Related papers: Topological Data Analysis of Task-Based fMRI Data …
As complex networks find applications in a growing range of disciplines, the diversity of naturally occurring and model networks being studied is exploding. The adoption of a well-developed collection of network taxonomies is a natural…
The human brain forms functional networks on all spatial scales. Modern fMRI scanners allow to resolve functional brain data in high resolutions, allowing to study large-scale networks that relate to cognitive processes. The analysis of…
Mild cognitive impairment (MCI) is characterized by subtle changes in cognitive functions, often associated with disruptions in brain connectivity. The present study introduces a novel fine-grained analysis to examine topological…
Smart systems that can accurately diagnose patients with mental disorders and identify effective treatments based on brain functional imaging data are of great applicability and are gaining much attention. Most previous machine learning…
The functional network of the brain continually adapts to changing environmental demands. The environmental changes closely connect with changes of active cognitive processes. In recent years, the network approach has emerged as a promising…
Persistent homology (PH) characterizes the shape of brain networks through the persistence features. Group comparison of persistence features from brain networks can be challenging as they are inherently heterogeneous. A recent scale-space…
Computational topologists recently developed a method, called persistent homology to analyze data presented in terms of similarity or dissimilarity. Indeed, persistent homology studies the evolution of topological features in terms of a…
Typical brain networks consist of many peripheral regions and a few highly central ones, i.e. hubs, playing key functional roles in cerebral inter-regional interactions. Studies have shown that networks, obtained from the analysis of…
This paper aims to discuss a method of quantifying the 'shape' of data, via a methodology called topological data analysis. The main tool within topological data analysis is persistent homology; this is a means of measuring the shape of…
Spatial transcriptomics studies are becoming increasingly large and commonplace, necessitating simultaneous analysis of a large number of spatially resolved variables. Correspondingly, a diverse range of methodologies have been proposed to…
Vascular networks play a crucial role in understanding brain functionalities. Brain integrity and function, neuronal activity and plasticity, which are crucial for learning, are actively modulated by their local environments, specifically…
Understanding brain connectivity has become one of the most important issues in neuroscience. But connectivity data can reflect either the functional relationships of the brain activities or the anatomical properties between brain areas.…
Complex networks encountered in biology are often characterized by significant structural diversity. Whether it be differences in the three-dimensional structure of allosteric proteins, or the variation among the micro-scale structures of…
Real-world networks often benefit from capturing both local and global interactions. Inspired by multi-modal analysis in brain imaging, where structural and functional connectivity offer complementary views of network organization, we…
This paper introduces a topological framework for interpreting the internal representations of Multilayer Perceptrons (MLPs). We construct a simplicial tower, a sequence of simplicial complexes connected by simplicial maps, that captures…
Network neuroscience shed some light on the functional and structural modifications occurring to the brain associated with the phenomenology of schizophrenia. In particular, resting-state functional networks have helped our understanding of…
Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…
Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be…
Understanding the structure of high-dimensional data is fundamental to neuroscience and other data-intensive scientific fields. While persistent homology effectively identifies basic topological features such as "holes," it lacks the…
In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals…