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New Designs with Block Size 7
AbstractAn imprimitive permutation group of order 4200 is used for the construction of a 2-(175,Ā 7,Ā 1) design. The design yields also a group divisible design 7āGDDand a generalized Bhaskar Rao designGBRD(25,Ā 100,Ā 28,Ā 7,Ā 7;Ā Z7)
Universal and Robust Distributed Network Codes
Random linear network codes can be designed and implemented in a distributed
manner, with low computational complexity. However, these codes are classically
implemented over finite fields whose size depends on some global network
parameters (size of the network, the number of sinks) that may not be known
prior to code design. Also, if new nodes join the entire network code may have
to be redesigned.
In this work, we present the first universal and robust distributed linear
network coding schemes. Our schemes are universal since they are independent of
all network parameters. They are robust since if nodes join or leave, the
remaining nodes do not need to change their coding operations and the receivers
can still decode. They are distributed since nodes need only have topological
information about the part of the network upstream of them, which can be
naturally streamed as part of the communication protocol.
We present both probabilistic and deterministic schemes that are all
asymptotically rate-optimal in the coding block-length, and have guarantees of
correctness. Our probabilistic designs are computationally efficient, with
order-optimal complexity. Our deterministic designs guarantee zero error
decoding, albeit via codes with high computational complexity in general. Our
coding schemes are based on network codes over ``scalable fields". Instead of
choosing coding coefficients from one field at every node, each node uses
linear coding operations over an ``effective field-size" that depends on the
node's distance from the source node. The analysis of our schemes requires
technical tools that may be of independent interest. In particular, we
generalize the Schwartz-Zippel lemma by proving a non-uniform version, wherein
variables are chosen from sets of possibly different sizes. We also provide a
novel robust distributed algorithm to assign unique IDs to network nodes.Comment: 12 pages, 7 figures, 1 table, under submission to INFOCOM 201
Recommendable block sizes: a case study on Finnish official variety trials of barley cultivars
Well-established results in the current statistical literature imply that plant breeders should use incomplete block designs wherever spatial variability exists and the number of treatments is large. But the theoretical position does not indicate the recommendable number of cultivars in an incomplete block. In this study we used data from 28 official variety trials conducted in Finland during the period 2001-2005 to study theffect of block size on the efficiency of testing pairwise yield differences of barley cultivars and cultivar rankings. In previous trials some 6-7 cultivars have usually been included in one block. Our results imply that the efficiency of testing procedures could be improved by using a block size as small as 4-5. The results further imply that if an experiment with an incomplete block design is well planned to mitigate the effects of within-block heterogeneity, the spatial mixed model techniques and the conventional analysis of variance techniques have approximately the same efficiency in testing pairwise yield differences. Thus, if appropriate blocking strategies are used in planning the trials, there is usually no need to change the conventional practice followed in statistical analysis
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Minimum aberration designs for discrete choice experiments
A discrete choice experiment (DCE) is a survey method that givesinsight into individual preferences for particular attributes.Traditionally, methods for constructing DCEs focus on identifyingthe individual effect of each attribute (a main effect). However, aninteraction effect between two attributes (a two-factor interaction)better represents real-life trade-offs, and provides us a better understandingof subjectsā competing preferences. In practice it is oftenunknown which two-factor interactions are significant. To address theuncertainty, we propose the use of minimum aberration blockeddesigns to construct DCEs. Such designs maximize the number ofmodels with estimable two-factor interactions in a DCE with two-levelattributes. We further extend the minimum aberration criteria toDCEs with mixed-level attributes and develop some general theoreticalresults
Past developments and future opportunities in the design and analysis of crop experiments
A review of papers on the statistical design and analysis of experiments published in the Journal of Agricultural Science, Cambridge, over the last 100 years is presented. The development of significant ideas in the practical design of field experiments is reviewed. Some possible future developments in the design of spatial field trials and computer-aided design of experiments are discussed
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