Cooperation in Kohonen Maps

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The Nerve and Geometric Realization

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Topological Waves for Robust Signal Processing Applications

Explores topological waves for robust signal processing applications, focusing on resistance to perturbations and the design paradigm of topological systems.

Categorical Perspective: Group Actions

Generalizes group actions beyond sets, providing a comprehensive framework for various mathematical contexts.

Ringed Spaces: Definitions and Properties

Covers the definitions and properties of ringed spaces, including morphisms and examples of locally ringed spaces.

Modular curves: Riemann surfaces and transition maps

Covers modular curves as compact Riemann surfaces, explaining their topology, construction of holomorphic charts, and properties.

Topology: Homotopy and Projective Spaces

Discusses homotopy, projective spaces, and the universal property of quotient spaces in topology.

Topology: Separation Criteria and Quotient Spaces

Discusses separation criteria and quotient spaces in topology, emphasizing their applications and theoretical foundations.

Homology of Riemann Surfaces

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

Topology: Homotopy and Cone Attachments

Discusses homotopy and cone attachments in topology, emphasizing their significance in understanding connected components and fundamental groups.