Li Ma, Qian Wang, Ulf-G. Meißner
During the last decades, numerous exotic states which cannot be explained by the conventional quark model have been observed in experiment. Some of them can be understood as two-body hadronic molecules, such as the famous $X(3872)$, analogous to deuteron in nuclear physics. Along the same line, the existence of the triton leaves an open question whether there is a bound state formed by three hadrons. Since, for a given potential, a system with large reduced masses is more easier to form a bound state, we study the $BBB^{\ast}$ system with the one-pion exchange potential as an exploratory step by solving the three-body Schrödinger Equation. We predict that a tri-meson molecular state for the $BBB^{\ast}$ system is probably existent as long as the molecular states of its two-body subsystem $BB^*$ exist.
Mao Li, Margaret H. Frank, Zoë Migicovsky
Colour patterning contributes to important plant traits that influence ecological interactions, horticultural breeding, and agricultural performance. High-throughput phenotyping of colour is valuable for understanding plant biology and selecting for traits related to colour during plant breeding. Here we present ColourQuant, an automated high-throughput pipeline that allows users to extract colour phenotypes from images. This pipeline includes methods for colour phenotyping using mean pixel values, Gaussian density estimator of Lab colour, and the analysis of shape-independent colour patterning by circular deformation.
Mao Li
In this paper we construct the Poincare line bundle for the stack of Higgs bundles on smooth projective curves and show that it induces a fully-faithful Fourier-Mukai transform on the category of quasi-coherent sheaves.
Jialiang Mao, Li Ma
Studying the human microbiome has gained substantial interest in recent years, and a common task in the analysis of these data is to cluster microbiome compositions into subtypes. This subdivision of samples into subgroups serves as an intermediary step in achieving personalized diagnosis and treatment. In applying existing clustering methods to modern microbiome studies including the American Gut Project (AGP) data, we found that this seemingly standard task, however, is very challenging in the microbiome composition context due to several key features of such data. Standard distance-based clustering algorithms generally do not produce reliable results as they do not take into account the heterogeneity of the cross-sample variability among the bacterial taxa, while existing model-based approaches do not allow sufficient flexibility for the identification of complex within-cluster variation from cross-cluster variation. Direct applications of such methods generally lead to overly dispersed clusters in the AGP data and such phenomenon is common for other microbiome data. To overcome these challenges, we introduce Dirichlet-tree multinomial mixtures (DTMM) as a Bayesian generative model for clustering amplicon sequencing data in microbiome studies. DTMM models the microbiome population with a mixture of Dirichlet-tree kernels that utilizes the phylogenetic tree to offer a more flexible covariance structure in characterizing within-cluster variation, and it provides a means for identifying a subset of signature taxa that distinguish the clusters. We perform extensive simulation studies to evaluate the performance of DTMM and compare it to state-of-the-art model-based and distance-based clustering methods in the microbiome context. Finally, we report a case study on the fecal data from the AGP to identify compositional clusters among individuals with inflammatory bowel disease and diabetes.
Shai Gorsky, Cliburn Chan, Li Ma
Flow cytometry (FCM) is the standard multi-parameter assay for measuring single cell phenotype and functionality. It is commonly used for quantifying the relative frequencies of cell subsets in blood and disaggregated tissues. A typical analysis of FCM data involves cell classification---that is, the identification of cell subgroups in the sample---and comparisons of the cell subgroups across samples or conditions. While modern experiments often necessitate the collection and processing of samples in multiple batches, analysis of FCM data across batches is challenging because differences across samples may occur due to either true biological variation or technical reasons such as antibody lot effects or instrument optics across batches. Thus a critical step in comparative analyses of multi-sample FCM data---yet missing in existing automated methods for analyzing such data---is cross-sample calibration, whose goal is to align corresponding cell subsets across multiple samples in the presence of technical variations, so that biological variations can be meaningfully compared. We introduce a Bayesian nonparametric hierarchical modeling approach for accomplishing both calibration and cell classification simultaneously in a unified probabilistic manner. Three important features of our method make it particularly effective for analyzing multi-sample FCM data: a nonparametric mixture avoids prespecifying the number of cell clusters; a hierarchical skew normal kernel that allows flexibility in the shapes of the cell subsets and cross-sample variation in their locations; and finally the "coarsening" strategy makes inference robust to departures from the model such as heavy-tailness not captured by the skew normal kernels. We demonstrate the merits of our approach in simulated examples and carry out a case study in the analysis of two multi-sample FCM data sets.
Patrick LeBlanc, Li Ma
Mixed-membership (MM) models such as Latent Dirichlet Allocation (LDA) have been applied to microbiome compositional data to identify latent subcommunities of microbial species. These subcommunities are informative for understanding the biological interplay of microbes and for predicting health outcomes. However, microbiome compositions typically display substantial cross-sample heterogeneities in subcommunity compositions -- that is, the variability in the proportions of microbes in shared subcommunities across samples -- which is not accounted for in prior analyses. As a result, LDA can produce inference which is highly sensitive to the specification of the number of subcommunities and often divides a single subcommunity into multiple artificial ones. To address this limitation, we incorporate the logistic-tree normal (LTN) model into LDA to form a new MM model. This model allows cross-sample variation in the composition of each subcommunity around some "centroid" composition that defines the subcommunity. Incorporation of auxiliary Pólya-Gamma variables enables a computationally efficient collapsed blocked Gibbs sampler to carry out Bayesian inference under this model. By accounting for such heterogeneity, our new model restores the robustness of the inference in the specification of the number of subcommunities and allows meaningful subcommunities to be identified.
Shai Gorsky, Li Ma
Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample size, making it difficult to apply them to massive data. Moreover, resampling is usually necessary to evaluate the statistical significance of the resulting test statistics at finite sample sizes, further worsening the computational burden. We introduce a scalable, resampling-free approach to testing the independence between two random vectors by breaking down the task into simple univariate tests of independence on a collection of 2x2 contingency tables constructed through sequential coarse-to-fine discretization of the sample space, transforming the inference task into a multiple testing problem that can be completed with almost linear complexity with respect to the sample size. To address increasing dimensionality, we introduce a coarse-to-fine sequential adaptive procedure that exploits the spatial features of dependency structures to more effectively examine the sample space. We derive a finite-sample theory that guarantees the inferential validity of our adaptive procedure at any given sample size. In particular, we show that our approach can achieve strong control of the family-wise error rate without resampling or large-sample approximation. We demonstrate the substantial computational advantage of the procedure in comparison to existing approaches as well as its decent statistical power under various dependency scenarios through an extensive simulation study, and illustrate how the divide-and-conquer nature of the procedure can be exploited to not just test independence but to learn the nature of the underlying dependency. Finally, we demonstrate the use of our method through analyzing a large data set from a flow cytometry experiment.
Li Ma, Weidong Bao, Xiaomin Zhu, Meng Wu, Yuan Wang, Yunxiang Ling, Wen Zhou
Flocking model has been widely used to control robotic swarm. However, with the increasing scalability, there exist complex conflicts for robotic swarm in autonomous navigation, brought by internal pattern maintenance, external environment changes, and target area orientation, which results in poor stability and adaptability. Hence, optimizing the flocking model for robotic swarm in autonomous navigation is an important and meaningful research domain.
Li Ma
In this paper, we study the existence of complete Yamabe metric with zero scalar curvature on an n-dimensional complete Riemannian manifold $(M,g_0)$, $n\geq 3$. Under suitable conditions about the initial metric, we show that there is a global fine solution to the Yamabe flow. The interesting point here is that we have no curvature assumption about the initial metric. We show that on an n-dimensional complete Riemannian manifold $(M,g_0)$ with non-negative Ricci curvature, $n\geq 3$, the Yamabe flow enjoys the local $L^1$-stability property from the view-point of the porous media equation. Complete Yamabe metrics with zero scalar curvature on an n-dimensional Riemannian model space are also discussed.
Li Ma
In this paper we study the gradient estimate for positive solutions of Schrodinger equations on locally finite graph. Then we derive Harnack's inequality for positive solutions of the Schrodinger equations. We also set up some results about Green functions of the Laplacian equation on locally finite graph. Interesting properties of Schrodinger equation are derived.
Li Ma, X. Y. Wang
In this paper, we study the schrodinger equation and wave equation with the Dirichlet boundary condition on a connected finite graph. The explicit expressions for solutions are given and the energy conservations are derived. Applications to the corresponding nonlinear problems are indicated.
Li Ma
In this paper, we consider the generalized lambda constant and the existence of ground states of the generalized Perelman's W-functional from a variational formulation. One result is concerned with the estimation of the generalized $λ$ constant. The other results are about the existence of ground states of generalized $F$-functional and W-functional both on a complete non-compact Riemannian manifold $(M,g)$ with positive injectivity radius and with Ricci curvature bounded from below. Our main results are Theorems 2,3 and 7. For the existence of the ground states we use Lions' concentration-compactness method.
Jiaojiao Li, Li Ma
In this paper, we study the finite time blowup of the generalized Euler ODE in the matrix geometry. We can extend Sullivan's result which is about the finite time blowup result of initial invertible linear operators to singular linear operators. we can give a complete answer to the question of Sullivan in the case when the initial matrix A is symmetric in the finite dimensional vector space W. Some open questions are proposed in the last part of the paper.
Li Ma, Jialiang Mao
We introduce a method---called Fisher exact scanning (FES)---for testing and identifying variable dependency that generalizes Fisher's exact test on $2\times 2$ contingency tables to $R\times C$ contingency tables and continuous sample spaces. FES proceeds through scanning over the sample space using windows in the form of $2\times 2$ tables of various sizes, and on each window completing a Fisher's exact test. Based on a factorization of Fisher's multivariate hypergeometric (MHG) likelihood into the product of the univariate hypergeometric likelihoods, we show that there exists a coarse-to-fine, sequential generative representation for the MHG model in the form of a Bayesian network, which in turn implies the mutual independence (up to deviation due to discreteness) among the Fisher's exact tests completed under FES. This allows an exact characterization of the joint null distribution of the $p$-values and gives rise to an effective inference recipe through simple multiple testing procedures such as Šidák and Bonferroni corrections, eliminating the need for resampling. In addition, FES can characterize dependency through reporting significant windows after multiple testing control. The computational complexity of FES is approximately linear in the sample size, which along with the avoidance of resampling makes it ideal for analyzing massive data sets. We use extensive numerical studies to illustrate the work of FES and compare it to several state-of-the-art methods for testing dependency in both statistical and computational performance. Finally, we apply FES to analyzing a microbiome data set and further investigate its relationship with other popular dependency metrics in that context.
Li Mao, Zhipeng Li, Biao Wu, Hongxing Xu
The quantum tunneling effects between two metallic plates are studied using the time dependent density functional theory. Results show that the tunneling is mainly dependent on the separation and the initial local field of the interstice between plates. The smaller separation and larger local field, the easier the electrons tunnels through the interstice. Our numerical calculation shows that when the separation is smaller than 0.6 nm the quantum tunneling dramatically reduce the enhancing ability of interstice between nanoparticles.
Li Ma
In this paper, we study the gradient estimate for positive solutions to the following nonlinear heat equation problem $$ u_t-Δu=au\log u+Vu, \ \ u>0 $$ on the compact Riemannian manifold $(M,g)$ of dimension $n$ and with non-negative Ricci curvature. Here $a\leq 0$ is a constant, $V$ is a smooth function on $M$ with $-ΔV\leq A$ for some positive constant $A$. This heat equation is a basic evolution equation and it can be considered as the negative gradient heat flow to $W$-functional (introduced by G.Perelman), which is the Log-Sobolev inequalities on the Riemannian manifold and $V$ corresponds to the scalar curvature.
Li Ma, Cheng Liang
In this paper, we propose a new non-local population model of logistic type equation on a bounded Lipschitz domain in the whole Euclidean space. This model preserves the L^2 norm, which is called mass, of the solution on the domain. We show that this model has the global existence, stability and asymptotic behavior at time infinity.
Li Ma, Liang Cheng
In this paper, we consider a kind of area preserving non-local flow for convex curves in the plane. We show that the flow exists globally, the length of evolving curve is non-increasing, and the curve converges to a circle in C^{\infty} sense as time goes into infinity.
Li Ma, Sheng-hua Du
In this paper, we extend the Reilly formula for drifting Laplacian operator and apply it to study eigenvalue estimate for drifting Laplacian operators on compact Riemannian manifolds boundary. Our results on eigenvalue estimates extend previous results of Reilly and Choi and Wang.
Li Ma
This paper has been withdrawn by the author due to the result being known