Analysis of Graph Theory

Analysis of Graph Theory In mathematics and computer science, graph theory is the study of graphs: mathematical structures used to model pair wise relations between objects from a certain collection. A graph is a very simple structure consisting of a set of vertices and a family of lines (possibly oriented), called edges (undirected) or arcs (directed), each of them linking some pair of vertices. An undirected graph may for example model conflicts between objects or persons. A directed graph (or digraph) may typically represent a communication network, or some domination relation between individuals, etc. The famous problem of the bridges of Kà ¶nigsberg, solved by Euler, is viewed as the first formal result in graph theory. This theory has developed during the second half of the 19th century (with Hamilton, Heawood, Kempe, Kirchhoff, Petersen, Tait), and has boomed since the 1930s (with Kà ¶nig, Hall, Kuratowski, Whitney, Erdà ¶s, Tutte, Edmonds, Berge, Lovà ¡sz, Seymour, and many other people). It is clearly related to Algebra, Topology, and other topics from Combinatorics. It applies to and gets motivating new problems from Computer Science, Operations Research, Game Theory, Decision Theory. â€Å"Because of its inherent simplicity, graph theory has a very wide range of applications in engineering, in physical, social, and biological sciences, in linguistics, and in numerous other areas. A graph can be used to represent almost any physical situation involving discrete objects and relationship among them† (Narsingh Deo). The term â€Å"graph† in mathematics has different meanings. There is a graph for the function and relation. Graphs, especially tree graphs and directed graphs appear in the computer and information sciences. Flowcharts for example are directed graphs. A flowchart is a visual representation of an algorithm. It is frequently used in the planning, development and structuring of an algorithm for solving a complex problem. The flowchart is regarded as an essential part of the documentation of any computer translation of the original algorithm (Seymour Lipschutz). There are two commonly used tools to help to document program logic (the algorithm). These are flowcharts and Pseudocode. Generally, flowcharts work well for small problems but Pseudocode is used for larger problems. Flowcharts are used in the design phase of software creation. It specifies the logical flow of a program. The semantics of a flowchart are totally concerned just with control flow-what happens first, and then what happens next, and so on. A flowchart is drawn using a small set of symbols with well-defined meanings. An elongated oval denotes the beginning of the program, where the execution commences. Passage of flow from the beginning, and at later stages, is denoted by edges with directional arrows. A box in the shape of a parallelogram denotes either an input (such as a READ), or an output (such as a PRINT). A rectangle denotes a computational step, such as addition, and a diamond-shaped box denotes a decision step. A diamond usually has one arrow leading in, and two or more leading out, denoting different ways the control can proceed from that point. A diamond is used in cases of decision statements like, If A is more than 7, proceed to multiply B and C; else, divide C and D. Example of flowchart which reads 2 numbers A and B, and prints them in decreasing order after assigning the larger number to BIG and smaller number to SMALL. â€Å"Essential computer mathematics† Seymour Lipschutz, 1987, page 101 A flowchart is a visual representation of sequence of operations performed to get the solution of the problem. They are usually drawn in early stages of programming project. They help with better communication between the programmers and their business customers. The flowcharts are very helpful with understanding complicated problems and programming logic, especially for people who do not work with (or understand) programming and coding. We can say that flowcharts are necessary for better documentation of complex programs. They also work as a guide during the system analysis and program development phase. If we have good flowchart for the programme the maintenance becomes easier, as the programmer can be more efficient in debugging process, as he can clearly see which parts he has to focus on. Flowcharts are also used in industrial and process engineering and management. The Unified Modelling Language (UML) created by the Three Amigos of software engineering borrows some of its basic ideas from the flowchart paradigm, although it is much more sophisticated. Visual Paradigm for UML is a professional tool that supports complete software lifecycle object-oriented analysis, object-oriented design, construction, testing and deployment. The UML modelling software helps to build quality applications faster and better. You can draw all types of class diagrams, reverse or generate code. It allows turning models into Java codes and Java codes into models. Graph theory is also helpful when building databases. Directed graphs (or digraphs) are a special case of graphs that constitute a powerful and convenient way of representing relationships between entities. In a digraph, entities are represented as nodes and relationships as directed lines or arrows that connect the nodes. The orientation of the arrows follows the flow of information in the digraph  ­. Digraphs offer a number of advantages to information visualization, with the most important of them being: comprehensibility the information that a digraph contains can be easily and accurately understood by humans and expressiveness- digraph topology bears non-trivial information. Case of graphical representation of logic rules, digraphs seem to be extremely appropriate. They can offer explanation of derived conclusions, since the series of inference steps in the graph can be easily detected and retraced. Also, by going backwards from the conclusion to the triggering conditions, on e can validate the truth of the inference result, gaining a means of proof visualization and validation. One of the examples can be found in the book â€Å"Automated Data Processing and Computations by David I. Donatoy. It is an example of geographic names database. An algorithm specifies how to quickly identify names that approximately match any specific name when searching the mentioned database. The algorithm identifies matching names by applying an artificial measure of name simplicity. A digraph index enables computer name searches that are carried out within this technique to be fast enough for Web application. The use of digraph index enables name search application to restrict comparisons to a small subset of the database name, speeding up processing. A digraph index lists in digraph sequence all digraphs found in the database of geo ­graphic names. The entry for a particular digraph consists of a set of pointers to all names in the geographic-names database that includes at least one occurrence of that digraph. Once the search-for name has itself been broken down into a list of its unique constituent digraphs, the digraph index can then be used to produce a candidate list containing only those names from the database that include at least one of the digraphs found in the search-for name. In most cases, several names in the candidate list will be referenced more than once (by different digraphs). After sorting the list of can ­didate names (thus, bringing together all occurrences of each particular candidate name), the number of occurrences of each candidate name can be counted. The number of occurrences of a candidate name will be the same as the number of unique digraphs a candidate name has in common with the search-for nam e. This number can be regarded as a first-approximation measure of a names similarity to the search-for name, with larger numbers corresponding to stronger similarity. Computer scientists have developed a great deal of theory about graphs and operations on them. One reason for this is because graphs can be used to represent many problems in computer science that are otherwise abstract. Finding a way to represent the solution to a problem as a graph can present new approaches to solving the problem or even lead directly to a solution derived from graph theory. This sort of technique is often used when discussing algorithmic efficiency and when trying to prove that a certain algorithm is NP-Complete; because many problems involving graphs, such as finding the shortest path to traverse all nodes (the Travelling Salesman Problem), are NP-Complete, if you can find a way to represent a problem as a graph and show that it is analogous to one of the other NP-Complete problems, then you can show the problem you are trying to solve is also NP-Complete, which gives you a hint that the solution will take a great deal of time. Another reason for using graphs is that many problems computers are used to solve involve representing relationships between objects, places, or concepts. Because graphs can be either directed or undirected, they are a flexible method of showing connections. For instance, you can describe who knows who in a room as a collection of nodes, each representing a person, and directed edges, each representing that one person knows another. Because graphs are so often used and because they allow the representation of many problems in computer science, they are a convenient means of expressing problems with which many people are comfortable. This familiarity simplifies the process of creating mental models of problems, which ultimately leads to better problem solving. Because computer science is a young discipline, it played essential role in development of graph theory. Mathematics plays essential role in computer science, as its language defines the generic structures and proves properties of those structures. Computer systems can be very complex and it is very difficult to have a clear picture of all details and keep the overview of the whole system. Computer science has put lots of effort to develop mathematically based frameworks to model computer systems. References: Gibbons, Alan (1985), Algorithmic graph theory, Cambridge University Press http://www-leibniz.imag.fr/GRAPH/english/overview.html http://www.bookrags.com/research/flowchart-wcs/ Brent Daviduck† Introduction to Programming in C++: Algorithms,  Flowcharts and Pseudocode† Narsingh Deo â€Å"Graph theory with applications to engineering and computer science†2004 An augmented directed graph base for application development Dan C. Clarke , 1982 Knoxville, Tennessee David I. Donato â€Å"Fast, Inclusive Searches for Geographic Names Using Digraphs† Chapter 1 of Book 7, Automated Data Processing and Computations, Section A, Algorithms, page 2-3 Quentin Charatan Aaron Kans â€Å"Java in two semesters†, The McGraw Hill, 2006, page 4-7 Seymour Lipschutz â€Å"Essential computer mathematics†, McGraw Hill 1987, page 95-107

Romanticism in Why Do I Love You, Sir?

Romanticism in â€Å"Why do I love You, Sir? † Many know of Emily Dickinson reclusive behavior, but very few know about her brief engagement to George Could, a student at Amherst College. Unfortunately, her wealthy father broke their engagement off because he was Just a poor student. It is believed that this disappointment triggered her initial withdrawal from society and the start of her life as a writer. She lived without marrying and devoted a significant amount of time to writing poetry and letters during a time now known as theAmerican Romanticism movement. This movement affected Emily writing and is evident in much of her poetry. Emily Dickinson displays many of the characteristics of the American Romantic period in her poem â€Å"Why do I Love You, sir? † First, an obvious connection to American Romanticism in this poem is Emily unconventional punctuation, short lines, and capitalization. Formerly, poems were structured strictly to fit into heroic couplets. In di verging from the ordinary, Emily used romanticism to destroy the authoritarian structure and give way for allowing he poet and reader to feel the way that each individual felt.With no guidelines, one is allowed to be free and let things flow into their ideal shape of religion. For example, the very first stanza, envoy do I love' You, Sir? † is oddly punctuated. The narrator is seemingly repeating a question that has been questioned of her which is suggested by the quotation marks around â€Å"why do I love. † This leads way that the narrator is quoting someone. Secondly, Emily use of nature to explain her simple answer â€Å"Because—† is also characteristic of the American Romantic poets.Romantics love nature because of its sensibility and connection to basic emotions. Nature's design is straightforward. Built to survive and reproduce are its only goals. There are there Just because. Emily first simplistic response is â€Å"The Wind does not require the G rass/ To Answer— Wherefore when He passes/ She cannot keep Her place†. Emily likens herself to blades of grass that are quivered by the wind. Just as when Sir passes she is shaken with Joy Just by his presence. Additionally, the wind does not solicit the grass to tell why it was affected.However, the wind did so inquire the answer would be because. Just as simple as can be Just like nature intended. Later on in the poem, Emily brings up lightening another major player in Mother Nature to further emphasize her argument. Lightening also doe not question why it's impulsive flash of brightness causes an eye to close, â€Å"Because He knows it cannot speak—â€Å". Still if it could express its feeling it will answer because. Thirdly, individualism is key to romantic poets. Her feelings are evident for however this Sir is and she is free in expressing her emotions.Whether Sir is God or secret crush, the reader's own interpretation is vital in this decision. The capit alization of he is significant in the fact that she is most likely referring to God. It is almost impossible to explain why someone has an affinity for a certain someone. Only nature can explain most simply and it answer is â€Å"Because—â€Å". Either way you cannot explain factually why you believe in God or why you had a love at first sight moment. Ultimately nature decides it all. It is as simple as â€Å"The Sunrises—Sire completely Me—/Because He's Sunrise—and I see?/Therefore—Then—/l loveIn conclusion, red is to a rose as Emily Dickinson is to Romantic poet. Emily encompasses all that is Romantic. She was original by revoking the structure of everyday poems of times before, using nature to explore feelings, and use nature as ways to exemplify the things we do. She also made the individual important and the main character to her poems. Overall, this poem is a great example of the legacy Emily Dickinson left to American literature. W orks Cited Dickinson, Emily. â€Å"Why Do I Love You, Sir? â€Å". Poem Hunter. Poem Hunter. N. D. Tuesday. 9 July 2013

Trader Joes - Free Essay Example

Sample details Pages: 3 Words: 854 Downloads: 10 Date added: 2017/09/23 Category Advertising Essay Type Narrative essay Did you like this example? 1. Trader Joe’s is a multi- billion dollar national chain through its ability to find cheap real state, store brands and smartly management practices. The company always encourage friendly, customer orientated employees who are ambitious and adventurous enjoy smiling and have strong sense of values. Each employee is encouraged to taste and learn about the products and to engage customer to share what they experienced. Trader Joe’s philosophy for their success is â€Å"HAPPY EMPLOYEES MAKE FOR HAPPY CUSTOMER’S. The company encourage multitasking, it is not unusual for store manager to sweep floor, stock shelves and run the register when needed. Company also encourages young teens who are working as part time and collecting money for their colleges. If we compare Trader Joe’s wages to other grocery stores, they pay 30% more to their employees. The simple reason lies is that Trader Joe’s knows that people looking for a new job look for money, but pay is not why employees generally remain with an organization. At Trader Joe’s, employees feel that they are taken care of and there is nothing to stop giving 100% of their abilities. 2. It is an old saying who is captain of the ship? Manager is always taken as the captain of the whole entire crew. Trader Joe’s always work on this theory so their managers are highly professional customer satisfaction experts, ambassadors, food tasters, personnel specialist, merchandisers, problem solvers and community volunteers. The management process work in the simple formula of planning, organizing, leading and controlling which sets clear rules for all the employees working in the company. Traders Joe’s offer their manager round six figure pay which is a biggest attraction among all others. Moreover Company’s non-union policy gives the management to lead their crew in more organized manner, controlling and monitoring everyone performance and taking immedia te actions as necessary. 3. Trader Joe’s knows that the stock of competence, knowledge and personality attributes embodied in the ability to perform labor so as to produce economic value. The Company is well known for treating employees with the measure of respect and dignity. Everyone come up with new ideas all of which are taken very seriously and often acted upon. Clearly the chain sees its own people as a way to build brand recognition for the store. The attitude within the corporate office is that the people it hires, trains and promotes are just an important as the low prices and products it carries. Trader Joe’s knows the importance of human capital it established a peer network in which managers talk to and work with each other on developing and implanting best practice at work. 4. Trader Joe’s always focus on a high level model of how their business receive raw materials from all over the world as input, add value to the raw material through vario us processes and sell the best and finished products to the customers. The Company is very famous for it’s in store brands which include wine, chocolates, cakes and bread. The unique idea of bringing all types of grocery from every ethnicity, region and culture bring all community people under one roof. It was a different concept back in those days to get grocery from Middle East, China, India and Africa, miles away from here, but this Company made this possible. The Company made a value reference model for making their products a success. The model structure work as a, 1) Research and Development 2) Design of Products, Services or Processes Production 3) Marketing and Sales 4) Distribution 5) Customer service. When they combine all these values in one product, the combine result did come out as a success. 5. Trader Joe’s blogs have at least 76% positive responses. Customers do talk about their candies, cake, chocolate and wine all the time. This Company is a big co mpetitor of Whole food market so it’s always focuses on the organic food. These days people are using more organic products with a big campaign â€Å"BACK TO BASICS†, Trader Joe’s is actively participating in it. Trader Joe’s locations and size of the store is always a catch for the customers, the Company focus on the location so they always open at the places where need of grocery stores is indeed. In the blogs customer did praise the fact that it’s a one stop shop for whatever they need for their pantry, fridge even cleaning supplies, not to forget their prices are very low which always attack customers especially in this economy. Trader Joe’s is a big competitor of Whole food market, Kroger and Alde so it sometimes faces some issues too, like these days Company is having issues with their seafood. An association name Green-Peace wants Trader Joe’s not to sell â€Å"Redlist Fishes†, people really want to be good by the planet so do Trader Joe’s. The Company also believes in Go-Green policy so the company is putting their heads up keeping all the products which is good for the environment and they are talking about their products in the store by giving flyers and showing in store cooking demos. Don’t waste time! Our writers will create an original "Trader Joes" essay for you Create order

Direct Instruction As An Instructional Approach - 936 Words

Direct Instruction is often associated with traditional lecture style teaching in the classroom and is most commonly used teaching method. Direct Instruction is an instructional approach that is teacher led either by lecture or demonstration and is structured and sequenced in nature (Hidden Curriculum, 2014). One of the fundamental characteristics of Direct Instruction is providing new material to the students’ by presenting the content into understandable and logical steps. Another characteristic of Direct Instruction is the review of previous lecture or assignment and the use of review to strengthen learning. Lastly, another characteristic of Direct Instruction is providing students’ with direct and independent practice, as well as providing advice with correctives from the instructor. During my time observing, most of the classes I observed focused heavily on direct instruction. I suppose this is due to that fact that there is a lot of material to cover in a short am ount of time, therefore the teacher starts with direct instruction and then moves on to other instructional approaches. For example, during my observation of the beginning of new content on pedigrees, the teacher relied heavily on lecture with the use of a Power Point presentation on the Smartboard. Throughout the lecture, the teacher explained and illustrated the content and model the skills needed. During the lesson, the students were guided to take notes on required information. The teacher presentedShow MoreRelatedThe Direct Instruction Approach Essay678 Words   |  3 PagesDirect Instruction There are various instructional approaches but one that is widely employed by many teachers is the direct instruction approach. This is the classic teaching style that many people remember during K-12 grade school. The teacher would stand in front of the class lecturing while writing on the black board. 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