42 citations · 59 across the 23 of their papers we have counts for
25 papers
Characterization of Minimal Degenerate Zero-One Reaction Networks
Yuanlin Chen, Xiaoxian Tang
A fundamental problem in the algebraic study of biochemical reaction networks is to characterize degeneracy. Two-dimensional zero-one networks, where each reactant appears with sto…
Detecting Nonproperness of Likelihood Equations
Xiaoxian Tang, Bican Xia, Tianqi Zhao
Given an algebraic statistical model, a challenging problem is classifying the data according to the number of positive critical points of the likelihood function. The positive cri…
The Ubiquity of Three Steady States: Minimal Multistable Zero-One Reaction Networks
Xiaoxian Tang, Jiandong Zhang
Biochemical networks with unit stoichiometry arise naturally in receptor-ligand binding and multisite phosphorylation systems. A central question is to identify which networks admi…
Obstruction of Absolute Concentration Robustness by Conservation Laws in Non-Redundant Zero-One Networks
Xinyi Si, Xiaoxian Tang
Absolute concentration robustness (ACR) is a structural property of biochemical reaction networks in which a species attains the same steady-state concentration at every positive s…
Hopf Bifurcations of Reaction Networks with Zero-One Stoichiometric Coefficients
Xiaoxian Tang, Kaizhang Wang
For the reaction networks with zero-one stoichiometric coefficients (or simply zero-one networks), we prove that if a network admits a Hopf bifurcation, then the rank of the stoich…
Projections of Tropical Fermat-Weber Points
Weiyi Ding, Xiaoxian Tang
In the tropical projective torus, it is not guaranteed that the projection of a Fermat-Weber point of a given data set is a Fermat-Weber point of the projection of the data set. In…
Multistationarity of Reaction Networks with One-Dimensional Stoichiometric Subspaces
Kexin Lin, Xiaoxian Tang, Zhishuo Zhang
We study the multistationarity for the reaction networks with one-dimensional stoichiometric subspaces, and we focus on the networks admitting finitely many positive steady states.…
Multistability of Reaction Networks with One-Dimensional Stoichiometric Subspaces
Xiaoxian Tang, Zhishuo Zhang
For the reaction networks with one-dimensional stoichiometric subspaces, we show the following results. (1) If the maximum number of positive steady states is an even number N, the…
Multistability of Small Reaction Networks
Xiaoxian Tang, Hao Xu
For three typical sets of small reaction networks (networks with two reactions, one irreversible and one reversible reaction, or two reversible-reaction pairs), we completely answe…
Tropical Support Vector Machine and its Applications to Phylogenomics
Xiaoxian Tang, Houjie Wang, Ruriko Yoshida
Most data in genome-wide phylogenetic analysis (phylogenomics) is essentially multidimensional, posing a major challenge to human comprehension and computational analysis. Also, we…
Dynamics of ERK regulation in the processive limit
Carsten Conradi, Nida Obatake, Anne Shiu +1
We consider a model of extracellular signal-regulated kinase (ERK) regulation by dual-site phosphorylation and dephosphorylation, which exhibits bistability and oscillations, but l…
Bistability of Sequestration Networks
Xiaoxian Tang, Jie Wang
We solve a conjecture on multiple nondegenerate steady states, and prove bistability for sequestration networks. More specifically, we prove that for any odd number of species, and…
Oscillations and bistability in a model of ERK regulation
Nida Obatake, Anne Shiu, Xiaoxian Tang +1
This work concerns the question of how two important dynamical properties, oscillations and bistability, emerge in an important biological signaling network. Specifically, we consi…
Computing Elimination Ideals and Discriminants of Likelihood Equations
Xiaoxian Tang, Timo De Wolff, Rukai Zhao
We develop a probabilistic algorithm for computing elimination ideals of likelihood equations, which is for larger models by far more efficient than directly computing Groebner bas…
Multistationarity in Structured Reaction Networks
Alicia Dickenstein, Mercedes Perez Millan, Anne Shiu +1
Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multi…
Principal component analysis and the locus of the Frechet mean in the space of phylogenetic trees
Tom M. W. Nye, Xiaoxian Tang, Grady Weyenberg +1
Most biological data are multidimensional, posing a major challenge to human comprehension and computational analysis. Principal component analysis is the most popular approach to…
New Upper Bounds for Equiangular Lines by Pillar Decomposition
Emily J. King, Xiaoxian Tang
We derive a procedure for computing an upper bound on the number of equiangular lines in various Euclidean vector spaces by generalizing the classical pillar decomposition develope…
A Probabilistic Algorithm for Computing Data-Discriminants of Likelihood Equations
Jose Israel Rodriguez, Xiaoxian Tang
An algebraic approach to the maximum likelihood estimation problem is to solve a very structured parameterized polynomial system called likelihood equations that have finitely many…
Convexity in Tree Spaces
Bo Lin, Bernd Sturmfels, Xiaoxian Tang +1
We study the geometry of metrics and convexity structures on the space of phylogenetic trees, which is here realized as the tropical linear space of all \ ultrametrics. The ${\rm C…
Data-Discriminants of Likelihood Equations
Jose Israel Rodriguez, Xiaoxian Tang
Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. The problem is to maximize the likelihood function with respect to given data on a statist…
Hierarchical Comprehensive Triangular Decomposition
Zhenghong Chen, Xiaoxian Tang, Bican Xia
The concept of comprehensive triangular decomposition (CTD) was first introduced by Chen et al. in their CASC'2007 paper and could be viewed as an analogue of comprehensive Grobner…
Special Algorithm for Stability Analysis of Multistable Biological Regulatory Systems
Hoon Hong, Xiaoxian Tang, Bican Xia
We consider the problem of counting (stable) equilibriums of an important family of algebraic differential equations modeling multistable biological regulatory systems. The problem…
Generic Regular Decompositions for Parametric Polynomial Systems
Zhenghong Chen, Xiaoxian Tang, Bican Xia
This paper presents a generalization of our earlier work in [19]. In this paper, the two concepts, generic regular decomposition (GRD) and regular-decomposition-unstable (RDU) vari…
Generic Regular Decompositions for Generic Zero-Dimensional Systems
Xiaoxian Tang, Zhenghong Chen, Bican Xia
Two new concepts, generic regular decomposition and regular-decomposition-unstable (RDU) variety for generic zero-dimensional systems, are introduced in this paper and an algorithm…