Maximally reliable Markov chains under energy constraints.

Signal-to-noise ratios in physical systems can be significantly degraded if the outputs of the systems are highly variable. Biological processes for which highly stereotyped signal generations are necessary features appear to have reduced their signal variabilities by employing multiple processing steps. To better understand why this multistep cascade structure might be desirable, we prove that the reliability of a signal generated by a multistate system with no memory (i.e., a Markov chain) is maximal if and only if the system topology is such that the process steps irreversibly through each state, with transition rates chosen such that an equal fraction of the total signal is generated in each state. Furthermore, our result indicates that by increasing the number of states, it is possible to arbitrarily increase the reliability of the system. In a physical system, however, an energy cost is associated with maintaining irreversible transitions, and this cost increases with the number of such transitions (i.e., the number of states). Thus, an infinite-length chain, which would be perfectly reliable, is infeasible. To model the effects of energy demands on the maximally reliable solution, we numerically optimize the topology under two distinct energy functions that penalize either irreversible transitions or incommunicability between states, respectively. In both cases, the solutions are essentially irreversible linear chains, but with upper bounds on the number of states set by the amount of available energy. We therefore conclude that a physical system for which signal reliability is important should employ a linear architecture, with the number of states (and thus the reliability) determined by the intrinsic energy constraints of the system.

Assessing necessary nutrient reduction for measurement planning in groundwater bodies.

For the Federal State of Lower Saxony, Germany, nitrogen management options are developed and implemented in three pilot areas using new participation approaches and technologies suitable for programs of measures to reduce diffuse pollution from agriculture. As a target value for water protection measures a nitrate concentration in percolation water of 50 mg/l as an average for a larger area defined by the groundwater bodies and their hydrogeological subdivisions has been defined. An integrative emission model is used to simulate the interactions between agricultural practice, nitrogen surpluses and the nitrogen flow through the soil and aquifer to the outflow into surface waters. The actual nitrate concentrations in percolation water are calculated for the entire Federal State of Lower Saxony considering site-characteristics, N-surpluses, water balance and denitrification in the soil. The tolerable N-surpluses needed to meet the environmental target are quantified as averages for each of the hydrogeological subdivisions by "backward" calculation using this model system. The required reduction of N-surpluses was estimated by comparing the tolerable N-surpluses with the actual state of nitrogen emission. For the evaluation of the amount and efficiency of water protection measures, the required reduction of N-surpluses to accomplish the environmental target is quantified, using the current status as a reference.