Signal Processing Techniques for Optical Transmission Based on Eigenvalue Communication

A minimum mean squared error (MMSE) equalizer is a way to effectively increase transmission performance for nonlinear Fourier transform (NFT) based communication systems. Other equalization schemes, based on nonlinear equalizer approaches or neural networks, are interesting for NFT transmission due to their ability to deal with nonlinear correlations of the NFTs’ eigenvalues and their coefficients. We experimentally investigated single- and dual-polarization long haul transmission with several modulation schemes and compared different equalization techniques including joint detection equalization and the use of neural networks. We observed that joint detection equalization provides range increases for shorter transmission distances while having low numeric complexity. We could further achieve bit error rates (BER) under HD-FEC for significant longer transmission distances in comparison to no equalization with different equalizers.<div><br></div><div>Manuscript received August 6, 2020; revised November 2, 2020; accepted December 8, 2020. Date of publication December 16, 2020;<br></div>

Signal Processing Techniques for Optical Transmission Based on Eigenvalue Communication

A minimum mean squared error (MMSE) equalizer is a way to effectively increase transmission performance for nonlinear Fourier transform (NFT) based communication systems. Other equalization schemes, based on nonlinear equalizer approaches or neural networks, are interesting for NFT transmission due to their ability to deal with nonlinear correlations of the NFTs’ eigenvalues and their coefficients. We experimentally investigated single- and dual-polarization long haul transmission with several modulation schemes and compared different equalization techniques including joint detection equalization and the use of neural networks. We observed that joint detection equalization provides range increases for shorter transmission distances while having low numeric complexity. We could further achieve bit error rates (BER) under HD-FEC for significant longer transmission distances in comparison to no equalization with different equalizers.<div><br></div><div>Manuscript received August 6, 2020; revised November 2, 2020; accepted December 8, 2020. Date of publication December 16, 2020;<br></div>

The Association between Urine Elements and Fasting Glucose Levels in a Community-Based Elderly People in Beijing

Epidemiological studies have demonstrated that various kinds of urinary element concentrations were different between healthy, prediabetes, and diabetes patients. Meanwhile, many studies have explored the relationship between element concentration and fasting blood glucose (FBG), but the association between joint exposure to co-existing elements and FBG level has not been well understood. The study explored the associations of joint exposure to co-existing urinary elements with FBG level in a cross-sectional design. 275 retired elderly people were recruited from Beijing, China. The questionnaire survey was conducted, and biological samples were collected. The generalized linear model (GLM) and two-phase Bayesian kernel machine regression (BKMR) model were used to perform in-depth association analysis between urinary elements and FBG. The GLM analysis showed that Zn, Sr, and Cd were significantly correlated with the FBG level, under control potential confounding factors. The BKMR analysis demonstrated 8 elements (Zn, Se, Fe, Cr, Ni, Cd, Mn, and Al) had a higher influence on FBG (Posterior inclusion probabilities >0.1). Further intensive analyses result of the BKMR model indicated that the overall estimated exposure of 8 elements was positively correlated with the FBG level and was statistically significant when all element concentrations were at their 65th percentile. Meanwhile, the BKMR analysis showed that Cd and Zn had a statistically significant association with FBG levels when other co-existing elements were controlled at different levels (25th, 50th or 75th percentile), respectively. The results of the GLM and BKMR model were inconsistent. The BKMR model could flexibly calculate the joint exposure to co-existing elements, evaluate the possible interaction effects and nonlinear correlations. The meaningful conclusions were found that it was difficult to get by traditional methods. This study will provide methodological reference and experimental evidence for the association between joint exposure to co-existing elements and FBG in elderly people.

An improved algorithm for the maximal information coefficient and its application

The maximal information coefficient (MIC) captures both linear and nonlinear correlations between variable pairs. In this paper, we proposed the BackMIC algorithm for MIC estimation. The BackMIC algorithm adds a searching back process on the equipartitioned axis to obtain a better grid partition than the original implementation algorithm ApproxMaxMI. And similar to the ChiMIC algorithm, it terminates the grid search process by the χ 2 -test instead of the maximum number of bins B( n , α ). Results on simulated data show that the BackMIC algorithm maintains the generality of MIC, and gives more reasonable grid partition and MIC values for independent and dependent variable pairs under comparable running times. Moreover, it is robust under different α in B( n , α ). MIC calculated by the BackMIC algorithm reveals an improvement in statistical power and equitability. We applied (1-MIC) as the distance measurement in the K-means algorithm to perform a clustering of the cancer/normal samples. The results on four cancer datasets demonstrated that the MIC values calculated by the BackMIC algorithm can obtain better clustering results, indicating the correlations between samples measured by the BackMIC algorithm were more credible than those measured by other algorithms.

Exploring adipogenic and myogenic circulatory biomarkers of recurrent pressure injury risk for persons with spinal cord injury

Purpose: To investigate linkages between circulatory adipogenic and myogenic biomarkers, gluteal intramuscular adipose tissue (IMAT), and pressure injury (PrI) history following spinal cord injury (SCI). Methods: This is an observational repeated-measures study of 30 individuals with SCI. Whole blood was collected regularly over 2-3 years. Circulatory adipogenic and myogenic gene expression was determined. IMAT was defined as above/below 15% (IMATd) or percentage (IMAT%). PrI history was defined as recurrent PrI (RPrI) or PrI number (nPrI). Model development used R packages (version 3.5.1). Univariate analysis screened for discriminating genes for downstream multivariate and combined models of averaged and longitudinal data for binary (RPrI/IMATd) and finer scales (nPrI/IMAT%). Results: For adipogenesis, Krüppel-like factor 4 was the top RPrI predictor together with resistin and cyclin D1, and sirtuin 2 was the top IMAT predictor. For myogenesis, the top RPrI predictor was dysferlin 2B, and pyruvate dehydrogenase kinase-4 was the top IMAT predictor together with dystrophin. Conclusion: Circulatory adipogenic and myogenic biomarkers have statistically significant relationships with PrI history and IMAT for persons with SCI. Biomarkers of interest may act synergistically or additively. Variable importance rankings can reveal nonlinear correlations among the predictors. Biomarkers of interest may act synergistically or additively, thus multiple genes may need to be included for prediction with finer distinction.

Measuring Independence between Statistical Randomness Tests by Mutual Information

The analysis of independence between statistical randomness tests has had great attention in the literature recently. Dependency detection between statistical randomness tests allows one to discriminate statistical randomness tests that measure similar characteristics, and thus minimize the amount of statistical randomness tests that need to be used. In this work, a method for detecting statistical dependency by using mutual information is proposed. The main advantage of using mutual information is its ability to detect nonlinear correlations, which cannot be detected by the linear correlation coefficient used in previous work. This method analyzes the correlation between the battery tests of the National Institute of Standards and Technology, used as a standard in the evaluation of randomness. The results of the experiments show the existence of statistical dependencies between the tests that have not been previously detected.

Scalable hierarchical clustering by composition rank vector encoding and tree structure

Supervised machine learning, especially deep learning based on a wide variety of neural network architectures, have contributed tremendously to fields such as marketing, computer vision and natural language processing. However, development of un-supervised machine learning algorithms has been a bottleneck of artificial intelligence. Clustering is a fundamental unsupervised task in many different subjects. Unfortunately, no present algorithm is satisfactory for clustering of high dimensional data with strong nonlinear correlations. In this work, we propose a simple and highly efficient hierarchical clustering algorithm based on encoding by composition rank vectors and tree structure, and demonstrate its utility with clustering of protein structural domains. No record comparison, which is an expensive and essential common step to all present clustering algorithms, is involved. Consequently, it achieves linear time and space computational complexity hierarchical clustering, thus applicable to arbitrarily large datasets. The key factor in this algorithm is definition of composition, which is dependent upon physical nature of target data and therefore need to be constructed case by case. Nonetheless, the algorithm is general and applicable to any high dimensional data with strong nonlinear correlations. We hope this algorithm to inspire a rich research field of encoding based clustering well beyond composition rank vector trees.