On the Terminal Location Uncertainty in Elliptical Footprints: Application in Air-to-Ground Links

Wireless transmitters (Txs) radiating directionally downwards often generate circular footprints on the ground. In certain scenarios, using elliptical cells can offer increased flexibility for providing user coverage, owing to the unique network characteristics. For instance, an elliptical footprint can be produced when a practical directional antenna with unequal azimuth and elevation half-power beamwidths is used in high-speed railway networks. Another common scenario involves the production of an elliptical footprint when an airborne Tx radiates at an angle by tilting its directional antenna by a few degrees. This paper aims to investigate, for the first time, the association between the random user location within an elliptical coverage area and the performance of a wireless communication link by considering these scenarios. We assume an unmanned aerial vehicle (UAV) as a Tx, although a tall cellular base station tower could also be employed without losing generality. To better understand the impact of random location, we derive relevant distance metrics and investigate the outage probability of the link for the two scenarios, taking both random terminal location and fading impairments into account. The findings may provide valuable insights into the performance of similar wireless systems.Comment: 23 pages, 11 figure

Chondrodystrophic dwarfism and multiple malformations in two sisters.

A genetic skeletal dysplasia with dwarfism, scoliosis and multiple skeletal defects was observed in two sisters. Only nine cases with similar features have been reported in the literature

Classical multivariate Hermite coordinate interpolation on n-dimensional grids

In this work, we study the Hermite interpolation on n-dimensional non-equally spaced, rectilinear grids over a field k of characteristic zero, given the values of the function at each point of the grid and the partial derivatives up to a maximum degree. First, we prove the uniqueness of the interpolating polynomial, and we further obtain a compact closed form that uses a single summation, irrespective of the dimensionality, which is algebraically simpler than the only alternative closed form for the n-dimensional classical Hermite interpolation [1]. We provide the remainder of the interpolation in integral form; moreover, we derive the ideal of the interpolation and express the interpolation remainder using only polynomial divisions, in the case of interpolating a polynomial function. Finally, we perform illustrative numerical examples to showcase the applicability and high accuracy of the proposed interpolant, in the simple case of few points, as well as hundreds of points on 3D-grids using a spline-like interpolation, which compares favorably to state-of-the-art spline interpolation methods

Degenerate solutions to the massless Dirac and Weyl equations and a proposed method for controlling the quantum state of Weyl particles

In a recent work we have shown that all solutions to the Weyl equation and a special class of solutions to the Dirac equation are degenerate, in the sense that they remain unaltered under the influence of a wide variety of different electromagnetic fields. In the present article our previous work is significantly extended, providing a wide class of degenerate solutions to the Dirac equation for massless particles. The electromagnetic fields corresponding to these solutions are calculated, giving also some examples regarding both spatially constant electromagnetic fields and electromagnetic waves. Further, some general forms of solutions to the Weyl equation are presented and the corresponding electromagnetic fields are calculated. Based on these results, a method for fully controlling the quantum state of Weyl particles through appropriate electromagnetic fields is proposed. Finally, the transition from degenerate to non-degenerate solutions as the particles acquire mass is discussed.Comment: Keywords: Dirac equation, Weyl equation, Degenerate solutions, Massless particles, Electromagnetic 4-potentials, Electromagnetic fields, Electromagnetic waves, Nearly degenerate solution

A general method for obtaining degenerate solutions to the Dirac and Weyl equations and a discussion on the experimental detection of degenerate states

In this work we describe a general method for obtaining degenerate solutions to the Dirac equation, corresponding to an infinite number of electromagnetic 4-potentials and fields, which are explicitly calculated. In more detail, using four arbitrary real functions, one can automatically construct a spinor which is solution to the Dirac equation for an infinite number of electromagnetic 4-potentials, defined by those functions. An interesting characteristic of these solutions is that, in the case of Dirac particles with non-zero mass, the degenerate spinors should be localized, both in space and time. Our method is also extended to the cases of massless Dirac and Weyl particles, where the localization of the spinors is no longer required. Finally, we propose two experimental methods for detecting the presence of degenerate states.Comment: In this version of the article we have added a discussion on the experimental detection of degenerate states, proposing two techniques based on electrical and optical measurement

A novel device for controlling the flow of information based on Weyl fermions and a method for manipulating the spatial distribution of Weyl particles

In this work we propose a novel device for controlling the flow of information using Weyl fermions. In more detail, based on a previous work of our group, we show that it is possible to fully control the flow of Weyl fermions on a sequence of different channels, by applying an electric field perpendicular to the direction of motion of the particles on each channel. In this way, we can transmit information, logical bits, depending on the existence or not of a Weyl current on each channel. We also show that the response time of this device is exceptionally low, less than 1 ps, for typical values of the parameters, providing the opportunity to control the flow of information at extremely high rates, of the order of 100 Pbps. This device also offers additional advantages, as low power consumption and robustness against electromagnetic perturbations, and is expected to find important applications in several fields, as telecommunications, signal processing, classical and quantum computing, etc. Finally, we demonstrate that Weyl fermions can be efficiently guided through the proposed device using appropriate magnetic fields

Automatic segmentation of the left ventricle cavity and myocardium in MRI data

A novel approach for the automatic segmentation has been developed to extract the epi-cardium and endo-cardium boundaries of the left ventricle (lv) of the heart. The developed segmentation scheme takes multi-slice and multi-phase magnetic resonance (MR) images of the heart, transversing the short-axis length from the base to the apex. Each image is taken at one instance in the heart's phase. The images are segmented using a diffusion-based filter followed by an unsupervised clustering technique and the resulting labels are checked to locate the (lv) cavity. From cardiac anatomy, the closest pool of blood to the lv cavity is the right ventricle cavity. The wall between these two blood-pools (interventricular septum) is measured to give an approximate thickness for the myocardium. This value is used when a radial search is performed on a gradient image to find appropriate robust segments of the epi-cardium boundary. The robust edge segments are then joined using a normal spline curve. Experimental results are presented with very encouraging qualitative and quantitative results and a comparison is made against the state-of-the art level-sets method

Roadmap on signal processing for next generation measurement systems

Signal processing is a fundamental component of almost any sensor-enabled system, with a wide range of applications across different scientific disciplines. Time series data, images, and video sequences comprise representative forms of signals that can be enhanced and analysed for information extraction and quantification. The recent advances in artificial intelligence and machine learning are shifting the research attention towards intelligent, data-driven, signal processing. This roadmap presents a critical overview of the state-of-the-art methods and applications aiming to highlight future challenges and research opportunities towards next generation measurement systems. It covers a broad spectrum of topics ranging from basic to industrial research, organized in concise thematic sections that reflect the trends and the impacts of current and future developments per research field. Furthermore, it offers guidance to researchers and funding agencies in identifying new prospects.AerodynamicsMicrowave Sensing, Signals & System

Rational swept surface constructions based on differential and integral sweep curve properties

A swept surface is generated from a profile curve and a sweep curve by employing the latter to define a continuous family of transformations of the former. By using polynomial or rational curves, and specifying the homogeneous coordinates of the swept surface as bilinear forms in the profile and sweep curve homogeneous coordinates, the outcome is guaranteed to be a rational surface compatible with the prevailing data types of CAD systems. However, this approach does not accommodate many geometrically intuitive sweep operations based on differential or integral properties of the sweep curve - such as the parametric speed, tangent, normal, curvature, arc length, and offset curves - since they do not ordinarily have a rational dependence on the curve parameter. The use of Pythagorean-hodograph (PH) sweep curves surmounts this limitation, and thus makes possible a much richer spectrum of rational swept surface types. A number of representative examples are used to illustrate the diversity of these novel swept surface forms - including the oriented-translation sweep, offset-translation sweep, generalized conical sweep, and oriented-involute sweep. In many cases of practical interest, these forms also have rational offset surfaces. Considerations related to the automated CNC machining of these surfaces, using only their high-level procedural definitions, are also briefly discussed