arXiv subjects

Min Tang

Publications and source records attributed to Min Tang.

At least 91 records · Page 5Linked to original sources

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.

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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.

math.AP↗

arXiv2017

On a problem of Nathanson

A set $A$ of nonnegative integers is an asymptotic basis of order $h$ if every sufficiently large integer can be represented as the sum of $h$ integers (not necessarily distinct) of $A$. An asymptotic basis $A$ of order $h$ is minimal if no proper subset of $A$ is an asymptotic basis of order $h$. In this paper, we resolve a problem of Nathanson on minimal asymptotic bases of order $h$.

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arXiv2017

Segmentation-by-Detection: A Cascade Network for Volumetric Medical Image Segmentation

We propose an attention mechanism for 3D medical image segmentation. The method, named segmentation-by-detection, is a cascade of a detection module followed by a segmentation module. The detection module enables a region of interest to come to attention and produces a set of object region candidates which are further used as an attention model. Rather than dealing with the entire volume, the segmentation module distills the information from the potential region. This scheme is an efficient solution for volumetric data as it reduces the influence of the surrounding noise which is especially important for medical data with low signal-to-noise ratio. Experimental results on 3D ultrasound data of the femoral head shows superiority of the proposed method when compared with a standard fully convolutional network like the U-Net.

cs.CV↗

arXiv2017

A deep level set method for image segmentation

This paper proposes a novel image segmentation approachthat integrates fully convolutional networks (FCNs) with a level setmodel. Compared with a FCN, the integrated method can incorporatesmoothing and prior information to achieve an accurate segmentation.Furthermore, different than using the level set model as a post-processingtool, we integrate it into the training phase to fine-tune the FCN. Thisallows the use of unlabeled data during training in a semi-supervisedsetting. Using two types of medical imaging data (liver CT and left ven-tricle MRI data), we show that the integrated method achieves goodperformance even when little training data is available, outperformingthe FCN or the level set model alone.

cs.CV↗

arXiv2017

The fractional diffusion limit of a kinetic model with biochemical pathway

Kinetic-transport equations that take into account the intra-cellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathematical studies have shown their interest and their relations to more standard models. Macroscopic equations of Keller-Segel type have been derived using parabolic scaling. Due to the randomness of receptor methylation or intra-cellular chemical reactions, noise occurs in the signaling pathways and affects the tumbling rate. Then, comes the question to understand the role of an internal noise on the behavior of the full population. In this paper we consider a kinetic model for chemotaxis which includes biochemical pathway with noises. We show that under proper scaling and conditions on the tumbling frequency as well as the form of noise, fractional diffusion can arise in the macroscopic limits of the kinetic equation. This gives a new mathematical theory about how long jumps can be due to the internal noise of the bacteria.

math.AP↗

arXiv2017

An accurate front capturing scheme for tumor growth models with a free boundary limit

We consider a class of tumor growth models under the combined effects of density-dependent pressure and cell multiplication, with a free boundary model as its singular limit when the pressure-density relationship becomes highly nonlinear. In particular, the constitutive law connecting pressure $p$ and density $ρ$ is $p(ρ)=\frac{m}{m-1} ρ^{m-1}$, and when $m \gg 1$, the cell density $ρ$ may evolve its support due to a pressure-driven geometric motion with sharp interface along the boundary of its support. The nonlinearity and degeneracy in the diffusion bring great challenges in numerical simulations, let alone the capturing of the singular free boundary limit. Prior to the present paper, there is lack of standard mechanism to numerically capture the front propagation speed as $m\gg 1$. In this paper, we develope a numerical scheme based on a novel prediction-correction reformulation that can accurately approximate the front propagation even when the nonlinearity is extremely strong. We show that the semi-discrete scheme naturally connects to the free boundary limit equation as $m \rightarrow \infty$, and with proper spacial discretization, the fully discrete scheme has improved stability, preserves positivity, and implements without nonlinear solvers. Finally, extensive numerical examples in both one and two dimensions are provided to verify the claimed properties and showcase good performance in various applications.

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