1. Summary of the Case
My manuscript The Weak Correlation Experimental Designs was submitted in February 2006 by e-mail into Editorial Department of Journal of Mathematical in Practice and Theory, which was published in Feb. 2009, [Mathematics in Practice and Theory, Vol.39, No. 3, 99-107, (2009) (In Chinese)]. Hereinafter referred to as He(2009). The publishing process was bizarrely long for three years.
In 2010, The Annals of Statistics published a paper (2010, Vol.38, No.3, 1460-1477),(referred to as Lin(2010)), which was written by four PhDs, C.Devon Lin, Derek Bingham, Randy R. Sitter and Boxin Tang from Simon Fraser University, Canada. The article was a revised and concise version of the Lin’s doctoral thesis. My system design was imitated, and the innovation elements including the definition of basic concepts, the existence theorem, the optimization objective function, the exchange algorithm, the stacking operator and the stacking principle for the orthogonal designs all appeared in Lin’s doctoral thesis.
The approval date of the thesis was June 20, 2008 (referred to as Lin(2008)), which was exactly 4th days before I receive the notice that my manuscript was waiting for printing. Stolen my manuscript under reviewing .
2. The Optimization Objective Function Was Exactly the Same
Figure 1: He(2009)’s Optimization Objective Function mcc
Figure 2: Lin(2008)’s (p.24) Optimization criterion (Lin(2010)p.13)
3. The Necessary Condition of the Existence Theorem Was the Same
Reference Translation: A necessary condition for the existence of the zero correlation arrays is that m is either an odd number greater than 3, or a multiple of 4. The zero correlation arrays don’t exist if the run size of the design is 4k + 2, where k is a positive integer.
Figure 3: He(2009)’s Existence Theorem ((He(2009)p.3, in Chinese)
Figure 4: Lin(2008)’s Existence Theorem 2.5, that is Lin(2010)p.7 theorem 2
4. Exchange Algorithm Was the Same
Reference Translation: Supposing two subscripts corresponding two components of x are i,j(i < j) respectively, and x0is a new vector obtained by exchanging the two components, then the relationship between two inner products is formula (2.4).
Figure 6: Lin’s Exchanging Algorithm (in Lin(2008)p.33,Lin(2010)p.10)
5. The Stacking Operation of the Designs and the Stacking Principle of the Orthogonal Designs Were the Same
Reference Translation: That both zero correlation arrays whose dimension are the same are stacked to each other, the result is still a zero correlation array. Let A = (a1,...,ap) and B =(b1,...,bp) be two m × p zero correlation arrays, stacking
them form a 2m × p array, C = (c1,...,cp ). We can write as formula (3.1).
Figure 7: He(2009)’s description and proof for the Stackability of the zero correlation matrices (He(2009)p.4)
Figure 8: The stacking principle in Lin(2008)p.40 (Lin(2010)p.8)