Parseval inequalities and lower bounds for variance-based sensitivity indices

Variance-based sensitivity indices for models with dependent inputs

Computational models are intensively used in engineering for risk analysis or prediction of future outcomes. Uncertainty and sensitivity analyses are of great help in these purposes. Although several methods exist to perform variance-based sensitivity analysis of model output with independent inputs only a few are proposed in the literature in the case of dependent inputs. This is explained by ...

Some Lower Bounds for Estrada Index

Upper and lower bounds for numerical radii of block shifts

For an n-by-n complex matrix A in a block form with the (possibly) nonzero blocks only on the diagonal above the main one, we consider two other matrices whose nonzero entries are along the diagonal above the main one and consist of the norms or minimum moduli of the diagonal blocks of A. In this paper, we obtain two inequalities relating the numeical radii of these matrices and also determine ...

Lower bounds for sensitivity of graph properties

We prove that the sensitivity of any non-trivial graph property on n vertices is at least b 12nc , provided n is sufficiently large.

Dual Lower Bounds for Approximate Degree and Markov-Bernstein Inequalities

The ε-approximate degree of a Boolean function f : {−1, 1} → {−1, 1} is the minimum degree of a real polynomial that approximates f to within ε in the `∞ norm. We prove several lower bounds on this important complexity measure by explicitly constructing solutions to the dual of an appropriate linear program. Our first result resolves the ε-approximate degree of the two-level AND-OR tree for any...