Feedback information rate and entropy in a discrete system†

A multi-state deterministic system controlled via a noisy Binary Symmetric Channel (BSC) is modelled by an equivalent Markov chain. The system performs a random walk whose mean deviation from zero is numerically equal to the expected number of steps between zero crossings, and whose entropy is equal to the average amount of transmitted control information between zero crossings. Simple expressions are found for the received control information and for the mutual information via the BSC.     

VICTIMS OR VICTORS? THE EFFECTS OF FORCED RELOCATIONS ON HOUSING SATISFACTION IN DUTCH CITIES

Urban restructuring is changing the face of many Western European cities. Old, relatively cheap dwellings are being demolished and replaced by new, more expensive ones. The spatial effects of this process have been extensively studied, but little is known about the residents who are forced to relocate so that their dwellings can be demolished or updated. We therefore studied how satisfied forced movers are with their current housing situation, and what factors contribute to this. Using data from four Dutch cities, we found that most displaced residents were quite satisfied with their new dwellings and neighborhoods. However, those with low incomes and those from ethnic minority groups were less satisfied with their homes and neighborhoods. We can explain their lower level of neighborhood satisfaction by the fact that they move to less desirable neighborhoods—for example, neighborhoods with higher concentrations of ethnic minorities.     

OPTIMAL OPERATION OF MULTIQUALITY WATER SUPPLY SYSTEMS-III: THE Q-C-H MODEL

A new technique for optimal operation of multiquality water supply systems is proposed. The technique, which is known as a Q-C-H (flow-quality-head) model, combines previously developed Sow-quality (Q-C) and flow-head (Q-H) models for optimal operation of water supply systems. The decision variables in the model are the operation of treatment plants, pumps and valves. The model minimizes the cost of water at sources, treatment, energy, and loss of agricultural yield when water quality is low. The model uses an iterative modified projected gradient method combined with the Complex method. As in the Q-C and Q-H models, the solution method is based on decomposition, dis-aggregation/aggregation approach, involving internal and external optimization. The decision variables of the external model are the flows in the loops of the network and the removal ratios at the treatment plants. The operation of the pumps and valves are the decision variables of the internal model. The method is demonstrated by application to an example problem.     

OPTIMAL OPERATION OF MULTI-QUALITY WATER SUPPLY SYSTEMS-II: THE Q-H MODEL

This paper describes the second in a series of three models for optimal operation of multi-quality water supply systems. This second model, which is termed the Q-H (flow-head) model, seeks to determine the optimal operation of pumps and valves, and does not consider water quality aspects. However, the model belongs to the group of three models Tor multi-quality systems because it is one of the two building blocks (the other is the flow-quality Q-C) of a full-llow-quality-head (Q-C-H) model. This Q-H model is based on continuous representations of the head-flow and power-flow functions of the pumping stations, which in turn results in a continuous non-convex optimization model. For a given flow distribution in the network, Q₀, the Q₀-H model is solved for the optimal operation of pumps and valves. The flow distribution is then modified by changing the circular flows, using a projected gradient method combined with the Complex Method which employs the results of the Q₀-H solution, such that the locally optimal solution at the next point has a better value of the objective function. The process is continued until one of the termination criteria is satisfied. The circular flows thus serve as decision variables in an external problem, while in the internal problem the decisions are the operation of pumps and valves. The method is demonstrated by application to a sample problem.     

OPTIMAL OPERATION OF MULTI-QUALITY WATER SUPPLY SYSTEMS-I: INTRODUCTION AND THE Q-C MODEL

One of three complementary models for optimal operation of multi-quality water supply systems is presented. The other two models are the subject of companion papers. The model, which is known as the Q-C (flow-quality) model, includes mass continuity of water and constituents. However, the hydraulic constraints do not appear explicitly. To prevent infeasibilities or unreasonable hydraulic conditions arising from the lack of hydraulic constraints, limits and a cost are associated with the flow in each pipe. The constraints in the model include dilution conditions which depend on flow direction. These dilution conditions are introduced into the model by an exponential function, resulting in a smooth continuous nonlinear programming problem, which is transformed into an equivalent problem and solved by a modified projected gradient method. The method is insensitive to scaling of variables, and the computational complexity depends only slightly on the number of water quality parameters. The method is demonstrated by application to two examples: the solution for a small network is presented in detail, and main results are shown for a larger one. The results of these two applications indicate the method's applicability to real networks.