arXiv subjects

Tianyi Pan

Publications and source records attributed to Tianyi Pan.

14 recordsLinked to original sources

arXiv2026

Polynomial mixing for the weakly damped stochastic nonlinear Schr\"odinger equation on the whole space

We consider the weakly damped stochastic nonlinear Schr\"odinger (NLS) equation on the real line, driven by a noise that is white in time and smooth in space. Assuming that the noise is sufficiently non-degenerate, we prove that the equation has a unique stationary measure in the class of probability measures concentrated on $H^2$, and establish polynomial mixing in the dual-Lipschitz metric over $H^1$. We do not impose any restriction on the size of the damping. The proof is based on a coupling argument, whose key ingredient is a Foia\c{s}-Prodi-type estimate in the $H^1$-norm, derived by means of a Lyapunov functional adapted to the linearized NLS dynamics. To compensate for the loss of compactness, we combine this estimate with a truncated Poincar\'e inequality and a space-time weight function quantifying the spatial decay of solutions.

math.PR↗

arXiv2026

A Unified Framework for Multiple Exposure Distributed Lag Non-Linear Models for Air Pollution Epidemiology

This study quantifies the association between air pollution and mortality in Ontario, Canada. Exposure-response relationships in air pollution epidemiology are complex due to three features: time-lagged associations, non-linear associations, and multiple pollutants. To address the first two features, two distinct classes of distributed lag non-linear model (DLNM) have been proposed, but extending them to multiple exposures and selecting an appropriate model remain challenging. We propose a unified framework for multiple exposure DLNMs, integrating model specification, estimation, selection and stacking. The framework applies to four different model structures: two additive and two proposed single-index DLNMs, all applicable to general outcome types, including the mortality counts in the motivating application. We develop an estimation approach that applies to all four models. Choosing among the candidate DLNMs is challenging a priori, and we derive an AIC to select among them. As an alternative to selecting a single model, we also extend a model stacking approach to combine inferences across the four DLNMs and propose an implementation scalable to our dataset with 106,346 observations. In the motivating analysis, the four DLNMs yield different estimates, and the proposed stacking approach identifies significant associations between respiratory mortality and a mixture of PM2.5, O3 and NO2.

stat.ME↗

arXiv2025

Estimating Associations Between Cumulative Exposure and Health via Generalized Distributed Lag Non-Linear Models using Penalized Splines

Quantifying associations between short-term exposure to ambient air pollution and health outcomes is an important public health priority. Many studies have investigated the association considering delayed effects within the past few days. Adaptive cumulative exposure distributed lag non-linear models (ACE-DLNMs) quantify associations between health outcomes and cumulative exposure that is specified in a data-adaptive way. While the ACE-DLNM framework is highly interpretable, it is limited to continuous outcomes and does not scale well to large datasets. Motivated by a large analysis of daily pollution and respiratory hospitalization counts in Canada between 2001 and 2018, we propose a generalized ACE-DLNM incorporating penalized splines, improving upon existing ACE-DLNM methods to accommodate general response types. We then develop a computationally efficient estimation strategy based on profile likelihood and Laplace approximate marginal likelihood with Newton-type methods. We demonstrate the performance and practical advantages of the proposed method through simulations. In application to the motivating analysis, the proposed method yields more stable inferences compared to generalized additive models with fixed exposures, while retaining interpretability.

stat.ME↗

arXiv2025

Strong well-posedness of the two-dimensional stochastic Navier-Stokes equation on moving domains

In this paper, we establish the strong($H^1$) well-posedness of the two dimensional stochastic Navier-Stokes equation with multiplicative noise on moving domains. Due to the nonlocality effect, this equation exhibits a ``piecewise" variational setting. Namely the global well-posedness of this equation is decomposed into the well-posedness of a family of stochastic partial differential equations(SPDEs) in the variational setting on each small time-interval. We first examine the well-posedness on each time interval, which does not have (nonhomogeneous) coercivity. Subsequently, we give an estimate of lower bound of length of the time-interval, which enables us to achieve the global well-posedness.

math.PR↗

arXiv2025

Stochastic Stefan problem on moving hypersurfaces: an approach by a new framework of nonhomogeneous monotonicity

The purpose of this paper is to establish the well-posedness of the stochastic Stefan problem on moving hypersurfaces. Through a specially designed transformation, it turns out we need to solve stochastic partial differential equations on a fixed hypersurface with a new kind of nonhomogeneous monotonicity involving a family of time-dependent operators. This new class of SPDEs is of independent interest and can also be applied to solve many other interesting models such as the stochastic $p$-Laplacian equations, stochastic Allen-Cahn equation and stochastic heat equations on time-dependent domains or hypersurfaces. (Monotone) Operator-valued calculus and geometric analysis of moving hypersurfaces play important roles in the study. Moreover, a forthcoming result on the well-posedness of stochastic 2D Navier-Stokes equation on moving domains is also based on our framework.

math.PR↗

arXiv2024

Large deviations of fully local monotone stochastic partial differential equations driven by gradient-dependent noise

Consider stochastic partial differential equations (SPDEs) with fully local monotone coefficients in a Gelfand triple $V\subseteq H\subseteq V^*$ $$ \left\{ \begin{align} &dX_t=A(t,X_t)dt+B(t,X_t)dW_t,\ t\in (0,T]\\\\& X_0=x\in H, \end{align} \right. $$ where $$A: [0,T] \times V\rightarrow V^*,\ \ B:[0,T]\times V\rightarrow\ L_2(U,H)$$ are measurable maps, $L_2(U,H)$ is the space of Hilbert-Schmidt operators from $U$ to $H$ and $W$ is a $U$-cylindrical Wiener process.\par In this paper, we establish a small noise large deviation principle(LDP) for the solutions {$u^\varepsilon$}$_{\varepsilon>0}$ of the above SPDEs. The main contribution of this paper is the much more generality of our framework than that of the existing results. In particular, the diffusion coefficient $B(t,\cdot)$ may depend on the gradient of the solutions, which is of great interest in the field of SPDEs, but there are few existing results on the topic of LDP. The broader scope of the fully local monotone setting leads us to use different strategies and techniques. A combination of the pseudomonotone technique and compactness arguement plays a crucial role in the whole paper. Our framework is very general to include many interesting models that could not be covered by existing work, including stochastic quasilinear SPDEs, stochastic convection diffusion equation, stochastic 2D Liquid crystal equation, stochastic $p$-Laplace equation with gradient-dependent noise, stochastic 2D Navier-Stokes equation with gradient-dependent noise etc.

math.PR↗

arXiv2023

Stochastic heat equations on moving domains

In this paper, we establish the well-posedness of stochastic heat equations on moving domains, which amounts to a study of infinite dimensional interacting systems. The main difficulty is to deal with the problems caused by the time-varying state spaces and the interaction of the particle systems. The interaction still occurs even in the case of additive noise. This is in contrast to stochastic heat equations in a fixed domain.

math.PR↗

arXiv2022

Large deviations of stochastic heat equations with logarithmic nonlinearity

In this paper, we establish a large deviation principle for the solutions to the stochastic heat equations with logarithmic nonlinearity driven by Brownian motion, which is neither locally Lipschitz nor locally monotone. Nonlinear versions of Gronwall's inequalities and Log-Sobolev inequalities play an important role.

math.PR↗

arXiv2020

Threat from being Social: Vulnerability Analysis of Social Network Coupled Smart Grid

Social Networks (SNs) have been gradually applied by utility companies as an addition to smart grid and are proved to be helpful in smoothing load curves and reducing energy usage. However, SNs also bring in new threats to smart grid: misinformation in SNs may cause smart grid users to alter their demand, resulting in transmission line overloading and in turn leading to catastrophic impact to the grid. In this paper, we discuss the interdependency in the social network coupled smart grid and focus on its vulnerability. That is, how much can the smart grid be damaged when misinformation related to it diffuses in SNs? To analytically study the problem, we propose the Misinformation Attack Problem in Social-Smart Grid (MAPSS) that identifies the top critical nodes in the SN, such that the smart grid can be greatly damaged when misinformation propagates from those nodes. This problem is challenging as we have to incorporate the complexity of the two networks concurrently. Nevertheless, we propose a technique that can explicitly take into account information diffusion in SN, power flow balance and cascading failure in smart grid integratedly when evaluating node criticality, based on which we propose various strategies in selecting the most critical nodes. Also, we introduce controlled load shedding as a protection strategy to reduce the impact of cascading failure. The effectiveness of our algorithms are demonstrated by experiments on IEEE bus test cases as well as the Pegase data set.

eess.SY↗

arXiv2017

Pseudo-Separation for Assessment of Structural Vulnerability of a Network

Based upon the idea that network functionality is impaired if two nodes in a network are sufficiently separated in terms of a given metric, we introduce two combinatorial \emph{pseudocut} problems generalizing the classical min-cut and multi-cut problems. We expect the pseudocut problems will find broad relevance to the study of network reliability. We comprehensively analyze the computational complexity of the pseudocut problems and provide three approximation algorithms for these problems. Motivated by applications in communication networks with strict Quality-of-Service (QoS) requirements, we demonstrate the utility of the pseudocut problems by proposing a targeted vulnerability assessment for the structure of communication networks using QoS metrics; we perform experimental evaluations of our proposed approximation algorithms in this context.

cs.DS↗

arXiv2017

Vulnerability of D2D Communications from Interconnected Social Networks

In this paper, we study how rumors in Online Social Networks (OSNs) may impact the performance of device-to-device (D2D) communication. As D2D is a new technology, people may choose not to use it when believed in rumors of its negative impacts. Thus, the cellular network with underlaying D2D is vulnerable to OSNs as rumors in OSNs may decrement the throughput of the cellular network in popular content delivery scenarios. To analyze the vulnerability, we introduce the problem of finding the most critical nodes in the OSN such that the throughput of a content delivery scenario is minimized when a rumor starts from those nodes. We then propose an efficient solution to the critical nodes detection problem. The severity of such vulnerability is supported by extensive experiments in various simulation settings, from which we observe up to $40\%$ reduction in network throughput.

cs.SI↗

arXiv2017

Scalable Bicriteria Algorithms for the Threshold Activation Problem in Online Social Networks

We consider the Threshold Activation Problem (TAP): given social network $G$ and positive threshold $T$, find a minimum-size seed set $A$ that can trigger expected activation of at least $T$. We introduce the first scalable, parallelizable algorithm with performance guarantee for TAP suitable for datasets with millions of nodes and edges; we exploit the bicriteria nature of solutions to TAP to allow the user to control the running time versus accuracy of our algorithm through a parameter $α\in (0,1)$: given $η> 0$, with probability $1 - η$ our algorithm returns a solution $A$ with expected activation greater than $T - 2 αT$, and the size of the solution $A$ is within factor $1 + 4 αT + \log ( T )$ of the optimal size. The algorithm runs in time $O \left( α^{-2}\log \left( n / η\right) (n + m) |A| \right)$, where $n$, $m$, refer to the number of nodes, edges in the network. The performance guarantee holds for the general triggering model of internal influence and also incorporates external influence, provided a certain condition is met on the cost-effectivity of seed selection.

cs.SI↗

arXiv2016

Leveraging Social Communities for Optimizing Cellular Device-to-Device Communications

Device-to-device (D2D) communications over licensed wireless spectrum has been recently proposed as a promising technology to meet the capacity crunch of next generation cellular networks. However, due to the high mobility of cellular devices, establishing and ensuring the success of D2D transmission becomes a major challenge. To this end, in this paper, a novel framework is proposed to enable devices to form multi-hop D2D connections in an effort to maintain sustainable communication in the presence of device mobility. To solve the problem posed by device mobility, in contrast to existing works, which mostly focus on physical domain information, a durable community based approach is introduced taking social encounters into context. It is shown that the proposed scheme can derive an optimal solution for time sensitive content transmission while also minimizing the cost that the base station pays in order to incentivize users to participate in D2D. Simulation results show that the proposed social community aware approach yields significant performance gain, in terms of the amount of traffic offloaded from the cellular network to the D2D tier, compared to the classical social-unaware methods.

cs.IT↗