Exact solutions for cluster-growth kinetics with evolving size and shape profiles

In this paper we construct a model for the simultaneous compaction by which clusters are restructured, and growth of clusters by pairwise coagulation. The model has the form of a multicomponent aggregation problem in which the components are cluster mass and cluster diameter. Following suitable approximations, exact explicit solutions are derived which may be useful for the verification of simulations of such systems. Numerical simulations are presented to illustrate typical behaviour and to show the accuracy of approximations made in deriving the model. The solutions are then simplified using asymptotic techniques to show the relevant timescales of the kinetic processes and elucidate the shape of the cluster distribution functions at large times.

STORM - a novel information fusion and cluster interpretation technique

Analysis of data without labels is commonly subject to scrutiny by unsupervised machine learning techniques. Such techniques provide more meaningful representations, useful for better understanding of a problem at hand, than by looking only at the data itself. Although abundant expert knowledge exists in many areas where unlabelled data is examined, such knowledge is rarely incorporated into automatic analysis. Incorporation of expert knowledge is frequently a matter of combining multiple data sources from disparate hypothetical spaces. In cases where such spaces belong to different data types, this task becomes even more challenging. In this paper we present a novel immune-inspired method that enables the fusion of such disparate types of data for a specific set of problems. We show that our method provides a better visual understanding of one hypothetical space with the help of data from another hypothetical space. We believe that our model has implications for the field of exploratory data analysis and knowledge discovery.