Related papers: Stochastic Graph Heat Modelling for Diffusion-base…
Complex networks are the representative graphs of interactions in many complex systems. Usually, these interactions are abstractions of the communication/diffusion channels between the units of the system. Real complex networks, e.g.…
Network theory provides a principled abstraction of the human brain: reducing a complex system into a simpler representation from which to investigate brain organisation. Recent advancement in the neuroimaging field are towards representing…
The joint analysis of biomedical data in Alzheimer's Disease (AD) is important for better clinical diagnosis and to understand the relationship between biomarkers. However, jointly accounting for heterogeneous measures poses important…
Early and accurate detection of Alzheimer's disease (AD) is crucial for enabling timely intervention and improving outcomes. However, developing reliable machine learning (ML) models for AD diagnosis is challenging due to limited labeled…
Graph neural networks (GNNs) have demonstrated significant promise in modelling relational data and have been widely applied in various fields of interest. The key mechanism behind GNNs is the so-called message passing where information is…
Graph generative modelling has become an essential task due to the wide range of applications in chemistry, biology, social networks, and knowledge representation. In this work, we propose a novel framework for generating graphs by adapting…
The aim of this article is to discuss the estimation of the diffusivity coefficient of a homogeneous metal rod from temperature values at a fixed point in the bar for different time instants. The time-dependent problem of heat conduction is…
Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely…
Graph is a prevalent discrete data structure, whose generation has wide applications such as drug discovery and circuit design. Diffusion generative models, as an emerging research focus, have been applied to graph generation tasks.…
We consider the steady heat transfer between a collection of impermeable obstacles immersed in an incompressible 2D potential flow, when each obstacle has a prescribed boundary temperature distribution. Inside the fluid, the temperature…
Alzheimer's disease (AD) is the most prevalent form of dementia. Traditional methods cannot achieve efficient and accurate diagnosis of AD. In this paper, we introduce a novel method based on dynamic functional connectivity (dFC) that can…
In this paper, we study the graph classification problem in vertex-labeled graphs. Our main goal is to classify the graphs comparing their higher-order structures thanks to heat diffusion on their simplices. We first represent…
In this work, a thermal energy transfer problem in a one-dimensional multilayer body is theoretically analyzed, considering diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, as well as…
Graph models are widely used to analyse diffusion processes embedded in social contacts and to develop applications. A range of graph models are available to replicate the underlying social structures and dynamics realistically. However,…
We propose a one-dimensional (1D) diffusion equation (heat equation) for systems in which the diffusion constant (thermal diffusivity) varies alternately with a spatial period $a$. We solve the time evolution of the field (temperature)…
Denoising Diffusion Probabilistic Models (DDPM) process images as a whole. Since adjacent pixels are highly likely to belong to the same object, we propose the Heat Diffusion Model (HDM) to further preserve image details and generate more…
Diffusion-based classifiers such as those relying on the Personalized PageRank and the Heat kernel, enjoy remarkable classification accuracy at modest computational requirements. Their performance however is affected by the extent to which…
Graph-based semi-supervised learning usually involves two separate stages, constructing an affinity graph and then propagating labels for transductive inference on the graph. It is suboptimal to solve them independently, as the correlation…
This paper explores the application diffusion maps as graph shift operators in understanding the underlying geometry of graph signals. The study evaluates the improvements in graph learning when using diffusion map generated filters to the…
Anatomical Landmark Detection is the process of identifying key areas of an image for clinical measurements. Each landmark is a single ground truth point labelled by a clinician. A machine learning model predicts the locus of a landmark as…