The objective of this paper is to find numerical bounds on the performances of algorithms for the placements of phasor measurement units (PMUs) in the power grid. Given noisy measurements and knowledge of the state correlation matrix, we use a linear minimum mean squared error estimator as the state estimator to formulate the PMU placement problem as an integer programming problem. Finding the ...

The Two-Dimensional Finite Bin Packing Problem (2BP) consists of determining the minimum number of large identical rectangles, bins, that are required for allocatingwithout overlapping a given set of rectangular items. The items are allocated into a bin with their edges always parallel or orthogonal to the bin edges. The problem is strongly NP-hard and finds many practical applications. In this...

We examine how the performance of a memoryless vector quantizer changes as a function of its training set size. Speci cally, we study how well the training set distortion predicts test distortion when the training set is a randomly drawn subset of blocks from the test or training image(s). Using the Vapnik-Chervonenkis dimension, we derive formal bounds for the di erence of test and training di...

Multistage stochastic mixed-integer programming is a powerful modeling paradigm appropriate for many problems involving a sequence of discrete decisions under uncertainty; however, they are difficult to solve without exploiting special structures. We present scenario-tree decomposition to establish bounds for unstructured multistage stochastic mixed-integer programs. Our method decomposes the s...

A large portion of the data that is collected in various application domains such as online social networking, finance, biomedicine, etc. is relational in nature. A subfield of Machine Learning namely; Statistical Relational Learning (SRL) is concerned with performing statistical inference on relational data. A defining property of relational data that separates it from independently and identi...

By defining two important terms called basic perturbation vectors and obtaining their linear bounds, we obtain the componentwise bounds for unitary factors upper triangular of generalized Schur decomposition. The diagonal elements invariant subspace are also derived. From former, present an bound a condition number eigenvalue. Furthermore, with numerical iterative method, nonlinear decompositio...

This paper focuses on the problem of scheduling n independent jobs on m identical parallel machines for the objective of minimizing total tardiness of the jobs. We develop dominance properties and lower bounds, and develop a branch and bound algorithm using these properties and lower bounds as well as upper bounds obtained from a heuristic algorithm. Computational experiments are performed on r...

New analytical upper bounds are derived for the performance of symbol-by-symbol maximum-likelihood (ML) Abend– Fritchman-type detectors for multi-amplitude/phase-modulated digital sequences transmitted over time-dispersive (generally) time-variant linear channels introducing finite Intersymbol Interference (ISI) and additive white Gaussian noise (AWGN). The proposed bounds are obtained starting...

Structural molecular biology is concerned with determining 3-dimensional representations of molecules. Various computational challenges arise in making such determinations, several of which have attracted some attention in the statistics and numerical optimization communities. One such problem is that of determining a 3-dimensional structure that is consistent with bounds on a molecule's intera...

We provide quantitative bounds on the characterization of multiparticle separable states by states that have locally symmetric extensions. The bounds are derived from two-particle bounds and relate to recent studies on quantum versions of de Finetti's theorem. We discuss algorithmic applications of our results, in particular a quasipolynomial-time algorithm to decide whether a multiparticle qua...