n(t,x)$ with initial assumptions are justified. Based on these properties, it can be extended globally in time near the equilibrium $(0,0,0)$. Considering the asymptotic behaviors of faster response CheZ turnover rate (i.e.,$\varepsilon\rightarrow 0$), one formally derives an anisotropic diffusion engineered Escherichia coli populations model (in short, AD-EECP) for which we find a key extra a priori estimate to overcome the difficulties coming from the nonlinearity of the diffusion structure. The local well-posedness and the positivity and local conservation laws for density and nutrient of the AD-EECP are justified. Furthermore, the global existence around the steady state $(\varrho_a, h_a, 0)$ with $\varrho_a \in [0, Λ_b)$ is obtained.

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arXiv2021

Human Listening and Live Captioning: Multi-Task Training for Speech Enhancement

With the surge of online meetings, it has become more critical than ever to provide high-quality speech audio and live captioning under various noise conditions. However, most monaural speech enhancement (SE) models introduce processing artifacts and thus degrade the performance of downstream tasks, including automatic speech recognition (ASR). This paper proposes a multi-task training framework to make the SE models unharmful to ASR. Because most ASR training samples do not have corresponding clean signal references, we alternately perform two model update steps called SE-step and ASR-step. The SE-step uses clean and noisy signal pairs and a signal-based loss function. The ASR-step applies a pre-trained ASR model to training signals enhanced with the SE model. A cross-entropy loss between the ASR output and reference transcriptions is calculated to update the SE model parameters. Experimental results with realistic large-scale settings using ASR models trained on 75,000-hour data show that the proposed framework improves the word error rate for the SE output by 11.82% with little compromise in the SE quality. Performance analysis is also carried out by changing the ASR model, the data used for the ASR-step, and the schedule of the two update steps.

eess.AS↗

arXiv2021

Multi-scale GCN-assisted two-stage network for joint segmentation of retinal layers and disc in peripapillary OCT images

An accurate and automated tissue segmentation algorithm for retinal optical coherence tomography (OCT) images is crucial for the diagnosis of glaucoma. However, due to the presence of the optic disc, the anatomical structure of the peripapillary region of the retina is complicated and is challenging for segmentation. To address this issue, we developed a novel graph convolutional network (GCN)-assisted two-stage framework to simultaneously label the nine retinal layers and the optic disc. Specifically, a multi-scale global reasoning module is inserted between the encoder and decoder of a U-shape neural network to exploit anatomical prior knowledge and perform spatial reasoning. We conducted experiments on human peripapillary retinal OCT images. The Dice score of the proposed segmentation network is 0.820$\pm$0.001 and the pixel accuracy is 0.830$\pm$0.002, both of which outperform those from other state-of-the-art techniques.

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arXiv2020

P-Cloth: Interactive Complex Cloth Simulation on Multi-GPU Systems using Dynamic Matrix Assembly and Pipelined Implicit Integrators

We present a novel parallel algorithm for cloth simulation that exploits multiple GPUs for fast computation and the handling of very high resolution meshes. To accelerate implicit integration, we describe new parallel algorithms for sparse matrix-vector multiplication (SpMV) and for dynamic matrix assembly on a multi-GPU workstation. Our algorithms use a novel work queue generation scheme for a fat-tree GPU interconnect topology. Furthermore, we present a novel collision handling scheme that uses spatial hashing for discrete and continuous collision detection along with a non-linear impact zone solver. Our parallel schemes can distribute the computation and storage overhead among multiple GPUs and enable us to perform almost interactive simulation on complex cloth meshes, which can hardly be handled on a single GPU due to memory limitations. We have evaluated the performance with two multi-GPU workstations (with 4 and 8 GPUs, respectively) on cloth meshes with 0.5-1.65M triangles. Our approach can reliably handle the collisions and generate vivid wrinkles and folds at 2-5 fps, which is significantly faster than prior cloth simulation systems. We observe almost linear speedups with respect to the number of GPUs.

cs.GR↗

arXiv2020

On an inverse problem in additive number theory

For a set $A$, let $P(A)$ be the set of all finite subset sums of $A$. In this paper, for a sequence of integers $B=\{1<b_1<b_2<\cdots\}$ and $3b_1+5\leq b_2\leq 6b_1+10$, we determine the critical value for $b_3$ such that there exists an infinite sequence $A$ of positive integers for which $P(A)=\mathbb{N}\setminus B$. This result shows that we partially solve the problem of Fang and Fang [`On an inverse problem in additive number theory', Acta Math. Hungar. 158(2019), 36-39].

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arXiv2020

On a subset sums problem of Chen and Wu

For a set $A$, let $P(A)$ be the set of all finite subset sums of $A$. We prove that if a sequence $B=\{11\leq b_1<b_2<\cdots\}$ satisfies $b_2=3b_1+5$, $b_3=3b_2+2$ and $b_{n+1}=3b_n+4b_{n-1}$ for all $n\geq 3$, then there is a sequence of positive integers $A=\{a_1<a_2<\cdots\}$ such that $P(A)=\mathbb{N}\setminus B$. This result shows that the answer to the problem of Chen and Wu [`The inverse problem on subset sums', European. J. Combin. 34(2013), 841-845] is negative.

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arXiv2020

Hierarchical Optimization Time Integration for CFL-rate MPM Stepping

We propose Hierarchical Optimization Time Integration (HOT) for efficient implicit time-stepping of the Material Point Method (MPM) irrespective of simulated materials and conditions. HOT is an MPM-specialized hierarchical optimization algorithm that solves nonlinear time step problems for large-scale MPM systems near the CFL-limit. HOT provides convergent simulations "out-of-the-box" across widely varying materials and computational resolutions without parameter tuning. As an implicit MPM time stepper accelerated by a custom-designed Galerkin multigrid wrapped in a quasi-Newton solver, HOT is both highly parallelizable and robustly convergent. As we show in our analysis, HOT maintains consistent and efficient performance even as we grow stiffness, increase deformation, and vary materials over a wide range of finite strain, elastodynamic and plastic examples. Through careful benchmark ablation studies, we compare the effectiveness of HOT against seemingly plausible alternative combinations of MPM with standard multigrid and other Newton-Krylov models. We show how these alternative designs result in severe issues and poor performance. In contrast, HOT outperforms the existing state-of-the-art, heavily optimized implicit MPM codes with an up to 10x performance speedup across a wide range of challenging benchmark test simulations.

cs.GR↗

arXiv2019

End-to-end detection-segmentation network with ROI convolution

We propose an end-to-end neural network that improves the segmentation accuracy of fully convolutional networks by incorporating a localization unit. This network performs object localization first, which is then used as a cue to guide the training of the segmentation network. We test the proposed method on a segmentation task of small objects on a clinical dataset of ultrasound images. We show that by jointly learning for detection and segmentation, the proposed network is able to improve the segmentation accuracy compared to only learning for segmentation. Code is publicly available at https://github.com/vincentzhang/roi-fcn.

cs.CV↗

arXiv2019

Mathematical Modelling and Analysis of Fractional Diffusion Induced by Intracellular Noise

In this paper we use an individual-based model and its associated kinetic equation to study the generation of long jumps in the motion of E. coli. These models relate the run-and-tumble process to the intracellular reaction where the intrinsic noise plays a central role. Compared with the previous work in [13] in which the parametric assumptions are mainly for mathematical convenience and not well-suited for either numerical simulation or comparison with experimental results, our current paper make use of biologically meaningful pathways and tumbling kernels. Moreover, using the individual-based model we can now perform numerical simulations. Power-law decay of the run length, which corresponds to Levy-type motions, are observed in our numerical results. The particular decay rate agrees quantitatively with the analytical result. We also rigorously recover the fractional diffusion equation as the limit of the kinetic model.

math.AP↗

arXiv2019

Some inverse results of sumsets

Let $h\geq 2$ and $A=\{a_0,a_1,\ldots,a_{k-1}\}$ be a finite set of integers. It is well-known that $\left|hA\right|=hk-h+1$ if and only if $A$ is a $k$-term arithmetic progression. In this paper, we give some nontrivial inverse results of the sets $A$ with some extrema the cardinalities of $hA$.

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arXiv2019

Towards understanding the boundary propagation speeds in tumor growth models

At the continuous level, we consider two types of tumor growth models: the cell density model, which is based on the fluid mechanical construction, is more favorable for scientific interpretation and numerical simulations; and the free boundary model, as the incompressible limit of the former, is more tractable when investigating the boundary propagation. In this work, we aim to investigate the boundary propagation speeds in those models based on asymptotic analysis of the free boundary model and efficient numerical simulations of the cell density model. We derive, for the first time, some analytical solutions for the free boundary model with pressures jumps across the tumor boundary in multi-dimensions with finite tumor sizes. We further show that in the large radius limit, the analytical solutions to the free boundary model in one and multiple spatial dimensions converge to traveling wave solutions. The convergence rate in the propagation speeds are algebraic in multi-dimensions as opposed to the exponential convergence in 1D. We also propose an accurate front capturing numerical scheme for the cell density model, and extensive numerical tests are provided to verify the analytical findings.

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arXiv2019

Accurate front capturing asymptotic preserving scheme for nonlinear gray radiative transfer equation

We develop an asymptotic preserving scheme for the gray radiative transfer equation. Two asymptotic regimes are considered: one is a diffusive regime described by a nonlinear diffusion equation for the material temperature; the other is a free streaming regime with zero opacity. To alleviate the restriction on time step and capture the correct front propagation in the diffusion limit, an implicit treatment is crucial. However, this often involves a large-scale nonlinear iterative solver as the spatial and angular dimensions are coupled. Our idea is to introduce an auxiliary variable that leads to a ``redundant" system, which is then solved with a three-stage update: prediction, correction, and projection. The benefit of this approach is that the implicit system is local to each spatial element, independent of angular variable, and thus only requires a scalar Newton's solver. We also introduce a spatial discretization with a compact stencil based on even-odd decomposition. Our method preserves both the nonlinear diffusion limit with correct front propagation speed and the free streaming limit, with a hyperbolic CFL condition.

math.NA↗

arXiv2019

Multiple asymptotics of Kinetic Equations with Internal States

The run and tumble process is well established in order to describe the movement of bacteria in response to a chemical stimulus. However the relation between the tumbling rate and the internal state of bacteria is poorly understood. The present study aims at deriving models at the macroscopic scale from assumptions on the microscopic scales. In particular we are interested in comparisons between the stiffness of the response and the adaptation time. Depending on the asymptotics chosen both the standard Keller-Segel equation and the flux-limited Keller-Segel (FLKS) equation can appear. An interesting mathematical issue arises with a new type of equilibrium equation leading to solution with singularities.

math.AP↗

arXiv2018

On asymptotic bases and minimal asymptotic bases

Let $\mathbb{N}$ denote the set of all nonnegative integers and $A$ be a subset of $\mathbb{N}$. Let $h\geq2$ and let $r_h(A,n)=\sharp \{ (a_1,\ldots,a_h)\in A^{h}: a_1+\cdots+a_h=n\}.$ The set $A$ is called an asymptotic basis of order $h$ if $r_h(A,n)\geq 1$ for all sufficiently large integers $n$. An asymptotic basis $A$ of order $h$ is minimal if no proper subset of $A$ is an asymptotic basis of order $h$. Recently, Chen and Tang resoved a problem of Nathanson on minimal asymptotic bases of order $h$. In this paper, we generalized this result to $g$-adic representations.

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arXiv2018

The restricted sumsets in $\mathbb{Z}_n$

Let $h\geq 2$ be a positive integer. For any subset $\mathcal{A}\subset \mathbb{Z}_n$, let $h^{\wedge}\mathcal{A}$ be the set of the elements of $\mathbb{Z}_n$ which are sums of $h$ distinct elements of $\mathcal{A}$. In this paper, we obtain some new results on $4^{\wedge}\mathcal{A}$ and $5^{\wedge}\mathcal{A}$. For example, we show that if $|\mathcal{A}|\geq 0.4045n$ and $n$ is odd, then $4^{\wedge}\mathcal{A}=\mathbb{Z}_{n}$; Under some conditions, if $n$ is even and $|\mathcal{A}|$ is close to $n/4$, then $4^{\wedge}\mathcal{A}=\mathbb{Z}_{n}$.

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arXiv2018

Illumination-aware Faster R-CNN for Robust Multispectral Pedestrian Detection

Multispectral images of color-thermal pairs have shown more effective than a single color channel for pedestrian detection, especially under challenging illumination conditions. However, there is still a lack of studies on how to fuse the two modalities effectively. In this paper, we deeply compare six different convolutional network fusion architectures and analyse their adaptations, enabling a vanilla architecture to obtain detection performances comparable to the state-of-the-art results. Further, we discover that pedestrian detection confidences from color or thermal images are correlated with illumination conditions. With this in mind, we propose an Illumination-aware Faster R-CNN (IAF RCNN). Specifically, an Illumination-aware Network is introduced to give an illumination measure of the input image. Then we adaptively merge color and thermal sub-networks via a gate function defined over the illumination value. The experimental results on KAIST Multispectral Pedestrian Benchmark validate the effectiveness of the proposed IAF R-CNN.

cs.CV↗

arXiv2018

Multispectral Pedestrian Detection via Simultaneous Detection and Segmentation

Multispectral pedestrian detection has attracted increasing attention from the research community due to its crucial competence for many around-the-clock applications (e.g., video surveillance and autonomous driving), especially under insufficient illumination conditions. We create a human baseline over the KAIST dataset and reveal that there is still a large gap between current top detectors and human performance. To narrow this gap, we propose a network fusion architecture, which consists of a multispectral proposal network to generate pedestrian proposals, and a subsequent multispectral classification network to distinguish pedestrian instances from hard negatives. The unified network is learned by jointly optimizing pedestrian detection and semantic segmentation tasks. The final detections are obtained by integrating the outputs from different modalities as well as the two stages. The approach significantly outperforms state-of-the-art methods on the KAIST dataset while remain fast. Additionally, we contribute a sanitized version of training annotations for the KAIST dataset, and examine the effects caused by different kinds of annotation errors. Future research of this problem will benefit from the sanitized version which eliminates the interference of annotation errors.

cs.CV↗

arXiv2018

Analysis and computation of some tumor growth models with nutrient: from cell density models to free boundary dynamics

In this paper, we study the tumor growth equation along with various models for the nutrient component, including the \emph{in vitro} model and the \emph{in vivo} model. At the cell density level, the spatial availability of the tumor density $n$ is governed by the Darcy law via the pressure $p(n)=n^γ$. For finite $γ$, we prove some a priori estimates of the tumor growth model, such as boundedness of the nutrient density, and non-negativity and growth estimate of the tumor density. As $γ\rightarrow \infty$, the cell density models formally converge to Hele-Shaw flow models, which determine the free boundary dynamics of the tumor tissue in the incompressible limit. We derive several analytical solutions to the Hele-Shaw flow models, which serve as benchmark solutions to the geometric motion of tumor front propagation. Finally, we apply a conservative and positivity preserving numerical scheme to the cell density models, with numerical results verifying the link between cell density models and the free boundary dynamical models.

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