22,071 research outputs found
Network growth model with intrinsic vertex fitness
© 2013 American Physical SocietyWe study a class of network growth models with attachment rules governed by intrinsic node fitness. Both the individual node degree distribution and the degree correlation properties of the network are obtained as functions of the network growth rules. We also find analytical solutions to the inverse, design, problems of matching the growth rules to the required (e.g., power-law) node degree distribution and more generally to the required degree correlation function. We find that the design problems do not always have solutions. Among the specific conditions on the existence of solutions to the design problems is the requirement that the node degree distribution has to be broader than a certain threshold and the fact that factorizability of the correlation functions requires singular distributions of the node fitnesses. More generally, the restrictions on the input distributions and correlations that ensure solvability of the design problems are expressed in terms of the analytical properties of their generating functions
Superconducting order parameter of SrRuO: a microscopic perspective
The character of the superconducting phase of SrRuO, is topic of a
longstanding discussion. The classification of the symmetry allowed order
parameters has relied on the tetragonal symmetry of the lattice and on
cylindrical Fermi surfaces, usually taken to be featureless, not including the
non-trivial symmetry aspects related to their orbital content. Here we show how
the careful account of the orbital degree of freedom in SrRuO, leads to
a much richer classification of order parameters. We analyse the stability and
degeneracy of these new order parameters from the perspective of the concept of
superconducting fitness and propose a new best order parameter candidate.Comment: 13 page
Fundamental Properties of the Evolution of Mutational Robustness
Evolution on neutral networks of genotypes has been found in models to
concentrate on genotypes with high mutational robustness, to a degree
determined by the topology of the network. Here analysis is generalized beyond
neutral networks to arbitrary selection and parent-offspring transmission. In
this larger realm, geometric features determine mutational robustness: the
alignment of fitness with the orthogonalized eigenvectors of the mutation
matrix weighted by their eigenvalues. "House of cards" mutation is found to
preclude the evolution of mutational robustness. Genetic load is shown to
increase with increasing mutation in arbitrary single and multiple locus
fitness landscapes. The rate of decrease in population fitness can never grow
as mutation rates get higher, showing that "error catastrophes" for genotype
frequencies never cause precipitous losses of population fitness. The
"inclusive inheritance" approach taken here naturally extends these results to
a new concept of dispersal robustness.Comment: 17 pages, 1 figur
Mutation-Selection Balance: Ancestry, Load, and Maximum Principle
We show how concepts from statistical physics, such as order parameter,
thermodynamic limit, and quantum phase transition, translate into biological
concepts in mutation-selection models for sequence evolution and can be used
there. The article takes a biological point of view within a population
genetics framework, but contains an appendix for physicists, which makes this
correspondence clear. We analyze the equilibrium behavior of deterministic
haploid mutation-selection models. Both the forward and the time-reversed
evolution processes are considered. The stationary state of the latter is
called the ancestral distribution, which turns out as a key for the study of
mutation-selection balance. We find that it determines the sensitivity of the
equilibrium mean fitness to changes in the fitness values and discuss
implications for the evolution of mutational robustness. We further show that
the difference between the ancestral and the population mean fitness, termed
mutational loss, provides a measure for the sensitivity of the equilibrium mean
fitness to changes in the mutation rate. For a class of models in which the
number of mutations in an individual is taken as the trait value, and fitness
is a function of the trait, we use the ancestor formulation to derive a simple
maximum principle, from which the mean and variance of fitness and the trait
may be derived; the results are exact for a number of limiting cases, and
otherwise yield approximations which are accurate for a wide range of
parameters. These results are applied to (error) threshold phenomena caused by
the interplay of selection and mutation. They lead to a clarification of
concepts, as well as criteria for the existence of thresholds.Comment: 54 pages, 15 figures; to appear in Theor. Pop. Biol. 61 or 62 (2002
- …