Data dimensionality reduction technique for clustering problem of metabolomics data

Learning prevalent patterns of co-morbidities in multichronic patients using population-based healthcare data

The prevalence of longstanding chronic diseases has increased worldwide, along with the average age of the population. As a result, an increasing number of people is affected by two or more chronic conditions simultaneously, and healthcare systems are facing the challenge of treating multimorbid patients effectively. Current therapeutic strategies are suited to manage each chronic condition separately, without considering the whole clinical condition of the patient. This approach may lead to suboptimal clinical outcomes and system inefficiencies (e.g. redundant diagnostic tests and inadequate drug prescriptions). We develop a novel methodology based on the joint implementation of data reduction and clustering algorithms to identify patterns of chronic diseases that are likely to co-occur in multichronic patients. We analyse data from a large adult population of multichronic patients living in Tuscany (Italy) in 2019 which was stratified by sex and age classes. Results demonstrate that (i) cardio-metabolic, endocrine, and neuro-degenerative diseases represent a stable pattern of multimorbidity, and (ii) disease prevalence and clustering vary across ages and between women and men. Identifying the most common multichronic profiles can help tailor medical protocols to patients' needs and reduce costs. Furthermore, analysing temporal patterns of disease can refine risk predictions for evolutive chronic conditions.

Improving reduced-order models through nonlinear decoding of projection-dependent outputs

A fundamental hindrance to building data-driven reduced-order models (ROMs) is the poor topological quality of a low-dimensional data projection. This includes behavior such as overlapping, twisting, or large curvatures or uneven data density that can generate nonuniqueness and steep gradients in quantities of interest (QoIs). Here, we employ an encoder-decoder neural network architecture for dimensionality reduction. We find that nonlinear decoding of projection-dependent QoIs, when embedded in a dimensionality reduction technique, promotes improved low-dimensional representations of complex multiscale and multiphysics datasets. When data projection (encoding) is affected by forcing accurate nonlinear reconstruction of the QoIs (decoding), we minimize nonuniqueness and gradients in representing QoIs on a projection. This in turn leads to enhanced predictive accuracy of a ROM. Our findings are relevant to a variety of disciplines that develop data-driven ROMs of dynamical systems such as reacting flows, plasma physics, atmospheric physics, or computational neuroscience.

Multi-order analytical solving computation of rainstorm causal decomposition during typhoons using a designed key-lock quasi-Newton optimizing derivation

To precisely identify multi-dimensional spatiotemporal rain-making parameters, generate an approximate Hessian matrix, and solve the nonlinear ill-posed problem, this study uses composite logical tangent hyperbolic functions to construct the rain-generating simulation model as nonlinear algebraic equations with designed key-lock quasi-Newton optimization for deriving multi-order objective functional derivatives for rainstorm causal decomposition into advanced functional, analytical solution (lock) and Newton's conditional constraints. Specifically, the rank-two approximate structure of the Levenberg-Marquardt and Broyden-Fletcher-Goldfarb-Shanno quasi-Newton algorithms are modified as the symmetric rank-four structure to efficiently calculate a positive definite stable Hessian and solve the constrained nonlinear rain-making threshold. The model projects various rain-making factors into multi-rank loading scores, characterizing rain-generating mechanisms and causal components as associated DNAs. To accelerate/modify directional convergence, avoid local minimum, and detect global optimum, the devised vectorized limited switchable step sizes are optimized using advanced double-bracketing approaches combined with candidate parameters' correction vectors (key) and referenced step-size distributions solved by Newton's constrained analytical solution to reduce heterogeneous differences and eliminate the conventional overestimated Hessian. The identified rain-making DNAs reveal that typhoons with similar DNAs move in similar directions. Specifically, rain-making DNAs in Taipei Category 1 were correlated with wind force/direction and cloud height along PCs 1, 3, 4, and 7, and those in Category 2 were correlated with cloud-cover distribution along PCs 1, 2, and 5. The identified rain-making thresholds of typhoons with constant direction/structure showed a weaker steady state, whereas the unsteady rest produced multi-peak rainfall hydrographs. Rain evolution analysis reveals that cloudy rainbands, carried by the wind field, move along the Tamsui River valley when traveling between northeast and south-southeast of Taipei; converge with gradient and geostrophic winds when traveling between east-northeast and southwest; merge with southwest monsoon when traveling between west-southwest and northeast of Kaohsiung.