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Cybersecurity: Introduction to Steganography
No full textThis is part of a series of lessons that teach 9th-12th graders about cybersecurity. This lesson begins with a reminder to the students about ethics and cybersecurity and is followed by a problem scenario that introduces the topic of steganography. Students are expected to contribute and explore options and solutions to the problem scenario, followed by a lesson on steganography where students will practice creating their own steganography models as examples. This lesson concludes by having the learners exchange their finished projects (a game) for fellow students to decode the clues as they play the game
Winant, G. (2021). The Next Shift: The Fall of Industry and the Rise of Health Care in Rust Belt America. Harvard University Press.
No full textOn the Ky Fan -norm of the -matrix of graphs
No full textLet and be the adjacency matrix and the degree diagonal matrix of a graph , respectively. Then is called Laplacian matrix of the graph . Let be a graph with vertices and edges. Then the -matrix of is defined as , where is the identity matrix. In this paper, we are interested in extremal properties of the Ky Fan -norm of the -matrix of graphs, which is closely related to the well known problems and results in spectral graph theory, such as the Laplacian spectral radius, the Laplacian spread, the sum of the largest Laplacian eigenvalues, the Laplacian energy, and other parameters. Some bounds on the Ky Fan -norm of the -matrix of graphs are given, and the extremal graphs are partly characterized. In addition, upper and lower bounds on the Ky Fan -norm of -matrix of trees, unicyclic graphs, and bicyclic graphs are determined, and the corresponding extremal graphs are characterized
Jordan chains of h-cyclic matrices, II
No full textMcDonald and Paparella [Linear Algebra Appl. 498 (2016), 145-159] gave a necessary condition on the structure of the Jordan chains of h-cyclic matrices. In this work, that necessary condition is shown to be sufficient. As a consequence, we provide a spectral characterization of nonsingular, h-cyclic matrices
A note on bounds for eigenvalues of nonsingular H-tensors
No full textA counterexample to a theorem in the paper ELA 29:3-16, (2015) is provided, and an upper bound on the H-spectral radius of H-tensors is given
Accurate computations with totally positive matrices applied to the computation of Gaussian quadrature formulae
No full textFor some families of classical orthogonal polynomials defined on appropriate intervals, it is shown that the corresponding Jacobi matrices are totally positive and their bidiagonal factorizations can be accurately computed. By exploiting these facts, an algorithm to compute with high relative accuracy the eigenvalues of those Jacobi matrices, and consequently the nodes of Gaussian quadrature formulae for those families of orthogonal polynomials, is presented. An algorithm is also presented for the computation of the eigenvectors of these Jacobi matrices, and hence the weights of Gaussian quadrature formulae. Although in this case high relative accuracy is not theoretically guaranteed, the numerical experiments with our algorithm provide very accurate results
Recovering the characteristic polynomial of a graph from entries of the adjugate matrix
No full textThe adjugate matrix of , denoted by , is the adjugate of the matrix , where is the adjacency matrix of . The polynomial reconstruction problem (PRP) asks if the characteristic polynomial of a graph can always be recovered from the multiset containing the characteristic polynomials of the vertex-deleted subgraphs of . Noting that the diagonal entries of are precisely the elements of , we investigate variants of the PRP in which multisets containing entries from successfully reconstruct the characteristic polynomial of . Furthermore, we interpret the entries off the diagonal of in terms of characteristic polynomials of graphs, allowing us to solve versions of the PRP that utilize alternative multisets to containing polynomials related to characteristic polynomials of graphs, rather than entries from
