5 papers
Hierarchical Minimum Variance Portfolios: A Theoretical and Algorithmic Approach
Gamal Mograby
We introduce a novel approach to portfolio optimization that leverages hierarchical graph structures and the Schur complement method to systematically reduce computational complexi…
Spectral decimation of piecewise centrosymmetric Jacobi operators on graphs
Gamal Mograby, Radhakrishnan Balu, Kasso A. Okoudjou +1
We study the spectral theory of a class of piecewise centrosymmetric Jacobi operators defined on an associated family of substitution graphs. Given a finite centrosymmetric matrix…
Spectra of three-peg Hanoi towers graphs
Brett Hungar, Gamal Mograby, Madison Phelps +2
We consider the relationship between the Laplacians on two sequences of planar graphs, one from the theory of self-similar groups and one from analysis on fractals. By establishing…
Discretization of the Koch Snowflake Domain with Boundary and Interior Energies
Malcolm Gabbard, Carlos Lima, Gamal Mograby +2
We study the discretization of a Dirichlet form on the Koch snowflake domain and its boundary with the property that both the interior and the boundary can support positive energy.…
Harmonic Gradients on Higher Dimensional Sierpinski Gaskets
Luke Brown, Giovanni Ferrer, Gamal Mograby +2
We consider criteria for the differentiability of functions with continuous Laplacian on the Sierpinski Gasket and its higher-dimensional variants , , proving results th…