相关论文: Topological inference on brain networks with appli…

Segmenting multiple objects (e.g., organs) in medical images often requires an understanding of their topology, which simultaneously quantifies the shape of the objects and their positions relative to each other. This understanding is…

While cognitive representations of an environment can last for days and even months, the synaptic architecture of the neuronal networks that underlie these representations constantly changes due to various forms of synaptic and structural…

Skin cancer is one of the most common cancers in the United States. As technological advancements are made, algorithmic diagnosis of skin lesions is becoming more important. In this paper, we develop algorithms for segmenting the actual…

Functional brain connectivity, as revealed through distant correlations in the signals measured by functional Magnetic Resonance Imaging (fMRI), is a promising source of biomarkers of brain pathologies. However, establishing and using…

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…

Inference of the network structure (e.g., routing topology) and dynamics (e.g., link performance) is an essential component in many network design and management tasks. In this paper we propose a new, general framework for analyzing and…

Investigation of human brain states through electroencephalograph (EEG) signals is a crucial step in human-machine communications. However, classifying and analyzing EEG signals are challenging due to their noisy, nonlinear and…

Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and…

Hierarchical Temporal Memory (HTM) is a computational theory of machine intelligence based on a detailed study of the neocortex. The Heidelberg Neuromorphic Computing Platform, developed as part of the Human Brain Project (HBP), is a…

Accurately characterizing higher-order interactions of brain regions and extracting interpretable organizational patterns from Functional Magnetic Resonance Imaging data is crucial for brain disease diagnosis. Current graph-based deep…

Most functional magnetic resonance imaging studies rely on estimates of hierarchically organized functional brain networks whose segregation and integration reflect the cognitive and behavioral changes in humans. However, most existing…

The topological morphology descriptor of a neuron is a multiset of intervals associated to the shape of the neuron represented as a tree. In practice, topological morphology descriptors are vectorized using persistence images, which can…

Neuroimaging produces data that are continuous in one or more dimensions. This calls for an inference framework that can handle data that approximate functions of space, for example, anatomical images, time--frequency maps and distributed…

Classification of large and dense networks based on topology is very difficult due to the computational challenges of extracting meaningful topological features from real-world networks. In this paper we present a computationally tractable…

The Persistent Homology Transform (PHT) was introduced in the field of Topological Data Analysis about 10 years ago, and has since been proven to be a very powerful descriptor of Euclidean shapes. The PHT consists of scanning a shape from…

Topological invariants have played a fundamental role in the advancement of theoretical high energy physics. Physicists have used several kinematic techniques to distinguish new physics predictions from the Standard Model (SM) of particle…

With the advances in high resolution neuroimaging, there has been a growing interest in the detection of functional brain connectivity. Complex network theory has been proposed as an attractive mathematical representation of functional…

The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world…

Brain network topology, derived from functional magnetic resonance imaging (fMRI), holds promise for improving Alzheimer's disease (AD) diagnosis. Current methods primarily focus on lower-order topological features, often overlooking the…

We propose PLLay, a novel topological layer for general deep learning models based on persistence landscapes, in which we can efficiently exploit the underlying topological features of the input data structure. In this work, we show…