A dynamic agent model is introduced with an annual random wealth multiplicative process followed by taxes paid according to a linear wealth-dependent tax rate. If poor agents pay higher tax rates than rich agents, eventually all wealth becomes concen
trated in the hands of a single agent. By contrast, if poor agents are subject to lower tax rates, the economic collective process continues forever.
An evolutionary tree is a cascade of bifurcations starting from a single common root, generating a growing set of daughter species as time goes by. Species here is a general denomination for biological species, spoken languages or any other entity ev
olving through heredity. From the N currently alive species within a clade, distances are measured through pairwise comparisons made by geneticists, linguists, etc. The larger is such a distance for a pair of species, the older is their last common ancestor. The aim is to reconstruct the past unknown bifurcations, i.e. the whole clade, from the knowledge of the N(N-1)/2 quoted distances taken for granted. A mechanical method is presented, and its applicability discussed.
A small and light polystyrene ball is released without initial speed from a certain height above the floor. Then, it falls on air. The main responsible for the friction force against the movement is the wake of successive air vortices which form behi
nd (above) the falling ball, a turbulent phenomenon. After the wake appears, the friction force compensates the Earth gravitational attraction and the ball speed stabilises in a certain limiting value Vl. Before the formation of the turbulent wake, however, the friction force is not strong enough, allowing the initially growing speed to surpass the future final value Vl. Only after the wake finally becomes long enough, the ball speed decreases and reaches the proper Vl.
We discovered a dynamic phase transition induced by sexual reproduction. The dynamics is a pure Darwinian rule with both fundamental ingredients to drive evolution: 1) random mutations and crossings which act in the sense of increasing the entropy (o
r diversity); and 2) selection which acts in the opposite sense by limiting the entropy explosion. Selection wins this competition if mutations performed at birth are few enough. By slowly increasing the average number m of mutations, however, the population suddenly undergoes a mutational degradation precisely at a transition point mc. Above this point, the bad alleles spread over the genetic pool of the population, overcoming the selection pressure. Individuals become selectively alike, and evolution stops. Only below this point, m < mc, evolutionary life is possible. The finite-size-scaling behaviour of this transition is exhibited for large enough chromosome lengths L. One important and surprising observation is the L-independence of the transition curves, for large L. They are also independent on the population size. Another is that mc is near unity, i.e. life cannot be stable with much more than one mutation per diploid genome, independent of the chromosome length, in agreement with reality. One possible consequence is that an eventual evolutionary jump towards larger L enabling the storage of more genetic information would demand an improved DNA copying machinery in order to keep the same total number of mutations per offspring.
We study the genetic behaviour of a population formed by haploid individuals which reproduce asexually. The genetic information for each individual is stored along a bit-string (or chromosome) with L bits, where 0-bits represent the wild-type allele
and 1-bits correspond to harmful mutations. Each newborn inherits this chromosome from its parent with some few random mutations: on average a fixed number m of bits are flipped. Selection is implemented according to the number N of 1-bits counted along the individuals chromosome: the smaller N the higher the probability an individual has to survive a new time step. Such a population evolves, with births and deaths, and its genetic distribution becomes stabilised after many enough generations have passed. The question we pose concerns the procedure of increasing L. The aim is to get the same distribution of relative genetic loads N/L among the equilibrated population, in spite of a larger L. Should we keep the same mutation rate m/L for different values of L? The answer is yes, which intuitively seems to be plausible. However, this conclusion is not trivial, according to our simulational results: the question involves also the population size.
The dynamic evolution at zero temperature of a uniform Ising ferromagnet on a square lattice is followed by Monte Carlo computer simulations. The system always eventually reaches a final, absorbing state, which sometimes coincides with a ground state
(all spins parallel), and sometimes does not (parallel stripes of spins up and down). We initiate here the numerical study of ``Chaotic Time Dependence (CTD) by seeing how much information about the final state is predictable from the randomly generated quenched initial state. CTD was originally proposed to explain how nonequilibrium spin glasses could manifest equilibrium pure state structure, but in simpler systems such as homogeneous ferromagnets it is closely related to long-term predictability and our results suggest that CTD might indeed occur in the infinite volume limit.
