When the number of runs is large, to search for uniform designs in the sense of low-discrepancy is an NP hard problem. The number of runs of most of the available uniform designs is small （≤50）. In this article, th...When the number of runs is large, to search for uniform designs in the sense of low-discrepancy is an NP hard problem. The number of runs of most of the available uniform designs is small （≤50）. In this article, the authors employ a kind of the so-called Hamming distance method to construct uniform designs with two- or three-level such that some resulting uniform designs have a large number of runs. Several infinite classes for the existence of uniform designs with the same Hamming distances between any distinct rows are also obtained simultaneously. Two measures of uniformity, the centered L2-discrepancy （CD, for short） and wrap-around L2-discrepancy （WD, for short）, are employed.展开更多
Functional magnetic resonance imaging(fMRI)is one of the leading brain mapping technologies for studying brain activity in response to mental stimuli.For neuroimaging studies utilizing this pioneering technology,there...Functional magnetic resonance imaging(fMRI)is one of the leading brain mapping technologies for studying brain activity in response to mental stimuli.For neuroimaging studies utilizing this pioneering technology,there is a great demand of high-quality experimental designs that help to collect informative data to make precise and valid inference about brain functions.This paper provides a survey on recent developments in experimental designs for fMRI studies.We briefly introduce some analytical and computational tools for obtaining good designs based on a specified design selection criterion.Research results about some commonly considered designs such as blocked designs,and m-sequences are also discussed.Moreover,we present a recently proposed new type of fMRI designs that can be constructed using a certain type of Hadamard matrices.Under certain assumptions,these designs can be shown to be statistically optimal.Some future research directions in design of fMRI experiments are also discussed.展开更多
An infinite family of is obtained, that is,(ν)≠￠ forυ ∈ N=N1UN2 U N3 where Using(υ),we give 2-(2υ;k1,k2;k1 + k2 -υ} supplementary difference sets withυ=(k1-υ)2 + (k2 - υ)2. Finally. we prove that if there ...An infinite family of is obtained, that is,(ν)≠￠ forυ ∈ N=N1UN2 U N3 where Using(υ),we give 2-(2υ;k1,k2;k1 + k2 -υ} supplementary difference sets withυ=(k1-υ)2 + (k2 - υ)2. Finally. we prove that if there exists an orthogonal design OD(4t;t,t,t,t) and(υ) ≠￠ then a Hadamard rnatrix of order 4tυ can be constructed.展开更多
基金This work was partially supported by the NNSF of China(10441001) the Project sponsored by SRF for ROCS (SEM) the NSF of Hubei Province. The second author's research was also partially supported by the Pre-studies Project of NBRP (2003CCA2400)
文摘When the number of runs is large, to search for uniform designs in the sense of low-discrepancy is an NP hard problem. The number of runs of most of the available uniform designs is small （≤50）. In this article, the authors employ a kind of the so-called Hamming distance method to construct uniform designs with two- or three-level such that some resulting uniform designs have a large number of runs. Several infinite classes for the existence of uniform designs with the same Hamming distances between any distinct rows are also obtained simultaneously. Two measures of uniformity, the centered L2-discrepancy （CD, for short） and wrap-around L2-discrepancy （WD, for short）, are employed.
文摘Functional magnetic resonance imaging(fMRI)is one of the leading brain mapping technologies for studying brain activity in response to mental stimuli.For neuroimaging studies utilizing this pioneering technology,there is a great demand of high-quality experimental designs that help to collect informative data to make precise and valid inference about brain functions.This paper provides a survey on recent developments in experimental designs for fMRI studies.We briefly introduce some analytical and computational tools for obtaining good designs based on a specified design selection criterion.Research results about some commonly considered designs such as blocked designs,and m-sequences are also discussed.Moreover,we present a recently proposed new type of fMRI designs that can be constructed using a certain type of Hadamard matrices.Under certain assumptions,these designs can be shown to be statistically optimal.Some future research directions in design of fMRI experiments are also discussed.
文摘An infinite family of is obtained, that is,(ν)≠￠ forυ ∈ N=N1UN2 U N3 where Using(υ),we give 2-(2υ;k1,k2;k1 + k2 -υ} supplementary difference sets withυ=(k1-υ)2 + (k2 - υ)2. Finally. we prove that if there exists an orthogonal design OD(4t;t,t,t,t) and(υ) ≠￠ then a Hadamard rnatrix of order 4tυ can be constructed.
