MOTIVATION: Compositional data are frequently encountered in many disciplines, such as in next-generation sequencing experiments widely used in biomedical studies. Regression analysis with compositional data as either responses or predictors has been well studied. However, when both responses and predictors are compositional, the inventory of analysis tools is surprisingly limited, especially in the high-dimensional setting. Among the few existing methods, most of them rely on a log-ratio transformation to move compositional data from the simplex to real numbers. Yet, a serious weakness of these methods is their failure to handle the substantial fraction of zeroes observed in data collected from next-generation sequencing experiments. RESULTS: To investigate associations between two high-dimensional multi-omics compositions, we propose a composition-on-composition (COC) regression analysis method which does not require log-ratio transformations and hence can handle zeroes in the data. To account for high dimensionality, we estimate regression coefficients using a penalized estimation equation approach. Finally, inference procedures for COC regression are also proposed. Superior performance of COC is demonstrated through both comprehensive numerical simulations and case studies. AVAILABILITY AND IMPLEMENTATION: Source R codes to implement COC method is available at https://github.com/nrios4/COC.

This work presents a novel and effective method for fitting multidimensional ellipsoids (i.e., ellipsoids embedded in [Formula: see text]) to scattered data in the contamination of noise and outliers. Unlike conventional algebraic or geometric fitting paradigms that assume each measurement point is a noisy version of its nearest point on the ellipsoid, we approach the problem as a Bayesian parameter estimate process and maximize the posterior probability of a certain ellipsoidal solution given the data. We establish a more robust correlation between these points based on the predictive distribution within the Bayesian framework, i.e., considering each model point as a potential source for generating each measurement. Concretely, we incorporate a uniform prior distribution to constrain the search for primitive parameters within an ellipsoidal domain, ensuring ellipsoid-specific results regardless of inputs. We then establish the connection between measurement point and model data via Bayes' rule to enhance the method's robustness against noise. Due to independent of spatial dimensions, the proposed method not only delivers high-quality fittings to challenging elongated ellipsoids but also generalizes well to multidimensional spaces. To address outlier disturbances, often overlooked by previous approaches, we further introduce a uniform distribution on top of the predictive distribution to significantly enhance the algorithm's robustness against outliers. Thanks to the uniform prior, our maximum a posterior probability coincides with a more tractable maximum likelihood estimation problem, which is subsequently solved by a numerically stable Expectation Maximization (EM) framework. Moreover, we introduce an ε-accelerated technique to expedite the convergence of EM considerably. We also investigate the relationship between our algorithm and conventional least-squares-based ones, during which we theoretically prove our method's superior robustness. To the best of our knowledge, this is the first comprehensive method capable of performing multidimensional ellipsoid-specific fitting within the Bayesian optimization paradigm under diverse disturbances. We evaluate it across lower and higher dimensional spaces in the presence of heavy noise, outliers, and substantial variations in axis ratios. Also, we apply it to a wide range of practical applications such as microscopy cell counting, 3D reconstruction, geometric shape approximation, and magnetometer calibration tasks. In all these test contexts, our method consistently delivers flexible, robust, ellipsoid-specific performance, and achieves the state-of-the-art results.

A small rotor eccentricity can produce a large unbalanced magnetic pull and even worse cause failure of the suspension control in the bearingless doubly salient electromagnetic machine. In order to ensure the stable suspension and improve the suspension performance, this paper investigates influence of the static rotor eccentricity from two aspects of average and instantaneous values of the suspension force by finite element analysis, which lays the foundation for the precise mathematical model and the eccentricity compensation control.