Physical Sciences and Mathematics | Open Access Articles

A Super Fast Algorithm For Estimating Sample Entropy, Weifeng Liu, Ying Jiang, Yuesheng Xu Apr 2022

A Super Fast Algorithm For Estimating Sample Entropy, Weifeng Liu, Ying Jiang, Yuesheng Xu

Mathematics & Statistics Faculty Publications

: Sample entropy, an approximation of the Kolmogorov entropy, was proposed to characterize complexity of a time series, which is essentially defined as − log(B/A), where B denotes the number of matched template pairs with length m and A denotes the number of matched template pairs with m + 1, for a predetermined positive integer m. It has been widely used to analyze physiological signals. As computing sample entropy is time consuming, the box-assisted, bucket-assisted, x-sort, assisted sliding box, and kd-tree-based algorithms were proposed to accelerate its computation. These algorithms require O(N²) or …

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Robust Testing Of Paired Outcomes Incorporating Covariate Effects In Clustered Data With Informative Cluster Size, Sandipan Dutta Jan 2022

Robust Testing Of Paired Outcomes Incorporating Covariate Effects In Clustered Data With Informative Cluster Size, Sandipan Dutta

Mathematics & Statistics Faculty Publications

Paired outcomes are common in correlated clustered data where the main aim is to compare the distributions of the outcomes in a pair. In such clustered paired data, informative cluster sizes can occur when the number of pairs in a cluster (i.e., a cluster size) is correlated to the paired outcomes or the paired differences. There have been some attempts to develop robust rank-based tests for comparing paired outcomes in such complex clustered data. Most of these existing rank tests developed for paired outcomes in clustered data compare the marginal distributions in a pair and ignore any covariate effect on …

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Rock Paintings, John Adam Jan 2022

Rock Paintings, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

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Rock Paintings: Solutions For Fermi Questions, September 2022, John Adam Jan 2022

Rock Paintings: Solutions For Fermi Questions, September 2022, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

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Recent Analytic Development Of The Dynamic Q-Tensor Theory For Nematic Liquid Crystals, Xiang Xu Jan 2022

Recent Analytic Development Of The Dynamic Q-Tensor Theory For Nematic Liquid Crystals, Xiang Xu

Mathematics & Statistics Faculty Publications

Liquid crystals are a typical type of soft matter that are intermediate between conventional crystalline solids and isotropic fluids. The nematic phase is the simplest liquid crystal phase, and has been studied the most in the mathematical community. There are various continuum models to describe liquid crystals of nematic type, and Q-tensor theory is one among them. The aim of this paper is to give a brief review of recent PDE results regarding the Q-tensor theory in dynamic configurations.

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On The Geometry Of The Multiplier Space Of ℓ^P_A, Christopher Felder, Raymond Cheng Jan 2022

On The Geometry Of The Multiplier Space Of ℓPA, Christopher Felder, Raymond Cheng

Mathematics & Statistics Faculty Publications

For p ∊ (1, ∞)\ {2}, some properties of the space M_p of multipliers on ℓ^p_Aare derived. In particular, the failure of the weak parallelogram laws and the Pythagorean inequalities is demonstrated for M_p. It is also shown that extremal multipliers on the ℓ^p_Aspaces are exactly the monomials, in stark contrast to the p = 2 case.