• Large-deviation theory for dilutedWishart random matrices 

      Pérez-Castillo, Isaac; Metz, Fernando Lucas (2018) [Artigo de periódico]
      Wishart random matrices with a sparse or diluted structure are ubiquitous in the processing of large datasets, with applications in physics, biology, and economy. In this work, we develop a theory for the eigenvalue ...
    • Locating eigenvalues of a symmetric matrix whose graph is unicyclic 

      Braga, Rodrigo Orsini; Rodrigues, Virginia Maria; Silva, Rafaela Oliveira da (2021) [Artigo de periódico]
      We present a linear-time algorithm that computes in a given real interval the number of eigenvalues of any symmetric matrix whose underlying graph is unicyclic. The algorithm can be applied to vertex- and/or edge-weighted ...
    • Locating eigenvalues of perturbed laplacian matrices of trees 

      Braga, Rodrigo Orsini; Rodrigues, Virginia Maria (2017) [Artigo de periódico]
      We give a linear time algorithm to compute the number of eigenvalues of any perturbed Laplacian matrix of a tree in a given real interval. The algorithm can be applied to weighted or unweighted trees. Using our method we ...
    • Locating eigenvalues of symmetric matrices - a survey 

      Hoppen, Carlos; Jacobs, David; Trevisan, Vilmar (2024) [Artigo de periódico]
      We survey algorithms for locating eigenvalues of symmetric matrices taking advantage of the underlying graph. We present applications in spectral graph theory.
    • Replica symmetry breaking in the transverse-field Ising spin-glass model : two fermionic representations 

      Santos, Eduardo Muccillo Monteiro; Theumann, Alba Graciela Rivas de (2005) [Artigo de periódico]
      We analyze the infinite range Ising spin glass in a transverse-field below the critical temperature by a one step replica symmetry breaking theory. The set of n replicas is divided in r blocks of m replicas each. We present ...
    • Robustness of the quadratic partial eigenvalue assignment using spectrum sensitivities for state and derivative feedback designs 

      Araújo, José Mario; Dórea, Carlos Eduardo Trabuco; Gonçalves, Luiz Marcos Garcia; Carvalho, Joao Batista da Paz; Datta, Biswa Nath (2018) [Artigo de periódico]
      Based on the notions of spectrum sensitivities, proposed by us earlier, we develop a novel optimization approach to deal with robustness in the closed-loop eigenvalues for partial quadratic eigenvalue assignment problem ...
    • Theory for the conditioned spectral density of noninvariant random matrices 

      Pérez-Castillo, Isaac; Metz, Fernando Lucas (2018) [Artigo de periódico]
      We develop a theoretical approach to compute the conditioned spectral density of N × N noninvariant random matrices in the limit N →∞. This large deviation observable, defined as the eigenvalue distribution conditioned to ...