Related papers: Topological Data Analysis for Directed Dependence …
Heterogeneous presentation of a neurological disorder suggests potential differences in the underlying pathophysiological changes that occur in the brain. We propose to model heterogeneous patterns of functional network differences using a…
Networks - collections of interacting elements or nodes - abound in the natural and manmade worlds. For many networks, complex spatiotemporal dynamics stem from patterns of physical interactions unknown to us. To infer these interactions,…
Coherence analysis plays a vital role in the study of functional brain connectivity. However, coherence captures only linear spectral associations, and thus can produce misleading findings when ignoring variations of connectivity in the…
Emerging brain network studies suggest that interactions between various distributed neuronal populations may be characterized by an organized complex topological structure. Many brain diseases are associated with altered topological…
This study integrates causal inference, graph analysis, temporal complexity measures, and machine learning to examine whether individual symptom trajectories can reveal meaningful diagnostic patterns. Testing on a longitudinal dataset of…
We present a topological framework for analysing neural time series that integrates Transfer Entropy (TE) with directed Persistent Homology (PH) to characterize information flow in spiking neural systems. TE quantifies directional influence…
The study of irreducible higher-order interactions has become a core topic of study in complex systems. Two of the most well-developed frameworks, topological data analysis and multivariate information theory, aim to provide formal tools…
Artificial Neural Networks (ANNs) require significant amounts of data and computational resources to achieve high effectiveness in performing the tasks for which they are trained. To reduce resource demands, various techniques, such as…
In increasingly many settings, data sets consist of multiple samples from a population of networks, with vertices aligned across these networks. For example, brain connectivity networks in neuroscience consist of measures of interaction…
This paper develops limit theorems for random variables with network dependence, without requiring the individuals in the network to be located in a Euclidean or metric space. This distinguishes our approach from most existing limit…
Over the last years, increasing evidence has fuelled the hypothesis that Autism Spectrum Disorder (ASD) is a condition of altered brain functional connectivity. The great majority of these empirical studies rely on functional magnetic…
Topological data analysis (TDA) detects geometric structure in biological data. However, many TDA algorithms are memory intensive and impractical for massive datasets. Here, we introduce a statistical protocol that reduces TDA's memory…
There is a wide availability of methods for testing normality under the assumption of independent and identically distributed data. When data are dependent in space and/or time, however, assessing and testing the marginal behavior is…
Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…
With the growth of information on the Web, most users heavily rely on information access systems (e.g., search engines, recommender systems, etc.) in their daily lives. During this procedure, modeling users' satisfaction status plays an…
Epilepsy is a neurological disorder arising from anomalies of the electrical activity in the brain, affecting about 0.5--0.8\% of the world population. Several studies investigated the relationship between seizures and brainwave…
One of the most important problems arising in time series analysis is that of bifurcation, or change point detection. That is, given a collection of time series over a varying parameter, when has the structure of the underlying dynamical…
Brain connectivity analysis based on magnetic resonance imaging is crucial for understanding neurological mechanisms. However, edge-based connectivity inference faces significant challenges, particularly the curse of dimensionality when…
This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to a wide variety of time-varying graphs. For…
Epileptic seizure detection and classification in clinical electroencephalogram data still is a challenge, and only low sensitivity with a high rate of false positives has been achieved with commercially available seizure detection tools,…