相关论文: Using persistent homology to reveal hidden informa…

Persistent homology (PH) is a recently developed theory in the field of algebraic topology to study shapes of datasets. It is an effective data analysis tool that is robust to noise and has been widely applied. We demonstrate a general…

Statistical similarities between neuronal spike trains could reveal significant information on complex underlying processing. In general, the similarity between synchronous spike trains is somewhat easy to identify. However, the similar…

Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…

Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…

Encoding models are used for predicting brain activity in response to sensory stimuli with the objective of elucidating how sensory information is represented in the brain. Encoding models typically comprise a nonlinear transformation of…

Identifying molecular signatures from complex disease patients with underlying symptomatic similarities is a significant challenge in the analysis of high dimensional multi-omics data. Topological data analysis (TDA) provides a way of…

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…

Understanding the interaction patterns among simultaneous recordings of spike trains from multiple neuronal units is a key topic in neuroscience. However, an optimal approach of assessing these interactions has not been established, as…

Persistent Homology (PH) is a fundamental tool in computational topology, designed to uncover the intrinsic geometric and topological features of data across multiple scales. Originating within the broader framework of Topological Data…

We present a novel method to explicitly incorporate topological prior knowledge into deep learning based segmentation, which is, to our knowledge, the first work to do so. Our method uses the concept of persistent homology, a tool from…

The relationship between a neuron's complex inputs and its spiking output defines the neuron's coding strategy. This is frequently and effectively modeled phenomenologically by one or more linear filters that extract the components of the…

Plasticity is one of the most important properties of the nervous system, which enables animals to adjust their behavior to the ever-changing external environment. Changes in synaptic efficacy between neurons constitute one of the major…

Topological data analysis is an emerging mathematical concept for characterizing shapes in multi-scale data. In this field, persistence diagrams are widely used as a descriptor of the input data, and can distinguish robust and noisy…

Convolutional neural networks (CNNs) are a standard tool for computer vision tasks such as image classification. However, typical model architectures may result in the loss of topological information. In specific domains such as…

This article presents a biological neural network model driven by inhomogeneous Poisson processes accounting for the intrinsic randomness of synapses. The main novelty is the introduction of local interactions: each firing neuron triggers…

For energy-efficient computation in specialized neuromorphic hardware, we present spiking neural coding, an instantiation of a family of artificial neural models grounded in the theory of predictive coding. This model, the first of its…

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 present a novel topological framework for analyzing functional brain signals using time-frequency analysis. By integrating persistent homology with time-frequency representations, we capture multi-scale topological features that…

Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. The output of persistent homology is a persistence diagram --…

Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…