Related papers: Growth Models And The Question Of Universality Cla…
We consider growth conditions for (frequently) Birkhoff-universal functions of exponential type with respect to the different rays emanating from the origin. For that purpose, we investigate their (conjugate) indicator diagram or,…
Human mobility is a fundamental process underpinning socioeconomic life and urban structure. Classic theories, such as egocentric activity spaces and central place theory, provide crucial insights into specific facets of movement, like…
We propose a generalized model for uniform recursive tree (URT) by introducing an imperfect growth process, which may generate disconnected components (clusters). The model undergoes an interesting phase transition from a singly connected…
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…
Cell growth in size is a complex process coordinated by intrinsic and environmental signals. In a recent work [Tzur et al., Science, 2009, 325:167-171], size distributions in an exponentially growing population of mammalian cells were used…
Tropical geometry gives a bound on the ranks of divisors on curves in terms of the combinatorics of the dual graph of a degeneration. We show that for a family of examples, curves realizing this bound might only exist over certain…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
A large class of the dynamical laws for causal sets described by a classical process of sequential growth yield a cyclic universe, whose cycles of expansion and contraction are punctuated by single `origin elements' of the causal set. We…
We show that the emergence of different surface patterns (ripples, dots) can be well understood by a suitable mapping onto the simplest nonequilibrium lattice gases and cellular automata.Using this efficient approach difficult, unanswered…
We show local higher integrability of derivative of a suitable weak solution to the surface growth model, provided a scale-invariant quantity is locally bounded. If additionally our scale-invariant quantity is small, we prove local…
In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often…
In this paper a comparison between first order microscopic and macroscopic differential models of crowd dynamics is established for an increasing number $N$ of pedestrians. The novelty is the fact of considering massive agents, namely…
We deal with consistency results for the existence of universal models in natural classes of models (more exactly--a somewhat weaker version). We apply a result on quite general family to T_feq and to the class of triangle-free graphs.
The Kardar-Parisi-Zhang universality class of stochastic surface growth is studied by exact field-theoretic methods. From previous numerical results, a few qualitative assumptions are inferred. In particular, height correlations should…
A most debated topic of the last years is whether simple statistical physics models can explain collective features of social dynamics. A necessary step in this line of endeavour is to find regularities in data referring to large scale…
We investigate a model of interacting clusters which compete for growth. For a finite assembly of coupled clusters, the largest one always wins, so that all but this one die out in a finite time. This scenario of `survival of the biggest'…
Deep neural networks come in many sizes and architectures. The choice of architecture, in conjunction with the dataset and learning algorithm, is commonly understood to affect the learned neural representations. Yet, recent results have…
It is still common wisdom amongst economists, politicians and lay people that economic growth is a necessity of our social systems, at least to avoid distributional conflicts. This paper challenges such belief moving from a purely physical…
Most models that try to explain economic growth indicate exponential growth paths. In recent years, however, a lively discussion has emerged considering the validity of this notion. In the empirical literature dealing with drivers of…
Logistic equations play a pivotal role in the study of any non linear evolution process exhibiting growth and saturation. The interest for the phenomenology, they rule, goes well beyond physical processes and cover many aspects of ecology,…