Higher-order Interactions in Brain Networks

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Topology in Complex Networks: Insights from Topological Data Analysis

Explores the role of higher-order topological properties in complex networks using topological data analysis for structural break and price anomaly detection.

Homology Theorem

Covers the proof of Theorem A, discussing homology, quotients, and isomorphisms.

Simplicial Homology Revisited

Covers the concept of simplicial homology, focusing on finite complexes and induced maps.

Approaches and Rationale of Simulation Neuroscience

Explores the overview, rationale, and strategies of simulation neuroscience, emphasizing the challenges of reconstructing and simulating the brain.

Topological Data Science

Delves into Topological Data Analysis, emphasizing the mathematical foundations of neural networks and exploring the manifold hypothesis and persistent homology.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Extensions to Exchangeability: Statistical Analysis of Network Data

Covers extensions to exchangeability in network data analysis, including graphon frameworks and edge exchangeability.

Homology Groups: Basics

Introduces reduced homology groups and explains their properties and applications in topology.

Topological Data Science

Delves into Topological Data Analysis, exploring the shape of data and its underlying structure through mathematical tools and concepts.

Excision: An Example

Covers the concept of excision in algebraic topology with a focus on simplicial and singular homology.