Buchstaber Invariants of Universal Complexes

Davis and Januszkiewicz introduced(real and complex) universal complexes to give an equivalent definition of characteristic maps of simple polytopes, which now can be seen as "colorings". The author derives an equivalent definition of Buchstaber invariants of a simplicial complex K, then interprets the difference of the real and complex Buchstaber invariants of K as the obstruction to liftings of nondegenerate simplicial maps from K to the real universal complex or the complex universal complex. It was proved by Ayzenberg that real universal complexes can not be nondegenerately mapped into complex universal complexes when dimension is 3. This paper presents that there is a nondegenerate map from 3-dimensional real universal complex to 4-dimensional complex universal complex.

Global sensitivity and uncertainty analysis of the VIP ecosystem model with an expanded soil nitrogen module for winter wheat-summer maize rotation system in the North China Plain

Accurately simulating the soil nitrogen(N)cycle is crucial for assessing food security and resource utilization efficiency.The accuracy of model predictions relies heavily on model parameterization.The sensitivity and uncertainty of the simulations of soil N cycle of winter wheat-summer maize rotation system in the North China Plain(NCP)to the parameters were analyzed.First,the N module in the Vegetation Interface Processes(VIP)model was expanded to capture the dynamics of soil N cycle calibrated with field measurements in three ecological stations from 2000 to 2015.Second,the Morris and Sobol algorithms were adopted to identify the sensitive parameters that impact soil nitrate stock,denitrification rate,and ammonia volatilization rate.Finally,the shuffled complex evolution developed at the University of Arizona(SCE-UA)algorithm was used to optimize the selected sensitive parameters to improve prediction accuracy.The results showed that the sensitive parameters related to soil nitrate stock included the potential nitrification rate,Michaelis constant,microbial C/N ratio,and slow humus C/N ratio,the sensitive parameters related to denitrification rate were the potential denitrification rate,Michaelis constant,and N2 O production rate,and the sensitive parameters related to ammonia volatilization rate included the coefficient of ammonia volatilization exchange and potential nitrification rate.Based on the optimized parameters,prediction efficiency was notably increased with the highest coefficient of determination being approximately 0.8.Moreover,the average relative interval length at the 95% confidence level for soil nitrate stock,denitrification rate,and ammonia volatilization rate were 11.92,0.008,and 4.26,respectively,and the percentages of coverage of the measured values in the 95% confidence interval were 68%,86%,and 92%,respectively.By identifying sensitive parameters related to soil N,the expanded VIP model optimized by the SCE-UA algorithm can effectively simulate the dynamics of soil nitrate stock,denitrification rate,and ammonia volatilization rate in the NCP.