Multiplicative local linear hazard estimation and best one-sided cross-validation

This paper develops detailed mathematical statistical theory of a new class of cross-validation techniques of local linear kernel hazards and their multiplicative bias corrections. The new class of cross-validation combines principles of local information and recent advances in indirect cross-validation. A few applications of cross-validating multiplicative kernel hazard estimation do exist in the literature. However, detailed mathematical statistical theory and small sample performance are introduced via this paper and further upgraded to our new class of best one-sided cross-validation. Best one-sided cross-validation turns out to have excellent performance in its practical illustrations, in its small sample performance and in its mathematical statistical theoretical performance

Boundary Integral Equations for the Laplace-Beltrami Operator

We present a boundary integral method, and an accompanying boundary element discretization, for solving boundary-value problems for the Laplace-Beltrami operator on the surface of the unit sphere $\S$ in $\mathbb{R}^3$. We consider a closed curve ${\cal C}$ on ${\cal S}$ which divides ${\cal S}$ into two parts ${\cal S}_1$ and ${\cal S}_2$. In particular, ${\cal C} = \partial {\cal S}_1$ is the boundary curve of ${\cal S}_1$. We are interested in solving a boundary value problem for the Laplace-Beltrami operator in $\S_2$, with boundary data prescribed on \C

Entangled single-wire NiTi material: a porous metal with tunable superelastic and shape memory properties

NiTi porous materials with unprecedented superelasticity and shape memory were manufactured by self-entangling, compacting and heat treating NiTi wires. The versatile processing route used here allows to produce entanglements of either superelastic or ferroelastic wires with tunable mesostructures. Three dimensional (3D) X-ray microtomography shows that the entanglement mesostructure is homogeneous and isotropic. The thermomechanical compressive behavior of the entanglements was studied using optical measurements of the local strain field. At all relative densities investigated here ($\sim$ 25 - 40$\%$), entanglements with superelastic wires exhibit remarkable macroscale superelasticity, even after compressions up to 25$\%$, large damping capacity, discrete memory effect and weak strain-rate and temperature dependencies. Entanglements with ferroelastic wires resemble standard elastoplastic fibrous systems with pronounced residual strain after unloading. However, a full recovery is obtained by heating the samples, demonstrating a large shape memory effect at least up to 16% strain.Comment: 31 pages, 10 figures, submitted to Acta Materiali

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

Minkowski-type and Alexandrov-type theorems for polyhedral herissons

Classical H.Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H.Minkowski uniqueness theorem due to A.D.Alexandrov are extended to a class of nonconvex polyhedra which are called polyhedral herissons and may be described as polyhedra with injective spherical image.Comment: 19 pages, 8 figures, LaTeX 2.0

On the Transferability of Knowledge among Vehicle Routing Problems by using Cellular Evolutionary Multitasking

Multitasking optimization is a recently introduced paradigm, focused on the simultaneous solving of multiple optimization problem instances (tasks). The goal of multitasking environments is to dynamically exploit existing complementarities and synergies among tasks, helping each other through the transfer of genetic material. More concretely, Evolutionary Multitasking (EM) regards to the resolution of multitasking scenarios using concepts inherited from Evolutionary Computation. EM approaches such as the well-known Multifactorial Evolutionary Algorithm (MFEA) are lately gaining a notable research momentum when facing with multiple optimization problems. This work is focused on the application of the recently proposed Multifactorial Cellular Genetic Algorithm (MFCGA) to the well-known Capacitated Vehicle Routing Problem (CVRP). In overall, 11 different multitasking setups have been built using 12 datasets. The contribution of this research is twofold. On the one hand, it is the first application of the MFCGA to the Vehicle Routing Problem family of problems. On the other hand, equally interesting is the second contribution, which is focused on the quantitative analysis of the positive genetic transferability among the problem instances. To do that, we provide an empirical demonstration of the synergies arisen between the different optimization tasks.Comment: 8 pages, 1 figure, paper accepted for presentation in the 23rd IEEE International Conference on Intelligent Transportation Systems 2020 (IEEE ITSC 2020

Dirac fermions at the H point of graphite: Magneto-transmission studies

We report on far infrared magneto-transmission measurements on a thin graphite sample prepared by exfoliation of highly oriented pyrolytic graphite. In magnetic field, absorption lines exhibiting a blue-shift proportional to sqrtB are observed. This is a fingerprint for massless Dirac holes at the H point in bulk graphite. The Fermi velocity is found to be c*=1.02x10^6 m/s and the pseudogap at the H point is estimated to be below 10 meV. Although the holes behave to a first approximation as a strictly 2D gas of Dirac fermions, the full 3D band structure has to be taken into account to explain all the observed spectral features.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

Noncommutative effective theory of vortices in a complex scalar field

We derive a noncommutative theory description for vortex configurations in a complex field in 2+1 dimensions. We interpret the Magnus force in terms of the noncommutativity, and obtain some results for the quantum dynamics of the system of vortices in that context