Methodology for identifying near-optimal interdiction strategies for a power transmission system

Previous methods for assessing the vulnerability of complex systems to intentional attacks or interdiction have either not been adequate to deal with systems in which flow readjusts dynamically (such as electricity transmission systems), or have been complex and computationally difficult. We propose a relatively simple, inexpensive, and practical method (“Max Line”) for identifying promising interdiction strategies in such systems. The method is based on a greedy algorithm in which, at each iteration, the transmission line with the highest load is interdicted. We apply this method to sample electrical transmission systems from the Reliability Test System developed by the Institute of Electrical and Electronics Engineers, and compare our method and results with those of other proposed approaches for vulnerability assessment. We also study the effectiveness of protecting those transmission lines identified as promising candidates for interdiction. These comparisons shed light on the relative merits of the various vulnerability assessment methods, as well as providing insights that can help to guide the allocation of scarce resources for defensive investment.     

Finger millet response to nitrogen,phosphorus and potassium in Kenya and Uganda

Finger millet (Eleusine coracana (L.) Gaertn) is an important food crop of semi-arid to sub-humid Africa where little is known of its response to applied nutrients. Yield responses to nitrogen (N), phosphorus (P) and potassium (K) together with a diagnostic treatment (S, Mg, Zn, B) were determined from field research conducted in western Kenya and eastern and central Uganda. Grain yield was not affected by applied nutrients in some sites in Kenya, likely due to other prevailing stresses. Grain yield increased with N application for all sites and years in Uganda by a mean of 127% from the no N treatment (0 N) yield of 1.00 Mg ha^?1. Grain yield increases ranged from 0.76 to 1.40 Mg ha^?1 with 30 kg N ha^?1 applied, with little added increase with >60 kg N ha^?1. The mean economically optimal rate for N in Uganda was 72 and 43 kg N ha^?1 with expected net returns to N of 166 and 279 $ ha^?1 when the N cost to grain value was 3 and 9 kg kg^?1, respectively. Yield was increased with P and K application at two of four production areas of Uganda. Yield was increased by >20% with application of Mg–S–Zn–B in addition to N–P–K for all sites in Uganda with foliar concentrations indicating possible S and B deficiency. There is great profit potential in Uganda, and less for Kenya for N, but not for P and K, application to finger millet. Response to S and B needs further exploration.     

Wheat nutrient response functions for the East Africa highlands

Wheat (Triticum æstivum L.) is an important East Africa highland crop but yields are low. Information is scarce for optimization of fertilizer use. Research was conducted to determine yield response functions for N, P and K, and to diagnose Mg–S–Zn–B deficiencies. The average grain yield increase in Rwanda due to N application was 1.5 Mg ha^?1 with a mean economically optimal rate (EOR) of 68 kg ha^?1 N. In Kenya and Tanzania, yield was increased by 29% with EOR N for two SY but unaffected by N rate for four other SY which on average had 50% of the soil organic C (SOC) as the N-responsive SY. Yield was increased, on average, with application of P and K by 0.47 and 0.23 Mg ha^?1, respectively, at EOR in Rwanda but effects were inconsistent for other SY where soil test K was higher than in Rwanda. Application of Mg–S–Zn–B resulted in 0.46 Mg ha^?1 more yield in Rwanda but did not affect yield at other SY where the average soil test values for these nutrients was 35% higher than in Rwanda. If the financially constrained farmer opts to apply the affordable fertilizer to twice as much land at 50% EOR compared with 100% EOR, the mean yield increase is reduced by 27% but production and PCR are increased by 43 and 72%, respectively. Nutrient effects were relatively consistent and positive in Rwanda, but less and less inconsistent elsewhere with generally less SOC, more K–Mg–S–Zn–B availability, and often lower yields.     

Maize-bean intercrop response to nutrient application relative to maize sole crop response

Maize-bean intercropping is important in sub-Saharan Africa. Maize sole crop (MSC) nutrient response has been much studied but data is scarce for determination of intercrop functions. A procedure for adapting MSC functions for the maize-bean intercrop was developed. Maize sole crop and intercrop responses were near parallel with notable exceptions for P in high potential areas for maize and for K. Mean intercrop bean yield with no nutrient application was about 0.4 Mg ha^?1 and increased on average by 24, 11 and ?3% with N, P and K application, respectively. Response function coefficients for MSC adjusted with the ratio of bean to maize grain value as the dependent variable accounted for nearly all variation in intercrop response coefficients providing the basis for determining intercrop response functions from MSC functions. Maize grain yield equivalent was less with MSC compared with intercrop; exceptions were for response to N in high potential areas and for bean to maize value ratios of two or less. The economically optimal rate of N and P were on average about 15% more but less for K with intercrop compared with MSC but with inconsistency. The economically optimal rate ranged widely with variation in the cost of nutrient use relative to grain value but generally without great effect on yield; an exception was a great effect on MSC yield response to N for high potential areas. Intercrop nutrient response functions can be reliably determined once maize sole crop functions are determined for a recommendation domain.