Digital objects in rhombic dodecahedron grid

Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In this paper, we describe a new coordinate system where every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. We also present the characterization of 3D digital lines and study it as the intersection of multiple digital planes. Characterization of 3D digital sphere with relevant topological features is proposed as well along with the 48-symmetry appearing in the new coordinate system

Spatial Representations in the Entorhino-Hippocampal Circuit

After a general introduction and a brief review of the available experimental data on spatial representations (chapter 2), this thesis is divided into two main parts. The first part, comprising the chapters from 3 to 6, is dedicated to grid cells. In chapter 3 we present and discuss the various models proposed for explaining grid cells formation. In chapter 4 and 5 we study our model of grid cells generation based on adaptation in the case of non-planar environments, namely in the case of a spherical environment and of three-dimensional space. In chapter 6 we propose a variant of the model where the alignment of the grid axes is induced through reciprocal inhibition, and we suggest that that the inhibitory connections obtained during this learning process can be used to implement a continuous attractor in mEC. The second part, comprising chapters from 7 to 10 is instead focused on place cell representations. In chapter 7 we analyze the differences between place cells and grid cells in terms on information content, in chapter 8 we describe the properties of attractor dynamics in our model of the Ca3 net- work, and in the following chapter we study the effects of theta oscillations on network dynamics. Finally, in Chapter 10 we analyze to what extent the learning of a new representation, can preserve the topology and the exact metric of physical space

Topological Self-Organisation: Using a particle-spring system simulation to generate structural space-filling lattices

The problem being addressed relates to the filling of a certain volume with a structural space frame network lattice consisting of a given number of nodes. A method is proposed that comprises a generative algorithm including a physical dynamic simulation of particle-spring system. The algorithm is able to arrange nodes in space and establish connections among them through local rules of self-organisation, thus producing space frame topologies. In order to determine the appropriateness of the method, an experiment is conducted that involves testing the algorithm in the case of filling the volume of a cube with multiple numbers of nodes. The geometrical, topological and structural aspects of the generated lattices are analysed and discussed. The results indicate that the method is capable of generating efficient space frame topologies that fill spatial envelopes

Neural encoding of the vertical plane in freely-moving rats

Grid cells produce a periodic hexagonal array of firing fields when the rat navigates on a horizontal 2D surface, and such regularity supports the hypothesis that they encode distances covered by the animal. This computation is thought to form the neural basis for path integration, and the medial entorhinal cortex (MEC), where grid cells are mostly found, is now believed to play a major role for the establishment of a cognitive map in the brain. However, while grid cells on the horizontal plane are invariant across different environments (they provide fixed spatial metrics), it is currently not known whether those distances vary in 3D space. Previous findings suggested that grid cells may be substantially incapable to perform path integration in the vertical plane and this thesis aimed to test a number of hypothesis to explain such an impairment. These results show that grid cells are not affected by experience with 3D locomotion; they are modulated by the orientation of the locomotion plane and on a climbing wall they display heavily distorted firing patterns with expanded but fewer fields. Based on these findings, the hypothesis that the inconsistency between horizontal and vertical maps may be due to the miscomputation of instantaneous speed was suggested. Preliminary results support the view that the speed signal carried by speed cells (single-unit level) and LFP theta oscillation (large ensembles) was substantially reduced suggesting an underestimation of speed during climbing. Put together these results support the hypothesis that the speed signal plays a crucial role for the generation of a regular grid. In the vertical dimension the speed signal is reduced and such impairment drives grid cells to expand and become more irregular. Overall these results demonstrate that the neural representation of space is therefore not symmetrical across dimensions but is instead anisotropic

Finite difference and finite volume methods for wave-based modelling of room acoustics

Wave-based models of sound propagation can be used to predict and synthesize sounds as they would be heard naturally in room acoustic environments. The numerical simulation of such models with traditional time-stepping grid-based methods can be an expensive process, due to the sheer size of listening environments (e.g., auditoriums and concert halls) and due to the temporal resolution required by audio rates that resolve frequencies up to the limit of human hearing. Finite difference methods comprise a simple starting point for such simulations, but they are known to suffer from approximation errors that may necessitate expensive grid refinements in order to achieve sufficient levels of accuracy. As such, a significant amount of research has gone into designing finite difference methods that are highly accurate while remaining computationally efficient. The problem of designing and using accurate finite difference schemes is compounded by the fact that room acoustics models require complex boundary conditions to model frequency-dependent wall impedances over non-trivial geometries. The implementation of such boundary conditions in a numerically stable manner has been a challenge for some time. Stable boundary conditions for finite difference room acoustics simulations have been formulated in the past, but generally they have only been useful in modelling trivial geometries (e.g., idealised shoebox halls). Finite volume methods have recently been shown to be a viable solution to the problem of complex boundary conditions over non-trivial geometries, and they also allow for the use of energy methods for numerical stability analyses. Finite volume methods lend themselves naturally to fully unstructured grids and they can simplify to the types of grids typically used in finite difference methods. This allows for room acoustics simulation models that balance the simplicity of finite difference methods for wave propagation in air with the detail of finite volume methods for the modelling of complex boundaries. This thesis is an exploration of these two distinct, yet related, approaches to wave-based room acoustic simulations. The overarching theme in this investigation is the balance between accuracy, computational efficiency, and numerical stability. Higher-order and optimised schemes in two and three spatial dimensions are derived and compared, towards the goal of finding accurate and efficient finite difference schemes. Numerical stability is analysed using frequency-domain analyses, as well as energy techniques whenever possible, allowing for stable and frequency-dependent boundary conditions appropriate for room acoustics modelling. Along the way, the use of non-Cartesian grids is investigated, geometric relationships between certain finite difference and finite volume schemes are explored, and some problems associated to staircasing effects at boundaries are considered. Also, models of sound absorption in air are incorporated into these numerical schemes, using physical parameters that are appropriate for room acoustic scenarios

Scanning transmission electron microscopy tomography and 4D-stem applied to the study of chiral and self-assembled nanoparticles

Over recent years, advances in nanotechnology have led to an increased interest towards engineering nanomaterials with defined morphologies, for applications where the nanoparticle shape plays a significant role in processes, such as in catalysis, drug delivery and optics. Therefore, it is essential to resolve the 3D morphology and structure of these materials in order to gain understanding about their physical and chemical properties for further optimization. Following this line of research, this thesis explores a set of experiments that makes use of Scanning Transmission Electron Microscopy (STEM), incorporating both STEM tomography and 4D-STEM techniques. These techniques were used to investigate the origin of chiral shapes in Tellurium (Te) bipyramidal nanoparticles, where it was determined that the chiral geometries of the nanoparticles arise from growth mediated by screw dislocations rather than chiral ligands used in their synthesis. Gold (Au) nanoparticle self-assembled superlattices were studied by electron tomography and their lattice structure was investigated through determination of the 3D nanoparticle positions. The superlattices were found to have different crystalline structures for different molecular weights of their protective ligands. Finally, gold nanoparticles that seemed to have a twisted bipyramidal geometry were investigated through electron tomography. A model was built from the reconstructed cross-sections which supported the conclusion that the asymmetry in the shape resulted from the arrangement of the facets rather than a twist. The analyses performed in this thesis were custom-developed building upon general electron microscopy and mathematical concepts, enabling their application towards different systems and materials

Phase separation in carbon:transition metal nanocomposite thin films

The structural evolution of carbon:transition metal (C:TM) nanocomposite thin films is investigated in two regimes: (i) surface diffusion governed regime occurring during the film growth and (ii) bulk diffusion dominated regime occurring during the post-deposition thermal annealing. C:V, C:Co, and C:Cu nanocomposite films were grown by ion beam co-sputtering. The influence of the metal type, metal content (15-40 at.%), substrate temperature (RT-500°C), and annealing temperature (300-700°C) on the structure and morphology of the composite is studied by the means of elastic recoil detection analysis, X-ray diffraction, transmission electron microscopy, and Raman spectroscopy. Vanadium (copper) is in carbidic (metallic) state in the whole temperature range of the study. In contrast, cobalt is in carbidic state up to 300°C and becomes metallic at higher growth temperatures. The nanoparticles in C:V films exhibit a globular shape at RT-500°C, whereas in C:Co and C:Cu films a growth transition from globular to elongated nanoparticles occurs around 300°C. The comparison of the Raman spectroscopy results from carbon reference and C:TM thin films shows that the presence of the metal during growth significantly enhances the formation of sixfold ring carbon clusters at temperatures as low as RT. The enhancement occurs independently of the nanoparticle size, shape, and phase, and metal content, and is related to processes taking place on the nanoparticle surface of the growing film rather than in the bulk. The degree of enhancement depends on the TM type and content. Post-deposition annealing of C:Co and C:Cu films at 700°C causes the metal segregation at the film surface, while no changes upon annealing occur in C:V films. In addition, cobalt brings about the carbon graphitization by a dissolution-diffusion-precipitation mechanism, similar to the metal-mediated crystallization of amorphous silicon or germanium. No graphitization upon annealing occurs in C:V, C:Cu, and carbon reference films.Die Strukturentwicklung in Kohlenstoff-Übergangsmetall-Nanokompositschichten wird in zwei Bereichen untersucht: (i) im oberflächendiffusionsgesteuerten Bereich während des Schichtwachstums und (ii) im bulkdiffusionsdominierten Bereich während des nachträglichen Temperns. C:V, C:Co und C:Cu Nanokompositschichten wurden durch Ionenstrahl Co-Sputtern hergestellt. Der Einfluss des Metalltyps, des Metallgehalts (15-40 at.%), der Substrattemperatur (RT-500°C) und der Temperatur beim Tempern (300-700°C) auf die Struktur und Morphologie des Komposits wird mittels elastischer Rückstoßteilchen-Analyse, Röntgenbeugung, Transmissionselektronenmikroskopie und Ramanspektroskopie untersucht. Vanadium (Kupfer) ist im gesamten Temperaturbereich der Studie in karbidischem (metallischen) Zustand. Im Gegensatz dazu befindet sich Kobalt bis zu einer Temperatur von 300°C in karbidischem Zustand und wird bei höheren Abscheidetemperaturen metallisch. Die Nanopartikel in C:V Filmen besitzen eine runde Form im Temperaturbereich von RT bis 500°C wohingegen bei den C:Co und C:Cu Filmen ein Übergang von runden zu länglichen Partikeln bei etwa 300°C zu beobachten ist. Der Vergleich der Ramanspektroskopieresultate der Kohlenstoffreferenzproben und der Nanokompositschichten zeigt, dass die Anwesenheit des Metalls während des Schichtwachstums die Bildung von sechsatomigen Kohlenstoffringclustern bei Temperaturen so niedrig wie Raumtemperatur deutlich fördert. Die Erhöhung tritt unabhängig von der Partikelgröße, -form und phase und unabhängig vom Metallgehalt auf, und betrifft eher Prozesse, die auf der Oberfläche der Nanopartikel während des Schichtwachstums stattfinden als im Bulk. Der Grad der Erhöhung hängt vom Metalltyp und -gehalt ab. Nachträgliches Tempern der C:Co und C:Cu Filme bei 700°C führt zur Segregation des Metalls an der Schichtoberfläche während in den C:V Filmen keine Veränderungen durch das Tempern auftreten. Des weiteren kommt es in den C:Co Filmen zur Graphitisierung des Kohlenstoffs durch einen „Lösungs-Diffusions-Ablagerungs“ Mechanismus ähnlich der metallvermittelten Kristallisierung in amorphem Silizium und Germanium. In den C:V, C:Cu und Kohlenstoffreferenzfilmen findet keine Graphitisierung während des Temperns statt