Affine Wa(A4), Quaternions, and Decagonal Quasicrystals

We introduce a technique of projection onto the Coxeter plane of an arbitrary higher dimensional lattice described by the affine Coxeter group. The Coxeter plane is determined by the simple roots of the Coxeter graph I2 (h) where h is the Coxeter number of the Coxeter group W(G) which embeds the dihedral group Dh of order 2h as a maximal subgroup. As a simple application we demonstrate projections of the root and weight lattices of A4 onto the Coxeter plane using the strip (canonical) projection method. We show that the crystal spaces of the affine Wa(A4) can be decomposed into two orthogonal spaces whose point groups is the dihedral group D5 which acts in both spaces faithfully. The strip projections of the root and weight lattices can be taken as models for the decagonal quasicrystals. The paper also revises the quaternionic descriptions of the root and weight lattices, described by the affine Coxeter group Wa(A3), which correspond to the face centered cubic (fcc) lattice and body centered cubic (bcc) lattice respectively. Extensions of these lattices to higher dimensions lead to the root and weight lattices of the group Wa(An), n>=4 . We also note that the projection of the Voronoi cell of the root lattice of Wa(A4) describes a framework of nested decagram growing with the power of the golden ratio recently discovered in the Islamic arts.Comment: 26 pages, 17 figure

A hybrid representation for modeling, interactive editing, and real-time visualization of terrains with volumetric features

Cataloged from PDF version of article.Terrain rendering is a crucial part of many real-time applications. The easiest way to process and visualize terrain data in real time is to constrain the terrain model in several ways. This decreases the amount of data to be processed and the amount of processing power needed, but at the cost of expressivity and the ability to create complex terrains. The most popular terrain representation is a regular 2D grid, where the vertices are displaced in a third dimension by a displacement map, called a heightmap. This is the simplest way to represent terrain, and although it allows fast processing, it cannot model terrains with volumetric features. Volumetric approaches sample the 3D space by subdividing it into a 3D grid and represent the terrain as occupied voxels. They can represent volumetric features but they require computationally intensive algorithms for rendering, and their memory requirements are high. We propose a novel representation that combines the voxel and heightmap approaches, and is expressive enough to allow creating terrains with caves, overhangs, cliffs, and arches, and efficient enough to allow terrain editing, deformations, and rendering in real time

Rate region analysis of multi-terminal neuronal nanoscale molecular communication channel

© 2017 IEEE. In this paper, we investigate the communication channel capacity among hippocampal pyramidal neurons. To this aim, we study the processes included in this communication and model them with realistic communication system components based on the existing reports in the physiology literature. We consider the communication between two neurons and reveal the effects of the existence of multiple terminals between these neurons on the achievable rate per spike. To this objective, we derive the power spectral density (PSD) of the signal in the output neuron and utilize it to calculate the rate region of the channel. Moreover, we evaluate the impacts of vesicle availability on the achievable rate by deriving the expected number of available vesicles in input neuron using a realistic vesicle release model. Simulation results show that number of available vesicles for release does not affect the achievable rate of neuro-spike communication with univesicular release model. However, in neurons that multiple vesicles can release from each synaptic terminal, achievable rate is significantly affected by depletion of vesicles. Moreover, we show that increasing the number of synaptic terminals between two neurons makes the synaptic connection stronger. Hence, it is an important factor in learning and memory, which occur in the hippocampal region of the brain based on the synaptic connectivity

Internet of Hybrid Energy Harvesting Things

© 2017 IEEE. Internet of Things (IoT) is a perfect candidate to realize efficient observation and management for Smart City concept. This requires deployment of large number of wireless devices. However, replenishing batteries of thousands, maybe millions of devices may be hard or even impossible. In order to solve this problem, Internet of Energy Harvesting Things (IoEHT) is proposed. Although the first studies on IoEHT focused on energy harvesting (EH) as an auxiliary power provisioning method, now completely battery-free and self-sufficient systems are envisioned. Taking advantage of diverse sources that the concept of Smart City offers helps us to fully appreciate the capacity of EH. In this way, we address the primary shortcomings of IoEHT; availability, unreliability, and insufficiency by the Internet of Hybrid EH Things (IoHEHT). In this paper, we survey the various EH opportunities, propose an hybrid EH system, and discuss energy and data management issues for battery-free operation. We mathematically prove advantages of hybrid EH compared to single source harvesting as well. We also point out to hardware requirements and present the open research directions for different network layers specific to IoHEHT for Smart City concept

Comparison of three-dimensional facial morphology between upright and supine positions employing three-dimensional scanner from live subjects

Facial soft tissue thicknesses (FSTT) measurements collected from Magnetic Resonance Imaging (MRI) and Computed Tomography (CT) imaging techniques are most commonly taken in the supine position for forensic craniofacial reconstruction. FSTT have been shown to be different in comparison to the upright position due to gravity. The variation of facial morphology between the upright and supine position of laser-scanned images taken from 44 individuals was investigated using volumetric analysis with deviation maps. Between 82.4% and 86.7% of the facial surface area were within the error range of ±2 mm between the supine and the upright position. This indicates that most anatomical landmarks taken from the MRI and CT data can be an accurate representative of the FSTT in the upright position. Seven landmarks located around the buccal region, masseteric region and the nasolabial region of the face showed the greatest FSTT deviation between the upright and supine position, thus these landmarks may affect the accuracy of facial reconstructions when using a CT or MRI database

Irreducible Heegner divisors in the period space of enriques surfaces

Reflection walls of certain primitive vectors in the anti-invariant sublattice of the K3 lattice define Heegner divisors in the period space of Enriques surfaces. We show that depending on the norm of these primitive vectors, these Heegner divisors are either irreducible or have two irreducible components. The two components are obtained as the walls orthogonal to primitive vectors of the same norm but of different type as ordinary or characteristic. © 2008 World Scientific Publishing Company

Evaluation of the relationship between the maxillary third molars and pterygomaxillary fissure by cephalometric radiographs

Background: The aim of this study is to evaluate the relationship between the third molars which are determined to be closely related to pterygomaxillary fissure (PTM) in cephalometric radiographs. Materials and methods: The material of this study was panoramic from 200 individuals (101 male, 99 female, mean age 19.02 ± 1.62) with three different skeletal malocclusion in the sagittal direction (class I: 109; class II: 66; class III: 25) and lateral cephalometric radiographs. It was observed that 151 of the patients included in this study had unilateral, 49 bilateral impacted maxillary third molars teeth. Angular and millimetric measurements (SNA°, SNB°, ANB°, PTM [Height-x], PTM [Width-y]) were made in accordance with the parameters determined on the lateral cephalometric radiographs of individuals. In this retrospective study, the relation of impaction with PTM evaluated on cephalometric radiographs, whether the impaction was unilateral or bilateral, was investigated in terms of skeletal anomaly. Chi-square test was used for the analysis. Results: Of the 200 individuals with impacted maxillary third molar, 99 were female and 101 were male. There is no statistical difference between them in terms of unilateral and bilateral impacted third molars (p > 0.05). Of the 200 patients, 109 patients were class I, 66 patients were class II, and 25 patients were class III. There is no statistical difference between unilateral and bilateral impacted cases in facial skeletal classification (p > 0.05). According to chi-square test results, the relationship between genders and PTM variable width and height (PTM-x and PTM-y) measurements were not statistically significant (p > 0.05). Conclusions: The fact that the third molar teeth are impacted bilaterally or unilaterally is not affected by PTM change

Performance analysis for capacitive electrical neural interfaces

Neural interfaces will pave the way for novel treatment methods for neural disorders, which are due to communication problems in nervous system. Such disorders include spinal cord injuries, Alzheimer's and Multiple Sclerosis. In this work, we present a novel neural stimulator, which will act as the transmitter part of a neural interface. We perform in detail physical analysis of such a device for the first time, considering the electrostatic and capacitive effects. We also establish the stimulation requirements of the post-synaptic neuron and support our findings with COMSOL simulations. This work will pave the way to the design of more efficient neural stimulators.This work was supported in part by the ERC project MINERVA (ERC-2013-CoG #616922), and the ERC Project MINERGRACE (ERC-2018-PoC #780645)

Saliency for animated meshes with material properties

We propose a technique to calculate the saliency of animated meshes with material properties. The saliency computation considers multiple features of 3D meshes including their geometry, material and motion. Each feature contributes to the final saliency map which is view independent; and therefore, can be used for view dependent and view independent applications. To verify our saliency calculations, we performed an experiment in which we use an eye tracker to compare the saliencies of the regions that the viewers look with the other regions of the models. The results confirm that our saliency computation gives promising results. We also present several applications in which the saliency information is used. © 2010 ACM