Related papers: Compositional Growth Models
We study size and growth distributions of products and business firms in the context of a given industry. Firm size growth is analyzed in terms of two basic mechanisms, i.e. the increase of the number of new elementary business units and…
We introduce a model of proportional growth to explain the distribution of business firm growth rates. The model predicts that the distribution is exponential in the central part and depicts an asymptotic power-law behavior in the tails…
Mathematical methods of analysis of data and of predicting growth are discussed. The starting point is the analysis of the growth rates, which can be expressed as a function of time or as a function of the size of the growing entity.…
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…
Many real-world systems can be usefully represented as sets of interacting components. Examples include computational systems, such as query processors and compilers, natural systems, such as cells and ecosystems, and social systems, such…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic…
We study Sutton's `microcanonical' model for the internal organisation of firms, that leads to non trivial scaling properties for the statistics of growth rates. We show that the growth rates are asymptotically Gaussian in this model, at…
The key idea of this model is that firms are the result of an evolutionary process. Based on demand and supply considerations the evolutionary model presented here derives explicitly Gibrat's law of proportionate effects as the result of…
Growth mixture models are an important tool for detecting group structure in repeated measures data. Unlike traditional clustering methods, they explicitly model the repeat measurements on observations, and the statistical framework they…
In the past many papers have appeared which simulated surface growth with different growth models. The results showed that, if models differed only slightly in their `growth' rules, the resulting surfaces may belong to different…
Compositional understanding is crucial for human intelligence, yet it remains unclear whether contemporary vision models exhibit it. The dominant machine learning paradigm is built on the premise that scaling data and model sizes will…
A step to consilience, starting with a deconstruction of the causality of uncertainty that is embedded in the fundamentals of growth and inequality, following a construction of aggregation laws that disclose the invariance principle across…
An extension of coupled maps is given which allows for the growth of the number of elements, and is inspired by the cell differentiation problem. The growth of elements is made possible first by clustering the phases, and then by…
This paper presents a simple model to measure the relative economic growth of economic systems. The model considers S-Shaped patterns of economic growth that, represented with a linear model, measure how an economic system grows in…
Providing diagnostic feedback about growth is crucial to formative decisions such as targeted remedial instructions or interventions. This paper proposed a longitudinal higher-order diagnostic classification modeling approach for measuring…
We study Bayesian estimation of finite mixture models in a general setup where the number of components is unknown and allowed to grow with the sample size. An assumption on growing number of components is a natural one as the degree of…
A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…
An important question in biology is how the relative size of different organs is kept nearly constant during growth of an animal. This property, called proportionate growth, has received increased attention in recent years. We discuss our…