In the movie Legally Blonde, a civil procedure professor tells her first-year students on their first day of class at Harvard Law School that Aristotle stated, “The law is reason free from passion.” Since Aristotle, there has been much written about whether passion and reason are complements or substitutes. In Two Conceptions of Emotion in Risk Regulation, Professor Dan M. Kahan analyzes two im...

Let A and C be self-adjoint operators such that the spectrum of A lies in a gap of the spectrum of C and let d > 0 be the distance between the spectra of A and C . We prove that under these assumptions the sharp value of the constant c in the condition ‖B‖ < cd implying the solvability of the operator Riccati equation XA−CX+XBX = B∗ is equal to √ 2. We also prove an extension of the Davis-Kahan...

Generalized matrix functions (GMFs) extend the concept of a matrix function to rectangular matrices via the singular value decomposition. Several applications involving directed graphs, Hamiltonian dynamical systems, and optimization problems with low-rank constraints require the action of a GMF of a large, sparse matrix on a vector. We present a new method for applying GMFs to vectors based on...

We introduce a randomized algorithm for computing the minimal-norm solution to an underdetermined system of linear equations. Given an arbitrary full-rank matrix Am×n with m < n, any vector bm×1, and any positive real number ε less than 1, the procedure computes a vector xn×1 approximating to relative precision ε or better the vector pn×1 of minimal Euclidean norm satisfying Am×n pn×1 = bm×1. T...

We study a model of opinion exchange in social networks where state the world is realized and every agent receives zero-mean noisy signal state. It known from Golub Jackson that under DeGroot dynamics agents reach consensus which close to when network large. The dynamics, however, highly non-robust presence single `bot' does not adhere updating rule, can sway public any other value.

it is well known that if the coefficient matrix in a linear system is large and sparse or sometimes not readily available, then iterative solvers may become the only choice. the block solvers are an attractive class of iterative solvers for solving linear systems with multiple right-hand sides. in general, the block solvers are more suitable for dense systems with preconditioner. in this paper,...

Abstract. Much of the work of Golub and his collaborators uses techniques of linear algebra to deal with problems in analysis, or employs tools from analysis to solve problems arising in linear algebra. Instances are described of such interdisciplinary work, taken from quadrature theory, orthogonal polynomials, and least squares problems on the one hand, and error analysis for linear algebraic ...

Rameen Beroukhim*, Gad Getz*, Leia Nghiemphu, Jordi Barretina, Teli Hsueh, David Linhart, Igor Vivanco, Jeffrey C. Lee, Julie H. Huang, Sethu Alexander, Jinyan Du, Tweeny Kau, Roman K. Thomas, Kinjal Shah, Horacio Soto, Sven Perner, John Prensner, Ralph M. Debiasi, Francesca Demichelis, Charlie Hatton, Mark A. Rubin, Levi A. Garraway, Stan F. Nelson, Linda Liau, Paul Mischel, Tim F. Cloughesy, ...