Difference Covering Arrays and Pseudo-Orthogonal Latin Squares

Difference arrays are used in applications such as software testing, authentication codes and data compression. Pseudo-orthogonal Latin squares are used in experimental designs. A special class of pseudo-orthogonal Latin squares are the mutually nearly orthogonal Latin squares (MNOLS) first discussed in 2002, with general constructions given in 2007. In this paper we develop row complete MNOLS from difference covering arrays. We will use this connection to settle the spectrum question for sets of 3 mutually pseudo-orthogonal Latin squares of even order, for all but the order 146

“It’s Killing Us!” Narratives of Black Adults About Microaggression Experiences and Related Health Stress

Perceived racism contributes to persistent health stress leading to health disparities. African American/Black persons (BPs) believe subtle, rather than overt, interpersonal racism is increasing. Sue and colleagues describe interpersonal racism as racial microaggressions: “routine” marginalizing indignities by White persons (WPs) toward BPs that contribute to health stress. In this narrative, exploratory study, Black adults (n= 10) were asked about specific racial microaggressions; they all experienced multiple types. Categorical and narrative analysis captured interpretations, strategies, and health stress attributions. Six iconic narratives contextualized health stress responses. Diverse mental and physical symptoms were attributed to racial microaggressions. Few strategies in response had positive outcomes. Future research includes development of coping strategies for BPs in these interactions, exploration of WPs awareness of their behaviors, and preventing racial microaggressions in health encounters that exacerbate health disparities

Bounds on data limits for all-to-all comparison from combinatorial designs

In situations where every item in a data set must be compared with every other item in the set, it may be desirable to store the data across a number of machines in such a way that any two data items are stored together on at least one machine. One way to evaluate the efficiency of such a distribution is by the largest fraction of the data it requires to be allocated to any one machine. The all-to-all comparison (ATAC) data limit for $m$ machines is a measure of the minimum of this value across all possible such distributions. In this paper we further the study of ATAC data limits. We observe relationships between them and the previously studied combinatorial parameters of fractional matching numbers and covering numbers. We also prove a lower bound on the ATAC data limit that improves on one of Hall, Kelly and Tian, and examine the special cases where equality in this bound is possible. Finally, we investigate the data limits achievable using various classes of combinatorial designs. In particular, we examine the cases of transversal designs and projective Hjelmslev planes.Comment: 16 pages, 1 figur