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Making statements based on opinion; back them up with references or personal experience. “1” in the matrix entry represent that there is an edge between two vertexes and “0” represent ‘No Edge’. Adjacency matrices. Let us learn how to implement Dijkstra’s Algorithm in C programming using Adjacency Matrix. Some Applications of BFS. BoostBreadthFirstSearchTree: vtkBoostBreadthFirstSearchTree: Breadth first search tree. Adjacency matrix Adjacency list (with crosslinks) Adj 4 1 124 2 4 13 3 4 1 1 1 0 0 0 1 1 410 3 2 1 3 1 23 4 Figure 24: Adjacency matrix and adjacency list for graphs. We will discuss two of them: adjacency matrix and adjacency list. If you find any of these codes not working Please comment on the Page, So that it can be corrected. For a Graph BFS (Breadth-first-search) traversal, we normally tend to keep an adjacency matrix as a. Each row in the matrix represent source vertices and each column represent destination vertices. Breadth first search (BFS) algorithm also starts at the root of the Tree (or some arbitrary node of a graph), but unlike DFS it explores the neighbor nodes first. Design and analysis of algorithms are a fundamental topic in computer science and engineering education. The typical Adjacency matrix has 0's along the diagonal, representing that there is no self-loop. Based on notes by E. See Also bfs_visitor and depth_first_search() Notes. Let the 2D array be adj[][], a slot adj[i][j] = 1 indicates that there is an edge from vertex i to vertex j. Undirected Graph 5. CodeProject, 503-250 Ferrand Drive Toronto Ontario, M3C 3G8 Canada +1 416-849-8900 x 100. Implementing Undirected Graphs in Python July 28, 2016 July 28, 2016 Anirudh Technical Adjacency List , Adjacency Matrix , Algorithms , Code Snippets , example , Graphs , Math , Python There are 2 popular ways of representing an undirected graph. Breadth First Search Analysis. If you want a pure Python adjacency matrix representation try networkx. In this traversal algorithm one node is selected and then all of the adjacent nodes are visited one by one. Adjacency matrix A two-dimensional matrix, in which the rows represent source vertices and columns represent destination vertices. Adjacency matrices. For nodes i and j which are not connected, the value depends on the representation:. Parameters: data (input graph) – Data to initialize graph. Like in the example above, for the first code the loop will run n number of times, so the time complexity will be n atleast and as the value of n will increase the time taken will also increase. Every node below has a node above known as the parent node. raw download clone embed report print Python 3. The advantage of DFS is it requires less memory compare to Breadth First Search(BFS). WhileQ6= ∅do. Questions Once you have completed the readings, answer the following questions in the reading09/README. From a cell you can either traverse to left, right, up or down. In this blog post I will describe how to form the adjacency matrix and adjacency list representation if a list of all edges is given. The algorithm starts at the root (top) node of a tree and goes as far as it can down a given branch (path), then backtracks until it finds an unexplored path, and then explores it. This module uses graphs which are stored in a matrix format. Tushar Roy - Coding Made Simple 342,137 views. 0 1 0 2 0 3 2 4. I am 70 years old and have been programming for 45 years. In this tutorial, you will understand the working of bfs algorithm with codes in C, C++, Java, and Python. For a Graph BFS (Breadth-first-search) traversal, we normally tend to keep an adjacency matrix as a. There are quite a few ways to represent a graph, the most common two are adjacency matrix and adjacency list. Indeed, the adjacency matrix structure wastes a lot of space. The disadvantage of BFS is it requires more memory compare to Depth First Search(DFS). Advanced Data Structures and Algorithms in Java using Data Structures/Algorithms/with Java Algorithms/Design/Analysis 4. Adjacency Matrix is a 2D array of size V x V where V is the number of vertices in a graph. For a Graph BFS (Breadth-first-search) traversal, we normally tend to keep an adjacency matrix as a. Show how to determine whether a directed graph G contains a universal sink, i. Finding a route from one location to another is a fundamental question in everyday life, and it shows up in many forms, from explicit questions (“Can you give me directions to get to the library from here?”, or “What prerequisites must I take in order to qualify for this class. This number will denote the number of vertices to follow. Breadth First Search (BFS) Technique In C++. If there is a connection from node i to node j, then G[i, j] = w, where w is the weight of the connection. A graph having n vertices, will have a dimension n x n. The steps are. Chou Department of Electrical and Computer Engineering University of California, Irvine, CA 92697-2625 USA [email protected] Both DFS and BFS can be used to solve this problem. Easier than breadth-first search. Let Gbe a graph with adjacency matrix Aand kbe a positive integer. For a graph with nvertices, an adjacency matrixis an n × nmatrix of 0s and 1s, where the entry in row iand column jis 1 if and only if the edge (i, j)is in the graph. In my Python implementation of Kruskal’s algorithm, I used an edge list. Thus, breadth-first search spends O (V + E) O(V+E) O (V + E) O, left parenthesis, V, plus, E, right parenthesis time visiting vertices. The major difference would be that instead of a simple queue used in BFS, we will use open list to store the neighboring reachable cells from the current node. Comparison: Adjacency list vs adjacency matrix To compare the two ways of representing edges, we will consider both the amount of space used, and the time required for some standard operations. First, you'll dive into understanding the pros and cons of adjacency matrices, adjacency lists, adjacency sets, and know when you would choose one data structure over another. Adjacency matrix. To get the minimum weight edge, we use min heap as a priority queue. For all v∈V \{s}dist(s,v) ←∞. DFS algorithm starts form a vertex “u” from graph. If the graph is undirected, the adjacency matrix will be symmetric. , it traverses along the increasing depth and upon reaching the end, it backtracks to the node from which it was started and then do the same with the sibling node. Martin C Brown. A NetworkX graph. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The algorithm starts at the root (top) node of a tree and goes as far as it can down a given branch (path), then backtracks until it finds an unexplored path, and then explores it. The disadvantage of BFS is it requires more memory compare to Depth First Search(DFS). Breadth-First Search algorithm follows a simple, level-based approach to solve a problem. Before jumping to actual coding lets discuss something about Graph and BFS. Adjacency Matrix is a 2D array of size V x V where V is the number of vertices in a graph. (Here a missing edge is represented by ∞. Breadth-First Search (BFS)for Undirected or Directed Graphs Recall that we can use an adjacency matrix to describe connectivity. the maximum degree and the adjacency matrix of the graph by calling the functions vcount(), Breadth-first search (BFS) from a. Lecture 30: Breadth-first search and Depth-first search on graphs Finding paths from one node to another. Adjacency Matrix is also used to represent weighted graphs. Note video explanations of implementations are specific to C++ and Java only 2) Practice Questions will be in Python It is recommended to prepare yourself with Fork Python if you are beginning with Python. First, you'll dive into understanding the pros and cons of adjacency matrices, adjacency lists, adjacency sets, and know when you would choose one data structure over another. each record of the linked list area appears on two adjacency lists: one for the node at each end of the represented edge. Breadth First Search is graph traversal algorithm which has many applications in most of the algorithms. Implementation of BFS in Python ( Breadth First Search ) Source Code: BFS in Python. If the new adjacency matrix is built in such a way that the first eight vertices are labelled by coordinates $(*,*,*,0)$ and the eight last vertices are $(*,*,*,1)$ ranked in the same order for the first 3 coordinates, the upper left block will simply be the ordinary (3D) adjacency matrix, The adjacency matrix of an undirected graph can also be represented in the form of an array. exploring = set() def edge_to_adjancency_matrix (self, n, edges): '''Convert the edges list to an adjancency matrix''' adj_mat = [[0 for i in range(n)] for j in range(n)] for edge in edges: i = edge[0] j = edge[1] adj_mat[i][j] = 1 return adj_mat def has_cyc (self, a, i, n. Overview of data types and objects. An adjacency matrix is one of the two common ways to represent a graph. Another matrix representation for a graph is the incidence matrix. In a sparse graph, an adjacency matrix will have a large memory overhead, and finding all neighbors of a vertex will be costly. To get the minimum weight edge, we use min heap as a priority queue. Let the 2D array be adj[][], a slot adj[i][j] = 1 indicates that there is an edge from vertex i to vertex j. Graphs and Graph Algorithms. Notice that the shortest path from the root to any other vertex is a path in this tree. Starting with that vertex it considers all edges to other vertices from that vertex. Browse other questions tagged python pandas data-analysis adjacency-matrix or ask your own question. An adjacency matrix requires (n2)storage and an adjacency list requires (n+e)storage (one entry for each vertex in Adj and each list has outdeg(v) entries, which when summed is (e. If the graph has some edges from i to j vertices, then in the adjacency matrix at i th row and j th column it will be 1 (or some non-zero value for weighted graph), otherwise that place will hold 0. Questions Once you have completed the readings, answer the following questions in the reading09/README. Now, we come to the code part of the Breadth First Search, in C. Design and analysis of algorithms are a fundamental topic in computer science and engineering education. Before attempting these exercises, you should read the posts about graphs, graph problems, and graph data structures. Home Courses Interview Preparation Course Representation of Graphs: Adjacency Matrix Representation of Graphs: Adjacency Matrix Instructor: admin Duration: 13 mins Full Screen. There are several possible ways to represent a graph inside the computer. Breadth first traversal or Breadth first Search is a recursive algorithm for searching all the vertices of a graph or tree data structure. — my journey as a worker bee in quant finance. depth first forest. they must be still evaluated. For a Graph BFS (Breadth-first-search) traversal, we normally tend to keep an adjacency matrix as a. Leonhard Euler is regarded to have started this area of Discrete Mathematics in 1736 by describing The Konigsberg Bridge Problem. Also Read: Depth First Search (DFS) Traversal of a Graph [Algorithm and Program] A Graph G = (V, E) is a collection of sets V and E where V is a collection of vertices and E is a collection of edges. Consider the directed graph. If the new adjacency matrix is built in such a way that the first eight vertices are labelled by coordinates $(*,*,*,0)$ and the eight last vertices are $(*,*,*,1)$ ranked in the same order for the first 3 coordinates, the upper left block will simply be the ordinary (3D) adjacency matrix, The adjacency matrix of an undirected graph can also be represented in the form of an array. Matrix as Graph * Leda Graph * Stanford GraphBase. G is an N-by-N sparse matrix that represents a directed graph. The Java implementations implement the corresponding interfaces in the Java Collections Framework. Path finding in a Maze Oct 2019 - Nov 2019. cpp demonstrates using the BGL Breadth-first search algorithm on the graph from Figure 6. Starting with that vertex it considers all edges to other vertices from that vertex. The adjacency matrix representation is attractive for its simplicity and for the fast random access to edge information in the graph it provides. Implementation of BFS in Python ( Breadth First Search ) Source Code: BFS in Python. Now, we come to the code part of the Breadth First Search, in C. AdjacentVertexIterator: vtkAdjacentVertexIterator: Get all vertices connected to a specified vertex. Leonhard Euler is regarded to have started this area of Discrete Mathematics in 1736 by describing The Konigsberg Bridge Problem. Here you will get Breadth First Search (BFS) Java program along with example. Here’s an implementation of the above in Python:. It starts from the Root node and then starts traversing to the next level of Tree and Graph. Algorithms Named parameters (used in many graph algorithms) Basic Operations copy_graph. The adjacency matrix shows which nodes are adjacent to one another. In the last post, we discussed how to represent a graph in a programmatic way using adjacency matrix and adjacency list representation. In the matrix, if there is an edge between two vertices, then a distance greater. Traits classes graph_traits; adjacency_list_traits; property_map. mmio - incidence matrix of the graph in MMIO format. Before we get started, you must be familiar with the main data structure involved in the Breadth-First Search algorithm. Now, we will do a regular Breadth first search on the graph. AdjMatrixGraph. Regardless of which way edges are represented, O(N) space will be needed to store information about the nodes (the space for the node objects themselves. Demaine and C. Now we star BFS from node 7 to get node 9 at maximum distance. * Graphs in Java [/graphs-in-java] * Representing Graphs in Code. java (using adjacency Lists) */ public class BFS {/** * Implementation of Breadth-First-Search using adjacency matrix. We traverse all the vertices of graph using breadth first search and use a min heap for storing the vertices not yet included in the MST. Some Applications of BFS. each record of the linked list area appears on two adjacency lists: one for the node at each end of the represented edge. They are from open source Python projects. Overview of data types and objects. – adjacency matrix – adjacency lists – Python: dict of dicts • Basic operations: traversals – breadth-first search – depth-first search 4/18/12 S. This queue stores all the nodes that we have to explore and each time a node is explored it is added to our set of visited nodes. Breadth-first search is a chart traversal calculation that begins navigating the diagram from the root node and investigates all the neighboring nodes. 1 ( Add new methods in BST ) Add the following new methods in BST. 4 Adjacency … - Selection from Data Structures and Algorithms in Python [Book]. Deﬁnition : A connected component is a subgraph that is internally. Breadth-first searching (BFS) is an algorithm for traversing or searching a path in a graph. And I build the matrix based on vertex index in ArrayList. Browse other questions tagged python pandas data-analysis adjacency-matrix or ask your own question. , Python: The Complete Reference, Publisher McGraw Hill Education. * This returns nothing (yet), it is meant to be a template for whatever you want to do with. Problem Solving with Algorithms and Data Structures using Python by By Brad Miller and. Depth-first search or DFS is also a searching technique like BFS. We can check each one of this properties. An adjacency matrix is a matrix of size n x n where n is the number of vertices in the graph. 1 Graphs 14. Two nodes are adjacent if there is an edge connecting them. Adjacency matrix for undirected graph is always symmetric. Deﬁnition : A connected component is a subgraph that is internally. Adjacency Matrices. of node 2 is node 1. Matrix as Graph * Leda Graph * Stanford GraphBase. Adjacency lists, in simple words, are the array of linked lists. When we are going to solve the maze from adjacency matrix, we have to again deal with BFS or DFS. Typically, the following structure is used to represent an edge. The typical Adjacency matrix has 0's along the diagonal, representing that there is no self-loop. These algorithms can be applied to traverse graphs or trees. Least Cost Method with algorithm and Example in c++ with C Language code Depth-first search ( DFS ) is an algorithm for traversing or searching. Adjacency list. 1 Graphs 14. The graph is going to be given by its adjacency list, not adjacency matrix. To represent such data structures in Python, all we need to use is a dictionary where the vertices (or nodes) will be stored as keys and the adjacent vertices as values. We will be using it to find the shortest path between two nodes in a graph. Python - Backtracking - Backtracking is a form of recursion. Coming back to our BFS discussion, the level of each vertex is stored in a separate array and so is the case for parent of each vertex. Greed is good. An adjacency matrix is one of the two common ways to represent a graph. Breadth-First Search (BFS)for Undirected or Directed Graphs Recall that we can use an adjacency matrix to describe connectivity. It starts at the tree root (or some arbitrary node of a graph, sometimes referred to as a 'search key') and explores the neighbor nodes first, before moving to the next level neighbors". Adjacency Matrix. The graph adjacency structure is implemented as a Python dictionary of dictionaries; the outer dictionary is keyed by nodes to values that are themselves dictionaries keyed by neighboring node to the edge. It has fast lookups to check for presence or absence of a specific edge, but slow to iterate over all edges. Objective: Given a 2d grid map of '1's (land) and '0's (water), count the number of islands. The Basic Network Diagram is a good choice when you want to map out a simple network. For a graph with nvertices, an adjacency matrixis an n × nmatrix of 0s and 1s, where the entry in row iand column jis 1 if and only if the edge (i, j)is in the graph. So after initialisation this list of possible paths only has one element, a list containing the current nodes index: <<555>> This list is then expanded as follows: For each element in the list: Take the tail of the list as the current node Check for connections from this node to other nodes (using the adjacency matrix) If there is a connection. finding the shortest path in a unweighted graph. • [note: Ak for large k is related to pagerank of vertices]of vertices] • undirected graph symmetric matrix • [eiligenvalues useflf hful for many graph algorithms, see Lecture 13 for. Browse other questions tagged python pandas data-analysis adjacency-matrix or ask your own question. A shortest path from vertex s to vertex t is a directed path from s to t with the property that no other such path has a lower weight. Undirected Graph 5. In it, each student is numbered from 0 to n-1 with n being the number of students. Path finding in a Maze Oct 2019 - Nov 2019. Hence this is one of the Best Data structures And Algorithms Training In Bangalore or Data Structures and Algorithms Training In Hyderabad. From WikiPedia: "Breadth-first search (BFS) is an algorithm for traversing or searching tree or graph data structures. Comparison: Adjacency list vs adjacency matrix To compare the two ways of representing edges, we will consider both the amount of space used, and the time required for some standard operations. /** Code for https://journaldev. In this tutorial, you will understand the working of bfs algorithm with codes in C, C++, Java, and Python. Use a set to cache the nodes that have been visited. The advantage of DFS is it requires less memory compare to Breadth First Search(BFS). 82 Leetcode Problem#1030. First, you'll dive into understanding the pros and cons of adjacency matrices, adjacency lists, adjacency sets, and know when you would choose one data structure over another. the maximum degree and the adjacency matrix of the graph by calling the functions vcount(), Breadth-first search (BFS) from a. Graphs and Graph Algorithms. java (using adjacency Lists) */ public class BFS {/** * Implementation of Breadth-First-Search using adjacency matrix. Depth-first search (DFS) is an algorithm for searching a graph or tree data structure. Returns the adjacency matrix of a graph as scipy csr matrix. The biggest advantage of using adjacency matrix representation is to look for a particular edge takes constant time. A graph is built on top of a dictionary indexed by its vertices, each item being the set of neighbours of the key vertex. Actually, the path that you get back from breadth-first search is the path from the source to the given vertex that uses the fewest number of edges. The adjacency matrix shows which nodes are adjacent to one another. If the corresponding optional Python packages are installed the data can also be a NumPy matrix or 2d ndarray, a SciPy sparse matrix, or a PyGraphviz gra. In our case S=0, A=1, B=2, C=3 and D=4. This can easily be shown by reducing from the Hamiltonian Cycle problem. When the name of a valid edge attribute is given here, the matrix returned will contain the default value at the places where there is no edge or the value of the given attribute where there is an edge. This is known as a breadth-first search, or BFS. The process to generate the adjacency matrix is relatively easy: first map every state to an index from 0 0 0 to s − 1 s-1 s − 1 where s s s is the number of states (I use a simple Python trick mentioned here to do this), and then go through each transition and increment the corresponding entry in the matrix. Breadth First Search is an algorithm which is used to search a Tree or Graph in the programming language. Here is the source code of the C++ program to display the breadth first method of traversing nodes in a graph along with a display of the start and end time of a visited node. Clustering of unlabeled data can be performed with the module sklearn. In the above pseudo-code, the event points are the labels on the right. In an abstract description, heap data structure is used to get the cell with lowest net cost around the current cell. they must be still evaluated. Python - Backtracking - Backtracking is a form of recursion. parenthesis property. With adjacency list representation, all vertices of a graph can be traversed in O(V+E) time using BFS. Due to the fact that many things can be represented as graphs, graph traversal has become a common task, especially used in data science and machine learning. of node 2 is node 1. The Dijkstra Algorithm is used to find the shortest path in a weighted graph. Hence this is one of the Best Data structures And Algorithms Training In Bangalore or Data Structures and Algorithms Training In Hyderabad. From WikiPedia: "Breadth-first search (BFS) is an algorithm for traversing or searching tree or graph data structures. Few programming languages provide direct support for graphs as a data type, and Python is no exception. Undirected Graphs Reference: Chapter 17-18, Algorithms in Java, 3 rd Edition, Robert Sedgewick. by counting all non-zero entries in the corresponding row of the adjacency matrix. The basic idea: Start from node $$a$$, and for all its neighbors, note that their distance is 1. The adjacency matrix is always square with size equal to the number of nodes in the graph. Example of a digraph. The breadth_first_search() function can be extended with user-defined actions that will be called a certain event points. Menu Dijkstra's Algorithm in Python 3 29 July 2016 on python, graphs, algorithms, Dijkstra. The advantage of DFS is it requires less memory compare to Breadth First Search(BFS). The adjacency matrix of an undirected graph will always be symmetric. All data structures are rigorously analyzed and implemented in Java and C++. Deﬁnition : A connected component is a subgraph that is internally. So the first thing we are going to assume is that the graph is given by its adjacency list. raw download clone embed report print Python 3. Description: This tutorial demonstrate how to create a graph using adjacency list and perform DFS and BFS. Just append a new vertex containing an empty list to the end of our ArrayList. As an example, we can represent the edges for the above graph using the following adjacency matrix. I am trying to create a maze-solving algorithm. An adjacency matrix is a way of representing a graph G = {V, E} as a matrix of booleans. (Recall that we can represent an n × nmatrix by a Python list of nlists, where each of the nlists is a list of nnumbers. 1 Breadth First Search # Let’s implement Breadth First Search in Python. In this blog post I will describe how to form the adjacency matrix and adjacency list representation if a list of all edges is given. • Adjacency matrix It’s the call stack of the python interpreter • Breadth First Search, Depth First Search. If the corresponding optional Python packages are installed the data can also be a NumPy matrix or 2d ndarray, a SciPy sparse matrix, or a PyGraphviz gra. Iterator Adaptors adjacency_iterator; inv_adjacency_iterator. An adjacency matrix is a matrix of size n x n where n is the number of vertices in the graph. CSci 231 Homework 9 Graph Algorithms CLRS Chapter 22, 24 1. All data structures are rigorously analyzed and implemented in Java and C++. - adjacency matrix - adjacency lists - Python: dict of dicts • Basic operations: traversals - breadth-first search - depth-first search 4/18/12 S. Description: This tutorial demonstrate how to create a graph using adjacency list and perform DFS and BFS. they must be still evaluated. Adjacency matrix A two-dimensional matrix, in which the rows represent source vertices and columns represent destination vertices. Actually, the path that you get back from breadth-first search is the path from the source to the given vertex that uses the fewest number of edges. Martin C Brown. We can implement this using an array of linked lists. endfor // A counter for the order: 4. The cheapest price from city 0 to city 2 with at most 1 stop costs 200, as marked red in the picture. Path from node 7 to node 9 is clearly the longest path. BFS Breadth First Search. × The SuiteSparse Matrix Collection (formerly the University of Florida Sparse Matrix Collection) is a widely used set of sparse matrix benchmarks collected from a wide range of applications. First of all, we need to get a representation of the graph, either adjacency matrix or adjacency list is OK. The graph adjacency structure is implemented as a Python dictionary of dictionaries; the outer dictionary is keyed by nodes to values that are themselves dictionaries keyed by neighboring node to the edge. * Graphs in Java [/graphs-in-java] * Representing Graphs in Code. Only the cost for one edge can be stored between each pair of vertices. NetworkX Overview. 1 ( Add new methods in BST ) Add the following new methods in BST. Adjacency Matrix Representation. If there is a connection from node i to node j, then G[i, j] = w, where w is the weight of the connection. There are two popular options for representing a graph, the first being an adjacency matrix (effective with dense graphs) and second an adjacency list (effective with sparse graphs). /***** * Compilation: javac AdjMatrixGraph. Learned Python during September 2017. Before attempting these exercises, you should read the posts about graphs, graph problems, and graph data structures. The disadvantage of BFS is it requires more memory compare to Depth First Search(DFS). ZigZag Conversion. 0 1 0 2 0 3 2 4. Then we can do this with a depth first search (DFS): – Initialize a dictionary ‘marked’ that tells us whether a node has been visited. Traits classes graph_traits; adjacency_list_traits; property_map. The Time complexity of both BFS and DFS will be O(V + E), where V is the number of vertices, and E is the number of Edges. 2 Data Structures for Graphs 14. in more than 20 kms. Use the Backtracking algorithm for the m-Coloring problem (Algorithm 5. The data can be an edge list, or any NetworkX graph object. Problem 2(CLRS 22. Weights could indicate distance, cost, etc. Different kind of graph are listed below:. I have a simple undirected graph in the form of a adjacency matrix. depth first forest. AKA roof-shaped matrix or connection matrix. At that point, it chooses the closest node and investigates all the unexplored nodes. See the about page for more information. Browse other questions tagged python breadth-first-search adjacency-list adjacency-matrix or ask your own question. (Python could use a list-of-lists) a) Complete the following adjacency matrix for the above graph. In this tutorial, you will learn what an adjacency matrix is. One way to represent graphs is through adjacency matrices. If you find any of these codes not working Please comment on the Page, So that it can be corrected. Martin C Brown. https://cs231n. Traits classes graph_traits; adjacency_list_traits; property_map. Adjacency list. In fact, in Python you must go out of your way to even create a matrix structure like the one in Figure 3. Matrix Cells in Distance Order. The adjacency matrix representation is best suited for dense graphs, graphs in which the number of edges is close to the maximal. Adjacency matrix. Disjaskra shortest path. Breadth-ﬁrst searchDepth-first search. One way is to use an adjacency matrix and the other is to use an adjacency list. Deﬁnition : A connected component is a subgraph that is internally. In this (short) tutorial, we're going to go over graphs, representing those graphs as adjacency lists/matrices, and then we'll look at using Breadth First Search (BFS) and Depth First Search (DFS) to traverse a graph. The adjacency matrix of a graph provides a method of counting these paths by calcu-lating the powers of the matrices. Adjacency matrix representation. BFS uses a queue data structure which is a 'First in, First Out' or FIFO data structure. A graph is a collection of nodes and edges. I have a simple undirected graph in the form of a adjacency matrix. The basic idea: Start from node $$a$$, and for all its neighbors, note that their distance is 1. Given Matrix / Problem Red Box → Where our 1 is located (what we want to find) Yellow Box → Location where we start the search The problem is very simple given n*n grid of matrix, there is going to be one element called ‘1’ and we want to find this value, in other words we want to know the coordinates of element 1. Adjacency Matrices. Steps to Solve Problems. The Basic Network Diagram is a good choice when you want to map out a simple network. If the solution is found the search stops. It can be useful in order to find whether the graph has connected components or not. The root of a tree is on top. Only the cost for one edge can be stored between each pair of vertices. Visit Stack Exchange. Another common graph data structure is an adjacency dictionary, a Python dictionary with a key for each node in the graph. This ensures that iterating through the neighbours of a vertex is still efficient in sparse graphs (as with adjacency lists) while at the same time checking for adjacency is expected constant-time (as with the adjacency matrix). Let's say the undirected graph is. The breadth_first_search() function can be extended with user-defined actions that will be called a certain event points. Problem Solving with Algorithms and Data Structures using Python by By Brad Miller and. 4 Adjacency … - Selection from Data Structures and Algorithms in Python [Book]. It starts at the tree root (or some arbitrary node of a graph, sometimes referred to as a 'search key') and explores the neighbor nodes first, before moving to the next level neighbors". It has fast lookups to check for presence or absence of a specific edge, but slow to iterate over all edges. adjacency list. The graph is going to be given by its adjacency list, not adjacency matrix. AdjMatrixGraph. The Overflow Blog Steps Stack Overflow is taking to help fight racism. This number will denote the number of vertices to follow. You may want to watch my general video on BFS first to understand how the algorithm works. Representing Graph using adjacency list & perform DFS & BFS. java implements the same API using the adjacency-matrix representation. A graph with N nodes can be represented by an (N x N) adjacency matrix G. Directed Graph. The adjacency list of the graph is as follows: A1 → 2 A2 → 4 A3 → 1 → 4 A4 → 2. Depth-first search. Implementation of BFS in Python ( Breadth First Search ) Source Code: BFS in Python. Toeplitz Matrix. Undirected Graph 5. If adjacency list is used to represent the graph, then using breadth first search, all the vertices can be traversed in O(V + E) time. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. When the name of a valid edge attribute is given here, the matrix returned will contain the default value at the places where there is no edge or the value of the given attribute where there is an edge. A graph with N nodes can be represented by an (N x N) adjacency matrix G. Graph-abstract data type,adjacency matrix,adjacency list, BFS,DFS, shortest path problem, spanning tree. node_stack = node_stack + children Take those nodes and push them onto the end of. In the case of a directed graph, if node is adjacent to node , there is an edge from to. 2 Adjacency List Structure 14. It is a two dimensional array with Boolean flags. In the matrix, if there is an edge between two vertices, then a distance greater. A shortest path from vertex s to vertex t is a directed path from s to t with the property that no other such path has a lower weight. We are given a matrix with R rows and C columns has cells with integer coordinates (r, c), where 0 = r R and 0 = c. In python it just takes few-code to transform an image into matrix form with color values. #' Here, we use the union-find algorithm #' #' Note: Python version takes 1. Can also be used to convert a graph to a tree. Implementation of BFS in Python ( Breadth First Search ) Source Code: BFS in Python. Python does not have built-in support for trees. The algorithm does this until the entire graph has been explored. A graph is a collection of nodes and edges. The execution time of this algorithm is very slow because the time complexity of this algorithm is exponential. Graphs are a nice visual representation of friendships but to compute the 2-friends of the hundreds of students required using a different representation called an adjacency matrix. def bfs (graph, start): """ Implementation of Breadth-First-Search (BFS) using adjacency matrix. If the graph is undirected, the adjacency matrix will be symmetric. Trainer explains one program and the students has to write the next programs with some extension of requirement. Graphs and Graph Algorithms. Matrix as Graph * Leda Graph * Stanford GraphBase; Implicit Graphs Multi-dimensional grid graph. In this article, you will learn with the help of examples the BFS algorithm, BFS pseudocode and the code of the breadth first search algorithm with implementation in C++, C, Java and Python programs. /** Code for https://journaldev. Use a set to cache the nodes that have been visited. Adjacency Matrix: Adjacency Matrix is a 2D array of size V x V where V is the number of vertices in a graph. class Solution (object): def __init__ (self): self. Also, a Depth First Search will tell us if two nodes are reachable or not. Demaine and C. The following Python code represents a graph using the edge list data structure. the algorithm finds the shortest path between source node and every other node. I am using an ArrayList for storing the vertex which is a letter label. From WikiPedia: "Breadth-first search (BFS) is an algorithm for traversing or searching tree or graph data structures. In mathematics and computer science, an adjacency matrix is a means of representing which vertices (or nodes) of a graph are adjacent to which other vertices. the maximum degree and the adjacency matrix of the graph by calling the functions vcount(), Breadth-first search (BFS) from a. * Graphs in Java [/graphs-in-java] * Representing Graphs in Code. The graph internal data structures are based on an adjacency list representation and implemented using Python dictionary datastructures. printMat: this function can be used to aid with debugging. The algorithm starts at the root (top) node of a tree and goes as far as it can down a given branch (path), then backtracks until it finds an unexplored path, and then explores it. The execution time of this algorithm is very slow because the time complexity of this algorithm is exponential. Dijkstra(G,s) finds all shortest paths from s to each other vertex in the graph, and shortestPath(G,s,t) uses Dijkstra to find the shortest path from s to t. Thus, breadth-first search spends O (V + E) O(V+E) O (V + E) O, left parenthesis, V, plus, E, right parenthesis time visiting vertices. The typical Adjacency matrix has 0's along the diagonal, representing that there is no self-loop. Remember, that we now to talk about a specific implementation, and, because we need to understand how this operations are going to be performed. Leiserson. 0 1 0 2 0 3 2 4. Let us learn how to implement Dijkstra’s Algorithm in C programming using Adjacency Matrix. DFS search starts from root node then traversal into left child node and continues, if item found it stops other wise it continues. Adjacency list. Generic graph. It traverses the graph by first checking the current node and then expanding it by adding its successors to the next level. Our aim is to traverse the graph by using the Breadth-First Search Algorithm. The matrix element is set to 1 when there is an edge present between the vertices. How can I register for the course?. ZigZag Conversion. WhileQ6= ∅do. Breadth First Search is graph traversal algorithm which has many applications in most of the algorithms. As its name suggests, it first explores the depth of the graph before the breadth i. Breadth First Search Analysis. e S, 0 > in a DICTIONARY [Pyt. Algorithm 1: BFS. shortest path. Use MathJax to format equations. Description: This tutorial demonstrate how to create a graph using adjacency list and perform DFS and BFS. This ensures that iterating through the neighbours of a vertex is still efficient in sparse graphs (as with adjacency lists) while at the same time checking for adjacency is expected constant-time (as with the adjacency matrix). The representation I chose will ressult in a very slow algorithm You can get a faster algorithm using adjacency list representation. printMat: this function can be used to aid with debugging. It traverses the graph by first checking the current node and then expanding it by adding its successors to the next level. Adjacency Matrix. Learned Python during September 2017. Implementation Level – Java & Scala Collections Framework. Each vertex (except the starting vertex) is discovered during the processing of one other vertex, so this defines the breadth-first search tree. Toeplitz Matrix. First, you'll dive into understanding the pros and cons of adjacency matrices, adjacency lists, adjacency sets, and know when you would choose one data structure over another. We will discuss two of them: adjacency matrix and adjacency list. Adjacency Matrix; Adjacency List; An adjacency matrix is a square matrix used to represent a finite graph. The major difference would be that instead of a simple queue used in BFS, we will use open list to store the neighboring reachable cells from the current node. Related Course: Python Programming Bootcamp: Go from zero to hero; Binary tree A binary tree is a data structure where every node has at most two children (left and right child). The first line in that file will be a single integer v. Typically, the following structure is used to represent an edge. Now, we come to the code part of the Breadth First Search, in C. Clash Royale CLAN TAG #URR8PPP. This article analyzes the adjacency matrix used for storing node-link information in an array. #' Here, we use the union-find algorithm #' #' Note: Python version takes 1. Advantages of BFS. – adjacency matrix – adjacency lists – Python: dict of dicts • Basic operations: traversals – breadth-first search – depth-first search 4/18/12 S. CodeProject, 503-250 Ferrand Drive Toronto Ontario, M3C 3G8 Canada +1 416-849-8900 x 100. There are two ways to traverse a graph: Depth First traversal, commonly called DFS and Breadth First traversal, commonly called as BFS. Leiserson. This ensures that iterating through the neighbours of a vertex is still efficient in sparse graphs (as with adjacency lists) while at the same time checking for adjacency is expected constant-time (as with the adjacency matrix). Toeplitz Matrix. Matrix Multiplication Calculator Here you can perform matrix multiplication with complex numbers online for free. The adjacency matrix representation is best suited for dense graphs, graphs in which the number of edges is close to the maximal. Demaine and C. Undirected Graph 5. Comparison: Adjacency list vs adjacency matrix To compare the two ways of representing edges, we will consider both the amount of space used, and the time required for some standard operations. 82 Leetcode Problem#1030. Breadth first search in java using Adjacency matrix and adjacency matrix (1) career (1) cluster of elements in array (1) coding (1) Combinations and Permutations (1) consecutive elements in array (1) Contacts problem using TRIE (1) correct equation (1) DAG (1) defining abstract methods in enum (1) defining methods in enum (1) Depth first search. md file in your assignments repository:. adjacency matrix. The algorithm does this until the entire graph has been explored. Both DFS and BFS can be used to solve this problem. Directed graph consider the direction of the connection between two nodes. In case a weight function w : E R is given, then a ij = w v i,v j. Advanced Data Structures and Algorithms in Java using Data Structures/Algorithms/with Java Algorithms/Design/Analysis 4. Depth-First Search and Breadth-First Search in Python 05 Mar 2014. The Basic Network Diagram is a good choice when you want to map out a simple network. In this matrix in each side V vertices are marked. There are quite a few ways to represent a graph, the most common two are adjacency matrix and adjacency list. We'll use this instance to explain graphs. Follow 116 views (last 30 days) muhammad ismat on 29 Jul 2015. We will start with one node and we will explore all the nodes (neighbor nodes) in the same level. Code Review Stack Exchange is a question and answer site for peer programmer code reviews. Adjacency Matrix Representation. BFS uses a queue data structure which is a 'First in, First Out' or FIFO data structure. Breadth First Search (BFS) Breadth First Search is one of the most simple graph algorithms. Depth-First Search and Breadth-First Search in Python 05 Mar 2014. cpp demonstrates using the BGL Breadth-first search algorithm on the graph from Figure 6. loops are not allowed in simple graphs. See Also bfs_visitor and depth_first_search() Notes. Actually, the path that you get back from breadth-first search is the path from the source to the given vertex that uses the fewest number of edges. Adjacency Matrix. In case a weight function w : E R is given, then a ij = w v i,v j. Look back to the previous lesson to see our abstract base class Graph. Breadth-first search (BFS) is an algorithm for traversing or searching tree or graph data structures. The book and accompanying source code are free ( libre and gratis ) and are released under a Creative Commons Attribution License. Learn how to code the BFS breadth first search graph traversal algorithm in Python in this tutorial. One way to represent graphs is through adjacency matrices. Compsci 201 Graphs, APTS, and More Part 1 of 5 4/17/2020 Compsci 201, Spring 2020 1 Susan Rodger April 17, 2020 W is for … • World Wide Web • Invented in 1989 – Sir Tim Berners Lee. Text and Reference. Depth-First Search and Breadth-First Search in Python 05 Mar 2014. Use the Backtracking algorithm for the m-Coloring problem (Algorithm 5. Due to the fact that many things can be represented as graphs, graph traversal has become a common task, especially used in data science and machine learning. Design and analysis of algorithms are a fundamental topic in computer science and engineering education. Undirected graphs Adjacency lists BFS DFS Euler tour 2 Undirected Graphs GRAPH. Breadth First Search Analysis. So after initialisation this list of possible paths only has one element, a list containing the current nodes index: <<555>> This list is then expanded as follows: For each element in the list: Take the tail of the list as the current node Check for connections from this node to other nodes (using the adjacency matrix) If there is a connection. loops are not allowed in simple graphs. A shortest path from vertex s to vertex t is a directed path from s to t with the property that no other such path has a lower weight. Coming back to our BFS discussion, the level of each vertex is stored in a separate array and so is the case for parent of each vertex. Objectives; 7. Depth-first search (DFS) is an algorithm for searching a graph or tree data structure. Compsci 201 Graphs, APTS, and More Part 1 of 5 4/17/2020 Compsci 201, Spring 2020 1 Susan Rodger April 17, 2020. Not a member of Pastebin yet? Sign Up, it unlocks many cool features!. This content is a collaboration of Dartmouth Computer Science professors Thomas Cormen and Devin Balkcom , plus the Khan Academy computing curriculum team. A lot of problems in real life are modeled as graphs, and we need to be able to represent those graphs in our code. OK, I Understand. This module uses graphs which are stored in a matrix format. The breadth_first_search() function can be extended with user-defined actions that will be called a certain event points. explored = set() self. Adjacency matrix representation. Python - [Graph] Adjacency Matrix. Adjacency lists are the right data structure for most applications of graphs. I am trying to create a maze-solving algorithm. Iterator Adaptors adjacency_iterator; inv_adjacency_iterator. finding the shortest path in a unweighted graph. Breadth First Search Practise Question. The Adjacency Matrix. We use the same Adjacency List that we used in our discussion of Graph Theory Basics. add in self-loops for all vertices), then you will still have a real symmetric matrix that is diagnoalizable. Assume all four edges of the grid are all surrounded by water. , it traverses along the increasing depth and upon reaching the end, it backtracks to the node from which it was started and then do the same with the sibling node. See Also bfs_visitor and depth_first_search() Notes. Returns the adjacency matrix of a graph as scipy csr matrix. Regardless of which way edges are represented, O(N) space will be needed to store information about the nodes (the space for the node objects themselves. Breadth First Search Utilizes the queue data structure as opposed to the stack that Depth First Search uses. Adjacency Matrix. The output is. Some Applications of BFS. 2 paths between vertices. to_dict_of_dicts which will return a dictionary-of-dictionaries format that can be addressed as a sparse matrix. Finding the longest simple path in general is NP-Hard. Breadth First Search Analysis. Adjacency matrix for undirected graph is always symmetric. Then, pick an. Time is mean of 16 BFS runs from different starting vertices. 8s w/out networkx and 54ms w/ networkx w/ sample. Adjacency Matrix is also used to represent weighted graphs. For undirected graphs, the matrix is symmetric since an edge {u, v} can be taken in either direction. Visit Stack Exchange. Depth-first search visits every vertex in the graph and checks every edge its edge. BFS Breadth First Search. BFS uses a queue data structure which is a 'First in, First Out' or FIFO data structure. In this matrix in each side V vertices are marked. Like in the example above, for the first code the loop will run n number of times, so the time complexity will be n atleast and as the value of n will increase the time taken will also increase. In case a weight function w : E R is given, then a ij = w v i,v j. When we are going to solve the maze from adjacency matrix, we have to again deal with BFS or DFS. Here is the source code of the C++ program to display the breadth first method of traversing nodes in a graph along with a display of the start and end time of a visited node. This can easily be shown by reducing from the Hamiltonian Cycle problem. The actions must be provided in the form of a visitor object, that is, an object who's type meets the requirements for a BFS Visitor. (Here a missing edge is represented by ∞. It is ignored for directed graphs. Now, we will do a regular Breadth first search on the graph. Breadth First Search Practise Question. In this post, we will see how to implement depth-first search(DFS) in java. Also supports colors for edges and vertices, plus depth-first-search and check for Eulerian characteristics. Use a set to cache the nodes that have been visited. This queue stores all the nodes that we have to explore and each time a node is explored it is added to our set of visited nodes. An adjacency matrix is a matrix of size n x n where n is the number of vertices in the graph. (Here a missing edge is represented by ∞. Initially, all the vertices are set to initial state. If the corresponding optional Python packages are installed the data can also be a NumPy matrix or 2d ndarray, a SciPy sparse matrix, or a PyGraphviz gra. We define a class thee which. Depth-First Search and Breadth-First Search in Python 05 Mar 2014. And actually, breadth-first search solves another problem that often we want to solve called the shortest path problem. adjacency list. From a cell you can either traverse to left, right, up or down. Algorithm for Depth First Search using Stack and Adjacency Matrix. Directed Graph. Directed graph consider the direction of the connection between two nodes. 1 Graph Traversals - BFS & DFS -Breadth First Search and Depth First Search - Duration. 1-6) Most graph algorithms that take an adjacency-matrix repre-sentation as input require time O(n2), but there are some exceptions. Breadth First Search Utilizes the queue data structure as opposed to the stack that Depth First Search uses. I would suggest Algorithm class to anyone who wants to learn Python with hands on approach. Let us learn how to implement Dijkstra’s Algorithm in C programming using Adjacency Matrix. Depth-first search (DFS) is an algorithm for searching a graph or tree data structure. The adjacency matrix of the graph depicted above is A = 8-1 010001 101110 010100 011010 010101 100010. 1 Edge List Structure 14. From WikiPedia: "Breadth-first search (BFS) is an algorithm for traversing or searching tree or graph data structures. Consider the below binary tree (which is a graph). For nodes i and j which are not connected, the value depends on the representation:. Overview of data types and objects. The output is. Depth-first search or DFS is also a searching technique like BFS. Graph theory and in particular the graph ADT (abstract data-type) is widely explored and implemented in the field of Computer Science and Mathematics. Breadth-first searching (BFS) is an algorithm for traversing or searching a path in a graph. Depth-first search visits every vertex in the graph and checks every edge its edge. Adjacency matrix Adjacency list (with crosslinks) Adj 4 1 124 2 4 13 3 4 1 1 1 0 0 0 1 1 410 3 2 1 3 1 23 4 Figure 24: Adjacency matrix and adjacency list for graphs. The concept was ported from mathematics and appropriated for the needs of computer science. Breadth-First Search algorithm follows a simple, level-based approach to solve a problem. Depth First Search is an algorithm used to search the Tree or Graph. BFS search starts from root node then traversal into next level of graph or tree and continues, if item found it stops other wise it continues. This technique uses the queue data structure to store the vertices or nodes and also to determine which vertex/node should be taken up. Grappghs and Matrix Algebra • can treat adjacency matrix as matrix • e. mmio - adjacency matrix of the graph in MMIO format _inc. Let the 2D array be adj[][], a slot adj[i][j] = 1 indicates that there is an edge from vertex i to vertex j. An interactive version of Problem Solving with Algorithms and Data Structures using Python. Depth-First Search and Breadth-First Search in Python 05 Mar 2014. Design and analysis of algorithms are a fundamental topic in computer science and engineering education. It starts at the tree root (or some arbitrary node of a graph, sometimes referred to as a 'search key') and explores the neighbor nodes first, before moving to the next level neighbors". adjacency matrix. Undirected Graphs Undirected graph. Breadth first traversal or Breadth first Search is a recursive algorithm for searching all the vertices of a graph or tree data structure. Adding a Vertex. Coming back to our BFS discussion, the level of each vertex is stored in a separate array and so is the case for parent of each vertex. We will start with one node and we will explore all the nodes (neighbor nodes) in the same level. Problem 2(CLRS 22. in more than 20 kms. #' #' In the Python-BCT, networkx is used to do the computation efficiently. A simple implementation in C is given below. Use a set to cache the nodes that have been visited. Data on edges and vertices must be stored externally. Consider the same undirected graph from an adjacency matrix. To get the minimum weight edge, we use min heap as a priority queue. The adjacency matrix representation is attractive for its simplicity and for the fast random access to edge information in the graph it provides. In this course, Working with Graph Algorithms in Python, you'll learn different kinds of graphs, their use cases, and how they're represented in code. AdjMatrixGraph. Let the 2D array be adj[][], a slot adj[i][j] = 1 indicates that there is an edge from vertex i to vertex j.
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# IEEE Transactions on Nanotechnology

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Displaying Results 1 - 25 of 51
• ### Performance Evaluation of UTBB FDSOI, FinFETs, and SOI FinFETs via Mechanical Stresses and Body Biasing

Publication Year: 2017, Page(s): 1
| | PDF (761 KB)

FinFETs and ultra-thin body and buried oxide fully depleted silicon on insulator (UTBB-FDSOI) are the main transistors currently used in advanced integrated circuits (ICs). The tunable electrical properties via back-biasing facilitate the threshold voltage adjustment and enable IC designers to achieve a highly efficient and low-power-consuming operation. This study compares the modulation rate bef... View full abstract»

• ### Continuous Fabrication of Highly Conductive and Transparent Ag Mesh Electrodes for Flexible Electronics

Publication Year: 2017, Page(s): 1
| | PDF (546 KB)

Flexible transparent conductive electrodes are essential components for flexible electronics and more functions are combined in such components for miniaturization and design flexibility. The embedded metal mesh, due to the merits of good transparency, conductivity and flexibility, is regarded as a promising candidate for transparent conductive electrodes. This study reports a continuous fabricati... View full abstract»

• ### Design and Simulation of a 128kb Embedded Non-Volatile Memory based on a Hybrid RRAM (HfO2) / 28nm FDSOI CMOS Technology

Publication Year: 2017, Page(s): 1
| | PDF (1677 KB)

Emerging Non-Volatile Memories (NVM) based on resistive switching mechanism such as RRAM are under intense R&D investigation by both academics and industries. They provide high write/read speed, low power and good endurance (e.g. >1012) beyond mainstream NVMs, enabling them to be a good candidate for Flash replacement in Micro-Controller Unit (MCU). This replacement could significantly decrease th... View full abstract»

• ### The effects of water on the dielectric properties of aluminum based nanocomposites

Publication Year: 2017, Page(s): 1
| | PDF (2650 KB)

A series of polyethylene nanocomposites was prepared utilizing aluminum nitride or alumina nano-powders with comparable morphologies. These were subsequently subjected to different conditioning regimes, namely prolonged storage in vacuum, the ambient laboratory environment or in water. The effect of filler loading and conditioning (i.e. water content) on their morphological and dielectric properti... View full abstract»

• ### Synthesis of CIS Quantum Dots in Low Temperature Regime: Effects of Precursor Composition and Temperature Ramps

Publication Year: 2017, Page(s): 1
| | PDF (1285 KB)

Copper Indium Sulfide (CIS) – based quantum dots (QDs) have strong potential for future large-scale applications in photovoltaic, display, and optoelectronic sectors, partly due to their minimal toxicity. CIS QDs are usually grown at temperatures over 200°C. In this work, we present a gram-scale, non-injection synthesis of CIS-based QDs in a low temperature regime and report, through... View full abstract»

• ### 3D nano-acoustic Bragg reflectors for CMOS embedded NEMS

Publication Year: 2017, Page(s): 1
| | PDF (1210 KB)

Integration of CMOS electronic circuits and electromechanical resonators has been pursued for a long time by many different research groups and even foundries. This would improve the overall performance of electromechanical oscillators and sensors. However, the postprocessing on the CMOS substrates that is necessary to attain this integration increases the production cost so much that it becomes n... View full abstract»

• ### Skybridge-3D-CMOS: A Fine-Grained 3D CMOS Integrated Circuit Technology

Publication Year: 2017, Page(s): 1
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Parallel and monolithic 3D integration directions realize 3D integrated circuits (ICs) by utilizing layer-by-layer implementations, with each functional layer being composed in 2D. In contrast, vertically-composed 3D CMOS has eluded us likely due to the seemingly insurmountable requirement of highly customized complex routing and regional 3D doping to form and connect CMOS pull-up and pull-down ne... View full abstract»

• ### Aluminum-doped Zinc Oxide Transparent Electrode Prepared by Atomic Layer Deposition for Organic Light Emitting Devices

Publication Year: 2017, Page(s): 1
| | PDF (931 KB)

Transparent conductive aluminum-doped zinc oxide (AZO) films are being introduced as alternatives to indium tin oxide (ITO) films, because they do not contain indium, which is expensive and toxic. In this study, the structural, electrical, and optical properties of AZO electrodes fabricated by atomic layer deposition (ALD) at a low temperature of 150 ℃ were examined by X-ray photoemission sp... View full abstract»

• ### Synthesis of RuO $_{2}$ Nanowires by Alkali-Assisted Oxidation of Ruthenium in Plasma Afterglow at Atmospheric Pressure

Publication Year: 2017, Page(s): 1
| | PDF (2014 KB) |  Media

RuO $_{2}$ nanowires are synthesized by oxidation of ruthenium thanks to a micro-post-discharge at atmospheric pressure. However, RuO $_{2}$ nanowires form islands. The growth mechanism depending on surface defects, the surface density of the nanowires is limited. We report on the influence of two alkali salts, NaCl and KCl, deposited a... View full abstract»

• ### The Effect of Ultrasonic Dispersion on the Surface Chemistry of Carbon Nanotubes in the Jeffamine D-230 Polyetheramine Medium

Publication Year: 2017, Page(s): 1
| | PDF (930 KB)

This paper studies changes in the surface chemistry of carbon nanotubes (CNTs) where they are under ultrasonication process in Jeffamine D-230 polyetheramine medium. Jeffamine is used as a curing agent in the nanocomposite manufacturing process. In the nanocomposite technology, ultrasonication process is employed as a method for dispersion of CNTs in a suspension. This research tries to investigat... View full abstract»

• ### Fabrication of planar back end of line compatible HfOx Complementary Resistive Switches

Publication Year: 2017, Page(s): 1
| | PDF (2132 KB)

This paper presents the fabrication, together with morphological and electrical characterizations of complementary resistive switches using the nanodamascene process. The asfabricated devices are fully embedded in an insulating oxide, opening the way for further process steps such as 3D monolithic integration. Complementary resistive switches electrical performance are consistent with resistive ra... View full abstract»

• ### Circuit Modeling of Waveguide Grating Nanostructures in Ultrathin Solar Cells

Publication Year: 2017, Page(s): 1
| | PDF (1502 KB)

In this paper, a circuit modeling is used to investigate the effects of waveguide grating nanostructures on the performance of ultrathin solar cells. The proposed method is based on transmission line equivalent circuit (TLEC) and it is identified for both of the transverse electric (TE) and transverse magnetic (TM) polarizations. Under assumption of weakcoupling condition, this method can effectiv... View full abstract»

• ### STEM: A Scheme for Two-phase Evaluation of Majority Logic

Publication Year: 2017, Page(s): 1
| | PDF (5581 KB)

The switching time of a magnet in a spin current based majority gate depends on the input vector combination, and this often restricts the speed of majority-based circuits. To address this issue, this work proposes a novel two-phase scheme to implement majority logic and evaluates it on an all-spin logic (ASL) majority-based logic structures. In Phase 1, the output is initialized to a preset value... View full abstract»

• ### Top-down technology for reconfigurable nanowire FETs with symmetric on-currents

Publication Year: 2017, Page(s): 1
| | PDF (1517 KB)

In this paper a technology for top-down single-gated Schottky barrier transistor is presented exhibiting the highest symmetry of on-currents for n- and p-conductance of such SOI based devices. The symmetry in the current-voltagecharacteristics is a mandatory requirement to realize circuits with reconfigurable nanowire field effect transistors (RFETs) whose channel can be switched electrostatically... View full abstract»

• ### Crystallinity of Silicon-Shells Deposited onto Germanium and Silicon Nanowires for Core-Shell Nanostructures and Nanotubes

Publication Year: 2017, Page(s): 1
| | PDF (645 KB)

Core-shell nanowires are an essential component of numerous nanoscale device concepts. In this work, germanium and silicon nanowires were synthesized bottom-up using the vapor-liquid-solid technique and successively modified with a silicon shell. The shell synthesis was studied with focus to the crystallinity but includes as well the electrical characteristics of n- and p-doped radial core-shell n... View full abstract»

• ### Numerical Modeling of Magnetic Nanoparticle and Carrier Fluid Interactions under Static and Double-Shear Flows

Publication Year: 2017, Page(s): 1
| | PDF (1161 KB)

Magnetic nanoparticles are widely utilized in smart materials; the most well-known application being magnetorheological (MR) fluids. In this paper, a comprehensive numerical model of magnetic nanoparticles and the carrier fluid interactions is presented. The soft sphere model approach is adopted to simulate the nanoparticle interactions at a coarse molecular level, with the consideration of both c... View full abstract»

• ### Ultrahigh Storage Densities via the Scaling of Patterned Probe Phase-Change Memories

Publication Year: 2017, Page(s): 1
| | PDF (722 KB)

The scaling potential of patterned probe phase-change memory (PP-PCM) cells is investigated, down to single-nanometer dimensions, using physically realistic simulations that combine electro-thermal modelling with a Gillespie Cellular Automata (GCA) phase-change model. For this study, a trilayer TiN/Ge $_2$ Sb $_2$ Te ... View full abstract»

• ### The unexpected complexity of filling double-wall carbon nanotubes with nickel (and iodine) 1D nanocrystals

Publication Year: 2017, Page(s): 1
| | PDF (1688 KB)

A variety of iodine-based 1D nanocrystals were introduced into double-wall carbon nanotubes (DWCNTs) using the molten phase method, as an intermediate step for ultimately obtaining encapsulated metal nanowires. Based on high-resolution transmission electron microscopy (HRTEM) observations using different imaging modes (bright field, dark field, scanning TEM) and associated analytical tools (electr... View full abstract»

• ### Interfacial Tuning for Detection of Cortisol in Sweat using ZnO Thin Films towards Wearable Biosensing

Publication Year: 2017, Page(s): 1
| | PDF (1031 KB)

We have demonstrated the detection of stress hormone cortisol from sweat using a flexible biosensing platform. Sweat based detection faces many challenges such as stability of electrodes, sensitivity and specificity. The surface states of zinc oxide (ZnO) can be leveraged for immobilizing various linker molecules for ultra-specific detection of biomolecules. In this study, we have used thiol based... View full abstract»

• ### Biomaterial gelatin film based crossbar structure resistive switching devices

Publication Year: 2017, Page(s): 1
| | PDF (966 KB)

Crossbar structural resistive switching devices (memristors) are fabricated using biomaterial gelatin film as the dielectric layer. The performance of the devices and the effects of gelatin film thickness and baking temperature are investigated. Results show that the optimal gelatin film thickness for the memristors is ~80 nm and baking temperature ~105 oC. The optimized memristors show a bipolar ... View full abstract»

• ### Performance enhancement in n-channel organic field-effect transistors using ferroelectric material as a gate dielectric

Publication Year: 2017, Page(s): 1
| | PDF (2475 KB)

Organic field-effect transistors were elaborated using N,N'-ditridecylperylene-3,4,9,10-tetracarboxylic diimide (PTCDI-C $_{13}$ ) as transport electron material and two polymeric insulators were used as gate dielectric : polymethyl methacrylate (PMMA), a low-k material widely used in OFETs and poly(vinylidenefluoride-co-trifluoroethylene) (P(VDF-TrFE)), a ferroelectr... View full abstract»

• ### Responsivity Enhancement of Metal-Insulator-Semiconductor Photodetectors on Silicon-On-Insulator Substrates by Plasmonic Nanoantennas

Publication Year: 2017, Page(s): 1
| | PDF (721 KB)

We report metal-insulator-semiconductor photodetectors fabricated on a silicon-on-insulator substrate, exhibiting an enhanced responsivity in the near-infrared due to the incorporation of Au-nanoantennas at the optical input port. The optimal antenna design and the photoresponse enhancements have been calculated using detailed finite-difference time-domain simulations. These nanoantennas modify th... View full abstract»

• ### Simulated Measurements of the Magnetic Behavior of New Dual-Mode Nanosized Contrast Agents

Publication Year: 2017, Page(s): 1
| | PDF (1582 KB)

Aim of this work was to perform simulated measurements of the magnetic behavior of a novel class of bimodal nanosized contrast agents (CAs), made of a silica core covered by smaller superparamagnetic nanoparticles (NPs) and designed to be detected through both ultrasound and magnetic resonance imaging (MRI), in order to compare their performance in terms of MRI signal enhancement with that of the ... View full abstract»

• ### Control of growth modes by carbon mediation in formation of Ge quantum dots on Si(100)

Publication Year: 2017, Page(s): 1
| | PDF (584 KB)

Control and mechanism analysis of a Ge quantum dot (QD) formation on a Si(100) substrate by using carbon (C)-mediated c(4×4) surface reconstruction (SR) and solid-phase epitaxy (SPE) methods were demonstrated. The Si surface was reconstructed via the formation of C-Si bonds before Ge deposition in the SR method, while the QDs were formed by annealing of an amorphous Ge/C/Si heterostructure ... View full abstract»

• ### Development of Dithienosilole-pyridalthiadiazole-based Copolymer as an Electron Donor in Organic Photovoltaic Cells

Publication Year: 2017, Page(s): 1
| | PDF (2008 KB) |  Media

The effect of nitrogen insertion in a benzothiadiazole (BT) moiety was investigated via the synthesis of a novel copolymer based on dithienosilole (DTS) and pyridalthiadiazole (PT), the heterocyclic counterpart. Stille cross coupling of the respectively electron rich and electron poor units yields poly[(4,4’-didodecyldithieno[3,2-b:2’,3’-d]silole-2,6-diyl)-alt-(2,1,3-pyridalth... View full abstract»

## Aims & Scope

The IEEE Transactions on Nanotechnology is devoted to the publication of manuscripts of archival value in the general area of nanotechnology, which is rapidly emerging as one of the fastest growing and most promising new technological developments for the next generation and beyond.

Full Aims & Scope

## Meet Our Editors

Editor-in-Chief
Fabrizio Lombardi
Dept. of ECE
Northeastern Univ.

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Example 3. The length of an arc is 35 m. If the radius of the circle is 14 m, find the angle subtended by the arc. Arc, Sagitta, and Diameter of a Circle. In the figure, ,a part of the circumference, is called ko (arc), the segment AB is called gen (chord), and the segment PR is ya (sagitta).The diameter PQ is called kei in Japanese. When we draw a chord for the arc PB and a sagitta for the chord, and continue to repeat this process with shorter chords, the shape derived by connecting these chords. Example 12: The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm 3 of wood has a mass of 0.6 g. Solution: Since, inner diameter = 24 cm ⇒ inner radius (r) = $$\frac{{24}}{2}cm$$ = 12 cm Since, outer diameter = 28 cm. Use Algebra to Calculate the Apothem & the Diameter of a Circular Saw Blade from its Arc Marks. It is possible to calculate this number using simple math or using trigonometry. Some carpenters and wood or old house researchers remember their algebra class. I do. Thank you Mrs. Revere. Calculate the Diameter from Arc Width & Height: find the Apothem. Find the Radius of a Circle from Arc Length. By Donna Blankenbecler. 9/8/15 5:00 AM. The video provides two example problems for finding the radius of a circle given the arc length. Problem one finds the radius given radians, and the second problem uses degrees. Common Core Standard: HSF-TF.A.1. Take the circumference divided by pi to find the diameter and divide the diameter by two to find the radius. How much fluid will fill a 3.5 inch by 12 inch cylinder? It is not possible to answer the question without knowing. Sep 18, 2012 · How much fluid will fill a 3.5 inch by 12 inch cylinder? It is not possible to answer the question without knowing which of the two given values is the height and whether the other number is the radius, diameter or circumference.It is not possible to answer the question without knowing which of the two given values is the height and whether the other number is the radius, diameter or .... Because the radian is based on the pure idea of "the radius being laid along the circumference", it often gives simple and natural results when used in mathematics. For example, look at the sine function for very small values: x (radians) 1: 0.1: 0.01: 0.001: sin(x) 0.8414710: 0.0998334:. 1. Set up the formula for arc length. The formula is , where equals the radius of the circle and equals the measurement of the arc's central angle, in degrees. [2] 2. Plug the length of the circle's radius into the formula. This information should be. 3. The sum of all central angle is 360°. 4. Jul 01, 2022 · Circumference of a Circle Formula The circumference of a circle is pi times its diameter. Circumference = π * Diameter What is the circumference of a circle? The circumference of a circle is pi times its diameter. The diameter of a circle is the distance from one edge to the other, passing through the center. It is twice the radius.. Circumference = pi x 2 x radius Area = pi x radius squared The radius squared is a square with units of square mm or square meters. pi scales up this square by just over 3 times. This square has an appropriately the same area as the circle. The diameter is equal to two times the radius of a circle. If we draw a straight line from the centre to any point on the circumference of a circle, it is called a radius. We can use the formula '2 * Pi * radius' to calculate the circumference of a circle, where 'radius' is the radius for that circle. So, we need only the value of the. Here, we will talk about three formulas of calculating the circumference of a circle . When the radius is given-The formula used when the radius of a circle is given is: C=2?r; Here, C is the circumference and r is the radius given. Lets learn this using an example-Calculate the circumference of circle with radius 14cm. Mar 5, 2014. I am doing an assignment that is asking for the user to put in the radius of a circle and the program figures out the area, diameter and circumference. It is using 2 different java programs to accomplish this. One with the info on how to get area, diameter and circumference and one is the demo that runs the program. The Volume of a Cylinder from the Height and Circumference calculator computes the volume of a right circular cylinder from the height (h) and circumference (c) of the base (see diagram). Practice Problem: Find the area and circumference of a circle with a diameter of 4 inches. Solution: One of the first rules of solving these types of problems involving circles is to carefully note whether we are dealing with the radius or the diameter. In this problem, the circle is described using the diameter, which is 4 inches. how to find diameter from circumference without radius von | Jul 2, 2022 | audible widget iphone | ludovico einaudi i giorni sheet music | Jul 2.

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text: Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 24 (2014), No. 1, 259--305Copyright Heldermann Verlag 2014 Bounded Conjugators for Real Hyperbolic and Unipotent Elements in Semisimple Lie Groups Andrew Sale IRMAR, Université de Rennes 1, 263 avenue du Général Leclerc, CS 74205, 35042 Rennes, France andrew.sale@some.oxon.org [Abstract-pdf] Let $G$ be a real semisimple Lie group with trivial centre and no compact factors. Given a conjugate pair of either real hyperbolic elements or unipotent elements $a$ and $b$ in $G$ we find a conjugating element $g \in G$ such that $d_G(1,g) \leq L(d_G(1,u)+d_G(1,v))$, where $L$ is a positive constant which will depend on some property of $a$ and $b$ (when $a,b$ are unipotent we require that the Lie algebra of $G$ is split). For the vast majority of such elements however, $L$ can be assumed to be a uniform constant. Keywords: Geometric group theory, conjugacy problem, semisimple Lie groups. MSC: 20F65, 20F10, 22E46, 53C35 [ Fulltext-pdf  (688  KB)] for subscribers only.


text:
This tutorial is hosted at davekleinschmidt.com/r-packages/.

# TL;DR

devtools makes it surprisingly easy to make a data package. There are lots of good reasons why you should (reproducibility, convenience, sharing, documenting).

1. devtools::create() the package skeleton
2. devtools::use_data_raw() and move raw data into data-raw/
3. Put data preprocessing script into data-raw/, which reads in raw data and at calls devtools::use_data(<processed data>) to save .RData formatted data files in data/.
4. Load package with devtools::load_all() to access data
5. Or install with devtools::install() and then library(<package name>).

The Github repository includes the Rmd source, and an example of how I’ve refactored an analysis along these lines, starting from an RMarkdown + CSV and ending up with an RMarkdown + a package.

If you want a sense of how this might work IRL, the example is based on this data package, which I’ve used for a couple of papers/presentations:

## Motivation

An R package is the basic unit of reproducible code. There are lots of reasons you might want to make one:

1. As a “personal library” of functions that you use across lots of projects (by copying and pasting).
2. For ctual software that you want to share with others so they can use it, too (things like lme4).
3. To hold data from your experiments in a way that’s easy to use, easy to share, and reproducibly tracks how the data was processed.

This guide focuses on the third use case. There are lots of good guides for the first case (Hilary Parker’s is the classic), and if you’re in the second camp you probably already know what you’re doing (and if not, Hadley Wickham’s R packages book is an excellent and thorough guide).

We’ll start from what used to be my default workflow (raw data file + R scripts to process and make figures etc.), and end up with an R package that allows you to both easily access pre-processed data and tracks how that data was generated from the raw form.

## Preliminaries

1. Install Rstudio.
2. Install devtools
3. Have some data you want to package, plus code to read it into R and process it into a useable form (in a .R or .Rmd file, etc.)

## What is a package?

To a first approximation, a minimal package is

• a directory with
• some R code in R/ and
• some metadata in DESCRIPTION (what the package is called, who made it, what it does, what other packages it depends on).

When you load a package with library or require, R looks in the package directory and runs the stuff.R files in R/.

## Packages can contain data

If there’s a data/ subdirectory in the package directory, R will also make any data files1 there available. In R, the dataset has the same name as the data file. There are (at least) three ways to access data from a package:

### Using package namespace

ggplot2::diamonds %>% head()
## Source: local data frame [6 x 10]
##
##   carat       cut  color clarity depth table price     x     y     z
##   (dbl)    (fctr) (fctr)  (fctr) (dbl) (dbl) (int) (dbl) (dbl) (dbl)
## 1  0.23     Ideal      E     SI2  61.5    55   326  3.95  3.98  2.43
## 2  0.21   Premium      E     SI1  59.8    61   326  3.89  3.84  2.31
## 3  0.23      Good      E     VS1  56.9    65   327  4.05  4.07  2.31
## 4  0.29   Premium      I     VS2  62.4    58   334  4.20  4.23  2.63
## 5  0.31      Good      J     SI2  63.3    58   335  4.34  4.35  2.75
## 6  0.24 Very Good      J    VVS2  62.8    57   336  3.94  3.96  2.48

### With library()

Then you can refer to datasets directly

library(ggplot2)
diamonds %>% head()
## Source: local data frame [6 x 10]
##
##   carat       cut  color clarity depth table price     x     y     z
##   (dbl)    (fctr) (fctr)  (fctr) (dbl) (dbl) (int) (dbl) (dbl) (dbl)
## 1  0.23     Ideal      E     SI2  61.5    55   326  3.95  3.98  2.43
## 2  0.21   Premium      E     SI1  59.8    61   326  3.89  3.84  2.31
## 3  0.23      Good      E     VS1  56.9    65   327  4.05  4.07  2.31
## 4  0.29   Premium      I     VS2  62.4    58   334  4.20  4.23  2.63
## 5  0.31      Good      J     SI2  63.3    58   335  4.34  4.35  2.75
## 6  0.24 Very Good      J    VVS2  62.8    57   336  3.94  3.96  2.48

But they’re not added to the global environment:

ls()
## character(0)

### With data()

This puts the requested dataset into the global environment:

data("diamonds", package="ggplot2")
ls()
## [1] "diamonds"

You can also get a listing of all the datasets in a package with data(package="ggplot2")

## How do I make a package

### Create the package skeleton

#### With RStudio (the easy way)

1. New Project -> New Directory -> R Package
2. Pick the name for your package (only letters, numbers, and .), and where it’ll live locally (defaults to ~/, your home directory).
3. Check the “Create git repository” because why not.
4. Click on the DESCRIPTION file, and edit it.
5. Put your code files in the R/ subdirectory.
6. Load the package (“Build” tab, More -> Load all; or ⌘-⇧-L)

#### With devtools (the slightly less easy way)

The devtools package is the back-end that RStudio uses to set up your package. It provides a convenient set of functions for doing those steps manually if you don’t like clicking on buttons (or don’t want to use RStudio):

1. Create the package skeleton with devtools::create('~/mypackage').
2. Edit the information in DESCRIPTION.
3. Put your code in the R/ subdirectory.

#### Manually (the dangerous, masochistic way)

You probably don’t want to do this. These are the steps that devtools and RStudio automate for you.

1. Create the DESCRIPTION file in your package-to-be directory.
2. Create an R/ subdirectory and put your code in there.

### Package workflow

The workflow when using a package is slightly different than you might be used to.

#### Local workflow

If you’re just working within the package directory, the steps are simple:

1. Edit code (or add data).
2. Re-load packge with devtools::load_all() (or ⌘-⇧-L in RStudio)

#### Installed package workflow

If you’re working from an installed package (e.g. to use across multiple projects), when you edit the package code you need to build, install, and reload it:

1. Edit code (or add data).
2. Re-generate documentation and namespace: devtools::document('/path/to/pkg')
3. Install: devtools::install('/path/to/pkg').
4. Reload: devtools::reload(inst('pkg')).

Note that you only need to do this if you edit something in the package.

### Documentation and exports

By default, all the functions and variables that are created in your package are private and not added to the global environment when you attach the package with library(). The NAMESPACE file tells R which things you want to export as part of the package’s namespace. The easiest, best, and most foolproof way to generate this file is using special comments before each function/variable you want to export. For instance:

#' Short description of what this does
#'
#' Longer description of what this does. Approximately a paragraph.
#'
#' @param x The first thing
#' @param y The second thing.
#' @return The thing that comes out of this function
#'
#' @export (do export this in NAMESPACE)
a_function <- function(x,y) {
return x+y
}

Then, you run devtools::document(), which will update NAMESPACE and create help files in, e.g., man/a_function.Rd. And you can call mypackage::a_function() now, or just a_function() after library(myfunction).

See the R packages book on documentation for more information on this.

For our purposes, this isn’t strictly necessary (if you’re just doing devtools::load_all(), but it’s important to know for later if you want to share this or devtools::install() your package.

## How do I put my data in the package

1. Just move the data files (.RData, .csv, etc.) in the data/ subdirectory of your package.

### Reproducibly, with devtools (good)

The version of the data that’s worth packaging is probably not pure, raw data, but data that’s been cleaned, proccessed, summarized, or collated in some way. Just dropping pre-processed data files into your package is bad for the same reason that it’s bad to do all your data analysis directly in the console: there’s no record of what you’ve done, and there’s no reliable way to reproduce it once you close R.

The solution is the same: create a script that covers all the steps you took from beginning (loading a CSV) to end (putting the final data files in data/). By including this script in your package along with the raw data, you get the convenience of having easy, fast access to the pre-processed data and all the benefits of reproducibility.

Here’s how:

1. Create a home for your raw raw data and preprocessing scripts to live in:

devtools::use_data_raw()
## Creating data-raw/
## Next:
## * Add data creation scripts in data-raw
## * Use devtools::use_data() to add data to package
2. Move raw data into data-raw/
3. Create an R script in data-raw/ that reads in the raw data, processes it, and puts it where it belongs. Such a script might look like this:

experiment1 <-
mutate(experiment = 1)
devtools::use_data(experiment1)

This saves data/experiment1.RData in your package directory (make sure you’ve setwd() to the package directory…)

4. Run this script to actually use the data (with source() or ⌘-⇧-S in RStudio). Now when you load the package, the dataset will be available as experiment1, already processed:

devtools::load_all()
## or use data() to put it in the global environment
data("experiment1")
5. You can save as many versions of the data as you’d like. For instance, if you want to have easy access to a sumamrized version of the dataset, you can save that, too:

experiment1_summary <-
experiment1 %>%
group_by(subject, condition, block) %>%
summarise(mean_rt = mean(rt))

devtools::use_data(experiment1_summary)
6. (Optionally): commit the script in git. In my (and Hadley’s) opinion, using git to track changes in your code is always a good idea, and it’s integrated right into RStudio.

I also like to commit at least the processed data, and the raw data if it doesn’t have personally identifiable information in it. You’ll need to do this if you’re going to distribute the package over github etc. If the data files are very large, you can use something like Git Large File Storage.

7. (Optionally): Document your datasets. This works basically the same as documenting other objects, with the exception that the object you document is the name of the data set. The convention is to put these in R/data.R:

#' Data from Experiment 1
#'
#' This is data from the first experiment ever to try XYZ using Mechanical
#' Turk workers.
#'
#' @format A data frame with NNNN rows and NN variables:
#' \describe{
#'   \item{subject}{Anonymized Mechanical Turk Worker ID}
#'   \item{trial}{Trial number, from 1..NNN}
#'   ...
#' }
"experiment1"

Writing this documentation is slightly annoying, but a very good idea if you intend to share your data (and that includes with your advisor, students, labmates, or, especially, future-you)

#### A few asides

You can, of course, do all of this from the R console. But, again, for the sake of reproducibility, it’s always better to put it in a script.

These scripts doesn’t have to live in data-raw/, but that’s where you put your raw data. And you don’t want to run it every time the package is loaded, so it shouldn’t go in R/.

Even if you’re packaging raw data, there’s still a good reason to do it this way: .RData files are much faster to read from disk than text-based formats like CSV. So every time you use this data, you’re saving a little bit of time (or a lot of time if your data is even medium sized). This reduces the friction associated with re-compiling your .Rmd files (say), or creating new sessions/.Rmd files for each analysis, which in turn makes it way easier to make sure your analysis is really reproducible and self-contained.

1. Data files can be lots of things: .RData, .csv, .R, etc. See ?data.


text:
# Calculating Hausdorff dimension in higher dimensional spaces

Research paper by M. A. Sánchez-Granero, M. Fernández-Martínez

Indexed on: 30 Mar '19Published on: 28 Mar '19Published in: arXiv - Mathematics - Metric Geometry

#### Abstract

In this paper, we prove the identity $\dim_{\textrm H}(F)=d\cdot \dim_{\textrm H}(\alpha^{-1}(F))$, where $\dim_{\textrm H}$ denotes Hausdorff dimension, $F\subseteq \mathbb{R}^d$, and $\alpha:[0,1]\to [0,1]^d$ is a function whose constructive definition is addressed from the viewpoint of the powerful concept of a fractal structure. Such a result stands particularly from some other results stated in a more general setting. Thus, Hausdorff dimension of higher dimensional subsets can be calculated from Hausdorff dimension of $1-$dimensional subsets of $[0,1]$. As a consequence, Hausdorff dimension becomes available to deal with the effective calculation of the fractal dimension in applications by applying a procedure contributed by the authors in previous works. It is also worth pointing out that our results generalize both Skubalska-Rafaj\l{}owicz and Garc\'{\i}a-Mora-Redtwitz theorems.


text:
# Math Help - volume of solid

1. ## volume of solid

et R be the region in the plane bounded by the x-axis and the line x=1 and the curve y= arc tan x
determine the volume of the solid obvtained by revolving R

any help pls

2. Originally Posted by alex83
et R be the region in the plane bounded by the x-axis and the line x=1 and the curve y= arc tan x
determine the volume of the solid obvtained by revolving R

any help pls
shells ...

$V = 2\pi \int_0^1 x \cdot \arctan(x) \, dx$

washers ...

$V = \pi \int_0^{\frac{\pi}{4}} 1 - \tan^2{y} \, dy$

washers looks like it may be easier to do ...

$1 - tan^2{y} = 1 - (sec^2{y} - 1) = 2 - sec^2{y}$

3. ## change the revolving axis

thanx for ur help

if i want to change the revolving axis to x=1 how does that effect the integral limits

4. Originally Posted by alex83
thanx for ur help

if i want to change the revolving axis to x=1 how does that effect the integral limits
doesn't affect the limits of integration ... it does affects the radius of revolution.


text:
# Coverages that are not pretopologies

A coverage on a category $C$ is a collection of covering families $\{u_i \to a\}$ for each object $a$ of $C$ such that for each arrow $b\to a$ there is a covering family for $b$ which fits into a commutative square with the original covering family.

A pretopology is an example of a coverage, but much stronger, in that the weak pullbacks are required to be pullbacks, covering families need to be closed under composition, and families consisting of a single isomorphism are covering.

In order to define sheaves, it is enough to start with a coverage, and indeed there is a very useful coverage on the category $Diff$ of finite dimensional smooth manifolds consisting of good open covers. Also, given a topological space, and a basis for the topology on it, one can define a coverage which is not a pretopology using these subsets.

However, the coverage of good open covers on $Diff$ does satisfy the 'covers compose' axiom of a pretopology, but not the other two, so is not in a sense completely general. What I would like to see is examples of coverages which satisfy zero, one or two but not all of the pretopology axioms, in various combinations. And, most importantly, are not contrived finite examples, but on categories which can be considered 'geometric' (probably should be extensive, or similar), like $Ring^{op}$, $Top$, $Diff$ and so on.

-
The natural coverage arising from the local ring axioms is a pullback-stable coverage on $\textbf{CRing}^\textrm{op}$, but not a pretopology. (Every covering family is a pair of localizations, so there's no chance of satisfying the transitivity axiom.) There's an obvious pretopology containing it, which is the usual Zariski pretopology. –  Zhen Lin Mar 15 '12 at 12:29
Slight correction: the "pullbacks" in a coverage are not even weak pullbacks; they are just commutative squares. –  Mike Shulman Mar 16 '12 at 5:09
Ah, yes. Just cones, then. I'll edit. –  David Roberts Mar 17 '12 at 0:51
on schemas category coverings maked by affine open immersion that make a topologically covering too, we have the composition axiom only. –  Buschi Sergio Mar 17 '12 at 14:36


text:
Why is gravity viewed as a curvature of spacetime and not the electromagnetic force? [duplicate]

There are four known forces in the universe. Two of these forces are the force of gravity and the force of electromagnetism. The first is the result of the mass of the object that has the gravity. The second is the result of charge in both the affected particle as well as the particles that generated the electrical and magnetic fields. Since both forces operate over spacetime why isn't there a model that common to both?

There is - gauge theory, and just as the Riemann tensor is the curvature of the Levi-Civita connection on the tangent bundle of spacetime, the electromagnetic field strength is the curvature of the gauge principal connection on a $\mathrm{U}(1)$-principal bundle over spacetime.


text:
## Monday, February 18, 2008

### Tomorrow's lecture

For tomorrow, could you brush up what you know Max $k$-ary Consistent Labeling(K,L) from HW1 problem #7 (also defined in the list of problems)? Thanks!

In particular, consider the $2$-ary (also called "binary" case): the constraint hyperedges now become normal edges, and the hypergraph becomes a normal graph. (Note that "strongly" and "weakly" satisfying mean the same thing now.)

Suppose such an instance is a bipartite graph $(U,V,E)$, with $|U| = |V| = n$; moreover, the instance is "regular" (i.e., the number of constraints involving each vertex is some $d$). Remind yourself that for such instances, it is NP-hard to infer whether the value is $1$ or less than $\eta < 1$.


text:
# Context Free Grammar

 Question 1
Consider the following context-free grammar where the set of terminals is $\{a,b,c,d,f\}$.

$\begin{array}{lll} S & \rightarrow & d \: a \: T \mid R \: f \\ T & \rightarrow & a \: S \: \mid \: b \: a \: T \: \mid \epsilon \\ R & \rightarrow & c \: a \: T \: R \: \mid \epsilon \end{array}$

The following is a partially-filled LL(1) parsing table.

Which one of the following choices represents the correct combination for the numbered cells in the parsing table ("blank" denotes that the corresponding cell is empty)?

 A A B B C C D D
GATE CSE 2021 SET-1   Theory of Computation
Question 1 Explanation:
 Question 2
The language which is generated by the grammar $S \rightarrow a S a\mid b S b\mid a\mid b$ over the alphabet of {a,b} is the set of
 A Strings that begin and end with the same symbol B All odd and even length palindromes C All odd length palindromes D All even length palindromes
ISRO CSE 2020   Theory of Computation
Question 2 Explanation:
 Question 3
Context free languages are closed under
 A union, intersection B union, kleene closure C intersection, complement D complement, kleene closure
ISRO CSE 2020   Theory of Computation
Question 3 Explanation:
 Question 4
A CFG (Context Free Grammar) is said to be in Chomsky Normal Form (CNF), if all the productions are of the form $\mathrm{A} \rightarrow \mathrm{BC}$ or $\mathrm{A} \rightarrow \mathrm{a}$. Let G be a CFG in CNF. To derive a string of terminals of length x, the number of products to be used is:
 A 2x-1 B 2x C 2x+1 D $2^{x}$
ISRO CSE 2018   Theory of Computation
Question 4 Explanation:
 Question 5
CFG (Context Free Grammar) is not closed under:
 A Union B Complementation C Kleene star D Product
ISRO CSE 2018   Theory of Computation
Question 5 Explanation:
 Question 6
Consider the following expression grammar G:
E$\rightarrow$E-T|T
T$\rightarrow$T+F|F
F$\rightarrow$(E)|id
Which of the following grammars is not left recursive, but is equivalent to G?
 A E$\rightarrow$E-T|T T$\rightarrow$T+F|F F$\rightarrow$(E)|id B E$\rightarrow$TE' E'$\rightarrow$TE'|$\in$ T$\rightarrow$T+F|F F$\rightarrow$(E)|id C E$\rightarrow$TX X$\rightarrow$-TX|$\in$ T$\rightarrow$FY Y$\rightarrow$+FY|$\in$ F$\rightarrow$(E)|id D E$\rightarrow$TX|(TX) X$\rightarrow$ -TX|+TX|$\in$ T $\rightarrow$id
GATE CSE 2017 SET-2   Theory of Computation
Question 6 Explanation:
 Question 7
Identify the language generated by the following grammar, where S is start variable.
S$\rightarrow$ XY
X$\rightarrow$ aX|a
Y $\rightarrow$aYb|$\in$
 A $\{a^{m}b^{n}|m\geq n,n \gt 0\}$ B $\{a^{m}b^{n}|m\geq n,n \geq 0\}$ C $\{a^{m}b^{n}|m\gt n,n\geq 0\}$ D $\{a^{m}b^{n}|m\gt n,n \gt 0\}$
GATE CSE 2017 SET-2   Theory of Computation
Question 7 Explanation:
 Question 8
Which of the following statements about parser is/are CORRECT?
I. Canonical LR is more powerful than SLR.
II. SLR is more powerful than LALR
III. SLR is more powerful than Canonical LR.
 A I only B II only C III only D II and III only
GATE CSE 2017 SET-2   Theory of Computation
Question 8 Explanation:
 Question 9
If G is grammar with productions
$S\rightarrow SaS|aSb|bSa|SS|\epsilon$
where S is the start variable, then which one of the following is not generated by G?
 A abab B aaab C abbaa D babba
GATE CSE 2017 SET-1   Theory of Computation
Question 9 Explanation:
 Question 10
Consider the following grammar.

P$\rightarrow$xQRS
Q$\rightarrow$yz|z
R$\rightarrow$w|$\varepsilon$
S$\rightarrow$y

 A {R} B {w} C {w, y} D {w, \$}
GATE CSE 2017 SET-1   Theory of Computation
Question 10 Explanation:
There are 10 questions to complete.

### 8 thoughts on “Context Free Grammar”

1. Please add a function to Sort the PYQs like (a) Older to Latest and (b) Latest to Older

• Dear Tirth,
It’s already sorted from latest to Older order for Subject and Topicwise practice. From the analysis it is observed that practice of latest questions are very important.

2. Question no 25th answer is wrong ,
it should be option A.

• Thank you shivam,