The High-throughput Chromosome Conformation Capture (Hi-C) technique combines the power of the Next Generation Sequencing technologies with chromosome conformation capture approach to study the 3D chromatin organization at the genome-wide scale. Although such a technique is quite recent, many tools are already available for pre-processing and analyzing Hi-C data, allowing to identify chromatin loops, topological associating domains and A/B compartments. However, only a few of them provide an exhaustive analysis pipeline or allow to easily integrate and visualize other omic layers.

We examine the constraints on the Yukawa regime from the nonminimally coupled curvature-matter gravity theory arising from deep underwater ocean experiments. We consider the geophysical experiment of Zumberge et al. [Phys. Rev. Lett. 67, 3051 (1991)] for searching deviations of Newton's inverse square law in ocean. In the context of nonminimally coupled curvature-matter theory of gravity the results of Zumberge et al. can be used to obtain an upper bound both on the strength a and range lambda of the Yukawa potential arising from the nonrelativistic limit of the nonminimally coupled theory.

This paper proposes improving the solve time of a bootstrap algebraic multigrid (AMG) designed previously by the authors. This is achieved by incorporating the information, a set of algebraically smooth vectors, generated by the bootstrap algorithm, in a single hierarchy by using sufficiently large aggregates, and these aggregates are compositions of aggregates already built throughout the bootstrap algorithm. The modified AMG method has good convergence properties and shows significant reduction in both memory and solve time.

We consider a variational model analyzed in March and Riey (Inverse Probl Imag 11(6): 997-1025, 2017) for simultaneous video inpainting and motion estimation. The model has applications in the field of recovery of missing data in archive film materials. A gray-value video content is reconstructed in a spatiotemporal region where the video data is lost. A variational method for motion compensated video inpainting is used, which is based on the simultaneous estimation of apparent motion in the video data.

The morphology of a mixture made of a polar active gel immersed in an isotropic passive fluid is studied numerically. Lattice Boltzmann method is adopted to solve the Navier-Stokes equation and coupled to a finite-difference scheme used to integrate the dynamic equations of the concentration and of the polarization of the active component. By varying the relative amounts of the mixture phases, different structures can be observed.

The rheological behaviour of an emulsion made of an active polar component and an isotropic passive fluid is studied by lattice Boltzmann methods. Different flow regimes are found by varying the values of the shear rate and extensile activity (occurring, e.g., in microtubule-motor suspensions).

We investigate nonlinear elliptic Dirichlet problems whose growth is driven by a general anisotropic N-function, which is not necessarily of power-type and need not satisfy the ? nor the ? -condition. Fully anisotropic, non-reflexive Orlicz-Sobolev spaces provide a natural functional framework associated with these problems. Minimal integrability assumptions are detected on the datum on the right-hand side of the equation ensuring existence and uniqueness of weak solutions.

We present here a comparison between collision-streaming and finite-difference lattice Boltzmann (LB) models. This study provides a derivation of useful formulae which help one to properly compare the simulation results obtained with both LB models. We consider three physical problems: the shock wave propagation, the damping of shear waves, and the decay of Taylor-Green vortices, often used as benchmark tests. Despite the different mathematical and computational complexity of the two methods, we show how the physical results can be related to obtain relevant quantities.

Let X={X1,X2,...,Xm} be a system of smooth vector fields in R^n satisfying the Hörmander's finite rank condition. We prove the following Sobolev inequality with reciprocal weights in Carnot-Carathéodory space G associated to system X (1?BRK(x)dx?BR|u|tK(x)dx)1/t<=CR??1?BR1K(x)dx?BR|Xu|2K(x)dx??1/2, where Xu denotes the horizontal gradient of u with respect to X. We assume that the weight K belongs to Muckenhoupt's class A_2 and Gehring's class G_?, where ? is a suitable exponent related to the homogeneous dimension.

We study an eigenvalue problem involving a fully anisotropic elliptic differential operator in arbitrary Orlicz-Sobolev spaces. The relevant equations are associated with constrained minimization problems for integral functionals depending on the gradient of competing functions through general anisotropic N-functions. In particular, the latter need neither be radial, nor have a polynomial growth, and are not even assumed to satisfy the so called \Delta_2-condition. The resulting analysis requires the development of some new aspects of the theory of anisotropic Orlicz-Sobolev spaces.