Balanced and strongly balanced Pk-designs

AbstractGiven a graph G, a G-decomposition of the complete graph Kv is a set of graphs, all isomorphic to G, whose edge sets partition the edge set of Kv. A G-decomposition of Kv is also called a G-design and the graphs of the partition are said to be the blocks. A G-design is said to be balanced if the number of blocks containing any given vertex of Kv is a constant.In this paper the concept of strongly balanced G-design is introduced and strongly balanced path-designs are studied. Furthermore, we determine the spectrum of those path-designs which are balanced, but not strongly balanced

Balanced directed cycle designs based on groups

AbstractA balanced directed cycle design with parameters (υ, k, λ) is a decomposition of the complete directed multigraph λK̄υ into edge disjoint directed cycles C̄k. The paper elaborates on the ‘difference method’ for constructing these designs from groups and obtains some new constructions and classification results for designs with large automorphism groups

Extending Morris Method: identification of the interaction graph using cycle-equitabe designs

International audienceThe paper presents designs that allow detection of mixed effects when performing preliminary screening of the inputs of a scalar function of $d$ input factors, in the spirit of Morris' Elementary Effects approach. We introduce the class of $(d,c)$-cycle equitable designs as those that enable computation of exactly $c$ second order effects on all possible pairs of input factors. Using these designs, we propose a fast Mixed Effects screening method, that enables efficient identification of the interaction graph of the input variables. Design definition is formally supported on the establishment of an isometry between sub-graphs of the unit cube $Q_d$ equipped of the Manhattan metric, and a set of polynomials in $(X_1,\ldots, X_d)$ on which a convenient inner product is defined. In the paper we present systems of equations that recursively define these $(d,c)$-cycle equitable designs for generic values of $c\geq 1$, from which direct algorithmic implementations are derived. Application cases are presented, illustrating the application of the proposed designs to the estimation of the interaction graph of specific functions

Counterfeits, Copying and Class

Consumers who want to express themselves by wearing contemporary clothing styles should not have to choose between expensive brands and counterfeit products. There should be a clear distinction in trademark law between illegal, counterfeit goods and perfectly legal (at least with respect to trademark law) knockoffs, in which aesthetically functional design attributes have been copied but trademarks have not. Toward that end, as a normative matter, the aesthetic features of products should not be registrable or protectable as trademarks or trade dress, regardless of whether they have secondary meaning, just as functional attributes of a utilitarian nature are not eligible for Lanham Act protection. With enough advertising, any product feature can acquire distinctiveness. Only the assertive deployment of functionality bars by courts can prevent the illegitimate and costly construction of trademark-based product monopolies. The purported trademark-related harms that stem from the production and distribution of noncounterfeit knockoffs are, in reality, the effects of legitimate competition based on attributes such as price, quality, consumer appeal, and retail availability, with which trademark law should not interfere. Repressing or illegalizing knockoffs illegitimately prevents lower income people from procuring and enjoying goods with aesthetic attributes that are not properly monopolized through trademark law, and probably perversely increases the demand for counterfeit items

Spartan Daily, October 10, 1979

Volume 73, Issue 26https://scholarworks.sjsu.edu/spartandaily/6524/thumbnail.jp

New results on path-decompositions and their down-links

In a recent paper the concept of \emph{down-link} from a $(K_v,\Gamma)$-design \cB to a $(K_n,\Gamma')$-design \cB' has been introduced. In the present paper the spectrum problems for $\Gamma'=P_4$ are studied. General results on the existence of path-decompositions and embeddings between path-decompositions playing a fundamental role for the construction of down-links are also presented