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Simulation of a multicomponent lipid bilayer having a fixed percentage of cholesterol is done to study phase transition leading to domain formation. The concept of random lattice has been used in simulation to account for the coupling…

Compositional data and multivariate count data with known totals are challenging to analyse due to the non-negativity and sum-to-one constraints on the sample space. It is often the case that many of the compositional components are highly…

We show that mixtures comprised of multicomponent systems typically are much more structurally complex than the sum of their parts; sometimes, infinitely more complex. We contrast this with the more familiar notion of statistical mixtures,…

Complex, multivariable systems are often analyzed by grouping their constituent units into components, sometimes referred to as latent features, which afford physical or biological interpretation. However, a priori many different types of…

Standard approaches to tackle high-dimensional supervised classification problem often include variable selection and dimension reduction procedures. The novel methodology proposed in this paper combines clustering of variables and feature…

In tasks like semantic parsing, instruction following, and question answering, standard deep networks fail to generalize compositionally from small datasets. Many existing approaches overcome this limitation with model architectures that…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

Biological sequencing data consist of read counts, e.g. of specified taxa and often exhibit sparsity (zero-count inflation) and overdispersion (extra-Poisson variability). As most sequencing techniques provide an arbitrary total count,…

Selecting an appropriate optimizer for a given problem is of major interest for researchers and practitioners. Many analytical optimizers have been proposed using a variety of theoretical and empirical approaches; however, none can offer a…

We study random composite structures considered up to symmetry that are sampled according to weights on the inner and outer structures. This model may be viewed as an unlabelled version of Gibbs partitions and encompasses multisets of…

The predominant knowledge-based approach to automated model construction, compositional modelling, employs a set of models of particular functional components. Its inference mechanism takes a scenario describing the constituent interacting…

This work investigates whether time series of natural phenomena can be understood as being generated by sequences of latent states which are ordered in systematic and regular ways. We focus on clinical time series and ask whether clinical…

An explanatory model for the emergence of evolvable units must display emerging structures that (1) preserve themselves in time (2) self-reproduce and (3) tolerate a certain amount of variation when reproducing. To tackle this challenge,…

Commercial adoption of automatic music composition requires the capability of generating diverse and high-quality music suitable for the desired context (e.g., music for romantic movies, action games, restaurants, etc.). In this paper, we…

Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…

Large monolithic generative models trained on massive amounts of data have become an increasingly dominant approach in AI research. In this paper, we argue that we should instead construct large generative systems by composing smaller…

In this article, we propose a covariance based method for combining partial data sets in the genotype to phenotype spectrum. In particular, an expectation-maximization algorithm that can be used to combine partially overlapping…

We are entering a new era in which software systems are becoming more and more complex and larger. So, the composition of such systems is becoming infeasible by manual means. To address this challenge, self-organising software models…

Compositional generalization is a crucial step towards developing data-efficient intelligent machines that generalize in human-like ways. In this work, we tackle a challenging form of distribution shift, termed compositional shift, where…

Homology-based invariants can be used to characterize the geometry of datasets and thereby gain some understanding of the processes generating those datasets. In this work we investigate how the geometry of a dataset changes when it is…