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Swarm Intelligence: Theoretical Proof That Empirical Techniques Are Optimal, Dmitry Iourinskiy, Scott A. Starks, Vladik Kreinovich, Stephen F. Smith
Swarm Intelligence: Theoretical Proof That Empirical Techniques Are Optimal, Dmitry Iourinskiy, Scott A. Starks, Vladik Kreinovich, Stephen F. Smith
Departmental Technical Reports (CS)
A natural way to distribute tasks between autonomous agents is to use swarm intelligence techniques, which simulate the way social insects (such as wasps) distribute tasks between themselves. In this paper, we theoretically prove that the corresponding successful biologically inspired formulas are indeed statistically optimal (in some reasonable sense).
Absolute Bounds On The Mean Of Sum, Product, Max, And Min: A Probabilistic Extension Of Interval Arithmetic, Scott Ferson, Lev Ginzburg, Vladik Kreinovich, Jorge Lopez
Absolute Bounds On The Mean Of Sum, Product, Max, And Min: A Probabilistic Extension Of Interval Arithmetic, Scott Ferson, Lev Ginzburg, Vladik Kreinovich, Jorge Lopez
Departmental Technical Reports (CS)
We extend the main formulas of interval arithmetic for different arithmetic operations x1*x2 to the case when, for each input xi, in addition to the interval [xi]=[xi-,xi+] of possible values, we also know its mean Ei (or an interval [Ei] of possible values of the mean), and we want to find the corresponding bounds for x1*x2 and its mean.