Eigenvalues associated to graphs are a well-studied subject. In particular the spectra of the adjacency matrix and of the Laplacian of random graphs G(n,p) are known quite precisely. We considerâ€¦ (More)

4 For graphs there exists a strong connection between spectral and combinatorial 5 expansion properties. This is expressed, e.g., by the discrete Cheeger inequality, the 6 lower bound of which statesâ€¦ (More)

We consider higher-dimensional generalizations of the normalized Laplacian and the adjacency matrix of graphs and study their eigenvalues for the Linialâ€“Meshulam model X(n, p) of random k-dimensionalâ€¦ (More)

Risk assessment for acute airborne exposure to volatile organic compounds (VOCs), including exposure to chemical warfare agents, requires consideration of local and systemic effects at highâ€¦ (More)

We introduce a generalization of the celebrated LovÃ¡sz theta number of a graph to simplicial complexes of arbitrary dimension. Our generalization takes advantage of real simplicial cohomology theory,â€¦ (More)

For graphs there exists a strong connection between spectral and combinatorial expansion properties. This is expressed, e.g., by the discrete Cheeger inequality, the lower bound of which states thatâ€¦ (More)

A basic statement in graph theory is that every inclusion-maximal forest is connected, i.e. a tree. Using a definiton for higher dimensional forests by Graham and LovÃ¡sz and the connectivity-relatedâ€¦ (More)

Simplicial Complexes. A (finite abstract) simplicial complex is a finite set system that is closed under taking subsets, i.e., F âŠ‚ H âˆˆ X implies F âˆˆ X. The sets F âˆˆ X are called faces of X. Theâ€¦ (More)