The existence of eigenfunctions for a class of fully anisotropic elliptic equations is established. The relevant equations are associated with constrained minimization problems for integral func- tionals depending on the gradient of competing functions through general anisotropic Young 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. In particular, our analysis requires the development of some new aspects of the theory of anisotropic Orlicz-Sobolev spaces.

We establish versions for fractional Orlicz-Sobolev seminorms, built upon Young functions, of the Bourgain-Brezis-Mironescu theorem on the limit as s->1^-, and of the Maz'ya-Shaposhnikova theorem on the limit as s-> 0^+ , dealing with classical fractional Sobolev spaces. As regards the limit as s->1^-, Young functions with an asymptotic linear growth are also considered in connection with the space of functions of bounded variation. Concerning the limit as s-> 0^+, Young functions fulfilling the \Delta_2-condition are admissible.

We establish versions for fractional Orlicz-Sobolev seminorms, built upon Young functions, of the Bourgain-Brezis-Mironescu theorem on the limit as s ->1^-, and of the Maz'ya-Shaposhnikova theorem on the limit as s->0^-, dealing with classical fractional Sobolev spaces. As regards the limit as s ->1^-, Young functions with an asymptotic linear growth are also considered in connection with the space of functions of bounded variation. Concerning the limit as s->0^+, Young functions fulfilling the \Delta_2-condition are admissible.

In this paper, we consider the problem of estimating multiple Gaussian Graphical Models from high-dimensional datasets. We assume that these datasets are sampled from different distributions with the same conditional independence structure, but not the same precision matrix. We propose jewel, a joint data estimation method that uses a node-wise penalized regression approach. In particular, jewel uses a group Lasso penalty to simultaneously guarantee the resulting adjacency matrix's symmetry and the graphs' joint learning.

To achieve high performance and high energy efficiency on near-future exascale computing systems, three key technology gaps needs to be bridged. These gaps include: energy efficiency and thermal control; extreme computation efficiency via HW acceleration and new arithmetics; methods and tools for seamless integration of reconfigurable accelerators in heterogeneous HPC multi-node platforms.

Linear solvers for large and sparse systems are a key element of scientific applications, and their efficient implementation is necessary to harness the computational power of current computers. Algebraic Multigrid (AMG) Preconditioners are a popular ingredient of such linear solvers; this is the motivation for the present work where we examine some recent developments in a package of AMG preconditioners to improve efficiency, scalability and robustness on extreme scale problems.

We numerically study the dynamic behavior under a symmetric shear flow of selected examples of concentrated phase emulsions with multicore morphology confined within a microfluidic channel. A variety of nonequilibrium steady states is reported. Under low shear rates, the emulsion is found to exhibit a solidlike behavior, in which cores display a periodic planetarylike motion with approximately equal angular velocity.

We provide a brief survey of our current developments in the simulation-based design of novel families of mesoscale porous materials using computational kinetic theory. Prospective applications on exascale computers are also briefly discussed and commented on, with reference to two specific examples of soft mesoscale materials: microfluid crystals and bi-continuous jels.

This work presents a microscale approach for simulating the dielectrophoresis assembly of polarizable particles under an external electric field. The model is shown to capture interesting dynamical and topological features, such as the formation of chains of particles and their incipient aggregation into hierarchical structures. A quantitative characterization in terms of the number and size of these structures is also discussed.