Related papers: Topologically Invariant Permutation Test
Persistent homology (PH) characterizes the shape of brain networks through persistence features. Group comparison of persistence features from brain networks can be challenging as they are inherently heterogeneous. A recent scale-space…
Subtle alterations in brain network topology often evade detection by traditional statistical methods. To address this limitation, we introduce a Bayesian inference framework for topological comparison of brain networks that…
This work introduces a novel framework for testing topological variability in weighted networks by combining Hodge decomposition with Wasserstein variance minimization. Traditional approaches that analyze raw edge weights are susceptible to…
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…
This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient…
Developing reliable methods to discriminate different transient brain states that change over time is a key neuroscientific challenge in brain imaging studies. Topological data analysis (TDA), a novel framework based on algebraic topology,…
Persistent homology has been applied to brain network analysis for finding the shape of brain networks across multiple thresholds. In the persistent homology, the shape of networks is often quantified by the sequence of $k$-dimensional…
Persistent homology offers a powerful tool for extracting hidden topological signals from brain networks. It captures the evolution of topological structures across multiple scales, known as filtrations, thereby revealing topological…
Multi-band insulating Bloch Hamiltonians with internal or spatial symmetries, such as particle-hole or inversion, may have topologically disconnected sectors of trivial atomic-limit (momentum-independent) Hamiltonians. We present a…
The study of topological properties by machine learning approaches has attracted considerable interest recently. Here we propose machine learning the topological invariants that are unique in non-Hermitian systems. Specifically, we train…
Topological invariants are crucial for characterizing topological systems. However, experimentally measuring them presents a significant challenge, especially in non-Hermitian systems where the biorthogonal eigenvectors are often necessary.…
We discuss and demonstrate an unsupervised machine-learning procedure to detect topological order in quantum many-body systems. Using a restricted Boltzmann machine to define a variational ansatz for the low-energy spectrum, we sample wave…
Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…
Topological invariants allow to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wavefunctions under twisted boundary…
We use methods from computational algebraic topology to study functional brain networks, in which nodes represent brain regions and weighted edges encode the similarity of fMRI time series from each region. With these tools, which allow one…
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…
Recently, graph theory has become a popular method for characterizing brain functional organization. One important goal in graph theoretical analysis of brain networks is to identify network differences across disease types or conditions.…
Understanding the common topological characteristics of the human brain network across a population is central to understanding brain functions. The abstraction of human connectome as a graph has been pivotal in gaining insights on the…
We consider the problem of testing positively dependent multiple hypotheses assuming that a prior information about the dependence structure is available. We propose two-step multiple comparisons procedures that exploit the prior…
We introduce an innovative, data-driven topological data analysis (TDA) technique for estimating the state spaces of dynamically changing functional human brain networks at rest. Our method utilizes the Wasserstein distance to measure…