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## Criticality and conformality in the random dimer model

In critical systems, the effect of a localized perturbation affects points that are arbitrarily far from the perturbation location. In this paper, we study the effect of localized perturbations on the solution of the random dimer problem in two …

## The planted $k$-factor problem

We consider the problem of recovering an unknown $k$-factor, hidden in a weighted random graph. For $k=1$ this is the planted matching problem, while the $k=2$ case is closely related to the planted travelling salesman problem. The inference problem …

## A combined model of aggregation, fragmentation, and exchange processes: insights from analytical calculations

We introduce a mean-field framework for the study of systems of interacting particles sharing a conserved quantity. The work generalises and unites the existing fields of asset-exchange models, often applied to socio-economic systems, and …

## How to study a persistent active glassy system

We explore glassy dynamics of dense assemblies of soft particles that are self-propelled by active forces. These forces have a fixed amplitude and a propulsion direction that varies on a timescale τp, the persistence timescale. Numerical simulations …

## Modelling the effect of ribosome mobility on the rate of protein synthesis

Abstract: Translation is one of the main steps in the synthesis of proteins. It consists of ribosomes that translate sequences of nucleotides encoded on mRNA into polypeptide sequences of amino acids. Ribosomes bound to mRNA move unidirectionally, …

## Dynamical instantons and activated processes in mean-field glass models

We focus on the energy landscape of a simple mean-field model of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for high-dimensional Gaussian landscapes with dynamical field theory. In particular, we consider Langevin …

## Localization and Universality of Eigenvectors in Directed Random Graphs

Although the spectral properties of random graphs have been a long-standing focus of network theory, the properties of right eigenvectors of directed graphs have so far eluded an exact analytic treatment. We present a general theory for the …

## Opinion dynamics with emergent collective memory: The impact of a long and heterogeneous news history

In modern society people are being exposed to numerous information, with some of them being frequently repeated or more disruptive than others. In this paper we use a model of opinion dynamics to study how this news impact the society. In particular, …

## Out-of-equilibrium phase diagram of the quantum random energy model

In this paper we study the out-of-equilibrium phase diagram of the quantum version of Derrida's random energy model, which is the simplest model of mean-field spin glasses. We interpret its corresponding quantum dynamics in Fock space as a …

## Precision of tissue patterning is controlled by dynamical properties of gene regulation networks

During development, gene regulatory networks allocate cell fates by partitioning tissues into spatially organised domains of gene expression. How the sharp boundaries that delineate these gene expression patterns arise, despite the stochasticity …