arXiv subjects

Jie Zhong

Publications and source records attributed to Jie Zhong.

At least 19 recordsLinked to original sources

arXiv2026

A Shape Design Approximation for Degenerate Partial Differential Equations and Its Application

In this paper, we focus on two types of degenerate partial differential equations: a degenerate elliptic equation and a degenerate parabolic equation. Significantly, both categories are characterized by the same principal operator. To obtain solutions for these equations, we introduce a novel approximation approach, termed the shape design approximation. As a practical application of this method, we derive a Carleman estimate for the backward degenerate parabolic equation. This estimate plays a pivotal role in establishing the null controllability of the degenerate parabolic equation. A notable advantage of employing the shape design approximation in deriving the Carleman estimate is that it enables us to bypass the requirement for second order derivatives in the degenerate equation. Usually, this has been a significant obstacle in the derivation of Carleman estimates for degenerate parabolic equations.

math.AP↗

arXiv2026

Quantitative Weak Unique Continuation on Annular Domains for Backward Degenerate Parabolic Equations with Degenerate Interior Points

In this paper, we establish a quantitative weak unique continuation theorem on an annular domain for a backward degenerate parabolic equation with a degenerate interior point. Our methodology hinges on approximating the solution of the degenerate parabolic equation through solutions of non-degenerate parabolic counterparts. Subsequently, we establish Carleman estimates for the non-degenerate parabolic equation across two separate domains. By virtue of these estimates, we deduce a quantitative weak unique continuation property for the degenerate parabolic equation, thereby substantiating the weak unique continuation result for the original degenerate parabolic equation.

math.AP↗

arXiv2026

Null Controllability for a Multi-Dimensional Degenerate Parabolic Equation with Degenerated Interior Point

In this study, we study the null controllability of a multi-dimensional degenerate parabolic equation characterized by a degenerate interior point. The control domain, which is an arbitrary inner region, does not encompass the degenerate point. To tackle this problem, we adopt a new approximation methodology. Specifically, we approximate the degenerate partial differential equations (PDEs) with a series of uniformly elliptic PDEs, notwithstanding their limited regularity. We then derive the Carleman estimate for these approximate uniformly parabolic equations and establish the observability inequality, which ultimately paves the way for demonstrating the null controllability of the system.

math.OC↗

arXiv2026

Hidden Boundary Trace Regularity and an Observability Estimate with Interior Remainder for Boundary-Degenerate Hyperbolic Equations

We study hidden boundary trace regularity for two-dimensional hyperbolic equations with boundary degeneracy governed by $\mcA\vp=-\Div(A\nabla \vp)$, where $A=\diag(1,r^\al)$ and $\al\in(0,1)$. We establish well-posedness in weighted Sobolev spaces and prove an $L^2$ trace estimate for the normal derivative on the nondegenerate side $r=1$. Using truncated geometries and Carleman weights adapted to the anisotropic degeneracy, we derive a large-time observability estimate with a lower-order interior remainder. We also identify a framework-level obstruction at the critical threshold $\al=1$: the weighted Dirichlet coercivity underlying the subcritical analysis loses uniformity and exhibits a logarithmic loss on truncated domains.

math.AP↗

arXiv2026

A Class of Degenerate Hyperbolic Equations with Neumann Boundary Conditions and Its Application to Observability

We establish a mixed observability inequality for a class of degenerate hyperbolic equations on the cylindrical domain $Ω= \mathbb{T} \times (0,1)$ with mixed Neumann Dirichlet boundary conditions. The degeneracy acts only in the radial variable, whereas the periodic angular variable allows propagation with a strong tangential component, making a direct top boundary observation delicate. For $α\in [1,2)$, we prove that the solution can be controlled by a boundary observation on the top boundary together with an interior observation on a narrow strip. The proof combines a weighted functional framework, improved regularity, a cutoff decomposition in the angular variable, a multiplier argument for the localized component, and an energy estimate for the remainder.

math.AP↗

arXiv2026

Shape Design for a Class of Degenerate Parabolic Equations with Boundary Point Degeneracy and Its Application to Boundary Observability

We study a class of degenerate parabolic equations with boundary point degeneracy in dimensions N>=2 and investigate the associated boundary observability problem by means of shape design. While one-dimensional degenerate models have been treated in the literature, the genuinely higher-dimensional case remains much more delicate because the degeneracy occurs at a boundary point and the boundary normal trace cannot be extracted directly near the singularity. We approximate the degenerate equation by a family of uniformly parabolic problems on truncated domains obtained by removing a small neighborhood of the degenerate point. Under a geometric condition on the boundary, we establish uniform estimates for the approximate problems, prove convergence to the solution of the original degenerate equation, and identify the convergence of the boundary normal derivatives under additional regularity. We then combine this approximation scheme with a parabolic Carleman estimate for the approximate backward equations and derive a boundary observability inequality for the limiting degenerate equation. In this way, we obtain a higher-dimensional parabolic counterpart of the shape-design program previously developed for degenerate hyperbolic equations.

math.AP↗

arXiv2026

Shape-Design Approximation for a Class of Degenerate Hyperbolic Equations with a Degenerate Boundary Point and Its Application to Observability

We study a class of degenerate hyperbolic equations in a bounded domain whose degeneracy occurs at a boundary point. We first develop the weighted functional framework, prove well-posedness of the degenerate problem, and establish regularity away from the degenerate point. We then introduce a shape-design approximation obtained by removing a small neighborhood of the degenerate boundary point, which yields uniformly non-degenerate hyperbolic problems on regularized domains. We prove that the regularized solutions converge to the solution of the original degenerate equation, including the convergence of the boundary normal derivatives away from the degenerate point. Finally, under a geometric condition on the observation boundary, we derive an observability inequality for the degenerate equation by combining the uniform observability of the regularized problems with the limit passage.

math.AP↗

arXiv2026

Non-homogeneous boundary value problems for second-order degenerate hyperbolic equations and their application

We study second-order hyperbolic equations with degenerate elliptic operators and non-homogeneous Dirichlet boundary inputs. We establish existence and regularity of weak solutions in weighted Sobolev spaces under mild assumptions on the degenerate weight. A Dirichlet map is constructed for the degenerate elliptic operator, leading to a solution theory that extends classical approaches to the degenerate setting. In particular, we derive energy estimates and well-posedness for boundary inputs of low regularity (in appropriate trace spaces), even though the classical Dirichlet-to-Neumann framework is not directly applicable in the degenerate setting. As an application, we prove an approximate controllability criterion, which generalizes the Hilbert Uniqueness Method to degenerate wave equations. Our framework accommodates higher-dimensional degenerate waves, non-homogeneous boundary conditions, and weighted functional analysis. We also illustrate how our criterion connects to higher-dimensional Grushin equations and waves with single-point degeneracy, and we highlight the remaining unique continuation/observability issue as an open problem.

math.AP↗

arXiv2025

Approximation of Elliptic Equations with Interior Single-Point Degeneracy and Its Application to Weak Unique Continuation Property

This paper investigates the quantitative weak unique continuation property (QWUCP) for a class of high-dimensional elliptic equations with interior point degeneracy. First, we establish well-posedness results in weighted function spaces. Then, using an innovative approximation method, we derive the three-ball theorem at the degenerate point. Finally, we apply the three-ball theorem to prove QWUCP for two different cases.

math.AP↗

arXiv2025

Fitness aligned structural modeling enables scalable virtual screening with AuroBind

Most human proteins remain undrugged, over 96% of human proteins remain unexploited by approved therapeutics. While structure-based virtual screening promises to expand the druggable proteome, existing methods lack atomic-level precision and fail to predict binding fitness, limiting translational impact. We present AuroBind, a scalable virtual screening framework that fine-tunes a custom atomic-level structural model on million-scale chemogenomic data. AuroBind integrates direct preference optimization, self-distillation from high-confidence complexes, and a teacher-student acceleration strategy to jointly predict ligand-bound structures and binding fitness. The proposed models outperform state-of-the-art models on structural and functional benchmarks while enabling 100,000-fold faster screening across ultra-large compound libraries. In a prospective screen across ten disease-relevant targets, AuroBind achieved experimental hit rates of 7-69%, with top compounds reaching sub-nanomolar to picomolar potency. For the orphan GPCRs GPR151 and GPR160, AuroBind identified both agonists and antagonists with success rates of 16-30%, and functional assays confirmed GPR160 modulation in liver and prostate cancer models. AuroBind offers a generalizable framework for structure-function learning and high-throughput molecular screening, bridging the gap between structure prediction and therapeutic discovery.

cs.LG↗

arXiv2023

Multi-Robot Geometric Task-and-Motion Planning for Collaborative Manipulation Tasks

We address multi-robot geometric task-and-motion planning (MR-GTAMP) problems in synchronous, monotone setups. The goal of the MR-GTAMP problem is to move objects with multiple robots to goal regions in the presence of other movable objects. We focus on collaborative manipulation tasks where the robots have to adopt intelligent collaboration strategies to be successful and effective, i.e., decide which robot should move which objects to which positions, and perform collaborative actions, such as handovers. To endow robots with these collaboration capabilities, we propose to first collect occlusion and reachability information for each robot by calling motion-planning algorithms. We then propose a method that uses the collected information to build a graph structure which captures the precedence of the manipulations of different objects and supports the implementation of a mixed-integer program to guide the search for highly effective collaborative task-and-motion plans. The search process for collaborative task-and-motion plans is based on a Monte-Carlo Tree Search (MCTS) exploration strategy to achieve exploration-exploitation balance. We evaluate our framework in two challenging MR-GTAMP domains and show that it outperforms two state-of-the-art baselines with respect to the planning time, the resulting plan length and the number of objects moved. We also show that our framework can be applied to underground mining operations where a robotic arm needs to coordinate with an autonomous roof bolter. We demonstrate plan execution in two roof-bolting scenarios both in simulation and on robots.

cs.RO↗

arXiv2023

Observability inequalities for the backward stochastic evolution equations and their applications

The present article delves into the investigation of observability inequalities pertaining to backward stochastic evolution equations. We employ a combination of spectral inequalities, interpolation inequalities, and the telegraph series method as our primary tools to directly establish observability inequalities. Furthermore, we explore three specific equations as application examples: a stochastic degenerate equation, a stochastic fourth order parabolic equation and a stochastic heat equation. It is noteworthy that these equations can be rendered null controllability with only one control in the drift term to each system.

math.OC↗

arXiv2023

Norm and time optimal control problems of stochastic heat equations

This paper investigates the norm and time optimal control problems for stochastic heat equations. We begin by presenting a characterization of the norm optimal control, followed by a discussion of its properties. We then explore the equivalence between the norm optimal control and time optimal control, and subsequently establish the bang-bang property of the time optimal control. These problems, to the best of our knowledge, are among the first to discuss in the stochastic case.

math.OC↗

arXiv2022

Zero-Shot Imitating Collaborative Manipulation Plans from YouTube Cooking Videos

People often watch videos on the web to learn how to cook new recipes, assemble furniture or repair a computer. We wish to enable robots with the very same capability. This is challenging; there is a large variation in manipulation actions and some videos even involve multiple persons, who collaborate by sharing and exchanging objects and tools. Furthermore, the learned representations need to be general enough to be transferable to robotic systems. On the other hand, previous work has shown that the space of human manipulation actions has a linguistic, hierarchical structure that relates actions to manipulated objects and tools. Building upon this theory of language for action, we propose a system for understanding and executing demonstrated action sequences from full-length, real-world cooking videos on the web. The system takes as input a new, previously unseen cooking video annotated with object labels and bounding boxes, and outputs a collaborative manipulation action plan for one or more robotic arms. We demonstrate performance of the system in a standardized dataset of 100 YouTube cooking videos, as well as in six full-length Youtube videos that include collaborative actions between two participants. We compare our system with a baseline system that consists of a state-of-the-art action detection baseline and show our system achieves higher action detection accuracy. We additionally propose an open-source platform for executing the learned plans in a simulation environment as well as with an actual robotic arm.

cs.RO↗

arXiv2022

A MIP-Based Approach for Multi-Robot Geometric Task-and-Motion Planning

We address multi-robot geometric task-and-motion planning (MR-GTAMP) problems in synchronous, monotone setups. The goal of the MR-GTAMP problem is to move objects with multiple robots to goal regions in the presence of other movable objects. To perform the tasks successfully and effectively, the robots have to adopt intelligent collaboration strategies, i.e., decide which robot should move which objects to which positions, and perform collaborative actions, such as handovers. To endow robots with these collaboration capabilities, we propose to first collect occlusion and reachability information for each robot as well as information about whether two robots can perform a handover action by calling motion-planning algorithms. We then propose a method that uses the collected information to build a graph structure which captures the precedence of the manipulations of different objects and supports the implementation of a mixed-integer program to guide the search for highly effective collaborative task-and-motion plans. The search process for collaborative task-and-motion plans is based on a Monte-Carlo Tree Search (MCTS) exploration strategy to achieve exploration-exploitation balance. We evaluate our framework in two challenging GTAMP domains and show that it can generate high-quality task-and-motion plans with respect to the planning time, the resulting plan length and the number of objects moved compared to two state-of-the-art baselines.

cs.RO↗

arXiv2022

Sensors Design for Large-Scale Boolean Networks via Pinning Observability

In this paper, a set of sensors is constructed via the pinning observability approach with the help of observability criteria given in [1] and [2], in order to make the given Boolean network (BN) be observable. Given the assumption that system states can be accessible, an efficient pinning control scheme is developed to generate an observable BN by adjusting the network structure rather than just to check system observability. Accordingly, the sensors are constructed, of which the form is consistent with that of state feedback controllers in the designed pinning control. Since this pinning control approach only utilizes node-to-node message communication instead of global state space information, the time complexity is dramatically reduced from $O(2^{2n})$ to $O(n^2+n2^d)$, where where $n$ and $d$ are respectively the node number of the considered BN and the largest in-degree of vertices in its network structure. Finally, we design the sensors for the reduced D. melanogaster segmentation polarity gene network and the T-cell receptor kinetics, respectively.

eess.SY↗

arXiv2021

Progressive Open-Domain Response Generation with Multiple Controllable Attributes

It is desirable to include more controllable attributes to enhance the diversity of generated responses in open-domain dialogue systems. However, existing methods can generate responses with only one controllable attribute or lack a flexible way to generate them with multiple controllable attributes. In this paper, we propose a Progressively trained Hierarchical Encoder-Decoder (PHED) to tackle this task. More specifically, PHED deploys Conditional Variational AutoEncoder (CVAE) on Transformer to include one aspect of attributes at one stage. A vital characteristic of the CVAE is to separate the latent variables at each stage into two types: a global variable capturing the common semantic features and a specific variable absorbing the attribute information at that stage. PHED then couples the CVAE latent variables with the Transformer encoder and is trained by minimizing a newly derived ELBO and controlled losses to produce the next stage's input and produce responses as required. Finally, we conduct extensive evaluations to show that PHED significantly outperforms the state-of-the-art neural generation models and produces more diverse responses as expected.

cs.CL↗

arXiv2021

A Stochastic Time Series Model for Predicting Financial Trends using NLP

Stock price forecasting is a highly complex and vitally important field of research. Recent advancements in deep neural network technology allow researchers to develop highly accurate models to predict financial trends. We propose a novel deep learning model called ST-GAN, or Stochastic Time-series Generative Adversarial Network, that analyzes both financial news texts and financial numerical data to predict stock trends. We utilize cutting-edge technology like the Generative Adversarial Network (GAN) to learn the correlations among textual and numerical data over time. We develop a new method of training a time-series GAN directly using the learned representations of Naive Bayes' sentiment analysis on financial text data alongside technical indicators from numerical data. Our experimental results show significant improvement over various existing models and prior research on deep neural networks for stock price forecasting.

q-fin.CP↗