Towards a robust algorithm to determine topological domains from colocalization data

One of the most important tasks in understanding the complex spatial organization of the genome consists in extracting information about this spatial organization, the function and structure of chromatin topological domains from existing experimental data, in particular, from genome colocalization (Hi-C) matrices. Here we present an algorithm allowing to reveal the underlying hierarchical domain structure of a polymer conformation from analyzing the modularity of colocalization matrices. We also test this algorithm on several model polymer structures: equilibrium globules, random fractal globules and regular fractal (Peano) conformations. We define what we call a spectrum of cluster borders, and show that these spectra behave strikingly differently for equilibrium and fractal conformations, allowing us to suggest an additional criterion to identify fractal polymer conformations

Lamplighter model of a random copolymer adsorption on a line

We present a model of an AB-diblock random copolymer sequential self-packaging with local quenched interactions on a one-dimensional infinite sticky substrate. It is assumed that the A-A and B-B contacts are favorable, while A-B are not. The position of a newly added monomer is selected in view of the local contact energy minimization. The model demonstrates a self-organization behavior with the nontrivial dependence of the total energy, $E$ (the number of unfavorable contacts), on the number of chain monomers, $N$: $E\sim N^{3/4}$ for quenched random equally probable distribution of A- and B-monomers along the chain. The model is treated by mapping it onto the "lamplighter" random walk and the diffusion-controlled chemical reaction of $X+X\to 0$ type with the subdiffusive motion of reagents.Comment: 8 pages, 5 figure

Statistics of randomly branched polymers in a semi-space

We investigate the statistical properties of a randomly branched 3--functional $N$--link polymer chain without excluded volume, whose one point is fixed at the distance $d$ from the impenetrable surface in a 3--dimensional space. Exactly solving the Dyson-type equation for the partition function $Z(N,d)=N^{-\theta} e^{\gamma N}$ in 3D, we find the "surface" critical exponent $\theta={5/2}$, as well as the density profiles of 3--functional units and of dead ends. Our approach enables to compute also the pairwise correlation function of a randomly branched polymer in a 3D semi-space.Comment: 15 pages 7 figsures; section VII is slightly reorganized, discussion is revise

Necklace-Cloverleaf Transition in Associating RNA-like Diblock Copolymers

We consider a ${\rm A}_m{\rm B}_n$ diblock copolymer, whose links are capable of forming local reversible bonds with each other. We assume that the resulting structure of the bonds is RNA--like, i.e. topologically isomorphic to a tree. We show that, depending on the relative strengths of A--A, A--B and B--B contacts, such a polymer can be in one of two different states. Namely, if a self--association is preferable (i.e., A--A and B--B bonds are comparatively stronger than A--B contacts) then the polymer forms a typical randomly branched cloverleaf structure. On the contrary, if alternating association is preferable (i.e. A--B bonds are stronger than A--A and B--B contacts) then the polymer tends to form a generally linear necklace structure (with, probably, some rear side branches and loops, which do not influence the overall characteristics of the chain). The transition between cloverleaf and necklace states is studied in details and it is shown that it is a 2nd order phase transition.Comment: 17 pages, 9 figure

When renormalizability is not sufficient: Coulomb problem for vector bosons

The Coulomb problem for vector bosons W incorporates a known difficulty; the boson falls on the center. In QED the fermion vacuum polarization produces a barrier at small distances which solves the problem. In a renormalizable SU(2) theory containing vector triplet (W^+,W^-,gamma) and a heavy fermion doublet F with mass M the W^- falls on F^+, to distances r ~ 1/M, where M can be made arbitrary large. To prevent the collapse the theory needs additional light fermions, which switch the ultraviolet behavior of the theory from the asymptotic freedom to the Landau pole. Similar situation can take place in the Standard Model. Thus, the renormalizability of a theory is not sufficient to guarantee a reasonable behavior at small distances for non-perturbative problems, such as a bound state problem.Comment: Four page

Quantum Hall fractions for spinless Bosons

We study the Quantum Hall phases that appear in the fast rotation limit for Bose-Einstein condensates of spinless bosonic atoms. We use exact diagonalization in a spherical geometry to obtain low-lying states of a small number of bosons as a function of the angular momentum. This allows to understand or guess the physics at a given filling fraction nu, ratio of the number of bosons to the number of vortices. This is also the filling factor of the lowest Landau level. In addition to the well-known Bose Laughlin state at nu =1/2 we give evidence for the Jain principal sequence of incompressible states at nu =p/(p+- 1) for a few values of p. There is a collective mode in these states whose phenomenology is in agreement with standard arguments coming e.g. from the composite fermion picture. At filling factor one, the potential Fermi sea of composite fermions is replaced by a paired state, the Moore-Read state. This is most clearly seen from the half-flux nature of elementary excitations. We find that the hierarchy picture does not extend up to the point of transition towards a vortex lattice. While we cannot conclude, we investigate the clustered Read-Rezayi states and show evidence for incompressible states at the expected ratio of flux vs number of Bose particles.Comment: RevTeX 4, 11 pages, 13 figure