The number of microbiome-related studies has notably increased the availability of data on human microbiome composition and function. These studies provide the essential material to deeply explore host-microbiome associations and their relation to the development and progression of various complex diseases. Improved data-analytical tools are needed to exploit all information from these biological datasets, taking into account the peculiarities of microbiome data, i.e., compositional, heterogeneous and sparse nature of these datasets. The possibility of predicting host-phenotypes based on taxonomy-informed feature selection to establish an association between microbiome and predict disease states is beneficial for personalized medicine. In this regard, machine learning (ML) provides new insights into the development of models that can be used to predict outputs, such as classification and prediction in microbiology, infer host phenotypes to predict diseases and use microbial communities to stratify patients by their characterization of state-specific microbial signatures. Here we review the state-of-the-art ML methods and respective software applied in human microbiome studies, performed as part of the COST Action ML4Microbiome activities. This scoping review focuses on the application of ML in microbiome studies related to association and clinical use for diagnostics, prognostics, and therapeutics. Although the data presented here is more related to the bacterial community, many algorithms could be applied in general, regardless of the feature type. This literature and software review covering this broad topic is aligned with the scoping review methodology. The manual identification of data sources has been complemented with: (1) automated publication search through digital libraries of the three major publishers using natural language processing (NLP) Toolkit, and (2) an automated identification of relevant software repositories on GitHub and ranking of the related research papers relying on learning to rank approach.

Investigations addressing correlation between antioxidant activity and theoretical descriptors are plentiful in the literature. This task is quite ambitious, bearing in mind the rather complicated interactions in living cells. In this study we have tried to simplify the problem by looking for direct correlations between calculated characteristics and scavenging activity, neglecting the specificity of cellular environment. To address the problem of antioxidant activity, a set of 20 phenolic compounds and their phenoxyl radicals were investigated at the unrestricted B3LYP level of theory using the 6-31+G(d,p) basis set. Three important descriptors of the considered compounds were related to the results of the DPPH scavenging activity. Significant linear correlations were obtained in several cases.

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The role of time delays in solid avascular tumour growth is considered. The model is formulated in terms of a reaction-diffusion equation and mass conservation law. Two main processes are taken into account-proliferation and apoptosis. We introduce time delay first in underlying apoptosis only and then in both processes. In the absence of necrosis the model reduces to one ordinary differential equation with one discrete delay which describes the changes of tumour radius. Basic properties of the model depending on the magnitude of delay are studied. Nonnegativity of solutions is investigated. Steady state and the Hopf bifurcation analysis are presented. The results are illustrated by computer simulations.

The goal of this paper is to construct a new algorithm for the numerical simulations of the evolution of tumour invasion and metastasis. By means of mathematical model equations and their numerical solutions we investigate how cancer cells can produce and secrete matrix degradative enzymes, degrade extracellular matrix, and invade due to diffusion and haptotactic migration. For the numerical simulations of the interactions between the tumour cells and the surrounding tissue, we apply numerical approximations, which are spectrally accurate and based on small amounts of grid-points. Our numerical experiments illustrate the metastatic ability of tumour cells.