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Mathematical method based on a direct or indirect analysis of growth rates is described. It is shown how simple assumptions and a relatively easy analysis can be used to describe mathematically complicated trends and to predict growth. Only…
In this paper, we define a class of slice mappings of several Clifford variables, and the corresponding slice regular mappings. Furthermore, we establish the growth theorem for slice regular starlike or convex mappings on the unit ball of…
The rising complexity of our terrestrial surrounding is an empirical fact. Details of this process evaded description in terms of physics for long time attracting attention and creating myriad of ideas including non-scientific ones. In this…
A modification of the symmetry approach for the classification of integrable differential-difference equations of the form $$ u_{n,t} = f_n(u_{n-1}, u_n, u_{n+1}), $$ where $n$ is a discrete integer variable, is presented (the well-known…
We present significantly advanced studies of the previously introduced physical growth mechanism and unite it with biochemical growth factors. Obtained results allowed formulating the general growth law which governs growth and evolutional…
We consider stochastic growth models for populations organized in colonies and subject to uniform catastrophes. To assess population viability, we analyze scenarios in which individuals adopt dispersion strategies after catastrophic events.…
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…
From the smallest biological systems to the largest cosmological structures, spatial domains undergo expansion and contraction. Within these growing domains, diffusive transport is a common phenomenon. Mathematical models have been widely…
In this paper, we define a class of additive random growth models whose growth is at least and at most linear and prove an asymptotic shape theorem for these models. This proof generalizes already known proofs for the classical contact…
In this comment, we show explicitly that the phenomenological model in which the quintessence field depends linearly on the energy density of the spatial curvature can provide acceleration for the universe, contrary to recent claims it…
This is a survey article based on the content of the plenary lecture given by Jos\'e A. Carrillo at the ICIAM23 conference in Tokyo. It is devoted to produce a snapshot of the state of the art in the analysis, numerical analysis,…
We propose a mathematical and a conceptual framework (called the `E-model' and the `event ontology' resp.) that encompasses and generalizes the `flash' ontology discussed in a recent paper by R. Tumulka (arXiv:quant-ph/0602208)
We discuss the issue of motivating the analysis of higher order gravity theories and their cosmologies and introduce a rule which states that these theories may be considered as a vehicle for testing whether certain properties may be of…
Time evolution of the classification scheme generated by the EqRank algorithm is studied with hep-th citation graph as an example. Intuitive expectations about evolution of an adequate classification scheme for a growing set of objects are…
A conceptual framework for variational formulations of physical theories is proposed. Such a framework is displayed here just for statics, but it is designed to be subsequently adapted to variational formulations of static field theories…
We consider a reaction-diffusion-advection equation arising from a biological model of migrating species. The qualitative properties of the globally attracting solution are studied and in some cases the limiting profile is determined. In…
While inflation gives an appealing explanation of observed cosmological data, there are a wide range of different inflation models, providing differing predictions for the initial perturbations. Typically models are motivated either by…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
A macroscopic theory for describing cellular states during steady-growth is presented, which is based on the consistency between cellular growth and molecular replication, as well as the robustness of phenotypes against perturbations.…
The phenomenon of quantum number fractionalization is explained. The relevance of non-trivial phonon field topology is emphasized.