29 citations · 65 across the 11 of their papers we have counts for
11 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…
Quantitative approach to Grover's quantum walk on graphs
Gamal Mograby, Radhakrishnan Balu, Kasso A. Okoudjou +1
In this paper, we study Grover's search algorithm focusing on continuous-time quantum walk on graphs. We propose an alternative optimization approach to Grover's algorithm on graph…
Gaps labeling theorem for the Bubble-diamond self-similar graphs
Elizabeth Melville, Gamal Mograby, Nikhil Nagabandi +2
Motivated by the appearance of fractals in several areas of physics, especially in solid state physics and the physics of aperiodic order, and in other sciences, including the quan…
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…
Spectral decimation of a self-similar version of almost Mathieu-type operators
Gamal Mograby, Radhakrishnan Balu, Kasso A. Okoudjou +1
We introduce self-similar versions of the one-dimensional almost Mathieu operators. Our definition is based on a class of self-similar Laplacians instead of the standard discrete L…
Hamiltonian systems, Toda lattices, Solitons, Lax Pairs on weighted Z-graded graphs
Gamal Mograby, Maxim Derevyagin, Gerald V. Dunne +1
We consider discrete one dimensional nonlinear equations and present the procedure of lifting them to Z-graded graphs. We identify conditions which allow one to lift one dimensiona…
Spectra of Perfect State Transfer Hamiltonians on Fractal-Like Graphs
Gamal Mograby, Maxim Derevyagin, Gerald V. Dunne +1
In this paper we study the spectral features, on fractal-like graphs, of Hamiltonians which exhibit the special property of perfect quantum state transfer: the transmission of quan…
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.…
Perfect quantum state transfer on diamond fractal graphs
Maxim Derevyagin, Gerald V. Dunne, Gamal Mograby +1
In the quest for designing novel protocols for quantum information and quantum computation, an important goal is to achieve perfect quantum state transfer for systems beyond the we…
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…