Let G be a graph on n vertices. A 2-lift of G is a graph H on 2n vertices, with a covering map π : H → G. It is not hard to see that all eigenvalues of G are also eigenvalues of H. In addition, H has n “new” eigenvalues. We conjecture that every d-regular graph has a 2-lift such that all new eigenvalues are in the range [−2 √ d− 1, 2 √ d− 1] (If true, this is tight , e.g. by the Alon-Boppana bo...

A high performance numerical technique in the study of aorto-coronaric bypass anastomoses configurations using steady Stokes equations is presented. The problem is first expressed as an optimal control problem. Then, by using an embedding method, the class of admissible shapes is replaced by a class of positive Borel measures. The optimization problem in measure space is then approximated by ...

Principal component analysis (PCA) has been widely used in analyzing high-dimensional data. It converts a set of observed data points possibly correlated variables into linearly uncorrelated via an orthogonal transformation. To handle streaming and reduce the complexities PCA, (subspace) online PCA iterations were proposed to iteratively update transformation by taking one point at time. Existi...

We develop a mathematical programming approach for the classical PSPACE hard restless bandit problem in stochastic optimization. We introduce a hierarchy of n (where n is the number of bandits) increasingly stronger linear programming relaxations, the last of which is exact and corresponds to the (exponential size) formulation of the problem as a Markov decision chain, while the other relaxatio...

Most optimization-based decision support systems are used repeatedly with only modest changes to input data from scenario to scenario. Unfortunately, optimization (mathematical programming) has a well-deserved reputation for amplifying small input changes into drastically different solutions. A previously optimal solution, or a slight variation of one, may still be nearly optimal in a new scena...

We propose an estimator for the mean of random variables in separable real Banach spaces using empirical characteristic function. Assuming that covariance operator variable is bounded a precise sense, we show proposed achieves optimal sub-Gaussian rate, except faster decaying mean-dependent term. Under mild condition, iterative refinement procedure can essentially eliminate term and provide shi...