The first critical evaluation of the mathematical modeling behind the critical positivity ratio was published by a group of Finnish researchers Luoma, Hämäläinen and Saarinen in 2008. The authors noted that "Only very limited explanations are given about the modeling process and the meaning and interpretation of its parameters. Thus, the reasoning behind the model equations remains unclear to the reader." Moreover, "the model also produces strange and previously unreported behavior under certain conditions. Thus, the predictive validity of the model also becomes problematic." Later in 2013, the critical positivity ratio aroused the skepticism of Nick Brown, a graduate student in applied positive psychology, who felt that the paper's mathematical claims underlying the critical positivity ratio were fundamentally flawed. Brown collaborated with physicist Alan Sokal and psychologist Harris Friedman on a re-analysis of the paper's data. They argued that Fredrickson and Losada's paper contained "numerous fundamental conceptual and mathematical errors", as did Losada's earlier work on positive psychology, which completely invalidated their claims. In their response, Hämäläinen and colleagues argued that there were no fundamental errors in the mathematics itself, but the problems relate to the interpretation and justification of the use of the model. Losada declined to respond to the criticism, indicating that he was too busy running his consulting business. Fredrickson wrote a response in which she conceded that the mathematical aspects of the critical positivity ratio were "questionable" and that she had "neither the expertise nor the insight" to defend them, but she maintained that the empirical evidence was solid. Brown and colleagues, whose response was published the next year, maintain that there is no evidence for the critical positivity ratio.