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In the context of countable groups of polynomial volume growth, we consider a large class of random walks that are allowed to take long jumps along multiple subgroups according to power law distributions. For such a random walk, we study…
We analyze the avalanche size distribution of the Abelian Manna model on two different fractal lattices with the same dimension d_g=ln(3)/ln(2), with the aim to probe for scaling behavior and to study the systematic dependence of the…
We investigate the evolutionary dynamics of an idealised model for the robust self-assembly of two-dimensional structures called polyominoes. The model includes rules that encode interactions between sets of square tiles that drive the…
Theories that attempt to explain the observed cosmic acceleration by modifying general relativity all introduce a new scalar degree of freedom that is active on large scales, but is screened on small scales to match experiments. We show…
While the animals' Fin-to-Limb evolution has been well-researched in biology, such morphological transformation remains under-adopted in the modern design of advanced robotic limbs. This paper investigates a novel class of overconstrained…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…
With the number of sequenced genomes now over one hundred, and the availability of rough functional annotations for a substantial proportion of their genes, it has become possible to study the statistics of gene content across genomes. Here…
We investigate the relation between a postulated skeleton expansion and the conformal limit of QCD. We begin by developing some consequences of an Abelian-like skeleton expansion, which allows one to disentangle running-coupling effects…
The observed general time-asymmetric behavior of macroscopic systems -- embodied in the second law of thermodynamics -- arises naturally from time-symmetric microscopic laws due to the great disparity between macro and micro-scales. More…
We are interested in modeling Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions. The population is modeled as a stochastic point process whose generator captures…
Constraints on the expansion history of the universe from measurements of cosmological distances make predictions for large-scale structure growth. Since these predictions depend on assumptions about dark energy evolution and spatial…
Understanding biological phenomena requires a systemic approach that incorporates different mechanisms acting on different spatial and temporal scales, since in organisms the workings of all components, such as organelles, cells, and organs…
We investigate the properties of the Lyman alpha forest as predicted by numerical simulations for a range of currently viable cosmological models. This is done in order to understand the dependencies of the forest on cosmological…
Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive.…
Among the infinite number of possible movements that can be produced, humans are commonly assumed to choose those that optimize criteria such as minimizing movement time, subject to certain movement constraints like signal-dependent and…
It has been widely believed that variability of the fine-structure constant alpha would imply detectable violations of the weak equivalence principle. This belief is not justified in general. It is put to rest here in the context of the…
Modularisation, repetition, and symmetry are structural features shared by almost all biological neural networks. These features are very unlikely to be found by the means of structural evolution of artificial neural networks. This paper…
It has long been recognized that tight relations link the mass, size, and characteristic velocity of galaxies. These scaling laws reflect the way in which baryons populate, cool, and settle at the center of their host dark matter halos; the…
A two-dimensional lattice system of non-interacting electrons in a homogeneous magnetic field with half a flux quantum per plaquette and a random potential is considered. For the large scale behavior a supersymmetric theory with collective…
One of the main objectives of modern cosmology is to explain the origin and evolution of cosmic structures at different scales. The principal force responsible for the formation of such structures is gravity. In a general relativistic…