The high-altitude landscape of western Tibet is one the most extreme environments in which humans have managed to introduce crop cultivation. To date, only sparse palaeoeconomic data been reported from this region. authors present archaeobotanical evidence five sites (dating late first millennium BC and early AD) located cold-arid Tibet. indicate that barley was widely grown region by c . 400 b...

Quantum multiple-valued decision diagrams (QMDD) are data structures that enable efficient representation and manipulation of unitary matrices representing reversible and quantum circuits. QMDDs are of the form of a rooted, directed, acyclic graph with initial and terminal vertices where each vertex is annotated with a variable name representing a circuit line. Directed paths from the intial to...

A celebrated theorem of Friedgut says that every function f : {0, 1}n → {0, 1} can be approximated by a function g : {0, 1}n → {0, 1} with ‖f − g‖2 ≤ ǫ which depends only on ef variables where If is the sum of the influences of the variables of f . Dinur and Friedgut later showed that this statement also holds if we replace the discrete domain {0, 1}n with the continuous domain [0, 1], under th...

This short communication concerns a class of Nash games in which the participants share some of the decision variables. An averaging method is developed in order to transform these games into standard Nash games. This technique is successfully applied to solve an example multileader, single-follower game described by Pang and Fukushima.