Boltzmann's Minimum Function

Reversible Function Synthesis with Minimum Garbage Outputs

Reversible functions are of interest in the design of low power CMOS circuits and in quantum computing. We describe a synthesis method for a proposed regular structure of generalized Toffoli gates. Multiple output functions are transformed into reversible functions with a minimum of number garbage outputs. The synthesis algorithm is greedy with one level look ahead. The synthesis results from b...

The Minimum Rank with Hysteresis Objective Function

The Routing Protocol for Low-Power and Lossy Networks (RPL) constructs routes by using Objective Functions that optimize or constrain the routes it selects and uses. This specification describes the Minimum Rank with Hysteresis Objective Function (MRHOF), an Objective Function that selects routes that minimize a metric, while using hysteresis to reduce churn in response to small metric changes....

Finding the Minimum of a Function

Adaptive query algorithms for finding the minimum of a function f are studied. The algorithms build on the earlier adaptive algorithms given in [5, 7]. The rate of convergence of these algorithms is estimated under various model assumptions on the function f . The first class of algorithms is analyzed when f satisfies a smoothness condition, e.g. f ∈ C, and an assumption on its level sets as gi...

Global Minimum Point of a Convex Function

In this paper we prove the existence of an unique global minimum point of a convex function under some smoothness conditions. Our proof permits us to calculate numerically such a minimum point utilizing a constructive homotopy method.

Minimum distance conditional variance function checking in heteroscedastic regression models