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Learning in weight spaces, where neural networks process the weights of other deep neural networks, has emerged as a promising research direction with applications in various fields, from analyzing and editing neural fields and implicit…

Growth-fragmentation processes describe the evolution of systems in which cells grow slowly and fragment suddenly. Despite originating as a way to describe biological phenomena, they have recently been found to describe the lengths of…

Many popular random partition models, such as the Chinese restaurant process and its two-parameter extension, fall in the class of exchangeable random partitions, and have found wide applicability in model-based clustering, population…

Multi-dimensional data streams, prevalent in applications like IoT, financial markets, and real-time analytics, pose significant challenges due to their high velocity, unbounded nature, and complex inter-dimensional dependencies. Sliding…

In this paper we develop a classification of real functions based on growth rates of repeated iteration. We show how functions are naturally distinguishable when considering inverses of repeated iterations. For example, $n+2\to 2n\to 2^n\to…

The dynamics of linear stochastic growth equations on growing substrates is studied. The substrate is assumed to grow in time following the power law $t^\gamma$, where the growth index $\gamma$ is an arbitrary positive number. Two different…

Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is…

This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…

Simple function classes have emerged as toy problems to better understand in-context-learning in transformer-based architectures used for large language models. But previously proposed simple function classes like linear regression or…

The velocity-dependent `one-scale' model of Martins and Shellard is used to study the evolution of a cosmic string network (and the corresponding loop population) in open universes. It is shown that in this case there is no linear scaling…

We study stochastic processes that generate non-growing complex networks without self-loops and multiple edges (simple graphs). The work concentrates on understanding and formulation of constraints which keep the rewiring stochastic…

The innumerable shapes of plant leaves present a challenge to the explanatory power of biophysical theory. A model is needed that can produce these shapes with a small set of parameters. This paper presents a simple model of leaf shape…

Accelerating cosmologies in extra dimensional spaces have been studied. These extra dimensional spaces are products of many spaces. The physical behaviors of accelerating cosmologies are investigated from Einstein's field equation in higher…

We introduce a general theory of quantitative and metric rewriting systems, namely systems with a rewriting relation enriched over quantales modelling abstract quantities. We develop theories of abstract and term-based systems, refining…

Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. We propose a class of spatially-based growing network models and investigate the relationship between the…

We give a survey of results regarding existence and regularity for autonomous functionals of linear growth that depend on the symmetric rather than the full gradients.

The cosmic string scenario in an open universe is developed -- including the equations of motion, a model of network evolution, the large angular scale CMB temperature anisotropy, and the power spectrum of density fluctuations produced by…

Many complex systems have been shown to share universal properties of organization, such as scale independence, modularity and self-similarity. We borrow tools from statistical physics in order to study structural preferential attachment…

The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher…

We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…