Erratum: Counting of level crossings for inertial random processes: Generalization of the Rice formula [Phys. Rev. E 107, 024111 (2023)].

This corrects the article DOI: 10.1103/PhysRevE.107.024111.

Counting of level crossings for inertial random processes: Generalization of the Rice formula.

We address the counting of level crossings for inertial stochastic processes. We review Rice's approach to the problem and generalize the classical Rice formula to include all Gaussian processes in their most general form. We apply the results to some second-order (i.e., inertial) processes of physical interest, such as Brownian motion, random acceleration and noisy harmonic oscillators. For all models we obtain the exact crossing intensities and discuss their long- and short-time dependence. We illustrate these results with numerical simulations.

Three-State Opinion Model on Complex Topologies.

We investigate opinion diffusion on complex networks and the interplay between the existence of neutral opinion states and non-trivial network structures. For this purpose, we apply a three-state opinion model based on magnetic-like interactions to modular complex networks, both synthetic and real networks extracted from Twitter. The model allows for tuning the contribution of neutral agents using a neutrality parameter. We also consider social agitation, encoded as a temperature, that accounts for random opinion changes that are beyond the agent neighborhood opinion state. Using this model, we study which topological features influence the formation of consensus, bipartidism, or fragmentation of opinions in three parties, and how the neutrality parameter and the temperature interplay with the network structure.

Improving free-energy estimates from unidirectional work measurements: theory and experiment.

We derive analytical expressions for the bias of the Jarzynski free-energy estimator from N nonequilibrium work measurements, for a generic work distribution. To achieve this, we map the estimator onto the random energy model in a suitable scaling limit parametrized by (logN)/µ, where µ measures the width of the lower tail of the work distribution, and then compute the finite-N corrections to this limit with different approaches for different regimes of (logN)/µ. We show that these expressions describe accurately the bias for a wide class of work distributions and exploit them to build an improved free-energy estimator from unidirectional work measurements. We apply the method to optical tweezers unfolding and refolding experiments on DNA hairpins of varying loop size and dissipation, displaying both near-Gaussian and non-Gaussian work distributions.

Derepression of Polycomb targets during pancreatic organogenesis allows insulin-producing beta-cells to adopt a neural gene activity program.

The epigenome changes that underlie cellular differentiation in developing organisms are poorly understood. To gain insights into how pancreatic beta-cells are programmed, we profiled key histone methylations and transcripts in embryonic stem cells, multipotent progenitors of the nascent embryonic pancreas, purified beta-cells, and 10 differentiated tissues. We report that despite their endodermal origin, beta-cells show a transcriptional and active chromatin signature that is most similar to ectoderm-derived neural tissues. In contrast, the beta-cell signature of trimethylated H3K27, a mark of Polycomb-mediated repression, clusters with pancreatic progenitors, acinar cells and liver, consistent with the epigenetic transmission of this mark from endoderm progenitors to their differentiated cellular progeny. We also identified two H3K27 methylation events that arise in the beta-cell lineage after the pancreatic progenitor stage. One is a wave of cell-selective de novo H3K27 trimethylation in non-CpG island genes. Another is the loss of bivalent and H3K27me3-repressed chromatin in a core program of neural developmental regulators that enables a convergence of the gene activity state of beta-cells with that of neural cells. These findings reveal a dynamic regulation of Polycomb repression programs that shape the identity of differentiated beta-cells.

Phase diagram, correlation gap, and critical properties of the coulomb glass.

We investigate the lattice Coulomb glass model in three dimensions via Monte Carlo simulations. No evidence for an equilibrium glass phase is found down to very low temperatures, although the correlation length increases rapidly near T = 0. A charge-ordered phase exists at low disorder. The transition to this phase is consistent with the random field Ising universality class, which shows that the interaction is effectively screened at moderate temperature. For large disorder, the single-particle density of states near the Coulomb gap satisfies the scaling relation g(epsilon, T) = T;{delta}f(|epsilon|/T) with delta = 2.01 +/- 0.05 in agreement with the prediction of Efros and Shklovskii. For decreasing disorder, a crossover to a larger effective exponent occurs due to the proximity of the charge-ordered phase.

Landscape of solutions in constraint satisfaction problems.

We present a theoretical framework for characterizing the geometrical properties of the space of solutions in constraint satisfaction problems, together with practical algorithms for studying this structure on particular instances. We apply our method to the coloring problem, for which we obtain the total number of solutions and analyze in detail the distribution of distances between solutions.

Cooperativity in two-state protein folding kinetics.

We present a solvable model that predicts the folding kinetics of two-state proteins from their native structures. The model is based on conditional chain entropies. It assumes that folding processes are dominated by small-loop closure events that can be inferred from native structures. For CI2, the src SH3 domain, TNfn3, and protein L, the model reproduces two-state kinetics, and it predicts well the average Phi-values for secondary structures. The barrier to folding is the formation of predominantly local structures such as helices and hairpins, which are needed to bring nonlocal pairs of amino acids into contact.