9,442 research outputs found
Pooling spaces associated with finite geometry
AbstractMotivated by the works of Ngo and Du [H. Ngo, D. Du, A survey on combinatorial group testing algorithms with applications to DNA library screening, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 55 (2000) 171β182], the notion of pooling spaces was introduced [T. Huang, C. Weng, Pooling spaces and non-adaptive pooling designs, Discrete Mathematics 282 (2004) 163β169] for a systematic way of constructing pooling designs; note that geometric lattices are among pooling spaces. This paper attempts to draw possible connections from finite geometry and distance regular graphs to pooling spaces: including the projective spaces, the affine spaces, the attenuated spaces, and a few families of geometric lattices associated with the orbits of subspaces under finite classical groups, and associated with d-bounded distance-regular graphs
A construction of pooling designs with surprisingly high degree of error correction
It is well-known that many famous pooling designs are constructed from
mathematical structures by the "containment matrix" method. In this paper, we
propose another method and obtain a family of pooling designs with surprisingly
high degree of error correction based on a finite set. Given the numbers of
items and pools, the error-tolerant property of our designs is much better than
that of Macula's designs when the size of the set is large enough
Pooling designs with surprisingly high degree of error correction in a finite vector space
Pooling designs are standard experimental tools in many biotechnical
applications. It is well-known that all famous pooling designs are constructed
from mathematical structures by the "containment matrix" method. In particular,
Macula's designs (resp. Ngo and Du's designs) are constructed by the
containment relation of subsets (resp. subspaces) in a finite set (resp. vector
space). Recently, we generalized Macula's designs and obtained a family of
pooling designs with more high degree of error correction by subsets in a
finite set. In this paper, as a generalization of Ngo and Du's designs, we
study the corresponding problems in a finite vector space and obtain a family
of pooling designs with surprisingly high degree of error correction. Our
designs and Ngo and Du's designs have the same number of items and pools,
respectively, but the error-tolerant property is much better than that of Ngo
and Du's designs, which was given by D'yachkov et al. \cite{DF}, when the
dimension of the space is large enough
On Information Pooling, Adaptability and Superefficiency in Nonparametric Function Estimation
The connections between information pooling and adaptability as well as superefficiency are considered. Separable rules, which figure prominently in wavelet and other orthogonal series methods, are shown to lack adaptability; they are necessarily not rate-adaptive. A sharp lower bound on the cost of adaptation for separable rules is obtained. We show that adaptability is achieved through information pooling. A tight lower bound on the amount of information pooling required for achieving rate-optimal adaptation is given. Furthermore, in a sharp contrast to the separable rules, it is shown that adaptive non-separable estimators can be superefficient at every point in the parameter spaces. The results demonstrate that information pooling is the key to increasing estimation precision as well as achieving adaptability and even superefficiency
Use of Statistical Outlier Detection Method in Adaptive\ud Evolutionary Algorithms
In this paper, the issue of adapting probabilities for Evolutionary Algorithm (EA) search operators is revisited. A framework is devised for distinguishing between measurements of performance and the interpretation of those measurements for purposes of adaptation. Several examples of measurements and statistical interpretations are provided. Probability value adaptation is tested using an EA with 10 search operators against 10 test problems with results indicating that both the type of measurement and its statistical interpretation play significant roles in EA performance. We also find that selecting operators based on the prevalence of outliers rather than on average performance is able to provide considerable improvements to\ud
adaptive methods and soundly outperforms the non-adaptive\ud
case
- β¦