ABSTRACT
We investigate the phase diagram of a fluid of hard-core disks confined to the surface of a sphere and whose interaction potential contains a short-range attraction followed by a long-range repulsive tail (SALR). Based on previous work in the bulk we derive a stability criterion for the homogeneous phase of the fluid, and locate a region of instability linked to the presence of a negative minimum in the spherical harmonics expansion of the interaction potential. The inhomogeneous phases contained within this region are characterized using a mean-field density functional theory. We find several inhomogeneous patterns that can be separated into three broad classes: cluster crystals, stripes, and bubble crystals, each containing topological defects. Interestingly, while the periodicity of inhomogeneous phases at large densities is mainly determined by the position of the negative minimum of the potential expansion, the finite size of the system induces a richer behavior at smaller densities.
ABSTRACT
MOTIVATION: Hi-C matrices are cornerstones for qualitative and quantitative studies of genome folding, from its territorial organization to compartments and topological domains. The high dynamic range of genomic distances probed in Hi-C assays reflects in an inherent stochastic background of the interactions matrices, which inevitably convolve the features of interest with largely non-specific ones. RESULTS: Here, we introduce and discuss essHi-C, a method to isolate the specific or essential component of Hi-C matrices from the non-specific portion of the spectrum compatible with random matrices. Systematic comparisons show that essHi-C improves the clarity of the interaction patterns, enhances the robustness against sequencing depth of topologically associating domains identification, allows the unsupervised clustering of experiments in different cell lines and recovers the cell-cycle phasing of single-cells based on Hi-C data. Thus, essHi-C provides means for isolating significant biological and physical features from Hi-C matrices. AVAILABILITY AND IMPLEMENTATION: The essHi-C software package is available at https://github.com/stefanofranzini/essHIC. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.
ABSTRACT
We investigate the formation of cluster crystals with multiply occupied lattice sites on a spherical surface in systems of ultra-soft particles interacting via repulsive, bounded pair potentials. Not all interactions of this kind lead to clustering: we generalize the criterion devised in C. N. Likos et al., Phys. Rev. E, 2001, 63, 031206 to spherical systems in order to distinguish between cluster-forming systems and fluids which display reentrant melting. We use both DFT and Monte Carlo simulations to characterize the behavior of the system, and obtain semi-quantitative agreement between the two. We find that the number of clusters is determined by the ratio between the size σ of the ultra-soft particles and the radius R of the sphere in such a way that each stable configuration spans a certain interval of σ/R. Furthermore, we study the effect of topological frustration on the system due to the sphere curvature by comparing the properties of disclinations, i.e., clusters with fewer than six neighbors, and non-defective clusters. Disclinations are shown to be less stable, contain fewer particles, and be closer to their neighbors than other lattice points: these properties are explained on the basis of geometric and energetic considerations.
