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High-order interaction occurs in various complex network, such as social network, bionetwork and network medicine. Comparing with that there are a lot of well-developed math tools (from graph theory) ...
Along with the rapid development of artificial intelligence (AI) technology, scientific research enters a new era of AI. Topology optimization (TO) and AI technology are recently showing a growing tre...
Modern algebraic topology sees equivariance arising in unexpected context. Equivariant cohomology carries rich structures but is much harder to compute. In 2009, Hill, Hopkins, and Ravenel solved the ...
Topology and entanglement are two powerful principles for characterizing the structure of complex quantum states. In a new paper in the journal Physical Review X, researchers from the University of Pe...
The study of Hamiltonian dynamical systems plays a fundamental role in many different contexts, both in pure and applied mathematics. Indeed, most of the physical laws ruling our everyday lives --the ...
This is the seventh annual Tech Topology Conference. It brings together established and beginning researchers from around the country for a weekend of mathematics in Atlanta. Check back soon for more ...
Computer experiments and calculations have had a profound influence on many areas covered by this Symposium. In 3-manifold theory the program SnapPea has been widely used to explore the landscape of 3...
As one of most important objects in mathematics, ‘manifold’ has provided us more and more insights and benefits. In the past half century, more and more different areas in mathematics have been inters...
Given the fundamental importance of moduli spaces and their applications in many different topics, we are organizing a week long conference titled "Moduli spaces and applications in geometry, topology...
An interesting example of a compact Hausdorff space that is often presented in beginning courses in topology is the unit square [0, 1]× [0, 1] with the lexicographic order topology. The closed subspac...
An understanding of stream network topology is necessary for a landscape-level perspective of stream hydrology and ecology. We present a method for quantifying stream network topology that overcomes c...
We discuss selected topics on the topology of moduli spaces of curves and maps, emphasizing their relationwith GromovWitten theory and integrable systems
SGDM (Sphere Grid Data Model) is an efficient method to deal with the global data because of the advantages of multi-resolution and hierarchy. However, SGDM has no distinct descriptions and lack of r...
In this paper we present a method for synthesis of decentralized controllers for multiple identical systems interconnected on a graph. We develop a synthesis procedure for controllers which will stabi...
In this paper we present a method for synthesis of decentralized controllers for systems interconnected on a graph. We develop a synthesis procedure which will achieve a specified level of performance...

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