EXISTENCE OF OPTIMAL STRONG PARTIALLY BALANCED DESIGNS

A strong partially balanced design SPBD（v, b, k; λ,0） whose b is the maximum number of blocks in all SPBD（v, b, k; λ, 0）, as an optimal strong partially balanced design, briefly OSPBD（v, k, λ） is studied. In investigation of authentication codes it has been found that the strong partially balanced design can be used to construct authentication codes. This note investigates the existence of optimal strong partially balanced design OSPBD（v, k, 1） for k = 3 and 4, and shows that there exists an OSPBD（v, k, 1） for any v ≥ k.

Statistical analysis of nitrogen use efficiency in Northeast China using multiple linear regression and Random Forest

Understanding the spatial-temporal dynamics of crop nitrogen(N)use efficiency(NUE)and the relationship with explanatory environmental variables can support land-use management and policymaking.Nevertheless,the application of statistical models for evaluating the explanatory variables of space-time variation in crop NUE is still under-researched.In this study,stepwise multiple linear regression(SMLR)and Random Forest(RF)were used to evaluate the spatial and temporal variation of NUE indicators(i.e.,partial factor productivity of N(PFPN);partial nutrient balance of N(PNBN))at county scale in Northeast China(Heilongjiang,Liaoning and Jilin provinces)from 1990 to 2015.Explanatory variables included agricultural management practices,topography,climate,economy,soil and crop types.Results revealed that the PFPN was higher in the northern parts and lower in the center of the Northeast China and PNBN increased from southern to northern parts during the 1990–2015 period.The NUE indicators decreased with time in most counties during the study period.The model efficiency coefficients of the SMLR and RF models were 0.44 and 0.84 for PFPN,and 0.67 and 0.89 for PNBN,respectively.The RF model had higher relative importance of soil and climatic covariates and lower relative importance of crop covariates compared to the SMLR model.The planting area index of vegetables and beans,soil clay content,saturated water content,enhanced vegetation index in November&December,soil bulk density,and annual minimum temperature were the main explanatory variables for both NUE indicators.This is the first study to show the quantitative relative importance of explanatory variables for NUE at a county level in Northeast China using RF and SMLR.This novel study gives reference measurements to improve crop NUE which is one of the most effective means of managing N for sustainable development,ensuring food security,alleviating environmental degradation and increasing farmer’s profitability.

A Note on Authentication Codes with Arbitration

By use of partially balanced t-designs (v,b, k;λ,0) that is constructed by the rational normal curves given by [5] and the Cartesian product given by [4],an authentication code with arbitration is constructed and its probability of success of attacks by the transmitter, the receiver and the opponent is obtained in this paper.

General Solution of Normal Equations in the Intra-Block Analysis of PBIB Designs with Four Associates

General solution of normal equations in the general intra-block analysis of partially balanced incomplete block designs involving four associates is presented in this talk as they are quite useful in practice. Only intra-block estimates are given as the necessary formulae for inter-block estimates can be derived from them by changing the parameters as discussed in Rao[5]. We have obtained the general formulae for computation of four types of efficiencies, the average efficiency factor and the variance of the estimated elementary treatment contrast of the four types of comparisons irrespective of the type of association scheme a PBIB Design follows.