We introduce the Linear Resource Temporal Network (LRTN), which consists of activities that consume or produce a resource, subject to absolute and relative metric temporal constraints; production and consumption is restricted to linear functions of activity duration. We show how to construct tight bounds for resource availability as a function of time in LRTNs; for a broad class of problems, th...

The problem of locating local maxima and minima of a function from approximate measurement results is vital for many physical applications: In spectral analysis, chemical species are identiied by locating local maxima of the spectra. In radioastronomy, sources of celestial radio emission, and their subcomponents, are identiied by locating local maxima of the measured brightness of the radio sky...

In this work, we derive a general class of multistep composite elementary landscapes and present the first non-trivial lower (upper) bounds on local minima (maxima) associated with elementary landscapes. © 2008 Elsevier Ltd. All rights reserved.

We provide necessary and sufficient conditions for hypercontractivity of the minima of nonnegative, i.i.d. random variables and of both the maxima of minima and the minima of maxima for such r.v.’s. It turns out that the idea of hypercontractivity for minima is closely related to small ball probabilities and Gaussian correlation inequalities.

Sparse grid interpolation is widely used to provide good approximations to smooth functions in high dimensions based on relatively few function evaluations. By using an efficient conversion from the interpolating polynomial provided by evaluations on a sparse grid to a representation in terms of orthogonal polynomials (gPC representation), we show how to use these relatively few function evalua...

This Letter presents a frequentist analysis of the hot and cold spots of the cosmic microwave background data collected by the Wilkinson Microwave Anisotropy Probe (WMAP). We compare the WMAP temperature statistics of extrema (number of extrema, mean excursion, variance, skewness and kurtosis of the excursion) to Monte Carlo simulations. We find that on average, the local maxima (high temperatu...

This paper presents a frequentist analysis of the hot and cold spots of the Cosmic Microwave Background (CMB) data collected by the Wilkinson Microwave Anisotropy Probe (WMAP). We compare the WMAP temperature statistics of extrema (number of extrema, mean excursion, variance, skewness and kurtosis of the excursion) to Monte-Carlo simulations. We find that, on average, the local maxima (high tem...

CHE based architecture for GA, on a single COTS FPGA, designed to perform optimization of single variable functions is presented in this chapter. The presented architecture’s ability to optimize is tested and validated with three different single variable functions. They are, a linear function, a quadratic function with only one global maximum, and a cubic function with one global maxima and lo...