arXiv subjects

Ning Zhong

Publications and source records attributed to Ning Zhong.

16 recordsLinked to original sources

arXiv2025

BleedOrigin: Dynamic Bleeding Source Localization in Endoscopic Submucosal Dissection via Dual-Stage Detection and Tracking

Intraoperative bleeding during Endoscopic Submucosal Dissection (ESD) poses significant risks, demanding precise, real-time localization and continuous monitoring of the bleeding source for effective hemostatic intervention. In particular, endoscopists have to repeatedly flush to clear blood, allowing only milliseconds to identify bleeding sources, an inefficient process that prolongs operations and elevates patient risks. However, current Artificial Intelligence (AI) methods primarily focus on bleeding region segmentation, overlooking the critical need for accurate bleeding source detection and temporal tracking in the challenging ESD environment, which is marked by frequent visual obstructions and dynamic scene changes. This gap is widened by the lack of specialized datasets, hindering the development of robust AI-assisted guidance systems. To address these challenges, we introduce BleedOrigin-Bench, the first comprehensive ESD bleeding source dataset, featuring 1,771 expert-annotated bleeding sources across 106,222 frames from 44 procedures, supplemented with 39,755 pseudo-labeled frames. This benchmark covers 8 anatomical sites and 6 challenging clinical scenarios. We also present BleedOrigin-Net, a novel dual-stage detection-tracking framework for the bleeding source localization in ESD procedures, addressing the complete workflow from bleeding onset detection to continuous spatial tracking. We compare with widely-used object detection models (YOLOv11/v12), multimodal large language models, and point tracking methods. Extensive evaluation demonstrates state-of-the-art performance, achieving 96.85% frame-level accuracy ($\pm\leq8$ frames) for bleeding onset detection, 70.24% pixel-level accuracy ($\leq100$ px) for initial source detection, and 96.11% pixel-level accuracy ($\leq100$ px) for point tracking.

cs.CV↗

arXiv2025

CATD: Unified Representation Learning for EEG-to-fMRI Cross-Modal Generation

Multi-modal neuroimaging analysis is crucial for a comprehensive understanding of brain function and pathology, as it allows for the integration of different imaging techniques, thus overcoming the limitations of individual modalities. However, the high costs and limited availability of certain modalities pose significant challenges. To address these issues, this paper proposes the Condition-Aligned Temporal Diffusion (CATD) framework for end-to-end cross-modal synthesis of neuroimaging, enabling the generation of functional magnetic resonance imaging (fMRI)-detected Blood Oxygen Level Dependent (BOLD) signals from more accessible Electroencephalography (EEG) signals. By constructing Conditionally Aligned Block (CAB), heterogeneous neuroimages are aligned into a latent space, achieving a unified representation that provides the foundation for cross-modal transformation in neuroimaging. The combination with the constructed Dynamic Time-Frequency Segmentation (DTFS) module also enables the use of EEG signals to improve the temporal resolution of BOLD signals, thus augmenting the capture of the dynamic details of the brain. Experimental validation demonstrates that the framework improves the accuracy of brain activity state prediction by 9.13% (reaching 69.8%), enhances the diagnostic accuracy of brain disorders by 4.10% (reaching 99.55%), effectively identifies abnormal brain regions, enhancing the temporal resolution of BOLD signals. The proposed framework establishes a new paradigm for cross-modal synthesis of neuroimaging by unifying heterogeneous neuroimaging data into a latent representation space, showing promise in medical applications such as improving Parkinson's disease prediction and identifying abnormal brain regions.

cs.CV↗

arXiv2024

Robust non-computability of dynamical systems and computability of robust dynamical systems

In this paper, we examine the relationship between the stability of the dynamical system $x^{\prime}=f(x)$ and the computability of its basins of attraction. We present a computable $C^{\infty}$ system $x^{\prime}=f(x)$ that possesses a computable and stable equilibrium point, yet whose basin of attraction is robustly non-computable in a neighborhood of $f$ in the sense that both the equilibrium point and the non-computability of its associated basin of attraction persist when $f$ is slightly perturbed. This indicates that local stability near a stable equilibrium point alone is insufficient to guarantee the computability of its basin of attraction. However, we also demonstrate that the basins of attraction associated with a structurally stable - globally stable (robust) - planar system defined on a compact set are computable. Our findings suggest that the global stability of a system and the compactness of the domain play a pivotal role in determining the computability of its basins of attraction.

math.LO↗

arXiv2023

Brain Structure-Function Fusing Representation Learning using Adversarial Decomposed-VAE for Analyzing MCI

Integrating the brain structural and functional connectivity features is of great significance in both exploring brain science and analyzing cognitive impairment clinically. However, it remains a challenge to effectively fuse structural and functional features in exploring the brain network. In this paper, a novel brain structure-function fusing-representation learning (BSFL) model is proposed to effectively learn fused representation from diffusion tensor imaging (DTI) and resting-state functional magnetic resonance imaging (fMRI) for mild cognitive impairment (MCI) analysis. Specifically, the decomposition-fusion framework is developed to first decompose the feature space into the union of the uniform and the unique spaces for each modality, and then adaptively fuse the decomposed features to learn MCI-related representation. Moreover, a knowledge-aware transformer module is designed to automatically capture local and global connectivity features throughout the brain. Also, a uniform-unique contrastive loss is further devised to make the decomposition more effective and enhance the complementarity of structural and functional features. The extensive experiments demonstrate that the proposed model achieves better performance than other competitive methods in predicting and analyzing MCI. More importantly, the proposed model could be a potential tool for reconstructing unified brain networks and predicting abnormal connections during the degenerative processes in MCI.

q-bio.NC↗

arXiv2022

Computing the exact number of periodic orbits for planar flows

In this paper, we consider the problem of determining the \emph{exact} number of periodic orbits for polynomial planar flows. This problem is a variant of Hilbert's 16th problem. Using a natural definition of computability, we show that the problem is noncomputable on the one hand and, on the other hand, computable uniformly on the set of all structurally stable systems defined on the unit disk. We also prove that there is a family of polynomial planar systems which does not have a computable sharp upper bound on the number of its periodic orbits.

math.DS↗

arXiv2021

Analytic one-dimensional maps and two-dimensional ordinary differential equations can robustly simulate Turing machines

In this paper, we analyze the problem of finding the minimum dimension $n$ such that a closed-form analytic map/ordinary differential equation can simulate a Turing machine over $\mathbb{R}^{n}$ in a way that is robust to perturbations. We show that one-dimensional closed-form analytic maps are sufficient to robustly simulate Turing machines; but the minimum dimension for the closed-form analytic ordinary differential equations to robustly simulate Turing machines is two, under some reasonable assumptions. We also show that any Turing machine can be simulated by a two-dimensional $C^{\infty}$ ordinary differential equation on the compact sphere $\mathbb{S}^{2}$.

math.LO↗

arXiv2021

Robustness of non-computability

Turing computability is the standard computability paradigm which captures the computational power of digital computers. To understand whether one can create physically realistic devices which have super-Turing power, one needs to understand whether it is possible to obtain systems with super-Turing capabilities which also have other desirable properties such as robustness to perturbations. In this paper we introduce a framework for analyzing whether a non-computability result is robust over continuous spaces. Then we use this framework to study the degree of robustness of several non-computability results which involve the wave equation, differentiation, and basins of attraction.

math.LO↗

arXiv2021

The set of hyperbolic equilibria and of invertible zeros on the unit ball is computable

In this note, we construct an algorithm that, on input of a description of a structurally stable planar dynamical flow $f$ defined on the closed unit disk, outputs the exact number of the (hyperbolic) equilibrium points and their locations with arbitrary accuracy. By arbitrary accuracy it is meant that any accuracy required by the input can be achieved. The algorithm can be further extended to a root-finding algorithm that computes the exact number of zeros as well the location of each zero of a continuously differentiable function $f$ defined on the closed unit ball of $\mathbb{R}^{d}$, provided that the Jacobian of $f$ is invertible at each zero of $f$; moreover, the computation is uniform in $f$.

math.LO↗

arXiv2021

MutualGraphNet: A novel model for motor imagery classification

Motor imagery classification is of great significance to humans with mobility impairments, and how to extract and utilize the effective features from motor imagery electroencephalogram(EEG) channels has always been the focus of attention. There are many different methods for the motor imagery classification, but the limited understanding on human brain requires more effective methods for extracting the features of EEG data. Graph neural networks(GNNs) have demonstrated its effectiveness in classifying graph structures; and the use of GNN provides new possibilities for brain structure connection feature extraction. In this paper we propose a novel graph neural network based on the mutual information of the raw EEG channels called MutualGraphNet. We use the mutual information as the adjacency matrix combined with the spatial temporal graph convolution network(ST-GCN) could extract the transition rules of the motor imagery electroencephalogram(EEG) channels data more effectively. Experiments are conducted on motor imagery EEG data set and we compare our model with the current state-of-the-art approaches and the results suggest that MutualGraphNet is robust enough to learn the interpretable features and outperforms the current state-of-the-art methods.

eess.SP↗

arXiv2019

Computability of the Solutions to Navier-Stokes Equations via Recursive Approximation

As one of the seven open problems in the addendum to their 1989 book "Computability in Analysis and Physics", Pour-El and Richards proposed ``... the recursion theoretic study of particular nonlinear problems of classical importance. Examples are the Navier-Stokes equation, the KdV equation, and the complex of problems associated with Feigenbaum's constant.'' In this paper, we approach the question of whether the Navier-Stokes Equation admits recursive solutions in the sense of Weihrauch's Type-2 Theory of Effectivity. A natural encoding (``representation'') is constructed for the space of divergence-free vector fields on 2-dimensional open square $Ω= (-1, 1)^2$. This representation is shown to render first the mild solution to the Stokes Dirichlet problem and then a strong local solution to the nonlinear inhomogeneous incompressible Navier-Stokes initial value problem uniformly computable. Based on classical approaches, the proofs make use of many subtle and intricate estimates which are developed in the paper for establishing the computability results.

math.AP↗

arXiv2017

Computing geometric Lorenz attractors with arbitrary precision

The Lorenz attractor was introduced in 1963 by E. N. Lorenz as one of the first examples of \emph{strange attractors}. However Lorenz' research was mainly based on (non-rigourous) numerical simulations and, until recently, the proof of the existence of the Lorenz attractor remained elusive. To address that problem some authors introduced geometric Lorenz models and proved that geometric Lorenz models have a strange attractor. In 2002 it was shown that the original Lorenz model behaves like a geometric Lorenz model and thus has a strange attractor. In this paper we show that geometric Lorenz attractors are computable, as well as their physical measures.

math.DS↗

arXiv2016

On Sharpness of the Local Kato Smoothing Property of Dispersive Wave Equations

Constantin and Saut showed in 1988 that solutions of the Cauchy problem for general dispersive equations $$ w_t +iP(D)w=0,\quad w(x,0)=q (x), \quad x\in \mathbb{R}^n, \ t\in \mathbb{R} , $$ enjoy the local smoothing property $$ q\in H^s (\R ^n) \implies w\in L^2 \Big (-T,T; H^{s+\frac{m-1}{2}}_{loc} \left (\R^n\right )\Big ) , $$ where $m$ is the order of the pseudo-differential operator $P(D)$. This property, now called local Kato smoothing, was first discovered by Kato for the KdV equation and implicitly shown later by Sjölin for the linear Schrödinger equation. In this paper, we show that the local Kato smoothing property possessed by solutions general dispersive equations in the 1D case is sharp, meaning that there exist initial data $q\in H^s \left (\R \right )$ such that the corresponding solution $w$ does not belong to the space $ L^2 \Big (-T,T; H^{s+\frac{m-1}{2} +ε}_{loc} \left (\R\right )\Big )$ for any $ε>0$.

math.AP↗

arXiv2014

An analytic system with a computable hyperbolic sink whose basin of attraction is non-computable

In many applications one is interested in finding the stability regions (basins of attraction) of some stationary states (attractors). In this paper we show that one cannot compute, in general, the basins of attraction of even very regular systems, namely analytic systems with hyperbolic asymptotically stable equilibrium points. To prove the main theorems, a new method for embedding a discrete-time system into a continuous-time system is developed.

math.LO↗

arXiv2011

Computability, Noncomputability, and Hyperbolic Systems

In this paper we study the computability of the stable and unstable manifolds of a hyperbolic equilibrium point. These manifolds are the essential feature which characterizes a hyperbolic system. We show that (i) locally these manifolds can be computed, but (ii) globally they cannot (though we prove they are semi-computable). We also show that Smale's horseshoe, the first example of a hyperbolic invariant set which is neither an equilibrium point nor a periodic orbit, is computable.

math.LO↗

arXiv2010

Proceedings Seventh International Conference on Computability and Complexity in Analysis

This volume of the Electronic Proceedings in Theoretical Computer Science (EPTCS) contains extended abstracts of talks to be presented at the Seventh International Conference on Computability and Complexity in Analysis (CCA 2010) that will take place in Zhenjiang, China, June 21-25, 2010. This conference is the seventeenth event in the series of CCA annual meetings. The CCA conferences are aimed at promoting the study and advancement of the theory of computability and complexity over real-valued data and its application.

cs.CC↗

arXiv2008

On Granular Knowledge Structures

Knowledge plays a central role in human and artificial intelligence. One of the key characteristics of knowledge is its structured organization. Knowledge can be and should be presented in multiple levels and multiple views to meet people's needs in different levels of granularities and from different perspectives. In this paper, we stand on the view point of granular computing and provide our understanding on multi-level and multi-view of knowledge through granular knowledge structures (GKS). Representation of granular knowledge structures, operations for building granular knowledge structures and how to use them are investigated. As an illustration, we provide some examples through results from an analysis of proceeding papers. Results show that granular knowledge structures could help users get better understanding of the knowledge source from set theoretical, logical and visual point of views. One may consider using them to meet specific needs or solve certain kinds of problems.

cs.AI↗