On the Markov Chain Tree Theorem in the Max Algebra
The Markov Chain Tree Theorem is extended to the max algebra and possible applications to ranking problems are discussed.
math.RA↗
arXiv subjects
Steve Kirkland
Publications and source records attributed to Steve Kirkland.
Spin systems dynamics and faults detection in threshold networks
We consider an agent on a fixed but arbitrary node of a known threshold network, with the task of detecting an unknown missing link/node. We obtain analytic formulas for the probability of success, when the agent's tool is the free evolution of a single excitation on an XX spin system paired with the network. We completely characterize the parameters allowing for an advantageous solution. From the results emerges an optimal (deterministic) algorithm for quantum search, therefore gaining a quadratic speed-up with respect to the optimal classical analogue, and in line with well-known results in quantum computation. When attempting to detect a faulty node, the chosen setting appears to be very fragile and the probability of success too small to be of any direct use.
quant-ph↗