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Shuli Chen

Publications and source records attributed to Shuli Chen.

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Connections as treatment: causal inference with edge interventions in networks

Causal inference has traditionally focused on interventions at the unit level. In many applications, however, the central question concerns the causal effects of connections between units, such as transportation links, social relationships, or collaborative ties. We develop a causal framework for edge interventions in networks, where treatments correspond to the presence or absence of edges. Our framework defines causal estimands under stochastic interventions on the network structure and introduces an inverse probability weighting estimator under an unconfoundedness assumption on edge assignment. We estimate edge probabilities using exponential random graph models, a widely used class of network models. We establish consistency and asymptotic normality of the proposed estimator. Finally, we apply our methodology to China's transportation network to estimate the causal impact of railroad connections on regional economic development.

stat.ME

Inverse spectral problem for glassy state relaxation approximated by Prony series

The stretched exponential relaxation function is used to analyze the relaxation of the glassy state data. Due to the singularity of this function at the origin, this function is inconvenient for data analysis. Concerning this, a Prony series approximation of the stretched exponential relaxation function (J. Mauro, Y. Mauro, 2018), which is the extended Burgers model (abbreviated by EBM) known for viscoelasticity equations, was introduced. In our previous paper [arXiv:2509.16714], we gave an inversion method to identify the relaxation tensor of the EBM using clustered eigenvalues of the quasi-static EBM. As a next important research subject of this study, we numerically examine the performance of the inversion method. The performance reveals that it is a powerful method of data analysis, analyzing the relaxation of the glassy state data.

math.NA

Clustered eigenvalue problem for glassy state relaxation and its inverse problem

For computational convenience, a Prony series approximation of the stretched exponential relaxation function of homogeneous glasses has been proposed (J. Mauro, Y. Mauro, 2018), which is the extended Burgers model known for viscoelasticity equations. The authors of [P. Loreti and D. Sforza, 2019] initiated a spectral analysis of glass relaxation along this line, and gave some numerical results on clusters of eigenvalues. A theoretical justification of the results and development of further numerical studies were left open. In this paper, we provide a complete theoretical justification of their results and their numerical verification. Besides these, we solve an inverse spectral problem for clusters of eigenvalues associated with the glass relaxation.

math.AP

Optimal decay constant for complete manifolds of positive scalar curvature with quadratic decay

We prove that if an orientable 3-manifold $M$ admits a complete Riemannian metric whose scalar curvature is positive and has at most $C$-quadratic decay at infinity for some $C > \frac{2}{3}$, then it decomposes as a (possibly infinite) connected sum of spherical manifolds and $\mathbb{S}^2\times \mathbb{S}^1$ summands. Consequently, $M$ carries a complete Riemannian metric of uniformly positive scalar curvature. The decay constant $\frac{2}{3}$ is sharp, as demonstrated by metrics on $\mathbb{R}^2 \times \mathbb{S}^1$. This improves a result of Balacheff, Gil Moreno de Mora Sard\`a, and Sabourau, and partially answers a conjecture of Gromov. The main tool is a new exhaustion result using $\mu$-bubbles. In dimensions $n = 4, 5$, we further extend results of Chodosh--Maximo--Mukherjee and Sweeney, and obtain topological obstructions to the existence of a complete Riemannian metric whose scalar curvature is positive and has at most $C$-quadratic decay at infinity for some $C > \frac{n-1}{n}$ on certain noncompact contractible $n$-manifolds.

math.DG

Interior control for surfaces with positive scalar curvature and its application

Let $M^{n}$, $n\in\{3,4,5\}$, be a closed aspherical $n$-manifold and $S\subset M$ a subset consisting of disjoint incompressible embedded closed aspherical submanifolds (possibly with different dimensions). When $n =3,4$, we show that $M\setminus S$ cannot admit any complete metric with positive scalar curvature. When $n=5$, we obtain the same result when $S$ contains a submanifold of codimension 1 or 2. The key ingredient is a new interior control for the extrinsic diameter of surfaces with positive scalar curvature.

math.DG

Direct inversion scheme of time-domain fluorescence diffuse optical tomography by asymptotic analysis of peak time

This paper proposes a direct inversion scheme for fluorescence diffuse optical tomography (FDOT) to reconstruct the location of a point target using the measured peak time of the temporal response functions. A sphere is defined for the target, with its radius determined by the peak time, indicating that the target lies on the sphere. By constructing a tetrahedron with edges determined by the radii, we identify the location of the target as the vertex of the tetrahedron. Asymptotically, we derive the relationship between the radius of the sphere and the peak time. Several numerical tests are implemented to demonstrate the accuracy and performance of the asymptotic relationship and the inversion scheme.

math.AP

Approximate peak time to time-domain fluorescence diffuse optical tomography for nonzero fluorescence lifetime

This paper concerns an inverse problem for fluorescence diffuse optical tomography (FDOT) reconstructing locations of multiple point targets from the measured temporal response functions. The targets are multiple fluorescent point objects with a nonzero fluorescence lifetime at unknown locations. Peak time, when the temporal response function of the fluorescence reaches its maximum, is a robust parameter of the temporal response function in FDOT because it is most less suffered by the artifacts, such as noise, and is easily determined by experiments. We derive an approximate peak time equation based on asymptotic analysis in an explicit way in the case of nonzero fluorescence lifetime when there are single and multiple point targets. The performance of the approximation is numerically verified. Then, we develop a bisection algorithm to reconstruct the location of a single point target from the algorithm proposed in [4] for the case of zero fluorescence lifetime. Moreover, we propose a boundary-scan algorithm for the reconstruction of locations of multiple point targets. Finally, several numerical experiments are implemented to show the efficiency and robustness of the addressed algorithms.

math.NA

Determining cell population size from cell fraction in cell plasticity models

Quantifying the size of cell populations is crucial for understanding biological processes such as growth, injury repair, and disease progression. Often, experimental data offer information in the form of relative frequencies of distinct cell types, rather than absolute cell counts. This emphasizes the need to devise effective strategies for estimating absolute cell quantities from fraction data. In response to this challenge, we present two computational approaches grounded in stochastic cell population models: the first-order moment method (FOM) and the second-order moment method (SOM). These methods explicitly establish mathematical mappings from cell fraction to cell population size using moment equations of the stochastic models. Notably, our investigation demonstrates that the SOM method obviates the requirement for a priori knowledge of the initial population size, highlighting the utility of incorporating variance details from cell proportions. The robustness of both the FOM and SOM methods was analyzed from different perspectives. Additionally, we extended the application of the FOM and SOM methods to various biological mechanisms within the context of cell plasticity models. Our methodologies not only assist in mitigating the inherent limitations of experimental techniques when only fraction data is available for detecting cell population size, but they also offer new insights into utilizing the stochastic characteristics of cell population dynamics to quantify interactions between different biomasses within the system.

q-bio.QM

Positive scalar curvature metrics and aspherical summands

We prove for $n\in\{3,4,5\}$ that the connected sum of a closed aspherical $n$-manifold with an arbitrary non-compact manifold does not admit a complete metric with nonnegative scalar curvature. In particular, a special case of our result answers a question of Gromov. More generally, we generalize the partial classification result of Chodosh, Li, and Liokumovich to the non-compact domination case with our newly-developed technique. Our result unifies all previous results of this type, and confirms the validity of Gromov's non-compact domination conjecture for closed aspherical manifolds of dimensions 3, 4, and 5.

math.DG

Bayesian Inference of Phenotypic Plasticity of Cancer Cells Based on Dynamic Model for Temporal Cell Proportion Data

Mounting evidence underscores the prevalent hierarchical organization of cancer tissues. At the foundation of this hierarchy reside cancer stem cells, a subset of cells endowed with the pivotal role of engendering the entire cancer tissue through cell differentiation. In recent times, substantial attention has been directed towards the phenomenon of cancer cell plasticity, where the dynamic interconversion between cancer stem cells and non-stem cancer cells has garnered significant interest. Since the task of detecting cancer cell plasticity from empirical data remains a formidable challenge, we propose a Bayesian statistical framework designed to infer phenotypic plasticity within cancer cells, utilizing temporal data on cancer stem cell proportions. Our approach is grounded in a stochastic model, adept at capturing the dynamic behaviors of cells. Leveraging Bayesian analysis, we explore the moment equation governing cancer stem cell proportions, derived from the Kolmogorov forward equation of our stochastic model. With improved Euler method for ordinary differential equations, a new statistical method for parameter estimation in nonlinear ordinary differential equations models is developed, which also provides novel ideas for the study of compositional data. Extensive simulations robustly validate the efficacy of our proposed method. To further corroborate our findings, we apply our approach to analyze published data from SW620 colon cancer cell lines. Our results harmonize with \emph{in situ} experiments, thereby reinforcing the utility of our method in discerning and quantifying phenotypic plasticity within cancer cells.

stat.AP

Index of minimal hypersurfaces in real projective spaces

We prove that for an embedded unstable one-sided minimal hypersurface of the $(n+1)$-dimensional real projective space, the Morse index is at least $n+2$, and this bound is attained by the cubic isoparametric minimal hypersurfaces. We also show that there exist closed embedded two-sided minimal surfaces in the 3-dimensional real projective space of each odd index by computing the index of the Lawson surfaces.

math.DG

A Generalization of the Geroch Conjecture with Arbitrary Ends

Using $\mu$-bubbles, we prove that for $3 \le n \le 7$, the connected sum of a Schoen-Yau-Schick $n$-manifold with an arbitrary manifold does not admit a complete metric of positive scalar curvature. When either $3 \le n \le 5$, $1 \le m \le n-1$ or $6 \le n \le 7$, $m \in \{1, n-2, n-1\}$, we also show the connected sum $(M^{n-m}\times \mathbb{T}^m) \# X^n$ where $X$ is an arbitrary manifold does not admit a metric of positive $m$-intermediate curvature. Here $m$-intermediate curvature is a new notion of curvature introduced by Brendle, Hirsch and Johne interpolating between Ricci and scalar curvature.

math.DG

Stable submanifolds in the product of projective spaces II

We prove that there do not exist odd-dimensional stable compact minimal immersions in the product of two complex projective spaces. We also prove that the only stable compact minimal immersions in the product of a quaternionic projective space with any other Riemannian manifold are the products of quaternionic projective subspaces with compact stable minimal immersions of the second manifold in the Riemmanian product. These generalize similar results of the second-named author of immersions with low dimensions or codimensions to immersions with arbitrary dimensions. In addition, we prove that the only stable compact minimal immersions in the product of a octonionic projective plane with any other Riemannian manifold are the products of octonionic projective subspaces with compact stable minimal immersions of the second manifold in the Riemmanian product.

math.DG

On the index of minimal surfaces with free boundary in a half-space

We study the Morse index of minimal surfaces with free boundary in a half-space. We improve previous estimates relating the Neumann index to the Dirichlet index and use this to answer a question of Ambrozio, Buzano, Carlotto, and Sharp concerning the non-existence of index two embedded minimal surfaces with free boundary in a half-space. We also give a simplified proof of a result of Chodosh and Maximo concerning lower bounds for the index of the Costa deformation family.

math.DG

On the generalized Erd\H{o}s--Kneser conjecture: proofs and reductions

Alon, Frankl, and Lov\'asz proved a conjecture of Erd\H{o}s that one needs at least $\lceil \frac{n-r(k-1)}{r-1} \rceil$ colors to color the $k$-subsets of $\{1, \dots, n\}$ such that any $r$ of the $k$-subsets that have the same color are not pairwise disjoint. A generalization of this problem where one requires $s$-wise instead of pairwise intersections was considered by Sarkaria. He claimed a proof of a generalized Erd\H{o}s--Kneser conjecture establishing a lower bound for the number of colors that reduces to Erd\H{o}s' original conjecture for ${s = 2}$. Lange and Ziegler pointed out that his proof fails whenever $r$ is not a prime. Here we establish this generalized Erd\H{o}s--Kneser conjecture for every $r$, as long as $s$ is not too close to $r$. Our result encompasses earlier results but is significantly more general. We discuss relations of our results to conjectures of Ziegler and of Abyazi Sani and Alishahi, and prove the latter in several cases.

math.CO

Jacobi-Trudi determinants over finite fields

In this paper, we work toward answering the following question: given a uniformly random algebra homomorphism from the ring of symmetric functions over the integers to a finite field $\mathbb{F}_q$, what is the probability that the Schur function $s_\lambda$ maps to zero? We show that this probability is always at least $1/q$ and is asymptotically $1/q$. Moreover, we give a complete classification of all shapes that can achieve probability $1/q$. In addition, we identify certain families of shapes where the corresponding Schur functions being sent to zero are independent events, and we look into the probability that a Schur functions is mapped to nonzero values in $\mathbb{F}_q$.

math.CO

Coincidences among skew dual stable Grothendieck polynomials

The question of when two skew Young diagrams produce the same skew Schur function has been well-studied. We investigate the same question in the case of stable Grothendieck polynomials, which are the K-theoretic analogues of the Schur functions. We prove a necessary condition for two skew shapes to give rise to the same dual stable Grothendieck polynomial. We also provide a necessary and sufficient condition in the case where the two skew shapes are ribbons.

math.CO