Related papers: Compositional Growth Models
One of approaches to quantum gravity is different models of a discrete pregeometry. An example of a discrete pregeometry on a microscopic scale is introduced. This is the particular case of a causal set. The causal set is a locally finite…
The Gini coefficient is an universally used measurement of income inequality. Intersectoral GDP contributions reveal the economic development of different sectors of the national economy. Linking intersectoral GDP contributions to Gini…
Existing models of network growth typically have one or two parameters or strategies which are fixed for all times. We introduce a general framework where feedback on the current state of a network is used to dynamically alter the values of…
Vegetation patterns, a natural phenomenon observed worldwide, are typically driven by spatially distributed feedback. However, the spatial colonization mechanisms of clonal plants, driven by the growth of a rhizome, are usually not…
Self-organisation lies at the core of fundamental but still unresolved scientific questions, and holds the promise of de-centralised paradigms crucial for future technological developments. While self-organising processes have been…
Several simple growth and decay models use concepts and measures from fractal geometry. Kinetic models relevant to condensed matter observations arerecalled. They should be specifically adapted with appropriate degrees of freedom in order…
The `pet fish' phenomenon is often cited as a paradigm example of the `non-compositionality' of human concept use. We show here how this phenomenon is naturally accommodated within a compositional distributional model of meaning. This model…
Since their introduction, diffusion models have quickly become the prevailing approach to generative modeling in many domains. They can be interpreted as learning the gradients of a time-varying sequence of log-probability density…
A common assumption in causal modeling posits that the data is generated by a set of independent mechanisms, and algorithms should aim to recover this structure. Standard unsupervised learning, however, is often concerned with training a…
We consider incorporation of particle detachment in Smoluchowski model of colloidal growth. Two approaches are considered, utilizing phenomenological rate equation and exact large-time results. Our main conclusion is that the value of the…
In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. Time dependence of metric represents the evolution of the stress-free (natural)…
Compositional data are contemporarily defined as positive vectors, the ratios among whose elements are of interest to the researcher. Financial statement analysis by means of accounting ratios a.k.a. financial ratios fulfils this definition…
Verhulst logistic curve either grows OR decays, depending on the {\it growth rate} parameter value. A similar situation is found in the Gompertz law about human mortality. However, growth can neither be infinite nor reach a finite steady…
Many socio-economic systems require positive economic growth rates to function properly. Given uncertainty about future growth rates and increasing evidence that economic growth is a driver of social and environmental crises, these growth…
The use of a hypothetical generative model was been suggested for causal analysis of observational data. The very assumption of a particular model is a commitment to a certain set of variables and therefore to a certain set of possible…
Transformers trained on huge text corpora exhibit a remarkable set of capabilities, e.g., performing basic arithmetic. Given the inherent compositional nature of language, one can expect the model to learn to compose these capabilities,…
Compositional data, such as regional shares of economic sectors or property transactions, are central to understanding structural change in economic systems across space and time. This paper introduces a spatiotemporal multivariate…
Multivariate functional data that are cross-sectionally compositional data are attracting increasing interest in the statistical modeling literature, a major example being trajectories over time of compositions derived from cause-specific…
Random matrix products arise in many science and engineering problems. An efficient evaluation of its growth rate is of great interest to researchers in diverse fields. In the current paper, we reformulate this problem with a generating…
Fund models are statistical descriptions of markets where all asset returns are spanned by the returns of a lower-dimensional collection of funds, modulo orthogonal noise. Equivalently, they may be characterised as models where the global…