Generalized Spatial Regression with Differential Regularization

We aim at analyzing geostatistical and areal data observed over irregularly shaped spatial domains and having a distribution within the exponential family. We propose a generalized additive model that allows to account for spatially-varying covariate information. The model is fitted by maximizing a penalized log-likelihood function, with a roughness penalty term that involves a differential quantity of the spatial field, computed over the domain of interest. Efficient estimation of the spatial field is achieved resorting to the finite element method, which provides a basis for piecewise polynomial surfaces. The proposed model is illustrated by an application to the study of criminality in the city of Portland, Oregon, USA

IGS: an IsoGeometric approach for Smoothing on surfaces

We propose an Isogeometric approach for smoothing on surfaces, namely estimating a function starting from noisy and discrete measurements. More precisely, we aim at estimating functions lying on a surface represented by NURBS, which are geometrical representations commonly used in industrial applications. The estimation is based on the minimization of a penalized least-square functional. The latter is equivalent to solve a 4th-order Partial Differential Equation (PDE). In this context, we use Isogeometric Analysis (IGA) for the numerical approximation of such surface PDE, leading to an IsoGeometric Smoothing (IGS) method for fitting data spatially distributed on a surface. Indeed, IGA facilitates encapsulating the exact geometrical representation of the surface in the analysis and also allows the use of at least globally $C^1-$continuous NURBS basis functions for which the 4th-order PDE can be solved using the standard Galerkin method. We show the performance of the proposed IGS method by means of numerical simulations and we apply it to the estimation of the pressure coefficient, and associated aerodynamic force on a winglet of the SOAR space shuttle

Proof of concept of a workflow methodology for the creation of basic canine head anatomy veterinary education tool using augmented reality

Neuroanatomy can be challenging to both teach and learn within the undergraduate veterinary medicine and surgery curriculum. Traditional techniques have been used for many years, but there has now been a progression to move towards alternative digital models and interactive 3D models to engage the learner. However, digital innovations in the curriculum have typically involved the medical curriculum rather than the veterinary curriculum. Therefore, we aimed to create a simple workflow methodology to highlight the simplicity there is in creating a mobile augmented reality application of basic canine head anatomy. Using canine CT and MRI scans and widely available software programs, we demonstrate how to create an interactive model of head anatomy. This was applied to augmented reality for a popular Android mobile device to demonstrate the user-friendly interface. Here we present the processes, challenges and resolutions for the creation of a highly accurate, data based anatomical model that could potentially be used in the veterinary curriculum. This proof of concept study provides an excellent framework for the creation of augmented reality training products for veterinary education. The lack of similar resources within this field provides the ideal platform to extend this into other areas of veterinary education and beyond

Numerical Contractor Renormalization Method for Quantum Spin Models

We demonstrate the utility of the numerical Contractor Renormalization (CORE) method for quantum spin systems by studying one and two dimensional model cases. Our approach consists of two steps: (i) building an effective Hamiltonian with longer ranged interactions using the CORE algorithm and (ii) solving this new model numerically on finite clusters by exact diagonalization. This approach, giving complementary information to analytical treatments of the CORE Hamiltonian, can be used as a semi-quantitative numerical method. For ladder type geometries, we explicitely check the accuracy of the effective models by increasing the range of the effective interactions. In two dimensions we consider the plaquette lattice and the kagome lattice as non-trivial test cases for the numerical CORE method. On the plaquette lattice we have an excellent description of the system in both the disordered and the ordered phases, thereby showing that the CORE method is able to resolve quantum phase transitions. On the kagome lattice we find that the previously proposed twofold degenerate S=1/2 basis can account for a large number of phenomena of the spin 1/2 kagome system. For spin 3/2 however this basis does not seem to be sufficient anymore. In general we are able to simulate system sizes which correspond to an 8x8 lattice for the plaquette lattice or a 48-site kagome lattice, which are beyond the possibilities of a standard exact diagonalization approach.Comment: 15 page

Frustration of the isotropic-columnar phase transition of colloidal hard platelets by a transient cubatic phase

Using simulations and theory, we show that the cubatic phase is metastable for three model hard platelets. The locally favored structures of perpendicular particle stacks in the fluid prevent the formation of the columnar phase through geometric frustration resulting in vitrification. Also, we find a direct link between structure and dynamic heterogeneities in the cooperative rotation of particle stacks, which is crucial for the devitrification process. Finally, we show that the life time of the glassy cubatic phase can be tuned by surprisingly small differences in particle shape.Comment: Submitted to Phys. Rev. Let