This page is intentionally left blank. The following document discusses algorithms for finding minimum spanning trees (MSTs) in graphs, including:
1) Methods for constructing graphs containing the MST generalize to higher dimensions, though some results are less informative in higher dimensions.
2) Yao's algorithm finds MSTs in higher dimensions in time proportional to the number of points raised to a power that depends on the dimension.
3) Agarwal et al. presented a more efficient method using bichromatic nearest neighbors, showing that finding MST edges is no harder than computing bichromatic nearest neighbors.
This document provides an overview of finite difference methods for solving partial differential equations. It introduces partial differential equations and various discretization methods including finite difference methods. It covers the basics of finite difference methods including Taylor series expansions, finite difference quotients, truncation error, explicit and implicit methods like the Crank-Nicolson method. It also discusses consistency, stability, and convergence of finite difference schemes. Finally, it applies these concepts to fluid flow equations and discusses conservative and transportive properties of finite difference formulations.
This document describes the R package gdistance, which calculates various distance measures and routes in geographic grids represented as rasters. It provides functions to calculate least-cost distances accounting for landscape heterogeneity, resistance distances modeling random walks, and random shortest paths. The package represents landscapes as transition matrices storing conductance values between raster cells. It calculates distances between points on these landscapes in a flexible way while correcting for projection and distance distortions.
Finite Element Analysis of Truss StructuresMahdi Damghani
The document discusses the finite element method (FEM) for analyzing truss structures. It begins with objectives of becoming familiar with FEM concepts for truss elements like stiffness matrices and assembling the global stiffness matrix. It then covers derivation of the element stiffness matrix in local coordinates, transforming it to global coordinates, and assembling the global stiffness matrix of the overall structure from the element matrices. Strain and stress calculations are also briefly discussed. Finally, an example problem is presented to demonstrate the FEM process for a simple truss structure.
The document discusses generating smooth trajectories for moving objects from an initial pose to a final pose over time. It describes how to create single-dimensional and multi-dimensional trajectories using polynomial and trapezoidal functions. It also covers generating multi-segment trajectories to smoothly move through via points without stopping by using polynomial blends between linear motion segments.
FINITE DIFFERENCE MODELLING FOR HEAT TRANSFER PROBLEMSroymeister007
This report provides a practical overview of numerical solutions to the heat equation using the finite difference method (FDM). The forward time, centered space (FTCS), the backward time, centered space (BTCS), and Crank-Nicolson schemes are developed, and applied to a simple problem in1volving the one-dimensional heat equation. Complete, working Matlab and FORTRAN codes for each program are presented. The results of running the codes on finer (one-dimensional) meshes, and with smaller time steps are demonstrated. These sample calculations show that the schemes realize theoretical predictions of how their truncation errors depend on mesh spacing and time step. The Matlab codes are straightforward and allow us to see the differences in implementation between explicit method (FTCS) and implicit methods (BTCS). The codes also allow us to experiment with the stability limit of the FTCS scheme.
A study on_contrast_and_comparison_between_bellman-ford_algorithm_and_dijkstr...Khoa Mac Tu
This document compares the Bellman-Ford algorithm and Dijkstra's algorithm for finding shortest paths in graphs. Both algorithms can be used to find single-source shortest paths, but Bellman-Ford can handle graphs with negative edge weights while Dijkstra's algorithm cannot. Bellman-Ford has a worst-case time complexity of O(n^2) while Dijkstra's algorithm has a better worst-case time complexity of O(n^2). However, Dijkstra's algorithm is more efficient in practice for graphs with non-negative edge weights. The document provides pseudocode to describe the procedures of each algorithm.
(1) The document derives an effective Einstein-Hilbert action from the original Einstein-Hilbert action by splitting it into two terms, one of which is a total divergence that can be ignored. (2) It then uses the resulting effective action to derive Einstein's field equations. (3) The derivation makes use of properties of the metric tensor, Christoffel symbols, Ricci tensor, and Riemann tensor to rewrite terms and arrive at the effective action and field equations.
Java3D is an Application Programming Interface used for writing 3D graphics applications and applets. This paper gives a short introduction of java3D, analyses the mathematics of Hermite, Bezier, FourPoints, B-Splines curve, and describes implementation of curve creation and curve
operations using Java3D API.
This document provides an overview of finite difference methods for solving partial differential equations. It introduces partial differential equations and various discretization methods including finite difference methods. It covers the basics of finite difference methods including Taylor series expansions, finite difference quotients, truncation error, explicit and implicit methods like the Crank-Nicolson method. It also discusses consistency, stability, and convergence of finite difference schemes. Finally, it applies these concepts to fluid flow equations and discusses conservative and transportive properties of finite difference formulations.
This document describes the R package gdistance, which calculates various distance measures and routes in geographic grids represented as rasters. It provides functions to calculate least-cost distances accounting for landscape heterogeneity, resistance distances modeling random walks, and random shortest paths. The package represents landscapes as transition matrices storing conductance values between raster cells. It calculates distances between points on these landscapes in a flexible way while correcting for projection and distance distortions.
Finite Element Analysis of Truss StructuresMahdi Damghani
The document discusses the finite element method (FEM) for analyzing truss structures. It begins with objectives of becoming familiar with FEM concepts for truss elements like stiffness matrices and assembling the global stiffness matrix. It then covers derivation of the element stiffness matrix in local coordinates, transforming it to global coordinates, and assembling the global stiffness matrix of the overall structure from the element matrices. Strain and stress calculations are also briefly discussed. Finally, an example problem is presented to demonstrate the FEM process for a simple truss structure.
The document discusses generating smooth trajectories for moving objects from an initial pose to a final pose over time. It describes how to create single-dimensional and multi-dimensional trajectories using polynomial and trapezoidal functions. It also covers generating multi-segment trajectories to smoothly move through via points without stopping by using polynomial blends between linear motion segments.
FINITE DIFFERENCE MODELLING FOR HEAT TRANSFER PROBLEMSroymeister007
This report provides a practical overview of numerical solutions to the heat equation using the finite difference method (FDM). The forward time, centered space (FTCS), the backward time, centered space (BTCS), and Crank-Nicolson schemes are developed, and applied to a simple problem in1volving the one-dimensional heat equation. Complete, working Matlab and FORTRAN codes for each program are presented. The results of running the codes on finer (one-dimensional) meshes, and with smaller time steps are demonstrated. These sample calculations show that the schemes realize theoretical predictions of how their truncation errors depend on mesh spacing and time step. The Matlab codes are straightforward and allow us to see the differences in implementation between explicit method (FTCS) and implicit methods (BTCS). The codes also allow us to experiment with the stability limit of the FTCS scheme.
A study on_contrast_and_comparison_between_bellman-ford_algorithm_and_dijkstr...Khoa Mac Tu
This document compares the Bellman-Ford algorithm and Dijkstra's algorithm for finding shortest paths in graphs. Both algorithms can be used to find single-source shortest paths, but Bellman-Ford can handle graphs with negative edge weights while Dijkstra's algorithm cannot. Bellman-Ford has a worst-case time complexity of O(n^2) while Dijkstra's algorithm has a better worst-case time complexity of O(n^2). However, Dijkstra's algorithm is more efficient in practice for graphs with non-negative edge weights. The document provides pseudocode to describe the procedures of each algorithm.
(1) The document derives an effective Einstein-Hilbert action from the original Einstein-Hilbert action by splitting it into two terms, one of which is a total divergence that can be ignored. (2) It then uses the resulting effective action to derive Einstein's field equations. (3) The derivation makes use of properties of the metric tensor, Christoffel symbols, Ricci tensor, and Riemann tensor to rewrite terms and arrive at the effective action and field equations.
Java3D is an Application Programming Interface used for writing 3D graphics applications and applets. This paper gives a short introduction of java3D, analyses the mathematics of Hermite, Bezier, FourPoints, B-Splines curve, and describes implementation of curve creation and curve
operations using Java3D API.
Coherence incoherence patterns in a ring of non-locally coupled phase oscilla...Ola Carmen
This document summarizes research on coherence-incoherence patterns in a ring of non-locally coupled phase oscillators. It introduces a model of phase oscillators with non-local coupling defined by a coupling function G. It shows that on a macroscopic level, the model dynamics can be described by a complex-valued order parameter evolving according to an explicit equation. Stable coherence-incoherence patterns correspond to standing wave solutions of this equation. The analysis formulates this as an infinite-dimensional nonlinear eigenvalue problem, which is then studied to classify possible patterns for different coupling functions G.
This document presents a methodology for mapping multidimensional transforms onto reconfigurable architectures like FPGAs. The methodology uses tensor product decompositions and permutation matrices to express transforms recursively in terms of lower-order blocks. This allows large transforms to be computed by combining many parallel, smaller transform blocks. Specific examples are given for mapping one-dimensional linear convolution and discrete cosine transforms. The overall goal is to provide a unified framework and design process for implementing multidimensional transforms in a modular, parallel architecture.
Xtc a practical topology control algorithm for ad hoc networks (synopsis)Mumbai Academisc
The XTC algorithm is a simple and scalable topology control algorithm for wireless ad-hoc networks that does not require knowledge of node positions or a unit disk graph. It operates in three steps: (1) each node orders its neighbors by link quality, (2) nodes exchange these rankings, and (3) each node independently selects its neighbors in the topology based on the exchanged rankings. The resulting topology is proven to be symmetric, connected, and low degree while remaining energy-efficient for communication. The algorithm is implemented and simulated in a scalable wireless network simulation using the XTC topology control method.
The document describes the Floyd-Warshall algorithm for finding shortest paths in a weighted graph. It discusses the all-pairs shortest path problem, previous solutions using Dijkstra's algorithm and dynamic programming, and then presents the Floyd-Warshall algorithm as another dynamic programming solution. The algorithm works by computing the shortest path between all pairs of vertices where intermediate vertices are restricted to a given set. It does this using a bottom-up computation in O(V^3) time and O(V^2) space.
The document describes the method of successive approximations to solve linear integral equations of the second kind. It presents the iterative scheme which begins with an initial approximation go(s) and calculates successive approximations gn(s). If gn(s) converges uniformly to a limit g(s) as n approaches infinity, then g(s) is the solution.
The iterative scheme leads to the Neumann series representation of the solution. For the series to converge, the condition |A|B < 1 must be satisfied. The resolvent kernel f(s,t;A) is defined as the limit of the iterated kernels Km(s,t). Examples are provided to demonstrate solving integral equations using this method.
This document provides exercises on Hawking radiation using scalar field theory in the Kruskal spacetime. It asks the student to find the radial equation for the scalar field and show that near the horizon, the field takes the form of ingoing and outgoing waves that are analytic in different coordinate systems. The document then derives the Klein-Gordon equation in Schwarzschild coordinates and uses separation of variables to obtain approximate solutions near the horizon. It shows that ingoing waves are regular on the future horizon but outgoing waves are not, and vice versa for the past horizon.
Numerical disperison analysis of sympletic and adi schemexingangahu
This document discusses numerical dispersion analysis of symplectic and alternating direction implicit (ADI) schemes for computational electromagnetic simulation. It presents Maxwell's equations as a Hamiltonian system that can be written as symplectic or ADI schemes by approximating the time evolution operator. Three high order spatial difference approximations - high order staggered difference, compact finite difference, and scaling function approximations - are analyzed to reduce numerical dispersion when combined with the symplectic and ADI schemes. The document derives unified dispersion relationships for the symplectic and ADI schemes with different spatial difference approximations, which can be used as a reference for simulating large scale electromagnetic problems.
1) The document discusses the mathematical analysis of a basic AC circuit consisting of a resistor and inductor connected in series and driven by an external sinusoidal voltage source.
2) Kirchhoff's voltage law is applied to derive the differential equation governing the circuit and the forced steady-state response is shown to be a sinusoidal current lagging the driving voltage by a phase angle.
3) Expressions are derived relating the phase lag to the circuit properties and defining the real and reactive power consumed based on the circuit response.
1) The document discusses dynamics modeling for robotic manipulators using the Denavit-Hartenberg representation and Lagrangian mechanics. It describes using the Euler-Lagrange method to derive equations of motion for robotic links by computing kinetic and potential energy terms.
2) As an example, dynamics equations are derived for a simple 1 degree-of-freedom robotic arm. Kinetic and potential energy expressions are written and the Lagrangian is computed to obtain the equation of motion.
3) State-space modeling basics are reviewed using the example of a damped spring-mass system, showing how to write the system dynamics as state-space matrices to evaluate responses like step response.
The document discusses the Nyquist stability criterion for analyzing the stability of sampled-data control systems. It begins by defining the Nyquist criterion and contour, and how they can be used to determine the number of closed-loop poles outside the unit circle (Z). It then provides an example showing how to apply the Nyquist criterion by plotting the loop gain and counting encirclements of the critical point. The document also discusses modifications to the Nyquist contour when open-loop poles are on the unit circle and defines the Nyquist criterion theorem.
I am Felix T. I am an Electrical Engineering Assignment Expert at eduassignmenthelp.com. I hold a Master’s. in Electrical Engineering, University of Greenwich, UK. I have been helping students with their Assignments for the past 7 years. I solve assignments related to Electrical Engineering.
Visit eduassignmenthelp.com or email info@eduassignmenthelp.com . You can also call on +1 678 648 4277 for any assistance with Electrical Engineering Assignments.
The phase field method models microstructure evolution using a single variable called the order parameter to represent the different phases and diffuse interfaces between them. The order parameter varies continuously from one value in one phase to another value in the other phase over the interface region. This allows the entire microstructure to be described with a single free energy functional and modeled simultaneously without explicitly tracking interface motion. While elegant, the phase field method relies on approximations and its predictions must be interpreted with an understanding of its limitations compared to sharp interface models.
This document discusses statically determinate and indeterminate beams. It introduces the concept of continuous beams, which have at least one hinged support and roller supports. The key equations for analyzing continuous beams are presented, including the three-moment equation. This equation relates the bending moments at the ends of adjacent beam segments and is used to solve for unknown support reactions and draw shear and moment diagrams. An example problem demonstrates applying the three-moment equation to determine reactions for a continuous beam with a single load.
This document is a literature review for a project on modeling fluid dynamics using spectral methods in MATLAB. It summarizes two key papers: (1) Balmforth et al.'s paper on modeling the dynamics of interfaces and layers in a stratified turbulent fluid, which derived coupled differential equations; and (2) Trefethen's book on spectral methods in MATLAB, which provided guidance on using Chebyshev polynomials and differentiation matrices. It also outlines the methodology used in Balmforth et al.'s paper and chapters from Trefethen's book on finite differences, Chebyshev points, and constructing Chebyshev differentiation matrices.
This document discusses strategies for parallelizing spectral methods. Spectral methods are global in nature due to their use of global basis functions, making them challenging to parallelize on fine-grained architectures. However, the document finds that spectral methods can be effectively parallelized. The main computational steps in spectral methods are the calculation of differential operators on functions and solving linear systems, both of which can exploit parallelism. Domain decomposition techniques may also help parallelize computations over non-Cartesian domains.
Digital control systems (dcs) lecture 18-19-20Ali Rind
This document discusses digital control systems and related topics such as difference equations, z-transforms, and mapping between the s-plane and z-plane. It begins with an outline of topics to be covered including difference equations, z-transforms, inverse z-transforms, and the relationship between the s-plane and z-plane. Examples are provided to illustrate difference equations, z-transforms, and mapping poles between the two planes. Standard z-transforms of discrete-time signals like the unit impulse and sampled step are also defined.
The document presents a combined algorithm for simplicial weight interpolation and extrapolation of multivariate functions. The algorithm takes a dataset of n-dimensional points with corresponding values and provides an interpolating function that is continuous on Rn along with its derivatives. It works by first checking if the point is in the dataset, then determining if it lies within a simplex, and using weight functions to calculate the value. If the point lies outside the simplicial complex, it instead uses the closest face to extrapolate the value. The algorithm provides continuous functions dependent on the basis and weight functions used to build the simplicial complex.
Top Tips and Tricks For Supporting Your Oracle Health Science Application UsersPerficient
1. Steven provides 5 tips for supporting Oracle Health Science Application users: using a Windows-based FTP program, adding a spellchecker for remote desktop connections, creating a single table with all audit information, allowing multiple logos for DCF reports, and changing report defaults from printer to file.
2. He discusses each tip in detail, providing screenshots and explanations.
3. Steven acknowledges colleagues at BioPharm Systems for their contributions to supporting users.
Coherence incoherence patterns in a ring of non-locally coupled phase oscilla...Ola Carmen
This document summarizes research on coherence-incoherence patterns in a ring of non-locally coupled phase oscillators. It introduces a model of phase oscillators with non-local coupling defined by a coupling function G. It shows that on a macroscopic level, the model dynamics can be described by a complex-valued order parameter evolving according to an explicit equation. Stable coherence-incoherence patterns correspond to standing wave solutions of this equation. The analysis formulates this as an infinite-dimensional nonlinear eigenvalue problem, which is then studied to classify possible patterns for different coupling functions G.
This document presents a methodology for mapping multidimensional transforms onto reconfigurable architectures like FPGAs. The methodology uses tensor product decompositions and permutation matrices to express transforms recursively in terms of lower-order blocks. This allows large transforms to be computed by combining many parallel, smaller transform blocks. Specific examples are given for mapping one-dimensional linear convolution and discrete cosine transforms. The overall goal is to provide a unified framework and design process for implementing multidimensional transforms in a modular, parallel architecture.
Xtc a practical topology control algorithm for ad hoc networks (synopsis)Mumbai Academisc
The XTC algorithm is a simple and scalable topology control algorithm for wireless ad-hoc networks that does not require knowledge of node positions or a unit disk graph. It operates in three steps: (1) each node orders its neighbors by link quality, (2) nodes exchange these rankings, and (3) each node independently selects its neighbors in the topology based on the exchanged rankings. The resulting topology is proven to be symmetric, connected, and low degree while remaining energy-efficient for communication. The algorithm is implemented and simulated in a scalable wireless network simulation using the XTC topology control method.
The document describes the Floyd-Warshall algorithm for finding shortest paths in a weighted graph. It discusses the all-pairs shortest path problem, previous solutions using Dijkstra's algorithm and dynamic programming, and then presents the Floyd-Warshall algorithm as another dynamic programming solution. The algorithm works by computing the shortest path between all pairs of vertices where intermediate vertices are restricted to a given set. It does this using a bottom-up computation in O(V^3) time and O(V^2) space.
The document describes the method of successive approximations to solve linear integral equations of the second kind. It presents the iterative scheme which begins with an initial approximation go(s) and calculates successive approximations gn(s). If gn(s) converges uniformly to a limit g(s) as n approaches infinity, then g(s) is the solution.
The iterative scheme leads to the Neumann series representation of the solution. For the series to converge, the condition |A|B < 1 must be satisfied. The resolvent kernel f(s,t;A) is defined as the limit of the iterated kernels Km(s,t). Examples are provided to demonstrate solving integral equations using this method.
This document provides exercises on Hawking radiation using scalar field theory in the Kruskal spacetime. It asks the student to find the radial equation for the scalar field and show that near the horizon, the field takes the form of ingoing and outgoing waves that are analytic in different coordinate systems. The document then derives the Klein-Gordon equation in Schwarzschild coordinates and uses separation of variables to obtain approximate solutions near the horizon. It shows that ingoing waves are regular on the future horizon but outgoing waves are not, and vice versa for the past horizon.
Numerical disperison analysis of sympletic and adi schemexingangahu
This document discusses numerical dispersion analysis of symplectic and alternating direction implicit (ADI) schemes for computational electromagnetic simulation. It presents Maxwell's equations as a Hamiltonian system that can be written as symplectic or ADI schemes by approximating the time evolution operator. Three high order spatial difference approximations - high order staggered difference, compact finite difference, and scaling function approximations - are analyzed to reduce numerical dispersion when combined with the symplectic and ADI schemes. The document derives unified dispersion relationships for the symplectic and ADI schemes with different spatial difference approximations, which can be used as a reference for simulating large scale electromagnetic problems.
1) The document discusses the mathematical analysis of a basic AC circuit consisting of a resistor and inductor connected in series and driven by an external sinusoidal voltage source.
2) Kirchhoff's voltage law is applied to derive the differential equation governing the circuit and the forced steady-state response is shown to be a sinusoidal current lagging the driving voltage by a phase angle.
3) Expressions are derived relating the phase lag to the circuit properties and defining the real and reactive power consumed based on the circuit response.
1) The document discusses dynamics modeling for robotic manipulators using the Denavit-Hartenberg representation and Lagrangian mechanics. It describes using the Euler-Lagrange method to derive equations of motion for robotic links by computing kinetic and potential energy terms.
2) As an example, dynamics equations are derived for a simple 1 degree-of-freedom robotic arm. Kinetic and potential energy expressions are written and the Lagrangian is computed to obtain the equation of motion.
3) State-space modeling basics are reviewed using the example of a damped spring-mass system, showing how to write the system dynamics as state-space matrices to evaluate responses like step response.
The document discusses the Nyquist stability criterion for analyzing the stability of sampled-data control systems. It begins by defining the Nyquist criterion and contour, and how they can be used to determine the number of closed-loop poles outside the unit circle (Z). It then provides an example showing how to apply the Nyquist criterion by plotting the loop gain and counting encirclements of the critical point. The document also discusses modifications to the Nyquist contour when open-loop poles are on the unit circle and defines the Nyquist criterion theorem.
I am Felix T. I am an Electrical Engineering Assignment Expert at eduassignmenthelp.com. I hold a Master’s. in Electrical Engineering, University of Greenwich, UK. I have been helping students with their Assignments for the past 7 years. I solve assignments related to Electrical Engineering.
Visit eduassignmenthelp.com or email info@eduassignmenthelp.com . You can also call on +1 678 648 4277 for any assistance with Electrical Engineering Assignments.
The phase field method models microstructure evolution using a single variable called the order parameter to represent the different phases and diffuse interfaces between them. The order parameter varies continuously from one value in one phase to another value in the other phase over the interface region. This allows the entire microstructure to be described with a single free energy functional and modeled simultaneously without explicitly tracking interface motion. While elegant, the phase field method relies on approximations and its predictions must be interpreted with an understanding of its limitations compared to sharp interface models.
This document discusses statically determinate and indeterminate beams. It introduces the concept of continuous beams, which have at least one hinged support and roller supports. The key equations for analyzing continuous beams are presented, including the three-moment equation. This equation relates the bending moments at the ends of adjacent beam segments and is used to solve for unknown support reactions and draw shear and moment diagrams. An example problem demonstrates applying the three-moment equation to determine reactions for a continuous beam with a single load.
This document is a literature review for a project on modeling fluid dynamics using spectral methods in MATLAB. It summarizes two key papers: (1) Balmforth et al.'s paper on modeling the dynamics of interfaces and layers in a stratified turbulent fluid, which derived coupled differential equations; and (2) Trefethen's book on spectral methods in MATLAB, which provided guidance on using Chebyshev polynomials and differentiation matrices. It also outlines the methodology used in Balmforth et al.'s paper and chapters from Trefethen's book on finite differences, Chebyshev points, and constructing Chebyshev differentiation matrices.
This document discusses strategies for parallelizing spectral methods. Spectral methods are global in nature due to their use of global basis functions, making them challenging to parallelize on fine-grained architectures. However, the document finds that spectral methods can be effectively parallelized. The main computational steps in spectral methods are the calculation of differential operators on functions and solving linear systems, both of which can exploit parallelism. Domain decomposition techniques may also help parallelize computations over non-Cartesian domains.
Digital control systems (dcs) lecture 18-19-20Ali Rind
This document discusses digital control systems and related topics such as difference equations, z-transforms, and mapping between the s-plane and z-plane. It begins with an outline of topics to be covered including difference equations, z-transforms, inverse z-transforms, and the relationship between the s-plane and z-plane. Examples are provided to illustrate difference equations, z-transforms, and mapping poles between the two planes. Standard z-transforms of discrete-time signals like the unit impulse and sampled step are also defined.
The document presents a combined algorithm for simplicial weight interpolation and extrapolation of multivariate functions. The algorithm takes a dataset of n-dimensional points with corresponding values and provides an interpolating function that is continuous on Rn along with its derivatives. It works by first checking if the point is in the dataset, then determining if it lies within a simplex, and using weight functions to calculate the value. If the point lies outside the simplicial complex, it instead uses the closest face to extrapolate the value. The algorithm provides continuous functions dependent on the basis and weight functions used to build the simplicial complex.
Top Tips and Tricks For Supporting Your Oracle Health Science Application UsersPerficient
1. Steven provides 5 tips for supporting Oracle Health Science Application users: using a Windows-based FTP program, adding a spellchecker for remote desktop connections, creating a single table with all audit information, allowing multiple logos for DCF reports, and changing report defaults from printer to file.
2. He discusses each tip in detail, providing screenshots and explanations.
3. Steven acknowledges colleagues at BioPharm Systems for their contributions to supporting users.
This document recommends 5 foods to help prevent cancer: soy, cruciferous vegetables like broccoli and cabbage, fish high in omega-3 fatty acids, green tea which contains catechins, and yellow/orange fruits and vegetables high in antioxidants. Soy, fish, and green tea are specifically called out for their links to reducing breast and colon cancers. Cruciferous vegetables, fish, and yellow/orange fruits and vegetables are highlighted for their cancer prevention properties.
The document discusses living worthily as a disciple of Christ, living fruitfully as a family, and living powerfully as a church. It emphasizes that with the Holy Spirit's power within us, we can overcome feelings of inadequacy and have breakthroughs. It encourages applying this by sharing life instead of just doing discipleship groups, loving people instead of just evangelizing, and participating instead of just attending church activities. The power for breakthroughs comes from allowing the indwelling Holy Spirit to strengthen us.
This document provides information about fertility issues, treatments, and the Fertility Partnership clinic. It discusses common causes of infertility for both men and women. It also outlines fertility treatments that may be used, including diagnostic procedures, ovulation induction, IUI, IVF and more. The document promotes the Fertility Partnership clinic as offering these treatments at lower costs than other clinics using the latest technologies. It introduces the clinic staff and describes their experience in fertility care.
Chinese New Year and Passover both originated as festivals celebrating new beginnings and liberation from danger. Both traditions involve spring cleaning of homes, taking time off from work, giving and receiving gifts, and hoping for a better future. Both also involve remembering past dangers - for Chinese New Year it was avoiding the beast Nian, and for Passover it was remembering freedom from slavery in Egypt and avoiding the plague of the firstborn.
The sermon discusses the presentation of Jesus in the temple as described in Luke 2:22-38. It notes that Mary and Joseph marveled at the good news they received about Jesus. However, Simeon then revealed that the good news would also be bad news for some, as Jesus' coming would cause division. Anna later confirmed that the bad news was ultimately good news, promising redemption. The sermon emphasizes that while the good news of Christmas was joyous, it was also costly, bringing hope, joy and peace through God coming near as Immanuel.
Cells have several organelles that allow them to perform essential functions for life. The nucleus contains DNA and controls the cell. The mitochondria produces ATP for energy. Plant cells also contain chloroplasts for photosynthesis, a cell wall, and a central vacuole. Other organelles include the endoplasmic reticulum for protein production, Golgi for packaging proteins, lysosomes for waste digestion, and ribosomes for protein synthesis. Together these organelles allow cells to obtain energy, make proteins, and reproduce themselves.
Bodyfuelz An Exciting New Business OpportunityRyan Fernando
India is seeing growing interest in sports and fitness from both adults and parents. BODYFUELZ, India's leading sports nutrition brand endorsed by Olympians, is looking for new dealerships. Dealerships require a small starting investment of Rs. 10,000-15,000 and provide promotional support. Interested parties should contact BODYFUELZ to learn more about becoming a dealer and starting a business with low capital requirements and support from the company.
1. Ribosomes are tiny granular structures found in cells that serve as sites for protein synthesis.
2. They are composed of RNA and proteins and exist in both prokaryotic and eukaryotic cells.
3. Ribosomes read mRNA to assemble amino acids into proteins through a process of initiation, elongation, and termination.
Tools of genetic engineering include restriction enzymes, DNA ligase, DNA polymerase, and cloning vectors. Restriction enzymes cut DNA at specific recognition sequences, leaving sticky or blunt ends. DNA ligase joins DNA fragments by sealing nicks in DNA strands. DNA polymerase synthesizes new strands of DNA using existing strands as templates. Cloning vectors, such as plasmids, are used to introduce foreign DNA into host cells for amplification. Key steps in gene cloning are isolation of the gene, restriction digestion, ligation into a vector, transformation into host cells, and screening for the recombinant DNA.
The document discusses various terms and measurements related to gear teeth. It defines terms like pitch circle, diametral pitch, module, addendum, dedendum, clearance, pressure angle, and helix angle. It also describes common methods for measuring individual elements of gear teeth, such as tooth thickness, pitch, and errors, using instruments like gear tooth calipers, constant chord method, and base tangent method. Sources of errors in gear manufacturing by generating and reproducing methods are also outlined.
Methods of Gene Transfer document discusses various methods of transferring genes into plants to create transgenic plants. It describes two main categories of gene transfer methods - physical and biological. Physical methods include microinjection, biolistics (gene gun), electroporation, and particle bombardment. Biological methods include Agrobacterium-mediated transformation, which involves using the bacteria Agrobacterium tumefaciens to transfer DNA into plant cells. The document also discusses transformation cassettes, selection of transgenic plants, analysis of transgenic plants, and some examples of commercially important transgenic crops like golden rice and Roundup Ready corn.
The document discusses weighted graphs and algorithms for finding minimum spanning trees and shortest paths in weighted graphs. It defines weighted graphs and describes the minimum spanning tree and shortest path problems. It then explains Prim's and Kruskal's algorithms for finding minimum spanning trees and Dijkstra's algorithm for finding shortest paths.
A NEW PARALLEL ALGORITHM FOR COMPUTING MINIMUM SPANNING TREEijscmc
Computing the minimum spanning tree of the graph is one of the fundamental computational problems. In
this paper, we present a new parallel algorithm for computing the minimum spanning tree of an undirected
weighted graph with n vertices and m edges. This algorithm uses the cluster techniques to reduce the
number of processors by fraction 1/f (n) and the parallel work by the fraction O ( 1 lo g ( f ( n )) ),where f (n) is an
arbitrary function. In the case f (n) =1, the algorithm runs in logarithmic-time and use super linear work on
EREWPRAM model. In general, the proposed algorithm is the simplest one.
A NEW PARALLEL ALGORITHM FOR COMPUTING MINIMUM SPANNING TREEijscmcj
Computing the minimum spanning tree of the graph is one of the fundamental computational problems. In this paper, we present a new parallel algorithm for computing the minimum spanning tree of an undirected weighted graph with vertices and edges. This algorithm uses the cluster techniques to reduce the number of processors by fraction and the parallel work by the fraction O ( 1 lo g ( f ( n )) ),where f (n) is an arbitrary function. In the case f (n) =1, the algorithm runs in logarithmic-time and use super linear work on EREWPRAM model. In general, the proposed algorithm is the simplest one.
This document describes Sollin's algorithm, also known as Boruvka's algorithm, for finding a minimum spanning tree (MST) of a connected, edge-weighted undirected graph. Sollin's algorithm is a greedy algorithm that works by repeatedly contracting edges of minimum weight to form subgraphs until a single vertex remains, resulting in an MST. The algorithm proceeds by first highlighting the cheapest outgoing edge for each vertex, then contracting edges to form subgraphs and repeating on each subgraph until an MST is produced. An example applying the algorithm to a graph is provided.
This document summarizes a survey on graph partitioning algorithms. It begins by defining the graph partitioning problem and describing its applications in areas like VLSI design and parallel finite element methods. It then provides an overview of several categories of sequential graph partitioning algorithms, including local improvement methods like Kernighan-Lin and Fiduccia-Mattheyses, as well as discussing parallel partitioning algorithms and conclusions from experimental comparisons of different approaches.
This document summarizes algorithms for finding connected components, topological sorting of directed acyclic graphs (DAGs), and finding minimal spanning trees in weighted undirected graphs. It describes:
1) Using breadth-first or depth-first search to find the connected components of an undirected graph by traversing from each unvisited vertex.
2) Topological sorting of DAGs by recursively traversing vertices in depth-first order and listing them in the order they are finished.
3) Kruskal's algorithm for finding a minimal spanning tree by adding edges in order of increasing weight if they do not form cycles.
This document discusses algorithms for solving the all-pairs shortest path problem in graphs. It defines the all-pairs shortest path problem as finding the shortest path between every pair of nodes in a graph. It then describes two main algorithms for solving this problem: Floyd-Warshall and Johnson's algorithm. Floyd-Warshall finds all-pairs shortest paths in O(n3) time using dynamic programming. Johnson's algorithm improves this to O(V2logV+VE) time by first transforming the graph to make edges positive, then running Dijkstra's algorithm from each node.
This document contains a summary of a lecture on graph analytics and complexity by Dr. Animesh Chaturvedi. It includes questions and answers on graph algorithms like minimum spanning tree (MST), single-source shortest path (SSSP) problems, and the Agrawal–Kayal–Saxena primality test. Sample algorithms are provided to calculate the average MST and average SSP of multiple graphs by combining the graphs and running standard algorithms. The document is in English and other languages with thank you messages at the end.
A comparison of efficient algorithms for scheduling parallel data redistributionIJCNCJournal
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The document discusses approximation algorithms for NP-complete problems. It introduces the concept of approximation ratios, which measure how close an approximate solution from a polynomial-time algorithm is to the optimal solution. The document then provides examples of approximation algorithms with a ratio of 2 for the vertex cover and traveling salesman problems. It also discusses using backtracking to find all possible solutions to the subset sum problem.
EDGE-TENACITY IN CYCLES AND COMPLETE GRAPHSijfcstjournal
It is well known that the tenacity is a proper measure for studying vulnerability and reliability in graphs.
Here, a modified edge-tenacity of a graph is introduced based on the classical definition of tenacity.
Properties and bounds for this measure are introduced; meanwhile edge-tenacity is calculated for cycle
graphs and also for complete graphs.
This document provides a summary of a lecture on graphs and algorithms. It discusses Hall's Theorem and provides a proof using induction. It then gives several examples of how Hall's Theorem can be applied, such as scheduling tasks among machines. The document also discusses maximum flows, the Konig-Egervary Theorem relating matchings and vertex covers, and Menger's Theorem relating disjoint paths and minimum cuts.
This document discusses minimum spanning trees and algorithms to find them. It begins by introducing the problem of laying cable in a new neighborhood along certain paths. It then defines spanning trees and minimum spanning trees. Two algorithms are described - Prim's and Kruskal's. Prim's grows the minimum spanning tree by adding one edge at a time, while Kruskal's grows a forest by adding edges until a single tree remains. The document applies Prim's algorithm to find the minimum spanning tree of a sample graph modeling the cable laying problem. It compares the time complexities of the two algorithms and discusses properties of minimum spanning trees.
This document discusses several graph algorithms:
1) Topological sort is an ordering of the vertices of a directed acyclic graph (DAG) such that for every edge from vertex u to v, u comes before v in the ordering. It can be used to find a valid schedule respecting dependencies.
2) Strongly connected components are maximal subsets of vertices in a directed graph such that there is a path between every pair of vertices. An algorithm uses depth-first search to find SCCs in linear time.
3) Minimum spanning trees find a subset of edges that connects all vertices at minimum total cost. Prim's and Kruskal's algorithms find minimum spanning trees using greedy strategies in O(E
This document discusses several graph algorithms:
1) Topological sort is an ordering of the vertices of a directed acyclic graph (DAG) such that for every edge from vertex u to v, u comes before v in the ordering. It can be used to find a valid schedule respecting dependencies.
2) Strongly connected components are maximal subsets of vertices in a directed graph such that there is a path between every pair of vertices. An algorithm uses depth-first search to find SCCs in linear time.
3) Minimum spanning trees find a subset of edges that connects all vertices at minimum total cost. Prim's and Kruskal's algorithms find minimum spanning trees using greedy strategies in O(E
This document discusses algorithms for solving the feedback vertex set problem, which aims to find the minimum number of nodes that need to be removed from a graph to make it acyclic. It describes several algorithms including a naive algorithm, fixed parameter tractable algorithm, 2-approximation algorithm, disjoint feedback vertex set algorithm, and randomized algorithm. For each algorithm, it provides definitions, pseudocode, and an example to illustrate how it works. The document concludes that this problem remains an active area of research to develop more efficient algorithms.
The document discusses graph representations and algorithms. It describes two common graph representations: adjacency matrix and adjacency list. It then explains traversal algorithms like breadth-first search and depth-first search. Spanning trees and minimum spanning trees are discussed along with Prim's and Kruskal's algorithms. Finally, it covers the single source shortest path problem and Dijkstra's algorithm for solving it on weighted graphs.
It is well known that the tenacity is a proper measure for studying vulnerability and reliability in graphs.
Here, a modified edge-tenacity of a graph is introduced based on the classical definition of tenacity.
Properties and bounds for this measure are introduced; meanwhile edge-tenacity is calculated for cycle
graphs and also for complete graphs.
This document discusses dynamic programming and algorithms for solving all-pair shortest path problems. It begins by defining dynamic programming as avoiding recalculating solutions by storing results in a table. It then describes Floyd's algorithm for finding shortest paths between all pairs of nodes in a graph. The algorithm iterates through nodes, calculating shortest paths that pass through each intermediate node. It takes O(n3) time for a graph with n nodes. Finally, it discusses the multistage graph problem and provides forward and backward algorithms to find the minimum cost path from source to destination in a multistage graph in O(V+E) time, where V and E are the numbers of vertices and edges.
This document discusses various algorithms for finding shortest paths in graphs, including Dijkstra's algorithm, breadth-first search (BFS), depth-first search (DFS), and Bellman-Ford algorithm. It provides pseudocode examples and explanations of how each algorithm works. It also covers properties of spanning trees, minimum spanning tree algorithms like Kruskal's and Prim's, and applications of spanning trees like network planning and routing protocols.
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তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
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Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
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2. A cycle in a graph is a simple closed walk. The Conjecture: For every bridgeless G and every
following Double Cover Conjecture is one of the cycle C of G, there is a cycle double cover of G
most famous problems in graph theory. It is due containing C.
independently to Szekeres [Sz] and Seymour [Se].
Partial results are too numerous to mention here. I
Conjecture: Every bridgeless graph has a refer the interested reader to the survey article by
collection of cycles which together contain every Jaeger [J].
edge exactly twice.
A dual form of the problem is called "Fulkerson's
The conjecture is almost easy. Form G_2 from G Conjecture".
by replacing each edge with two parallel edges.
Then G_2 has every vertex of even degree. It
follows easily from induction that G_2 has an edge
partition into cycles. However, some of these
cycles may be of length two and hence do not
correspond to cycles in a double cover of G.
A stumbling block to inductive proofs has been
found in many different contexts. Namely, suppose
that each edge e is assigned a weight w(e) = 1 or 2
so that at each vertex the sum of the weights is
even. Can we find a cycle cover so that each edge e
is used w(e) times? No. A counterexample is
formed from the Petersen graph (of course) by
assigning weights 2 on a perfect matching and
weights 1 on two disjoint 5-cycles.
There are several variations of a topological nature.
For example there is the Circular Embedding
Conjecture.
Conjecture: Every 2-connected graph has an
embedding in some surface such that each face is
bounded by a simple cycle.
The face boundaries form a cycle double cover.
The two conjectures are equivalent for cubic
graphs, but the second is stronger for noncubic
graphs. An even stronger conjecture asserts that the
faces of the circular embedding can be properly 5-
colored. Likewise one could require the embedding
to be in an orientable surface.
A stronger conjecture due to Goddyn [G] allows
you to fix one cycle in the cover.
4. Algorithm proceeds in two steps: - (1) Test Case 13. To achieve this, now we make use of the
Generation Step [9] and (2) Optimization Step [10]. bridges that we found out / stored at the end of step
10.
4.1 Test Case Generation [9] Criteria:- 14. From the original graph, we now remove all the
edges that occur in the MST found in step 12 but
1. First of all, the user provides us with the SRS do not occur in the set of bridges. Our motive
(Software Requirement Specification) of the behind this is that we do not want to make the
software that he/she wants to get developed. graph disconnected at any point of time.
2. Based upon this SRS, a UML state chart diagram 15. Say, we obtain graph G’ after step 14. Now we
for the SUT is prepared either manually or using again apply step 11 (i.e. MST finding algorithm) on
some software tool which can automatically build a this particular graph to obtain another MST.
UML diagram on feeding it with a SRS. 16. Now, step 15 is repeated until we are left with
3. Based upon this UML diagram, the specification only the set of bridges. Or, in other words, we are
in terms of the states and transitions among them is able to find as many spanning trees of the original
provided to the software that has been built for this state transition diagram / graph as possible.
purpose to obtain the state transition diagram.
4. Note that, we also need to provide the weight /
cost associated with each transition (which is 4.2 Optimization [10] Criteria:-
actually provided by the user based on his/her
requirements). Also, a key value is associated with 1. The graph based approach to software testing,
each of the state which is initially ∞ (infinity) for that we have proposed here, uses the concept of
all the states. Minimal Spanning Tree.
5. We will ignore self loops, if any, in the UML 2. A Minimal Spanning Tree T of a graph G covers
diagram, while building the state transition all the vertices V of G and only those edges which
diagram. The reason being that test sequence do not form any cycle among themselves.
generation, in our case, is primarily based upon 3. These edges are such that the total weight of tree,
Prim Jarnik Algorithm, which does not take into got by summing the weights of the containing
account the self loops (like any other minimal edges, is the minimum among all possible trees in
spanning tree finding algorithm) while calculating graph G.
the MST. Once a vertex gets added in the cloud, it 4. Based on this, any path from the initial node to
immediately gets removed from the heap of other the terminal node, via any frontier node, carries the
vertices which are yet to be taken into account. least weight among all the paths via that particular
6. Regarding parallel edges between any two states frontier node.
(s1 & s2, with weight say, w), that is equivalent to 5. In each iteration ‘i’, as we delete some edges, as
adding a new state (s3) in between those two states, described in the above Test Sequence Generation
such that the transition from s1 to s3 carries weight Algorithm, the path from the starting node to the
zero and that from s3 to s2 carries weight w. terminal node via any frontier node (say p [i]), is
7. After taking into account all the above points, we always carrying the least weight due to loop
apply the algorithm on the graph obtained after step invariance property of the proposed algorithm.
no. 5. 6. In this way, the path got in the first iteration of
8. Now, there might be some cut edges / bridges in the Test Sequence Generating Algorithm (i.e. p [1])
the graph (discussed in section 3.3). is the most optimal path in the graph from the
9. So, our first step is to apply the bridge finding starting to the terminal node.
algorithm described in section 3.4 to the graph. 7. In the ith iteration, the path got between the
10. Once we get all the cut edges in this graph, we starting and the terminal node, i.e. p [i], is the ith
store them in a suitable data structure (say an array) most optimal path.
for easy reference in later steps of the algorithm. 8. Thus by applying the proposed Test Sequence
11. Now, we aim for finding the minimal spanning Generation Algorithm, we get all possible
tree (MST) in the graph on the basis of the key transitions from the starting node to the terminal
associated with each node and weight associated node, and these paths are generated according to a
with every transition. ranking associated with them based on their
12. This is the first MST that we obtain at the end optimality.
of this step. Now, our aim is to find all the other 9. The set of paths got from the Test Sequence
MST’s of this particular graph so that we are able Generation Algorithm is the Optimal Test
to cover all the transitions. Sequence that covers all the States and the
Transitions in the State Transition Graph.
6. size O.n=2i / (1 · i · log n) and so that each MST
edge is the solution to one of the closest pair
Higher dimensional MSTs problems.
The methods described above, for constructing Proof: For simplicity of exposition we demonstrate
graphs containing the minimum spanning tree, all the result in the case that d D 2; the higher
generalize to higher dimensions. However Lemma dimensional versions follow analogously. If pq is a
2 is not so informative, because the Delaunay minimum spanning tree edge, and w is a double
triangulation may form a complete graph. Lemma 3 wedge having sufficiently small interior angle, with
is more useful; Yao [115] used it to find minimum p in one half of w and q in the other, then pq must
spanning trees in time O.n2¡²d / where for any have the minimum distance over all such pairs
dimension d, ²d is a (very small) constant. Agarwal defined by the points in w. Therefore if F is a
et al. [2] found a more efficient method for high family of double wedges with sufficiently
dimensional minimum spanning trees, via small interior angles, such that for each pair of
bichromatic nearest neighbors. If we are given two points .p; q/ some double wedge w.p; q/ in F has p
sets of points, one set colored red and the other on one side and q on the other, then every MST
colored blue, the bichromatic nearest neighbor pair edge pq is the bichromatic closest pair for wedge
is simply the shortest red-blue edge in the complete w.p; q/. Suppose the interior angle required is
geometric graph. It is not hard to show that this 2¼=k. We can divide the space around each point p
edge must belong to the minimum spanning tree, so into k wedges, each having that interior angle.
finding bichromatic nearest neighbors is no harder Suppose edge pq falls inside wedge w. We find a
than computing minimum spanning trees. Agarwal collection of
et al. show that it is also no easier; the two double wedges, with sides parallel tow, that is
problems are equivalent to within a polylogarithmic guaranteed to contain pq. By repeating the
factor. The intersection of any d halfspaces forms a construction k times, we are guaranteed to find a
simplicial cone, with an apex where the three double wedge containing each possible edge.
bounding hyperplanes meet. We define a double For simplicity, assume that the sides of wedge w
cone to be the union of two simplicial cones, where are horizontal and vertical. In the actual
the halfspaces defining the second cone are construction, w will have a smaller angle than ¼=2,
opposite those defining the first cone on the same but the details are similar. First choose a horizontal
bounding hyperplanes. Such a double cone line with at most n=2 points above it, and at most
naturally defines a pair of point sets, one in each n=2 points below. We continue recursively with
cone. Define the opening angle of a cone to be the each of these two subsets; therefore if the line does
maximum angle uvw where v is the apex and u and not cross pq, then pq is contained in a closest pair
w are in the cone. The opening angle of a double problem generated in one of the two recursive
cone is just that of either of the two cones forming subproblems. At this point we have two sets, above
it. and below the line. We next choose a vertical line,
Lemma 4 (Agarwal et al.). There is a constant ® again dividing the point set in half. We continue
such that, if pq is a minimum spanning tree edge, recursively with the pairs of sets to the left of the
and PQ are the points in the two sides of a double line, and to the right of the line. If the line does 4
cone with opening angle at most ®, with p 2 P and Figure 2. A fair split tree. not cross pq, then pq will
q 2 Q, then pq is the bichromatic nearest neighbor be covered by a recursive subproblem. If both lines
pair of P and Q. crossed pq, so that it was not covered by any
The proof involves using Lemma 3 to show that p recursive subproblem, then w.p; q/ can be taken to
and q must be mutual bichromatic nearest be one of two bichromatic closest pair problems
neighbors. It then uses geometric properties of formed by opposite pairs of the quadrants formed
cones to show that, if there were a closer pair p0q0, by the two lines. The inner recursion (along the
then pp0 and qq0 would also have to be smaller vertical lines) gives rise to one subproblem
than pq, contradicting the property of minimum containing p at each level of the recursion, and each
spanning trees that any two points are connected by level halves the total number of points, so p ends
a path with the shortest possible maximum edge up involved in one problem of each possible size
length. One can then use this result to find a graph n=2i . The outer recursion generates an inner
containing the minimum spanning tree, by solving recursion at each possible
a collection of bichromatic closest pair problems size, giving i problems total of each size n=2i . The
defined by a sequence of double cones, such that construction must be repeated for each of the k
any edge of the complete geometric graph is wedge angles, multiplying the bounds by O.1/. 2
guaranteed to be contained by some double cone. Theorem 2 (Agarwal et al.). We can compute the
Lemma 5 (Agarwal et al.). Given a set of n points Euclidean minimum spanning tree of a d-
in Rd , we can form a hierarchical collection of O.n dimensionalpoint set in randomized expected time
logd¡1 n/ bi-chromatic closest pair problems, so O..n log n/4=3/ for d D 3, or deterministically in
that each point is involved in O.i d¡1/ problems of