arXiv subjects

Ard A Louis

Publications and source records attributed to Ard A Louis.

3 recordsLinked to original sources

arXiv2026

Beyond Typical Strings: Sampling the Complexity Landscape

Uniform random sampling of strings is overwhelmingly dominated by high-complexity strings, leaving the much smaller set of low- and intermediate-complexity strings largely unexplored. Here, we adapt the nested neutral set estimator (NNSE), a Monte Carlo rare-event sampling method, to estimate the distribution P(K) of complexity values for binary strings of fixed length. NNSE allows us to explore the full complexity landscape, including exponentially rare low-complexity regions that are inaccessible to direct sampling, for string lengths up to several hundred. We apply the method to several widely used complexity measures: Lempel-Ziv 76 (LZ76), Lempel-Ziv 78 (LZ78), context tree weighting (CTW), the block decomposition method (BDM), and block entropy. We further introduce uniform complexity weighting (UCW), which gives equal weight to different complexity levels rather than to individual strings. This approach provides a dataset-independent framework for comparing complexity measures across their full range and reveals substantial differences between measures for low- and intermediate-complexity strings that are largely hidden by conventional uniform sampling. Using the NNSE to perform UCW sampling allows us to compare complexity measures across their full range in a dataset-independent way. This reveals differences in their behavior for low- and intermediate-complexity strings that are practically inaccessible to conventional uniform sampling.

cs.IT↗

arXiv2014

The arrival of the frequent: how bias in genotype-phenotype maps can steer populations to local optima

Genotype-phenotype (GP) maps specify how the random mutations that change genotypes generate variation by altering phenotypes, which, in turn, can trigger selection. Many GP maps share the following general properties: 1) The number of genotypes $N_G$ is much larger than the number of selectable phenotypes; 2) Neutral exploration changes the variation that is accessible to the population; 3) The distribution of phenotype frequencies $F_p=N_p/N_G$, with $N_p$ the number of genotypes mapping onto phenotype $p$, is highly biased: the majority of genotypes map to only a small minority of the phenotypes. Here we explore how these properties affect the evolutionary dynamics of haploid Wright-Fisher models that are coupled to a simplified and general random GP map or to a more complex RNA sequence to secondary structure map. For both maps the probability of a mutation leading to a phenotype $p$ scales to first order as $F_p$, although for the RNA map there are further correlations as well. By using mean-field theory, supported by computer simulations, we show that the discovery time $T_p$ of a phenotype $p$ similarly scales to first order as $1/F_p$ for a wide range of population sizes and mutation rates in both the monomorphic and polymorphic regimes. These differences in the rate at which variation arises can vary over many orders of magnitude. Phenotypic variation with a larger $F_p$ is therefore be much more likely to arise than variation with a small $F_p$. We show, using the RNA model, that frequent phenotypes (with larger $F_p$) can fix in a population even when alternative, but less frequent, phenotypes with much higher fitness are potentially accessible. In other words, if the fittest never `arrive' on the timescales of evolutionary change, then they can't fix. We call this highly non-ergodic effect the `arrival of the frequent'.

q-bio.PE↗

arXiv2002

Exotic fluids and crystals of soft polymeric colloids

We discuss recent developments and present new findings in the colloidal description of soft polymeric macromolecular aggregates. For various macromolecular architectures, such as linear chains, star polymers, dendrimers and polyelectrolyte stars, the effective interactions between suitably chosen coordinates are shown to be ultrasoft, i.e., they either remain finite or diverge very slowly at zero separation. As a consequence, the fluid phases have unusual characteristics, including anomalous pair correlations and mean-field like thermodynamic behaviour. The solid phases can exhibit exotic, strongly anisotropic as well as open crystal structures. For example, the diamond and the A15-phase are shown to be stable at sufficiently high concentrations. Reentrant melting and clustering transitions are additional features displayed by such systems, resulting in phase diagrams with a very rich topology. We emphasise that many of these effects are fundamentally different from the usual archetypal hard sphere paradigm. Instead, we propose that these fluids fall into the class of mean-field fluids.

cond-mat.soft↗