Horizontal Edges Research Articles

Critical scaling for an anisotropic percolation system on $\Z ^2$

In this article, we consider an anisotropic finite-range bond percolation model on $\mathbb {Z}^2$. On each horizontal layer $\{ (x,i)\colon x \in \mathbb {Z}\}$ we have edges $\langle (x,i),(y,i)\rangle $ for $1 \le |x-y|\le N$. There are also vertical edges connecting two nearest neighbor vertices on distinct layers $\langle (x,i),(x,i+1)\rangle $ for $x,i \in \mathbb {Z}$. On this graph we consider the following anisotropic independent percolation model: horizontal edges are open with probability $1/(2N)$, while vertical edges are open with probability $\epsilon $ to be suitably tuned as $N$ grows to infinity. The main result tells that if $\epsilon = \kappa N^{-2/5}$, we see a phase transition in $\kappa $: positive and finite constants $C_1, C_2$ exist so that there is no percolation if $\kappa <C_1$ while percolation occurs for $\kappa >C_2$. The question is motivated by a result on the analogous layered ferromagnetic Ising model at mean field critical temperature [11, J. Stat. Phys. 161, (2015), 91–123] for which the authors showed the existence of multiple Gibbs measures for a fixed value of the vertical interaction and conjectured a change of behavior in $\kappa $ when the vertical interaction suitably vanishes as $\kappa \gamma ^{b}$, where $1/\gamma $ is the range of the horizontal interaction. For the product percolation model we have a value of $b$ that differs from what was conjectured in that paper. The proof relies on the analysis of the scaling limit of the critical branching random walk that dominates the growth process restricted to each horizontal layer and a careful analysis of the true horizontal growth process, which is interesting by itself. This is inspired by works on the long range contact process [17, Probab. Th. Rel. Fields 102, (1995), 519–545]. A renormalization scheme is used for the percolative regime.

Stability of a suspension bridge with structural damping

We investigate the exponential stability of a rectangular plate equation assumed to be hinged on its vertical edges and free on its remaining horizontal edges. Our problem models the deformation of a suspension bridge under a structural damping.

The Analytical Aspect of Pressure Dependence and the Change of Edge Crack Propagation of Horizontal Layer

The receiving of plain problem by analytical appearance with horizontal edges on the endless layer of propagation of the vertical crack and the dependence of the inner pressure of crack is observed. It supposed that the bottom edge of the layer is fixed to absolutely hard semi-flatness, but the upper edge is free. In this respect, we have tried to get the propagation measure of the opening and the analytical aspect of pressure change dependence acting inside it, by method of local modifications using the received solutions. The corresponding methods of approximate illustration of functional dependence are used. In the environment of the opening and the received measure of crack propagation the analytical expressions of distribution of stresses give the full image of peculiarities of those dependences for that immeasurable domain and correspond to the received results by method of modifications. The received formulas may be applied by solving concrete applicable problems and in studies of opportunities of cracks’ propagation for environment of fragile material. Those opportunities are increasing moreover if we take into account that the solutions are received for immeasurable environment.

A Compact Circularly Polarized Antenna With Directional Pattern for Wearable Off-Body Communications

This letter presents a geometrically simple and compact circularly polarized antenna with unidirectional radiation characteristics for off-body communications. The proposed antenna is based on a microstrip-line monopole extension from a coplanar waveguide and a protruded stub from one side of the coplanar ground plane along the length of the monopole. The orthogonal components of equal amplitudes required for circular polarization are induced using the vertical stub and the horizontal edge of the coplanar ground plane. To control the radiation of the antenna towards the human body, a flexible, high-permittivity laminated substrate is used as a reflector. The topological simplicity of the antenna permits a small number of adjustable variables and therefore a reduced computational cost of the parameter tuning process. The total footprint of the proposed antenna is only $0.23\lambda _{o}\,\times\, 0.24\lambda _{o}$ = 0.05 $\boldsymbol{\lambda }_{\bf{o}}^2$ at the lowest operating frequency. The antenna is numerically and experimentally characterized in the free space and on a real human volunteer. The simulated and measured reflection coefficient indicates that the operating range of the antenna extends from 5.16 to 6.13 GHz range with 100% bandwidth overlap between the impedance bandwidth and the axial-ratio bandwidth. The peak gain of the antenna is 6.22 dBic with a stable radiation pattern in the + z -direction, high efficiency of 90%, and 0.131 W/g specific absorption rate (SAR). The antenna can be used for Unlicensed National Information Infrastructure (U-NII) worldwide band and Industrial, Scientific, and Medical (ISM) 5.8 GHz band.

Edge Detection Algorithm for $Musca-Domestica$ Inspired Vision System

Compound vision sensors, mimicking the compound eye of the common housefly, possess motion hyperacuity, resulting in better motion detection and tracking capabilities as compared to traditional camera systems. Therefore, these sensors have applications requiring near instantaneous obstacle avoidance in its field-of-view. However, the obstacle detection algorithms used by current compound vision systems are insufficient to enable these capabilities due to their ability to only detect horizontal or vertical edges. In this paper, we propose an improved edge detection and location algorithm for fly inspired vision sensors which can correctly classify horizontal, vertical, forward diagonal, and backward diagonal edges.

Quantum gravity on a square graph

We perform functional-integral quantisation of the moduli of all quantum metrics defined as square-lengths a on the edges of a Lorentzian quadrilateral graph. Noting that the partition function factorises into a theory for the spacelike edges and its conjugate for the timelike ones, we determine correlation functions and find a fixed relative uncertainty for the edge square-lengths relative to their expected value . The expected value of the geometry is a rectangle where parallel edges have the same square-length. We compare with the simpler theory of a quantum scalar field on such a rectangular background. We also look at quantum metric fluctuations relative to a rectangular background, a theory which is finite and which at large rectangle scales resembles a pair of scalar fields on the vertical and horizontal edges with Planckian mass.

Intensity gradient based edge detection for pixelated communication systems

Pixelated optical communication systems transmit data using a series of encoded pixelated images. The decoding of these pixelated images is important for reliable data communication. This study proposes a novel intensity gradient-based edge detection (IGED) method for the received pixelated images. In the first stage of the proposed edge detection algorithm, the intensity difference of neighbouring pixels is calculated in the horizontal or vertical direction depending on the presence of a horizontal or vertical edge. In the second stage, the false edge pixels whose intensity values are less than the threshold are removed. Next, slopes are calculated between the consecutive edge pixels and the appropriate lines are found considering the slopes that have almost the same value. The new IGED method performs edge detection without requiring any anchor pixel blocks. This study also provides a description of a misalignment correction algorithm suitable for pixelated images. Next, the effectiveness of the proposed IGED method is tested through an experimental demonstration. It is shown that the IGED method can properly detect the edges even for pixelated images affected by rotational misalignment. For a given transmitter resolution, the proposed method provides better data rates than the existing methods.

Damping performance of annular anti-motion structures on a cylindrical floating drilling production storage and offloading system

Using anti-motion structures is one of the most common methods of improving motion performance of cylindrical floating drilling production storage and offloading system (FDPSO). In order to study the damping performance of annular anti-motion structures, basin model experiments and numerical simulations are carried out. By using six different annular anti-motion structures, the influence of different factors, including horizontal gaps, edges, and removal of horizontal plates are investigated. Numerical results are validated by the basin model test for further research. Specifically, with computational fluid dynamics (CFD) simulations the flow fields around the structures are presented and correlated with the experimental measurements. Results show that horizontal gaps can improve the damping performance, especially in roll. Meanwhile edges can also benefit the damping of anti-motion structure. With respect to the annular anti-motion structure, outer edges perform better than inner ones. Removing upper plate decreases the roll damping coefficients but removing lower plate increases it. In general, in order to maximize damping performance, outer edges and horizontal gaps can be added to annular anti-motion structures.

Tailored Nanopatterning by Controlled Continuous Nanoinscribing with Tunable Shape, Depth, and Dimension.

We present that the tailored nanopatterning with tunable shape, depth, and dimension for diverse application-specific designs can be realized by utilizing controlled dynamic nanoinscribing (DNI), which can generate bur-free plastic deformation on various flexible substrates via continuous mechanical inscription of a small sliced edge of a nanopatterned mold in a compact and vacuum-free system. Systematic controlling of prime DNI processing parameters including inscribing force, temperature, and substrate feed rate can determine the nanopattern depths and their specific profiles from rounded to angular shapes as a summation of the force-driven plastic deformation and heat-driven thermal deformation. More complex nanopatterns with gradient depths and/or multidimensional profiles can also be readily created by modulating the horizontal mold edge alignment and/or combining sequential DNI strokes, which otherwise demand laborious and costly procedures. Many practical user-specific applications may benefit from this study by tailor-making the desired nanopattern structures within desired areas, including precision machine and optics components, transparent electronics and photonics, flexible sensors, and reattachable and wearable devices. We demonstrate one vivid example in which the light diffusion direction of a light-emitting diode can be tuned by application of specifically designed DNI nanopatterns.

Spatial Variability of the Physicochemical Properties of Soils from Seasonally Flooded Forest Fragments on a Tropical Plain

Flooded ecosystems are conditioned to seasonal floods that promote specific soil conditions, such as low oxygen, hydromorphism, and peculiar chemical reactions. These environments are dependent on flood pulses that determine specific ecological conditions. Ipucas are seasonally flooded discontinuous forest patches that occur exclusively in the Araguaia Plain in Central Brazil. They are located 0.40 to 1.20 m lower than the surrounding plain, which promotes an accumulation of rainwater for five to six months of the year, being entirely or partially dry during the dry season. The aim of this study was to evaluate the horizontal (centre and edge) and vertical (depths: 0–0.20 m and 0.20–0.40 m) variability of physicochemical parameters in Ipucas soils, attempting to establish the importance of flood pulses and the leaching of surrounding areas in soil formation and composition. Samples were collected during the dry season in three Ipucas of similar size and circularity using a Dutch auger. The results reveal that flood pulses promote the deposition of sediments eroded from the surrounding plain, homogenizing the characteristics of the surface soil, from the edge to the centre of the Ipucas. However, biogeochemical processes, also linked to temporary flooding, account for the differences between the surface and deeper soil horizons because anoxic conditions during flooding promote chemical reactions characteristic of anaerobic environments, modifying the pH and organic matter content, in addition to the gleying of soils subjected to flooding, which are then covered by sediments after the dry season. Finally, Ipucas soils are susceptible to anthropic changes and are dependent on seasonal flood pulses.

Random Walks on Comb-Type Subsets of $$\mathbb {Z}^2$$

We study the path behavior of the simple symmetric walk on some comb-type subsets of $${{\mathbb {Z}}}^2$$ which are obtained from $${{\mathbb {Z}}}^2$$ by removing all horizontal edges belonging to certain sets of values on the y-axis. We obtain some strong approximation results and discuss their consequences.

The Application of Theta Method to Potential Field Gradient Tensor Data for Edge Detection of Complex Geological Structures

Edge detection of magnetized structures is an important application of magnetic filters for geological interpretations. In this way, one can mention methods of the potential field derivatives which are categorized into: methods based on scalar potential field and potential field gradient tensor (PGT) data. Using five independent signal components, methods based on the PGT matrices have higher accuracy than methods based on scalar potential field data. Investigations of various methods of edge detection show that as geologic conditions become more complex, they greatly lose their efficacy and sometimes suffer from distortions. These distortions probably result from the Gibbs phenomenon which occurs in the process of computing the potential field data derivatives. This phenomenon creates false edges and incorrect interpretations of data. The thetaPGT method addresses this phenomenon by combining the PGT matrix and the previously derived theta map method. The maximum value of thetaPGT delineates the horizontal edge of geologic contacts. Achieved results by applying the thetaPGT method on simple and then complex synthetic magnetic models demonstrates higher accuracy of the proposed method in comparison with the analytic signal, theta and horizontal directional theta (HDT) methods. The new method has no sensitivity to depth and strike, and also doesn’t create additional edges. Furthermore, it has lower noise sensitivity and significantly reduces the effect of the Gibbs phenomenon. Finally, applying this method on real magnetic data from the Varzeghan area, northwest Iran, with respect to other methods reveals more details of structures in the area and characterized false faults resulting from the Gibbs phenomenon.

Experimental and Numerical Study on Mixed Crack Propagation Characteristics in Rock-Like Material Under Uniaxial Loading

The cracks of rock mass were in complicated geometric distribution, whose propagation characteristics and stress distribution change with the geometric distribution accordingly. In this research, propagation tests on mixed crack (horizontal edge cracks and inclined cracks) were conducted to analyze the propagation characteristics and stress distribution by lab tests and numerical modelling. The failure mode of specimens in Group 1 and Group 2 was the mixed crack (shear crack and tensile crack) and the coalescence of the pre-existing cracks propagation, respectively. The crack initiating from edge crack was the mixed crack–shear crack and tensile crack, and the crack initiating from inclined crack was the wing crack–tensile crack. The peak of energy index appeared in the crack initiation, coalescence and specimen failure. The energy release of an inclined crack was less than that of an edge crack. The existence of pre-existing inclined crack resulted in the strength decrease of specimens. Stress concentration produced in the tips of the pre-existing cracks, and the concentration degree of edge cracks was much bigger than that of inclined cracks. The mechanism of buried structure water inrush was illustrated in this study. The working faces and buried structure could be simplified as the horizontal edge crack and inclined crack. The buried structure (inclined cracks) propagated and connected with the mining damage zone (horizontal edge cracks) and confined aquifer, so that water inrush paths were formed in the buried structure (similar to macroscopic cracks formed by the pre-existing crack propagation). This research provides a reference for the study on the water inrush in the buried structure.

Estimating the location of magnetic sources using magnetic gradient tensor data

In this paper, a new method for the interpretation of magnetic sources is developed using magnetic gradient tensor data. The total magnetisation direction of each magnetic source is estimated, and the magnetic gradient tensor is transformed into tensor data, which would be produced by the same sources with vertical magnetisation. Furthermore, the horizontal edges of the broad steep-sided magnetic sources are estimated from the ratio of the sum of absolute values of the eigenvalues (SAE) and Bzz of the transformed magnetic gradient tensor. The depth estimation of the magnetic sources is obtained using a modified Euler deconvolution method that eliminates the structural index from the equations. The process was tested on both synthetic and measured magnetic data. The results show that this method reduces considerably the effects of total magnetisation and is tolerant to the noise of the data. In addition, this method calculates vertical locations without any prior information about the structural index of the source.

S − r ways on a graph-lattice

Graph-lattice has vertices at points with non-negative integer coordinates. Each vertex has two outgoing edges: horizontal edge and vertical edge to the neighboring vertices (right and top). We considered the problem of reachability for s — r ways. s — r way consists of alternating pieces of horizontal edges or vertical edges, each piece consisting of horizontal arcs (with the exception of, perhaps, the final) has a length that is a multiple of s, and each piece consisting of vertical edges (with the exception of, perhaps, the final) has a length that is a multiple of r. We obtained formulas for the number of s — r ways, leading from the vertex to the vertex. In the second part we investigate the problem of random walks via s — r ways. The process of random walk on the s — r paths isn’t Markov process. It is shown that it is locally reduced to the Markov process on the subgraph which determined by the starting vertex.

Regular switching components

We consider a problem of Discrete Tomography which consists of reconstructing a finite lattice set S⊂Z2 from given horizontal and vertical X-rays (i.e. with prescribed numbers of points in each row and column). Without additional requirements, the problem can be solved in polynomial time. Many variants require the solution to be in a chosen class A. For instance, the problem is NP-complete for the class A=H∩V of HV-convex lattice sets and it is polynomial for the class A=H∩V∩P of HV-convex polyominoes. Twenty years after these results, the problem's complexity remains unknown for A=C, the class of C-convex lattice sets (i.e. two-dimensional lattice polytopes).The main difficulty to solve this problem comes from combinatorial structures called switching components. Switching components are closed path with horizontal and vertical edges such that the solutions S are composed of either the elements of even or of odd indices. This binary choice can be encoded by a Boolean variable associated with the switching component and the convexity constraints are simply encoded by SAT clauses (2-clauses for HV-convexity and 3-clauses for C-convexity).The purpose of the paper is to investigate the properties of the switching components and the consequences of the convexity requirements. We divide the switching components in two classes: regular if their turning angle is constant, irregular otherwise. We prove that adjacent regular switching components have the same Boolean values. This property allows us to merge them into extended switching components. We prove that if all switching components are regular, then the extended switching components are all independent (then the number of solutions with the considered feet is 2n, where n is the number of extended switching components). Finally, we prove that they are geometrically ordered.

Compressed ghost edge imaging

In this paper, we propose an advanced framework of ghost edge imaging, named compressed ghost edge imaging (CGEI). In the scheme, a set of structured speckle patterns with pixel shifting are illuminated on an unknown object, and the output is collected by a bucket detector without any spatial resolution. By using compressed sensing algorithm, we obtain the horizontal and vertical edge information of the unknown object with the bucket detector detection results and the known structured speckle patterns. The edge is finally constructed by the two-dimentional edge information. The experimental and numerical simulations results show that the proposed scheme has a higher quality and reduces the number of measurements, in comparison with the existed edge detection schemes based on ghost imaging.

Shear behavior of non-persistent joints in concrete and gypsum specimens using combined experimental and numerical approaches

In this paper, shear behavior of non-persistent joint surrounded in concrete and gypsum layers has been investigated using experimental test and numerical simulation. Two types of mixture were prepared for this study. The first type consists of water and gypsum that were mixed with a ratio of water/gypsum of 0.6. The second type of mixture, water, sand and cement were mixed with a ratio of 27%, 33% and 40% by weight. Shear behavior of a non-persistent joint embedded in these specimens is studied. Physical models consisting of two edge concrete layers with dimensions of 160 mm by 130 mm by 60 mm and one internal gypsum layer with the dimension of 16 mm by 13 mm by 6 mm were made. Two horizontal edge joints were embedded in concrete beams and one angled joint was created in gypsum layer. Several analyses with joints with angles of 0o, 30o, and 60o degree were conducted. The central fault places in 3 different positions. Along the edge joints, 1.5 cm vertically far from the edge joint face and 3 cm vertically far from the edge joint face. All samples were tested in compression using a universal loading machine and the shear load was induced because of the specimen geometry. Concurrent with the experiments, the extended finite element method (XFEM) was employed to analyze the fracture processes occurring in a non-persistent joint embedded in concrete and gypsum layers using Abaqus, a finite element software platform. The failure pattern of non-persistent cracks (faults) was found to be affected mostly by the central crack and its configuration and the shear strength was found to be related to the failure pattern. Comparison between experimental and corresponding numerical results showed a great agreement. XFEM was found as a capable tool for investigating the fracturing mechanism of rock specimens with non-persistent joint.

High-Throughput Deblocking Filter Architecture Using Quad Parallel Edge Filter for H.264 Video Coding Systems

With the increasing demand in electronic gadgets expecting better video quality for multimedia applications, various coding standards evolved for the past two decades and optimization on the architectures of the various modules used in the video codec is most popular. In this paper, an efficient architecture for deblocking filter used to smoothen the pixels of the decompressed video data is proposed, which utilizes both pipelining and parallelism. The filtering process follows a sequential order as filtering vertical edges of luma block and chroma block followed by the horizontal edges of the luma block and chroma block. Three pipeline stages are used and four edges, either vertical or horizontal are filtered in parallel. Internal buffers which hold the sub-blocks read from the external frame buffers are accessed in a ping pong fashion to filter the adjacent sub-edges and thus reducing the external memory access cycles. Due to parallelism with novel edge filtering order, self-transposing mechanism, and ping pong buffer access, the throughput is increased. The proposed quad parallel edge deblocking filter architecture is implemented using Synopsys 90 nm library. It achieves a target area of 19.8 K and can process a Macro Block in 58 clock cycles.

Sparsely encoded distinctive visual features for object recognition

An image feature descriptor named “sparsely encoded distinctive visual features (SEDVF)” is proposed for object recognition. SEDVF is built with the integration of local and global visual features. Visual information on edge orientation, magnitude, color, and pixel intensity is sparsely encoded by a bit plane slicing technique. Distinctive features are obtained using winner-takes-all principle. Edge gradient multiorientation detector method (EGMOD) is proposed to obtain the gradient orientations. EGMOD extracts four-directional (horizontal, vertical, and both diagonal) edge information with the proposed multioriented Scharr operator in YIQ color space. Magnitude features are extracted by incorporating chromatic information along horizontal and vertical directions in the RGB color space. SEDVF can be used as a color feature descriptor that has good discriminative power of visual features. The proposed descriptor is extensively tested for performance evaluation using K-nearest neighbor classifier on three standard datasets, including Columbia object image library, Amsterdam library of object images, and PVOC 2007, respectively. Experimental results reveal outperformance of SEDVF as compared to the state-of-the-art object recognition methods.