Search results for: laplacian vertex PI eigenvalues
116 Vehicle to Vehicle Communication: Collision Avoidance Scenarios
Authors: Ahmed Emad, Ahmed Salah, Abdelrahman Magdy, Omar Rashid, Mohammed Adel
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This research paper discusses vehicle-to-vehicle technology as an important application of linear algebra. This communication technology represents an efficient and promising application to help to ensure the safety of the drivers by warning them when a crash possibility is close. The major link that combines our topic with linear algebra is the Laplacian matrix. Some main definitions used in the V2V were illustrated, such as VANET and its characteristics. The V2V technology could be applied in different applications with different traffic scenarios and various ways to warn car drivers. These scenarios were simulated programs such as MATLAB and Python to test how the V2V system would respond to the different scenarios and warn the car drivers exposed to the threat of collisions.Keywords: V2V communication, vehicle to vehicle scenarios, VANET, FCW, EEBL, IMA, Laplacian matrix
Procedia PDF Downloads 111115 Existence and Concentration of Solutions for a Class of Elliptic Partial Differential Equations Involving p-Biharmonic Operator
Authors: Debajyoti Choudhuri, Ratan Kumar Giri, Shesadev Pradhan
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The perturbed nonlinear Schrodinger equation involving the p-biharmonic and the p-Laplacian operators involving a real valued parameter and a continuous real valued potential function defined over the N- dimensional Euclidean space has been considered. By the variational technique, an existence result pertaining to a nontrivial solution to this non-linear partial differential equation has been proposed. Further, by the Concentration lemma, the concentration of solutions to the same problem defined on the set consisting of those elements where the potential function vanishes as the real parameter approaches to infinity has been addressed.Keywords: p-Laplacian, p-biharmonic, elliptic PDEs, Concentration lemma, Sobolev space
Procedia PDF Downloads 201114 Biologically Inspired Small Infrared Target Detection Using Local Contrast Mechanisms
Authors: Tian Xia, Yuan Yan Tang
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In order to obtain higher small target detection accuracy, this paper presents an effective algorithm inspired by the local contrast mechanism. The proposed method can enhance target signal and suppress background clutter simultaneously. In the first stage, a enhanced image is obtained using the proposed Weighted Laplacian of Gaussian. In the second stage, an adaptive threshold is adopted to segment the target. Experimental results on two changeling image sequences show that the proposed method can detect the bright and dark targets simultaneously, and is not sensitive to sea-sky line of the infrared image. So it is fit for IR small infrared target detection.Keywords: small target detection, local contrast, human vision system, Laplacian of Gaussian
Procedia PDF Downloads 426113 Exploring Counting Methods for the Vertices of Certain Polyhedra with Uncertainties
Authors: Sammani Danwawu Abdullahi
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Vertex Enumeration Algorithms explore the methods and procedures of generating the vertices of general polyhedra formed by system of equations or inequalities. These problems of enumerating the extreme points (vertices) of general polyhedra are shown to be NP-Hard. This lead to exploring how to count the vertices of general polyhedra without listing them. This is also shown to be #P-Complete. Some fully polynomial randomized approximation schemes (fpras) of counting the vertices of some special classes of polyhedra associated with Down-Sets, Independent Sets, 2-Knapsack problems and 2 x n transportation problems are presented together with some discovered open problems.Keywords: counting with uncertainties, mathematical programming, optimization, vertex enumeration
Procedia PDF Downloads 312112 Total Chromatic Number of Δ-Claw-Free 3-Degenerated Graphs
Authors: Wongsakorn Charoenpanitseri
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The total chromatic number χ"(G) of a graph G is the minimum number of colors needed to color the elements (vertices and edges) of G such that no incident or adjacent pair of elements receive the same color Let G be a graph with maximum degree Δ(G). Considering a total coloring of G and focusing on a vertex with maximum degree. A vertex with maximum degree needs a color and all Δ(G) edges incident to this vertex need more Δ(G) + 1 distinct colors. To color all vertices and all edges of G, it requires at least Δ(G) + 1 colors. That is, χ"(G) is at least Δ(G) + 1. However, no one can find a graph G with the total chromatic number which is greater than Δ(G) + 2. The Total Coloring Conjecture states that for every graph G, χ"(G) is at most Δ(G) + 2. In this paper, we prove that the Total Coloring Conjectur for a Δ-claw-free 3-degenerated graph. That is, we prove that the total chromatic number of every Δ-claw-free 3-degenerated graph is at most Δ(G) + 2.Keywords: total colorings, the total chromatic number, 3-degenerated, CLAW-FREE
Procedia PDF Downloads 144111 Deciding Graph Non-Hamiltonicity via a Closure Algorithm
Authors: E. R. Swart, S. J. Gismondi, N. R. Swart, C. E. Bell
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We present an heuristic algorithm that decides graph non-Hamiltonicity. All graphs are directed, each undirected edge regarded as a pair of counter directed arcs. Each of the n! Hamilton cycles in a complete graph on n+1 vertices is mapped to an n-permutation matrix P where p(u,i)=1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n+1. We first create exclusion set E by noting all arcs (u, v) not in G, sufficient to code precisely all cycles excluded from G i.e. cycles not in G use at least one arc not in G. Members are pairs of components of P, {p(u,i),p(v,i+1)}, i=1, n-1. A doubly stochastic-like relaxed LP formulation of the Hamilton cycle decision problem is constructed. Each {p(u,i),p(v,i+1)} in E is coded as variable q(u,i,v,i+1)=0 i.e. shrinks the feasible region. We then implement the Weak Closure Algorithm (WCA) that tests necessary conditions of a matching, together with Boolean closure to decide 0/1 variable assignments. Each {p(u,i),p(v,j)} not in E is tested for membership in E, and if possible, added to E (q(u,i,v,j)=0) to iteratively maximize |E|. If the WCA constructs E to be maximal, the set of all {p(u,i),p(v,j)}, then G is decided non-Hamiltonian. Only non-Hamiltonian G share this maximal property. Ten non-Hamiltonian graphs (10 through 104 vertices) and 2000 randomized 31 vertex non-Hamiltonian graphs are tested and correctly decided non-Hamiltonian. For Hamiltonian G, the complement of E covers a matching, perhaps useful in searching for cycles. We also present an example where the WCA fails.Keywords: Hamilton cycle decision problem, computational complexity theory, graph theory, theoretical computer science
Procedia PDF Downloads 334110 1D Klein-Gordon Equation in an Infinite Square Well with PT Symmetry Boundary Conditions
Authors: Suleiman Bashir Adamu, Lawan Sani Taura
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We study the role of boundary conditions via -symmetric quantum mechanics, where denotes parity operator and denotes time reversal operator. Using the one-dimensional Schrödinger Hamiltonian for a free particle in an infinite square well, we introduce symmetric boundary conditions. We find solutions of the 1D Klein-Gordon equation for a free particle in an infinite square well with Hermitian boundary and symmetry boundary conditions, where in both cases the energy eigenvalues and eigenfunction, respectively, are obtained.Keywords: Eigenvalues, Eigenfunction, Hamiltonian, Klein- Gordon equation, PT-symmetric quantum mechanics
Procedia PDF Downloads 344109 A Contribution to the Polynomial Eigen Problem
Authors: Malika Yaici, Kamel Hariche, Tim Clarke
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The relationship between eigenstructure (eigenvalues and eigenvectors) and latent structure (latent roots and latent vectors) is established. In control theory eigenstructure is associated with the state space description of a dynamic multi-variable system and a latent structure is associated with its matrix fraction description. Beginning with block controller and block observer state space forms and moving on to any general state space form, we develop the identities that relate eigenvectors and latent vectors in either direction. Numerical examples illustrate this result. A brief discussion of the potential of these identities in linear control system design follows. Additionally, we present a consequent result: a quick and easy method to solve the polynomial eigenvalue problem for regular matrix polynomials.Keywords: eigenvalues/eigenvectors, latent values/vectors, matrix fraction description, state space description
Procedia PDF Downloads 429108 Random Matrix Theory Analysis of Cross-Correlation in the Nigerian Stock Exchange
Authors: Chimezie P. Nnanwa, Thomas C. Urama, Patrick O. Ezepue
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In this paper we use Random Matrix Theory to analyze the eigen-structure of the empirical correlations of 82 stocks which are consistently traded in the Nigerian Stock Exchange (NSE) over a 4-year study period 3 August 2009 to 26 August 2013. We apply the Marchenko-Pastur distribution of eigenvalues of a purely random matrix to investigate the presence of investment-pertinent information contained in the empirical correlation matrix of the selected stocks. We use hypothesised standard normal distribution of eigenvector components from RMT to assess deviations of the empirical eigenvectors to this distribution for different eigenvalues. We also use the Inverse Participation Ratio to measure the deviation of eigenvectors of the empirical correlation matrix from RMT results. These preliminary results on the dynamics of asset price correlations in the NSE are important for improving risk-return trade-offs associated with Markowitz’s portfolio optimization in the stock exchange, which is pursued in future work.Keywords: correlation matrix, eigenvalue and eigenvector, inverse participation ratio, portfolio optimization, random matrix theory
Procedia PDF Downloads 303107 A Combined Error Control with Forward Euler Method for Dynamical Systems
Authors: R. Vigneswaran, S. Thilakanathan
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Variable time-stepping algorithms for solving dynamical systems performed poorly for long time computations which pass close to a fixed point. To overcome this difficulty, several authors considered phase space error controls for numerical simulation of dynamical systems. In one generalized phase space error control, a step-size selection scheme was proposed, which allows this error control to be incorporated into the standard adaptive algorithm as an extra constraint at negligible extra computational cost. For this generalized error control, it was already analyzed the forward Euler method applied to the linear system whose coefficient matrix has real and negative eigenvalues. In this paper, this result was extended to the linear system whose coefficient matrix has complex eigenvalues with negative real parts. Some theoretical results were obtained and numerical experiments were carried out to support the theoretical results.Keywords: adaptivity, fixed point, long time simulations, stability, linear system
Procedia PDF Downloads 279106 Analytical Solutions to the N-Dimensional Schrödinger Equation with a Collective Potential Model to Study Energy Spectra Andthermodynamic Properties of Selected Diatomic Molecules
Authors: BenedictI Ita, Etido P. Inyang
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In this work, the resolutions of the N-dimensional Schrödinger equation with the screened modified Kratzerplus inversely quadratic Yukawa potential (SMKIQYP) have been obtained with the Greene-Aldrich approximation scheme using the Nikiforov-Uvarov method. The eigenvalues and the normalized eigenfunctions are obtained. We then apply the energy spectrum to study four (HCl, N₂, NO, and CO) diatomic molecules. The results show that the energy spectra of these diatomic molecules increase as quantum numbers increase. The energy equation was also used to calculate the partition function and other thermodynamic properties. We predicted the partition function of CO and NO. To check the accuracy of our work, the special case (Modified Kratzer and screened Modified Kratzer potentials) of the collective potential energy eigenvalues agrees excellently with the existing literature.Keywords: Schrödinger equation, Nikiforov-Uvarov method, modified screened Kratzer, inversely quadratic Yukawa potential, diatomic molecules
Procedia PDF Downloads 53105 Location-Domination on Join of Two Graphs and Their Complements
Authors: Analen Malnegro, Gina Malacas
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Dominating sets and related topics have been studied extensively in the past few decades. A dominating set of a graph G is a subset D of V such that every vertex not in D is adjacent to at least one member of D. The domination number γ(G) is the number of vertices in a smallest dominating set for G. Some problems involving detection devices can be modeled with graphs. Finding the minimum number of devices needed according to the type of devices and the necessity of locating the object gives rise to locating-dominating sets. A subset S of vertices of a graph G is called locating-dominating set, LD-set for short, if it is a dominating set and if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. The location-domination number λ(G) is the minimum cardinality of an LD-set for G. The complement of a graph G is a graph Ḡ on same vertices such that two distinct vertices of Ḡ are adjacent if and only if they are not adjacent in G. An LD-set of a graph G is global if it is an LD-set of both G and its complement Ḡ. The global location-domination number λg(G) is defined as the minimum cardinality of a global LD-set of G. In this paper, global LD-sets on the join of two graphs are characterized. Global location-domination numbers of these graphs are also determined.Keywords: dominating set, global locating-dominating set, global location-domination number, locating-dominating set, location-domination number
Procedia PDF Downloads 146104 Inequality for Doubly Warped Product Manifolds
Authors: Morteza Faghfouri
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In this paper we establish a general inequality involving the Laplacian of the warping functions and the squared mean curvature of any doubly warped product isometrically immersed in a Riemannian manifold.Keywords: integral submanifolds, S-space forms, doubly warped product, inequality
Procedia PDF Downloads 252103 Independence and Path Independence on Cayley Digraphs of Left Groups and Right Groups
Authors: Nuttawoot Nupo, Sayan Panma
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A semigroup S is said to be a left (right) zero semigroup if S satisfies the equation xy=x (xy=y) for all x,y in S. In addition, the semigroup S is called a left (right) group if S is isomorphic to the direct product of a group and a left (right) zero semigroup. The Cayley digraph Cay(S,A) of a semigroup S with a connection set A is defined to be a digraph with the vertex set S and the arc set E(Cay(S,A))={(x,xa) | x∈S, a∈A} where A is any subset of S. All sets in this research are assumed to be finite. Let D be a digraph together with a vertex set V and an arc set E. Let u and v be two different vertices in V and I a nonempty subset of V. The vertices u and v are said to be independent if (u,v)∉E and (v,u)∉E. The set I is called an independent set of D if any two different vertices in I are independent. The independence number of D is the maximum cardinality of an independent set of D. Moreover, the vertices u and v are said to be path independent if there is no dipath from u to v and there is no dipath from v to u. The set I is called a path independent set of D if any two different vertices in I are path independent. The path independence number of D is the maximum cardinality of a path independent set of D. In this research, we describe a lower bound and an upper bound of the independence number of Cayley digraphs of left groups and right groups. Some examples corresponding to those bounds are illustrated here. Furthermore, the exact value of the path independence number of Cayley digraphs of left groups and right groups are also presented.Keywords: Cayley digraphs, independence number, left groups, path independence number, right groups
Procedia PDF Downloads 200102 Optical Signal-To-Noise Ratio Monitoring Based on Delay Tap Sampling Using Artificial Neural Network
Authors: Feng Wang, Shencheng Ni, Shuying Han, Shanhong You
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With the development of optical communication, optical performance monitoring (OPM) has received more and more attentions. Since optical signal-to-noise ratio (OSNR) is directly related to bit error rate (BER), it is one of the important parameters in optical networks. Recently, artificial neural network (ANN) has been greatly developed. ANN has strong learning and generalization ability. In this paper, a method of OSNR monitoring based on delay-tap sampling (DTS) and ANN has been proposed. DTS technique is used to extract the eigenvalues of the signal. Then, the eigenvalues are input into the ANN to realize the OSNR monitoring. The experiments of 10 Gb/s non-return-to-zero (NRZ) on–off keying (OOK), 20 Gb/s pulse amplitude modulation (PAM4) and 20 Gb/s return-to-zero (RZ) differential phase-shift keying (DPSK) systems are demonstrated for the OSNR monitoring based on the proposed method. The experimental results show that the range of OSNR monitoring is from 15 to 30 dB and the root-mean-square errors (RMSEs) for 10 Gb/s NRZ-OOK, 20 Gb/s PAM4 and 20 Gb/s RZ-DPSK systems are 0.36 dB, 0.45 dB and 0.48 dB respectively. The impact of chromatic dispersion (CD) on the accuracy of OSNR monitoring is also investigated in the three experimental systems mentioned above.Keywords: artificial neural network (ANN), chromatic dispersion (CD), delay-tap sampling (DTS), optical signal-to-noise ratio (OSNR)
Procedia PDF Downloads 77101 Study Secondary Particle Production in Carbon Ion Beam Radiotherapy
Authors: Shaikah Alsubayae, Gianluigi Casse, Carlos Chavez, Jon Taylor, Alan Taylor, Mohammad Alsulimane
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Ensuring accurate radiotherapy with carbon therapy requires precise monitoring of radiation dose distribution within the patient's body. This monitoring is essential for targeted tumor treatment, minimizing harm to healthy tissues, and improving treatment effectiveness while lowering side effects. In our investigation, we employed a methodological approach to monitor secondary proton doses in carbon therapy using Monte Carlo simulations. Initially, Geant4 simulations were utilized to extract the initial positions of secondary particles formed during interactions between carbon ions and water. These particles included protons, gamma rays, alpha particles, neutrons, and tritons. Subsequently, we studied the relationship between the carbon ion beam and these secondary particles. Interaction Vertex Imaging (IVI) is valuable for monitoring dose distribution in carbon therapy. It provides details about the positions and amounts of secondary particles, particularly protons. The IVI method depends on charged particles produced during ion fragmentation to gather information about the range by reconstructing particle trajectories back to their point of origin, referred to as the vertex. In our simulations regarding carbon ion therapy, we observed a strong correlation between some secondary particles and the range of carbon ions. However, challenges arose due to the target's unique elongated geometry, which hindered the straightforward transmission of forward-generated protons. Consequently, the limited protons that emerged mostly originated from points close to the target entrance. The trajectories of fragments (protons) were approximated as straight lines, and a beam back-projection algorithm, using recorded interaction positions in Si detectors, was developed to reconstruct vertices. The analysis revealed a correlation between the reconstructed and actual positions.Keywords: radiotherapy, carbon therapy, monitoring of radiation dose, interaction vertex imaging
Procedia PDF Downloads 31100 Standard Model-Like Higgs Decay into Displaced Heavy Neutrino Pairs in U(1)' Models
Authors: E. Accomando, L. Delle Rose, S. Moretti, E. Olaiya, C. Shepherd-Themistocleous
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Heavy sterile neutrinos are almost ubiquitous in the class of Beyond Standard Model scenarios aimed at addressing the puzzle that emerged from the discovery of neutrino flavour oscillations, hence the need to explain their masses. In particular, they are necessary in a U(1)’ enlarged Standard Model (SM). We show that these heavy neutrinos can be rather long-lived producing distinctive displaced vertices and tracks. Indeed, depending on the actual decay length, they can decay inside a Large Hadron Collider (LHC) detector far from the main interaction point and can be identified in the inner tracking system or the muon chambers, emulated here through the Compact Muon Solenoid (CMS) detector parameters. Among the possible production modes of such heavy neutrino, we focus on their pair production mechanism in the SM Higgs decay, eventually yielding displaced lepton signatures following the heavy neutrino decays into weak gauge bosons. By employing well-established triggers available for the CMS detector and using the data collected by the end of the LHC Run 2, these signatures would prove to be accessible with negligibly small background. Finally, we highlight the importance that the exploitation of new triggers, specifically, displaced tri-lepton ones, could have for this displaced vertex search.Keywords: beyond the standard model, displaced vertex, Higgs physics, neutrino physics
Procedia PDF Downloads 10399 Thermal Behaviors of the Strong Form Factors of Charmonium and Charmed Beauty Mesons from Three Point Sum Rules
Authors: E. Yazıcı, H. Sundu, E. Veli Veliev
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In order to understand the nature of strong interactions and QCD vacuum, investigation of the meson coupling constants have an important role. The knowledge on the temperature dependence of the form factors is very important for the interpretation of heavy-ion collision experiments. Also, more accurate determination of these coupling constants plays a crucial role in understanding of the hadronic decays. With the increasing of CM energies of the experiments, researches on meson interactions have become one of the more interesting problems of hadronic physics. In this study, we analyze the temperature dependence of the strong form factor of the BcBcJ/ψ vertex using the three point QCD sum rules method. Here, we assume that with replacing the vacuum condensates and also the continuum threshold by their thermal version, the sum rules for the observables remain valid. In calculations, we take into account the additional operators, which appear in the Wilson expansion at finite temperature. We also investigated the momentum dependence of the form factor at T = 0, fit it into an analytic function, and extrapolate into the deep time-like region in order to obtain a strong coupling constant of the vertex. Our results are consistent with the results existing in the literature.Keywords: QCD sum rules, thermal QCD, heavy mesons, strong coupling constants
Procedia PDF Downloads 14798 Genetic Variation among the Wild and Hatchery Raised Populations of Labeo rohita Revealed by RAPD Markers
Authors: Fayyaz Rasool, Shakeela Parveen
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The studies on genetic diversity of Labeo rohita by using molecular markers were carried out to investigate the genetic structure by RAPAD marker and the levels of polymorphism and similarity amongst the different groups of five populations of wild and farmed types. The samples were collected from different five locations as representatives of wild and hatchery raised populations. RAPAD data for Jaccard’s coefficient by following the un-weighted Pair Group Method with Arithmetic Mean (UPGMA) for Hierarchical Clustering of the similar groups on the basis of similarity amongst the genotypes and the dendrogram generated divided the randomly selected individuals of the five populations into three classes/clusters. The variance decomposition for the optimal classification values remained as 52.11% for within class variation, while 47.89% for the between class differences. The Principal Component Analysis (PCA) for grouping of the different genotypes from the different environmental conditions was done by Spearman Varimax rotation method for bi-plot generation of the co-occurrence of the same genotypes with similar genetic properties and specificity of different primers indicated clearly that the increase in the number of factors or components was correlated with the decrease in eigenvalues. The Kaiser Criterion based upon the eigenvalues greater than one, first two main factors accounted for 58.177% of cumulative variability.Keywords: variation, clustering, PCA, wild, hatchery, RAPAD, Labeo rohita
Procedia PDF Downloads 40697 A Study of Secondary Particle Production from Carbon Ion Beam for Radiotherapy
Authors: Shaikah Alsubayae, Gianluigi Casse, Carlos Chavez, Jon Taylor, Alan Taylor, Mohammad Alsulimane
Abstract:
Achieving precise radiotherapy through carbon therapy necessitates the accurate monitoring of radiation dose distribution within the patient's body. This process is pivotal for targeted tumor treatment, minimizing harm to healthy tissues, and enhancing overall treatment effectiveness while reducing the risk of side effects. In our investigation, we adopted a methodological approach to monitor secondary proton doses in carbon therapy using Monte Carlo (MC) simulations. Initially, Geant4 simulations were employed to extract the initial positions of secondary particles generated during interactions between carbon ions and water, including protons, gamma rays, alpha particles, neutrons, and tritons. Subsequently, we explored the relationship between the carbon ion beam and these secondary particles. Interaction vertex imaging (IVI) proves valuable for monitoring dose distribution during carbon therapy, providing information about secondary particle locations and abundances, particularly protons. The IVI method relies on charged particles produced during ion fragmentation to gather range information by reconstructing particle trajectories back to their point of origin, known as the vertex. In the context of carbon ion therapy, our simulation results indicated a strong correlation between some secondary particles and the range of carbon ions. However, challenges arose due to the unique elongated geometry of the target, hindering the straightforward transmission of forward-generated protons. Consequently, the limited protons that did emerge predominantly originated from points close to the target entrance. Fragment (protons) trajectories were approximated as straight lines, and a beam back-projection algorithm, utilizing interaction positions recorded in Si detectors, was developed to reconstruct vertices. The analysis revealed a correlation between the reconstructed and actual positions.Keywords: radiotherapy, carbon therapy, monitor secondary proton doses, interaction vertex imaging
Procedia PDF Downloads 4196 Two-Dimensional Observation of Oil Displacement by Water in a Petroleum Reservoir through Numerical Simulation and Application to a Petroleum Reservoir
Authors: Ahmad Fahim Nasiry, Shigeo Honma
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We examine two-dimensional oil displacement by water in a petroleum reservoir. The pore fluid is immiscible, and the porous media is homogenous and isotropic in the horizontal direction. Buckley-Leverett theory and a combination of Laplacian and Darcy’s law are used to study the fluid flow through porous media, and the Laplacian that defines the dispersion and diffusion of fluid in the sand using heavy oil is discussed. The reservoir is homogenous in the horizontal direction, as expressed by the partial differential equation. Two main factors which are observed are the water saturation and pressure distribution in the reservoir, and they are evaluated for predicting oil recovery in two dimensions by a physical and mathematical simulation model. We review the numerical simulation that solves difficult partial differential reservoir equations. Based on the numerical simulations, the saturation and pressure equations are calculated by the iterative alternating direction implicit method and the iterative alternating direction explicit method, respectively, according to the finite difference assumption. However, to understand the displacement of oil by water and the amount of water dispersion in the reservoir better, an interpolated contour line of the water distribution of the five-spot pattern, that provides an approximate solution which agrees well with the experimental results, is also presented. Finally, a computer program is developed to calculate the equation for pressure and water saturation and to draw the pressure contour line and water distribution contour line for the reservoir.Keywords: numerical simulation, immiscible, finite difference, IADI, IDE, waterflooding
Procedia PDF Downloads 29195 An Improved Adaptive Dot-Shape Beamforming Algorithm Research on Frequency Diverse Array
Authors: Yanping Liao, Zenan Wu, Ruigang Zhao
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Frequency diverse array (FDA) beamforming is a technology developed in recent years, and its antenna pattern has a unique angle-distance-dependent characteristic. However, the beam is always required to have strong concentration, high resolution and low sidelobe level to form the point-to-point interference in the concentrated set. In order to eliminate the angle-distance coupling of the traditional FDA and to make the beam energy more concentrated, this paper adopts a multi-carrier FDA structure based on proposed power exponential frequency offset to improve the array structure and frequency offset of the traditional FDA. The simulation results show that the beam pattern of the array can form a dot-shape beam with more concentrated energy, and its resolution and sidelobe level performance are improved. However, the covariance matrix of the signal in the traditional adaptive beamforming algorithm is estimated by the finite-time snapshot data. When the number of snapshots is limited, the algorithm has an underestimation problem, which leads to the estimation error of the covariance matrix to cause beam distortion, so that the output pattern cannot form a dot-shape beam. And it also has main lobe deviation and high sidelobe level problems in the case of limited snapshot. Aiming at these problems, an adaptive beamforming technique based on exponential correction for multi-carrier FDA is proposed to improve beamforming robustness. The steps are as follows: first, the beamforming of the multi-carrier FDA is formed under linear constrained minimum variance (LCMV) criteria. Then the eigenvalue decomposition of the covariance matrix is performed to obtain the diagonal matrix composed of the interference subspace, the noise subspace and the corresponding eigenvalues. Finally, the correction index is introduced to exponentially correct the small eigenvalues of the noise subspace, improve the divergence of small eigenvalues in the noise subspace, and improve the performance of beamforming. The theoretical analysis and simulation results show that the proposed algorithm can make the multi-carrier FDA form a dot-shape beam at limited snapshots, reduce the sidelobe level, improve the robustness of beamforming, and have better performance.Keywords: adaptive beamforming, correction index, limited snapshot, multi-carrier frequency diverse array, robust
Procedia PDF Downloads 9894 Robust Segmentation of Salient Features in Automatic Breast Ultrasound (ABUS) Images
Authors: Lamees Nasser, Yago Diez, Robert Martí, Joan Martí, Ibrahim Sadek
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Automated 3D breast ultrasound (ABUS) screening is a novel modality in medical imaging because of its common characteristics shared with other ultrasound modalities in addition to the three orthogonal planes (i.e., axial, sagittal, and coronal) that are useful in analysis of tumors. In the literature, few automatic approaches exist for typical tasks such as segmentation or registration. In this work, we deal with two problems concerning ABUS images: nipple and rib detection. Nipple and ribs are the most visible and salient features in ABUS images. Determining the nipple position plays a key role in some applications for example evaluation of registration results or lesion follow-up. We present a nipple detection algorithm based on color and shape of the nipple, besides an automatic approach to detect the ribs. In point of fact, rib detection is considered as one of the main stages in chest wall segmentation. This approach consists of four steps. First, images are normalized in order to minimize the intensity variability for a given set of regions within the same image or a set of images. Second, the normalized images are smoothed by using anisotropic diffusion filter. Next, the ribs are detected in each slice by analyzing the eigenvalues of the 3D Hessian matrix. Finally, a breast mask and a probability map of regions detected as ribs are used to remove false positives (FP). Qualitative and quantitative evaluation obtained from a total of 22 cases is performed. For all cases, the average and standard deviation of the root mean square error (RMSE) between manually annotated points placed on the rib surface and detected points on rib borders are 15.1188 mm and 14.7184 mm respectively.Keywords: Automated 3D Breast Ultrasound, Eigenvalues of Hessian matrix, Nipple detection, Rib detection
Procedia PDF Downloads 29593 On the Girth of the Regular Digraph of Ideals of a Commutative Ring
Authors: Masoud Karimi
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Let R be a commutative ring. The regular digraph of ideals of R, which is denoted by Γ(R), is a digraph whose vertex-set is the set of all non-trivial ideals of R and, for every two distinct vertices I and J, there is an arc from I to J, whenever I contains a non-zero-divisor on J. In this article, we show that an indecomposable Noetherian ring R is Artinian local if and only if Z(I)=Z(R) for every non-nilpotent ideal I. Then we conclude that the girth of Γ(R) is not equal to four.Keywords: commutative ring, girth, regular digraph, zero-divisor
Procedia PDF Downloads 24292 Kemmer Oscillator in Cosmic String Background
Authors: N. Messai, A. Boumali
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In this work, we aim to solve the two dimensional Kemmer equation including Dirac oscillator interaction term, in the background space-time generated by a cosmic string which is submitted to an uniform magnetic field. Eigenfunctions and eigenvalues of our problem have been found and the influence of the cosmic string space-time on the energy spectrum has been analyzed.Keywords: Kemmer oscillator, cosmic string, Dirac oscillator, eigenfunctions
Procedia PDF Downloads 55391 Upper Bounds on the Paired Domination Number of Cubic Graphs
Authors: Bin Sheng, Changhong Lu
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Let G be a simple undirected graph with no isolated vertex. A paired dominating set of G is a dominating set which induces a subgraph that has a perfect matching. The paired domination number of G, denoted by γₚᵣ(G), is the size of its smallest paired dominating set. Goddard and Henning conjectured that γₚᵣ(G) ≤ 4n/7 holds for every graph G with δ(G) ≥ 3, except the Petersen Graph. In this paper, we prove this conjecture for cubic graphs.Keywords: paired dominating set, upper bound, cubic graphs, weight function
Procedia PDF Downloads 20190 On a Generalization of the Spectral Dichotomy Method of a Matrix With Respect to Parabolas
Authors: Mouhamadou Dosso
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This paper presents methods of spectral dichotomy of a matrix which compute spectral projectors on the subspace associated with the eigenvalues external to the parabolas described by a general equation. These methods are modifications of the one proposed in [A. N. Malyshev and M. Sadkane, SIAM J. MATRIX ANAL. APPL. 18 (2), 265-278, 1997] which uses the spectral dichotomy method of a matrix with respect to the imaginary axis. Theoretical and algorithmic aspects of the methods are developed. Numerical results obtained by applying methods presented on matrices are reported.Keywords: spectral dichotomy method, spectral projector, eigensubspaces, eigenvalue
Procedia PDF Downloads 5589 The Application of Video Segmentation Methods for the Purpose of Action Detection in Videos
Authors: Nassima Noufail, Sara Bouhali
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In this work, we develop a semi-supervised solution for the purpose of action detection in videos and propose an efficient algorithm for video segmentation. The approach is divided into video segmentation, feature extraction, and classification. In the first part, a video is segmented into clips, and we used the K-means algorithm for this segmentation; our goal is to find groups based on similarity in the video. The application of k-means clustering into all the frames is time-consuming; therefore, we started by the identification of transition frames where the scene in the video changes significantly, and then we applied K-means clustering into these transition frames. We used two image filters, the gaussian filter and the Laplacian of Gaussian. Each filter extracts a set of features from the frames. The Gaussian filter blurs the image and omits the higher frequencies, and the Laplacian of gaussian detects regions of rapid intensity changes; we then used this vector of filter responses as an input to our k-means algorithm. The output is a set of cluster centers. Each video frame pixel is then mapped to the nearest cluster center and painted with a corresponding color to form a visual map. The resulting visual map had similar pixels grouped. We then computed a cluster score indicating how clusters are near each other and plotted a signal representing frame number vs. clustering score. Our hypothesis was that the evolution of the signal would not change if semantically related events were happening in the scene. We marked the breakpoints at which the root mean square level of the signal changes significantly, and each breakpoint is an indication of the beginning of a new video segment. In the second part, for each segment from part 1, we randomly selected a 16-frame clip, then we extracted spatiotemporal features using convolutional 3D network C3D for every 16 frames using a pre-trained model. The C3D final output is a 512-feature vector dimension; hence we used principal component analysis (PCA) for dimensionality reduction. The final part is the classification. The C3D feature vectors are used as input to a multi-class linear support vector machine (SVM) for the training model, and we used a multi-classifier to detect the action. We evaluated our experiment on the UCF101 dataset, which consists of 101 human action categories, and we achieved an accuracy that outperforms the state of art by 1.2%.Keywords: video segmentation, action detection, classification, Kmeans, C3D
Procedia PDF Downloads 4288 Hamiltonian Paths and Cycles Passing through Prescribed Edges in the Balanced Hypercubes
Authors: Dongqin Cheng
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The n-dimensional balanced hypercube BHn (n ≥ 1) has been proved to be a bipartite graph. Let P be a set of edges whose induced subgraph consists of pairwise vertex-disjoint paths. For any two vertices u, v from different partite sets of V (BHn). In this paper, we prove that if |P| ≤ 2n − 2 and the subgraph induced by P has neither u nor v as internal vertices, or both of u and v as end-vertices, then BHn contains a Hamiltonian path joining u and v passing through P. As a corollary, if |P| ≤ 2n−1, then the BHn contains a Hamiltonian cycle passing through P.Keywords: interconnection network, balanced hypercube, Hamiltonian cycle, prescribed edges
Procedia PDF Downloads 16687 Metric Dimension on Line Graph of Honeycomb Networks
Authors: M. Hussain, Aqsa Farooq
Abstract:
Let G = (V,E) be a connected graph and distance between any two vertices a and b in G is a−b geodesic and is denoted by d(a, b). A set of vertices W resolves a graph G if each vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G. In this paper line graph of honeycomb network has been derived and then we calculated the metric dimension on line graph of honeycomb network.Keywords: Resolving set, Metric dimension, Honeycomb network, Line graph
Procedia PDF Downloads 144