INTRODUCTION Previous work in our laboratory showed that postural sway power in a group of six healthy adults was significantly larger in response to a periodic sum-of-sinusoids (SOS), compared to a spectrally similar non-periodic SOS [1], but only at the highest component frequency of the stimulus (0.5Hz). The objective of the current study was to determine whether this behavior could be repro...

Sequences of generalized Lagrangian duals and their SOS (sums of squares of polynomials) relaxations for a POP (polynomial optimization problem) are introduced. Sparsity of polynomials in the POP is used to reduce the sizes of the Lagrangian duals and their SOS relaxations. It is proved that the optimal values of the Lagrangian duals in the sequence converge to the optimal value of the POP usin...

In this thesis, we investigate theoretical and numerical advantages of a novel representation for Sum of Squares (SOS) decomposition of univariate and multivariate polynomials. This representation formulates a SOS problem by interpolating a polynomial at a finite set of sampling points. As compared to the conventional coefficient method of SOS, the formulation has a low rank property in its con...

• Device-independent randomness certification through a family of Bell expressions. Using the sum-of-squares (SOS) technique optimal quantum value expression is obtained. Many copies maximally entangled states provide an advantage over single copy. We demonstrate to what extent many two-qubit enable for generating greater amount certified than that can be from Although it appears dimension syst...

Y = β0 + (β1 + β2)X1 + and we may get a good estimate of Y estimating 2 parameters instead of 3. Our estimate will be a bit biased but we may lower our variance considerably creating an estimate with smaller expected prediciton error than the least squares estimate. We won’t be able to interpret the estimated parameter, but our prediction may be good. In subset selection regression we select a ...

Several models in data analysis are estimated by minimizing the objective function defined as the residual sum of squares between the model and the data.A necessary and sufficient condition for the existence of a least squares estimator is that the objective function attains its infimum at a unique point. It is shown that the objective function for Parafac-2 need not attain its infimum, and tha...