On the efficient Monte Carlo implementation of path integrals

We demonstrate that the Levy-Ciesielski implementation of Lie-Trotter products enjoys several properties that make it extremely suitable for path-integral Monte Carlo simulations: fast computation of paths, fast Monte Carlo sampling, and the ability to use different numbers of time slices for the different degrees of freedom, commensurate with the quantum effects. It is demonstrated that a Monte Carlo simulation for which particles or small groups of variables are updated in a sequential fashion has a statistical efficiency that is always comparable to or better than that of an all-particle or all-variable update sampler. The sequential sampler results in significant computational savings if updating a variable costs only a fraction of the cost for updating all variables simultaneously or if the variables are independent. In the Levy-Ciesielski representation, the path variables are grouped in a small number of layers, with the variables from the same layer being statistically independent. The superior performance of the fast sampling algorithm is shown to be a consequence of these observations. Both mathematical arguments and numerical simulations are employed in order to quantify the computational advantages of the sequential sampler, the Levy-Ciesielski implementation of path integrals, and the fast sampling algorithm.Comment: 14 pages, 3 figures; submitted to Phys. Rev.

The Relationship of Left Ventricular Trabeculation to Ventricular Function and Structure Over a 9.5-Year Follow-Up The MESA Study

Left ventricular (LV) trabeculation is highly variable among individuals and is increased in some diseases (e.g., congenital heart disease or cardiomyopathies), but its significance in population-representative individuals is unknown

Spin-orbit torques in L10_0-FePt/Pt thin films driven by electrical and thermal currents

Using the linear response formalism for the spin-orbit torque (SOT) we compute from first principles the SOT in a system of two layers of L1$_0$-FePt(001) deposited on an fcc Pt(001) substrate of varying thickness. We find that at room temperature the values of the SOTs that are even and odd with respect to magnetization generally lie in the range of values measured and computed for Co/Pt bilayers. We also observe that the even SOT is much more robust with respect to changing the number of layers in the substrate, and as a function of energy it follows the general trend of the even SOT exerted by the spin Hall current in fcc Pt. The odd torque, on the other hand, is strongly affected by modification of the electronic structure for a specific energy window in the limit of very thin films. Moreover, taking the system at hand as an example, we compute the values of the thermal spin-orbit torque (T-SOT). We predict that the gradients of temperature which can be experimentally created in this type of systems will cause a detectable torque on the magnetization. We also underline the correlation between the even T-SOT and the spin Nernst effect, thus motivating a more intensive experimental effort aimed at observation of both phenomena.Comment: 8 pages, 4 figure

Topological Data Analysis of Task-Based fMRI Data from Experiments on Schizophrenia

We use methods from computational algebraic topology to study functional brain networks, in which nodes represent brain regions and weighted edges encode the similarity of fMRI time series from each region. With these tools, which allow one to characterize topological invariants such as loops in high-dimensional data, we are able to gain understanding into low-dimensional structures in networks in a way that complements traditional approaches that are based on pairwise interactions. In the present paper, we use persistent homology to analyze networks that we construct from task-based fMRI data from schizophrenia patients, healthy controls, and healthy siblings of schizophrenia patients. We thereby explore the persistence of topological structures such as loops at different scales in these networks. We use persistence landscapes and persistence images to create output summaries from our persistent-homology calculations, and we study the persistence landscapes and images using $k$-means clustering and community detection. Based on our analysis of persistence landscapes, we find that the members of the sibling cohort have topological features (specifically, their 1-dimensional loops) that are distinct from the other two cohorts. From the persistence images, we are able to distinguish all three subject groups and to determine the brain regions in the loops (with four or more edges) that allow us to make these distinctions

Electronic structure, imaging contrast and chemical reactivity of graphene moir\'e on metals

Realization of graphene moir\'e superstructures on the surface of 4d and 5d transition metals offers templates with periodically modulated electron density, which is responsible for a number of fascinating effects, including the formation of quantum dots and the site selective adsorption of organic molecules or metal clusters on graphene. Here, applying the combination of scanning probe microscopy/spectroscopy and the density functional theory calculations, we gain a profound insight into the electronic and topographic contributions to the imaging contrast of the epitaxial graphene/Ir(111) system. We show directly that in STM imaging the electronic contribution is prevailing compared to the topographic one. In the force microscopy and spectroscopy experiments we observe a variation of the interaction strength between the tip and high-symmetry places within the graphene moir\'e supercell, which determine the adsorption cites for molecules or metal clusters on graphene/Ir(111).Comment: submitted on Sep, 6th 201

Higher-dimensional Wannier interpolation for the modern theory of the Dzyaloshinskii-Moriya interaction: Application to Co-based trilayers

We present an advanced first-principles formalism to evaluate the Dzyaloshinskii-Moriya interaction (DMI) in its modern theory as well as Berry curvatures in complex spaces based on a higher-dimensional Wannier interpolation. Our method is applied to the Co-based trilayer systems Ir$_\delta$Pt$_{1-\delta}$/Co/Pt and Au$_\gamma$Pt$_{1-\gamma}$/Co/Pt, where we gain insights into the correlations between the electronic structure and the DMI, and we uncover prominent sign changes of the chiral interaction with the overlayer composition. Beyond the discussed phenomena, the scope of applications of our Wannier-based scheme is particularly broad as it is ideally suited to study efficiently the Hamiltonian evolution under the slow variation of very general parameters.Comment: 8 pages, 3 figures, contribution to Special Topics "New ab initio approaches to explore emergent phenomena in quantum matters" in J. Phys. Soc. Jp