Ard Louis

Abstract:

Double-descent curves in neural networks describe the phenomenon that the generalisation error initially descends with increasing parameters, then grows after reaching an optimal number of parameters which is less than the number of data points, but then descends again in the overparameterized regime. In this paper, we use techniques from random matrix theory to characterize the spectral distribution of the empirical feature covariance matrix as a width-dependent perturbation of the spectrum of the neural network Gaussian process (NNGP) kernel, thus establishing a novel connection between the NNGP literature and the random matrix theory literature in the context of neural networks. Our analytical expressions allow us to explore the generalisation behavior of the corresponding kernel and GP regression. Furthermore, they offer a new interpretation of double-descent in terms of the discrepancy between the width-dependent empirical kernel and the width-independent NNGP kernel.

Abstract:

We introduce oxNA, a new model for the simulation of DNA–RNA hybrids that is based on two previously developed coarse-grained models—oxDNA and oxRNA. The model naturally reproduces the physical properties of hybrid duplexes, including their structure, persistence length, and force-extension characteristics. By parameterizing the DNA–RNA hydrogen bonding interaction, we fit the model’s thermodynamic properties to experimental data using both average-sequence and sequence-dependent parameters. To demonstrate the model’s applicability, we provide three examples of its use—calculating the free energy profiles of hybrid strand displacement reactions, studying the resolution of a short R-loop, and simulating RNA-scaffolded wireframe origami.

Abstract:

We introduce oxNA, a new model for the simulation of DNA-RNA hybrids which is based on two previously developed coarse-grained models—oxDNA and oxRNA. The model naturally reproduces the physical properties of hybrid duplexes including their structure, persistence length and force-extension characteristics. By parameterising the DNA-RNA hydrogen bonding interaction we fit the model's thermodynamic properties to experimental data using both average-sequence and sequence-dependent parameters. To demonstrate the model's applicability we provide three examples of its use—calculating the free energy profiles of hybrid strand displacement reactions, studying the resolution of a short R-loop and simulating RNA-scaffolded wireframe origami.

Abstract:

Phenotype robustness, defined as the average mutational robustness of all the genotypes that map to a given phenotype, plays a key role in facilitating neutral exploration of novel phenotypic variation by an evolving population. By applying results from coding theory, we prove that the maximum phenotype robustness occurs when genotypes are organized as bricklayer's graphs, so-called because they resemble the way in which a bricklayer would fill in a Hamming graph. The value of the maximal robustness is given by a fractal continuous everywhere but differentiable nowhere sums-of-digits function from number theory. Interestingly, genotype-phenotype maps for RNA secondary structure and the hydrophobic-polar (HP) model for protein folding can exhibit phenotype robustness that exactly attains this upper bound. By exploiting properties of the sums-of-digits function, we prove a lower bound on the deviation of the maximum robustness of phenotypes with multiple neutral components from the bricklayer's graph bound, and show that RNA secondary structure phenotypes obey this bound. Finally, we show how robustness changes when phenotypes are coarse-grained and derive a formula and associated bounds for the transition probabilities between such phenotypes.