TY - JOUR A1 - Mireles, Victor A1 - Conrad, Tim T1 - Decomposing biological systems into reusable modules reveals characteristic module size distributions N2 - One of the widely recognized features of biological systems is their modularity. The modules that comprise biological systems are said to be redeployed and combined across several conditions. In this work, we analyze to what extent are these modules indeed reusable as compared to randomized versions of a system. We develop a notion of modular decompositions of systems that allows for modules to overlap while maximizing the number of times a module is reused across several conditions. Different biological systems present modules whose reusability ranges from the condition specific to the constitutive, although their average reusability is not always higher than random equivalents of the system. These decompositions reveal a distinct distribution of module sizes in real biological systems. This distribution stems, in part, from the peculiar usage pattern of the elements of biological systems, and constitutes a new angle to study the evolution of modularity. Y1 - 2016 ER - TY - JOUR A1 - Conrad, Tim A1 - Mireles, Victor T1 - Minimum-overlap clusterings and the sparsity of overcomplete decompositions of binary matrics JF - Procedia Computer Science N2 - Given a set of n binary data points, a widely used technique is to group its features into k clusters. In the case where n {\ensuremath{<}} k, the question of how overlapping are the clusters becomes of interest. In this paper we approach the question through matrix decomposition, and relate the degree of overlap with the sparsity of one of the resulting matrices. We present analytical results regarding bounds on this sparsity, and a heuristic to estimate the minimum amount of overlap that an exact grouping of features into k clusters must have. As shown below, adding new data will not alter this minimum amount of overlap. Y1 - 2015 U6 - https://doi.org/10.1016/j.procs.2015.05.500 VL - 51 SP - 2967 EP - 2971 ER - TY - JOUR A1 - Mireles, Victor A1 - Conrad, Tim T1 - Reusable building blocks in biological systems JF - Journal of the Royal Society Interface N2 - One of the most widely recognized features of biological systems is their modularity. The modules that constitute biological systems are said to be redeployed and combined across several conditions, thus acting as building blocks. In this work, we analyse to what extent are these building blocks reusable as compared with those found in randomized versions of a system. We develop a notion of decompositions of systems into phenotypic building blocks, which allows them to overlap while maximizing the number of times a building block is reused across several conditions. Different biological systems present building blocks whose reusability ranges from single use (e.g. condition specific) to constitutive, although their average reusability is not always higher than random equivalents of the system. These decompositions reveal a distinct distribution of building block sizes in real biological systems. This distribution stems, in part, from the peculiar usage pattern of the elements of biological systems, and constitutes a new angle to study the evolution of modularity. Y1 - 2018 U6 - https://doi.org/10.1098/rsif.2018.0595 VL - 15 IS - 149 SP - 1 EP - 10 ER -