The tool consists of only two Parts  a board covered with flannel and objects having fluzzy and napped backing.
The principle involved is the interlooking of fibres of two rough or hairy surfaces, so that the pieces pressed on to a background which is hard and vertical will stay. It can be illustrated on a larger scale by pressing two tooth brushes or hair brushes together, so the bristle inter1ook. In case of flannel graph similar principle of friction helps an object to cling to the surface of the board. The flannel board is usually painted to depict a background scene appropriate to the story being told. Paper cutouts of characters and objects in the story are then placed on the board, and moved around, as the story unfolds. These cutouts are backed, either with flannel, or with some other substance that adheres lightly to the flannel background, such as coarse sandpaper. Plain, undecorated flannel boards can also be used as a visual aid during presentations, allowing the speaker to display and remove charts and graphs as needed.
Advantages:
* Permits numerous and varied arrangements of visua1 materials. * Is appealing, because the audience is fascinated in watching the steps in the presentation. * Permits the development of a complete story.
* Permits the use of either chart or small pieces of material. * Promotes conscientious planning, which must precede the development of the material in the first place.
Disadvantages:
* Transportation and storing of boards and materials is a problem. * Suitable tables to support boards must be available.
* Time and cost of making material for presentation present a problem. * Cost of boards themselves can't be overlooked.
* Presentation is limited a new idea involves a lapse of time before the new material...
...V. Adamchik
1
Graph Theory
Victor Adamchik Fall of 2005
Plan
1. Basic Vocabulary 2. Regular graph 3. Connectivity 4. Representing Graphs
Introduction
A.Aho and J.Ulman acknowledge that “Fundamentally, computer science is a science of abstraction.” Computer scientists must create abstractions of realworld problems that can be represented and manipulated in a computer. Sometimes the process of abstraction is simple. For example, we use a logic to design a computer circuits. Another example  scheduling final exams. For successful scheduling we have to take into account associations between courses, students and rooms. Such set of connections between items is modeled by graphs. Let me reiterate, in our model the set of items (courses, students and rooms) won't be much helpful. We also have to have a set of connections between pairs of items, because we need to study the relationships between connections. The basic idea of graphs were introduced in 18th century by the great Swiss mathematician Leonhard Euler. He used graphs to solve the famous Königsberg bridge problem. Here is a picture (taken from the internet)
V. Adamchik
21127: Concepts of Mathematics
German city of Königsberg (now it is Russian Kaliningrad) was situated on the river Pregel. It had a park situated on the banks of the river and two islands. Mainland and islands were joined by seven bridges. A problem was whether it...
...Paul Erdos and Alfred Renyi. Their work suggested that systems such as communications could be effectively modelled by connecting nodes with randomly placed links. Their simple approach revitalised graph theory and led to the emergence of the field of random networks.
An important prediction of random network theory is regardless of the random placement of links most nodes will still have approximately the same number of links. In fact, in a random network the nodes follow a Poisson distribution with a bell shape (see Fig.1). Random networks are also called exponential, because the probability that a node is connected to k other sites decreases exponentially for large k. This is better described by the famous small world networks. It was Watts and Strogatz in 1998 that recognised that a class of random graphs could be categorised as small world networks. They noted that graphs could be classified according to their clustering coefficient and their diameter. Many random graphs show a small diameter and also have a small clustering coefficient. What Strogatz and Watts found was that in real world networks the diameter is still small but has a clustering coefficient significantly higher than expected by random chance. Watts and Strogatz thus proposed a simple model of random graphs with (a) a small diameter and (b) a large clustering coefficient.
I wasn't until 1998 when AlbertLászlǒ Barabási...
...LAB # 1
Graph Matching
Principles of Physics I Laboratory
Breanna Wilhite
Introduction
In this lab motion will be represented by graphs that plots distance and velocity vs. time. A motion detector will be used to measure the time it takes for a high frequency sound pulse to travel from the detector to an object and back. By using this method sound can determine the distance to the object, or its position. This device will determine in what direction the woman in the video was walking and how fast she was walking. This information will be plotted on a graph and show the motion as the woman moves, whether she speed up or slowed down. Logger Pro will use the change in position to calculate the object’s velocity and acceleration. All of this information is in graph form. A qualitative analysis of the graphs of motion will help you develop an understanding of the concepts of kinematics.
Theory
The motion of an object can be measured using a motion detector. The detector helps in knowing where an object is according to an indication point. How fast and in what direction an object is moving, and how an object is accelerating is necessary in understanding the kinematics graphs.
The Motion detector uses pulses of ultrasound that bounces off of an object to determine the position of the person/object. As the person moves, the change in its position is measured many times each second....
...Graphs
Data Structures and Algorithms
Prepared by: Engr. Martinez
Graph Concepts
Graph Concepts
Graphs are of 2 types
Undirected Graph
Undirected Graph examples
Directed Graph
Directed Graph example
Directed Graph
Directed GraphGraph Relationships
Graph RelationshipsGraph Relationships
Basic terms involved in graphs:
Basic terms involved in graphs:
Basic terms involved in graphs:
Degree of vertex
The number of edges incident onto the vertex For an undirected graph The degree of a vertex u is the number of edges connected to u. For a directed graph The outdegree of a vertex u is the number edges leaving u, and its indegree is the number of edges ending at u
Degree of vertex
Edges are of 2 types
Directed edge: A directed edge between the vertices vi and vj is an ordered pair. It is denoted by . Undirected edge: An undirected edge between the vertices vi and vj is an unordered pair. It is denoted by (vi,vj).
Different Types of Graphs
Subgraph Connected graph Completely connected graph
1. Subgraphs
A subgraph of a graph G = (V,E) is a...
...Graphs and Function
What is the relation between the graphs and function and how was it applied in the real world?
Graphs are frequently used in national magazines and newspaper to present information about things such as the world’s busiest airports (O’Hare in China is first, Heathrow in London is sixth), about the advertisingdollar receivers in the United States (newspaper are first, radio is fourth) and about NCAA men’s golf team title winner (Yael is first, Houston is second). The function concept is very closely connected to graphs, and functions are the heart of mathematics.
I gathered my information from books especially algebra books and some are from the internet. I went to the library to look for some books and I borrowed some so I have many resources of information.
Many reallife relations between two quantities expressed in the form of equation are functions. To visualize these relationships, geometric figures called graphs are used. Modern technology provides us with graphing utilities needed to draw these graphs as well as enhance man’s knowledge of graphing techniques. Scientist and astronomers identify, visualize, and explore graphical patterns useful in analyzing data about the universe. Economist and businessmen draw mathematical models to find curves of best fit. Generally, the use of function and graphs is found in every...
...Baker Machine Company
Layout
Problem 3.4. (Summary)
Baker Machine is considering two alternative layouts. We will compare the WeightedDistance Scores using rectilinear distance* of the two block plans to determine which alternative layout is better.
Alternative Layout 1 Alternative Layout 2
3  6  4 
5  1  2 
3  1  4 
5  6  2 
* rectilinear distance – the distance between two points with a series 90degree turns, as along city blocks
Data
Baker Machine Company is a job shop that specialized in precision parts for firms in the aerospace industry. The current block plan is as follows:
3  4  2 
1  5  6 
The weighteddistance score for the current layout is 115.
 Closeness Matrix       
       
  Trips Between Departments  
 Department  1  2  3  4  5  6 
1  Burr and grind    7  16   10  5 
2  Numerically controlled (NC) equipment      4   
3  Shipping and receiving       9  9 
4  Lathes and drills        3 
5  Tool crib        3 
6  Inspection        
Solution
To determine which alternative layout is better we calculate the weighted distance, wd, scores of the two block plans.
Layouts can be assessed using the Layout solver of OM Explorer.
Solution (continue)
Alternative Layout 1
Solver  Layout 
       

   
...
...Graph Theory
GraphsGraph: A graph consists of a nonempty set of points or vertices, and a set of edges that link together the vertices. A simple real world example of a graph would be your house and the corner store. Where the house and the store are the vertices and the road between them is the edge connecting the two vertices.
Or a graph is a network consisting of vertices (or nodes) and edges (V,E)
Simple Graph
A graph can take on many forms: directed or undirected.
Directed Graph: A directed graph is one in which the direction of any given edge is defined.
Or A graph with directed edges = directed graph (digraph)
Directed edges = arcs
Directed Graph
Undirected Graph: An undirected graph is one in which the direction of any given edge is not defined. Conversely, in an undirected graph you can move in both directions between vertices. Or a graph with undirected edges is called undirected graph.
Undirected graph
Mixed Graph: A graph is one in which contains both directed...
...Trees and Graphs
Pat Hanrahan
Tree Drawing
Page 1
Why Trees?
Hierarchies
File systems and web sites
Organization charts
Categorical classifications
Similiarity and clustering
Branching processes
Genealogy and lineages
Phylogenetic trees
Decision processes
Indices or search trees
Decision trees
Tournaments
Two Major Visual Representations
Connection: Node / Link Diagrams
Containment / Enclosure
F6
G6
H6
J36
U8
B10
C30
L7 M7
V12
O4 P4 Q4 R4 S4 T4
W8
Page 2
[Furbringer]
C. Elegans Cell Lineage
[Sulston]
Page 3
Page 4
Page 5
Page 6
Classic Tree Drawing
Preorder or inorder traversal
DepthInOrder Traversal
0
1
2
3
4
5
6
7
0 1 2 3 4 5 6 7 8 9 10 11 13 14 15
Similarly for preorder, postorder
Note: width = n1
Page 7
Aesthetic Criteria
1.
Nodes at the same levels should be aligned
2.
Maintain the relative ordering of left and
right subtrees
3.
Parent should be centered over the children
4.
A tree and its mirror image should be
drawn as reflections of each other
5.
A subtree should be drawn the same way
regardless of where it occurs in the tree
RheingoldTilford Algorithm
E. Rheingold, J. Tilford, Tidier drawing of trees, IEEE Trans.
Software Engineering, SE7(2), pp. 223228. 1981
Page 8
RheingoldTilford Algorithm
Left contour
Left threads
Right contour
Right threads
E. Rheingold, J. Tilford, Tidier drawing of...