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Urban transportation systems grow over time as city populations grow and move and their transportation needs evolve. Typical network growth models, such as preferential attachment, grow the network node by node whereas rail and metro…
The exact general evolution of circular strings in $2+1$ dimensional de Sitter spacetime is described closely and completely in terms of elliptic functions. The evolution depends on a constant parameter $b$, related to the string energy,…
The growth function is the generating function for sizes of spheres around the identity in Cayley graphs of groups. We present a novel method to calculate growth functions for automatic groups with normal form recognizing automata that…
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…
Additive models form a widely popular class of regression models which represent the relation between covariates and response variables as the sum of low-dimensional transfer functions. Besides flexibility and accuracy, a key benefit of…
From genomes and ecosystems to bureaucracies and cities, the growth of complex systems occurs by adding new types of functions and expanding existing ones. We present a simple generative model that generalizes the Yule-Simon process by…
The spacetime discreteness of causal set theory has enabled the formulation of novel spacetime dynamics. In these so-called "growth" dynamics, a causal set spacetime is generated probabilistically by means of a random walk on certain tree…
We introduce and study algebraic dynamical systems generated by triangular systems of rational functions. We obtain several results about the degree growth and linear independence of iterates as well as about possible lengths of…
In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…
The Burrows-Wheeler Transform is a string transformation that plays a fundamental role for the design of self-indexing compressed data structures. Over the years, researchers have successfully extended this transformation outside the…
The aim of this article is to provide characterizations for subadditivity-like growth conditions for the so-called associated weight functions in terms of the defning weight sequence. Such growth requirements arise frequently in the…
A novel mechanism for the production of a cosmic network of fundamental superstrings based on a time-varying string tension has been recently proposed in the context of a kinating background driven by the volume modulus of string…
Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon…
Polyregular functions form a robust class of string-to-string functions with polynomial growth, as evidenced by Bojanczyk (2018). This class admits numerous descriptions and enjoys several closure properties. Most notably, polyregular…
Complex networks serve as abstract models for understanding real-world complex systems and provide frameworks for studying structured dynamical systems. This article addresses limitations in current studies on the exploration of individual…
Real-world growth processes and scalings have been broadly categorized into three growth regimes with distinctly different properties and driving forces. The first two are characterized by a positive and constant feedback between growth and…
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…
In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected…