Nonlinear Boundary Value Problems via Minimization on Orlicz-Sobolev Spaces

We develop arguments on convexity and minimization of energy functionals on Orlicz-Sobolev spaces to investigate existence of solution to the equation \displaystyle -\mbox{div} (\phi(|\nabla u|) \nabla u) = f(x,u) + h \mbox{in} \Omega under Dirichlet boundary conditions, where $\Omega \subset {\bf R}^{N}$ is a bounded smooth domain, $\phi : (0,\infty)\longrightarrow (0,\infty)$ is a suitable continuous function and $f: \Omega \times {\bf R} \to {\bf R}$ satisfies the Carath\'eodory conditions, while $h$ is a measure.Comment: 14 page

Real space mapping of topological invariants using artificial neural networks

Topological invariants allow to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wavefunctions under twisted boundary conditions. However, those procedures do not allow to calculate a topological invariant by evaluating the system locally, and thus require information about the wavefunctions in the whole system. Here we show that artificial neural networks can be trained to identify the topological order by evaluating a local projection of the density matrix. We demonstrate this for two different models, a 1-D topological superconductor and a 2-D quantum anomalous Hall state, both with spatially modulated parameters. Our neural network correctly identifies the different topological domains in real space, predicting the location of in-gap states. By combining a neural network with a calculation of the electronic states that uses the Kernel Polynomial Method, we show that the local evaluation of the invariant can be carried out by evaluating a local quantity, in particular for systems without translational symmetry consisting of tens of thousands of atoms. Our results show that supervised learning is an efficient methodology to characterize the local topology of a system.Comment: 9 pages, 6 figure

Non-Linear Supersymmetric σ\sigma -Models and their Gauging in the Atiyah-Ward Space-Time

We present a supersymmetric non-linear \s-model built up in the $N=1$ superspace of Atiyah-Ward space-time. A manifold of the K\"ahler type comes out that is restricted by a particular decomposition of the K\"ahler potential. The gauging of the \s-model isometries is also accomplished in superspace.Comment: 15 pages, Latex, no figure

Endometriosis: A Rare Cause of Large Bowel Obstruction.

Large bowel obstruction can result in significant morbidity and mortality, especially in cases of acute complete obstruction. There are many possible causes, the most common in adults being colorectal cancer. Endometriosis is a benign disease, and the most affected extragenital location is the bowel, especially the rectosigmoid junction. However, transmural involvement and acute occlusion are very rare events. We report an exceptional case of acute large bowel obstruction as the initial presentation of endometriosis. The differential diagnosis of colorectal carcinoma may be challenging, and this case emphasizes the need to consider intestinal endometriosis in females at a fertile age presenting with gastrointestinal symptoms and an intestinal mass causing complete large bowel obstruction.info:eu-repo/semantics/publishedVersio