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Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Counter Machines And Crystallographic Structures, Natasha Jonoska, Mile Krajcevski, Gregory Mccolm
Counter Machines And Crystallographic Structures, Natasha Jonoska, Mile Krajcevski, Gregory Mccolm
Mathematics and Statistics Faculty Publications
One way to depict a crystallographic structure is by a periodic (di)graph, i.e., a graph whose group of automorphisms has a translational subgroup of finite index acting freely on the structure. We establish a relationship between periodic graphs representing crystallographic structures and an infinite hierarchy of intersection languages DCLd,d=0,1,2,…, within the intersection classes of deterministic context-free languages. We introduce a class of counter machines that accept these languages, where the machines with d counters recognize the class DCLd. An intersection of d languages in DCL1 defines DCLd. We prove that there is …
Ehugs: Enhanced Hierarchical Unbiased Graph Shrinkage For Efficient Groupwise Registration, Guorong Wu, Xuewei Peng, Shihui Ying, Qian Wang, Pew-Thian Yap, Dan Shen, Dinggang Shen
Ehugs: Enhanced Hierarchical Unbiased Graph Shrinkage For Efficient Groupwise Registration, Guorong Wu, Xuewei Peng, Shihui Ying, Qian Wang, Pew-Thian Yap, Dan Shen, Dinggang Shen
Mathematics and Statistics Faculty Publications
Effective and efficient spatial normalization of a large population of brain images is critical for many clinical and research studies, but it is technically very challenging. A commonly used approach is to choose a certain image as the template and then align all other images in the population to this template by applying pairwise registration. To avoid the potential bias induced by the inappropriate template selection, groupwise registration methods have been proposed to simultaneously register all images to a latent common space. However, current groupwise registration methods do not make full use of image distribution information for more accurate registration. …