Related papers: Scaling Function, Universality and Analytical Solu…
Much of our understanding of ecological and evolutionary mechanisms derives from analysis of low-dimensional models: with few interacting species, or few axes defining "fitness". It is not always clear to what extent the intuition derived…
The scaling theory of irreversible aggregation is discussed in some detail. First, we review the general theory in the simplest case of binary reactions. We then extend consideration to ternary reactions, multispecies aggregation,…
A finite size scaling theory, originally developed only for transitions to absorbing states [Phys. Rev. E {\bf 92}, 062126 (2015)], is extended to distinct sorts of discontinuous nonequilibrium phase transitions. Expressions for quantities…
We investigate the error threshold for the emergence of quasispecies in the Eigen model. By mapping to to an effective Hamiltonian ruled by the "imaginary-time" Schr\"odinger equation, a variational ansatz is proposed and applied to…
When traversing a symmetry breaking second order phase transition at a finite rate, topological defects form whose number dependence on the quench rate is given by simple power laws. We propose a general approach for the derivation of such…
We derive a trade-off relation between the accuracy of implementing a desired unitary evolution using a restricted set of free unitaries and the size of the assisting system, in terms of the resource generating/losing capacity of the target…
Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We reveal the finite-size scaling law of the survival…
Residential segregation is analyzed via the Schelling model, in which two types of agents attempt to optimize their situation according to certain preferences and tolerance levels. Several variants of this work are focused on urban or…
A general procedure to formulate asexual (unstructured, deterministic) population dynamical models resulting from individual pairwise interactions is proposed. Individuals are characterized by a continuous strategy that represents all their…
We consider discrete models of kinetic rough interfaces that exhibit space-time scale-invariance in height-height correlation. A generic scaling theory implies that the dynamical structure factor of the height profile can uniquely…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
Linking the microscopic and macroscopic behavior is at the heart of many natural and social sciences. This apparent similarity conceals essential differences across disciplines: while physical particles are assumed to optimize the global…
While the use of spatial agent-based and individual-based models has flourished across many scientific disciplines, the complexities these models generate are often difficult to manage and quantify. This research reduces population-driven,…
We analyze the growth statistics of Swedish trade unions and find a universal functional form for the probability distribution of growth rates of union size, and a power law dependence of the standard deviation of this distribution on the…
The growth function of populations is central in biomathematics. The main dogma is the existence of density dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the population. One important…
A punctuated equilibrium model of biological evolution with relative fitness between different species being the fundamental driving force of evolution is introduced. Mutation is modeled as a fitness updating cellular automaton process…
We demonstrate the non-universal behavior of finite size scaling in (1+1) dimension of a nonlinear discrete growth model involving extended particles in generalized point of view. In particular, we show the violation of the universal nature…
In evolutionary dynamics, well-mixed populations are almost always associated with all-to-all interactions; mathematical models are based on complete graphs. In most cases, these models do not predict fixation probabilities in groups of…
In an evolutionary system in which the rules of mutation are local in nature, the number of possible outcomes after $m$ mutations is an exponential function of $m$ but with a rate that depends only on the set of rules and not the size of…
Methods of general applicability are searched for in swarm intelligence with the aim of gaining new insights about natural swarms and to develop design methodologies for artificial swarms. An ideal solution could be a `swarm calculus' that…