Udit Kumar

Student at Chandigarh University

Graph Theory

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node. A graph ‘G’ is a set of vertex, called nodes ‘v’ which are connected by edges, called links ‘e'. Thus G= (v , e). Vertex (Node): A node v is an intersection point of a graph. It denotes a location such as a city, a road intersection, or a transport terminal (stations, harbours, and airports). Edge (Link): An edge e is a link between two nodes. A link denotes movements between nodes. It has a direction that is generally represented as an arrow. If an arrow is not used, it means the link is bi-directional.Transport geography can be defined by a graph. Most networks, namely road, transit, and rail networks, are defined more by their links than by nodes. But it is not true for all transportation networks. For instance, air networks are defined more by their nodes than by their links since links are mostly not clearly defined. A telecommunication system can also be represented as a network. Mobile telephone networks or the internet is the considered the most complex graph. However, cell phones and antennas can be represented as nodes whereas links could be individual phone calls. The core of the internet or servers can also be represented as nodes while the physical infrastructure between them, like fiber optic cables, can act as links. This suggests that all transport networks can be represented by graph theory in some way.

Number Theory

Number theory is a branch of pure mathematics devoted to the study of the natural numbers and the integers. It is the study of the set of positive whole numbers which are usually called the set of natural numbers. As it holds the foundational place in the discipline, Number theory is also called "The Queen of Mathematics".The number theory helps discover interesting relationships between different sorts of numbers and to prove that these are true . Number Theory is partly experimental and partly theoretical. Experimental part leads to questions and suggests ways to answer them. The theoretical part tries to devise an argument which gives a conclusive answer to the questions. Here are the steps to follow: 1. Accumulate numerical data 2. Examine the data and find the patterns and relationships. 3. Formulate conjectures that explain the patterns and relationships. 4. Test the conjectures by collecting additional data and check whether the new information fits or not 5. Devise an argument that conjectures are correct. All the steps are important in number theory and in mathematics. A scientific theory is an ability to predict the outcome of experiments. In mathematics one requires the step of a proof, that is, a logical sequence of assertions, starting from known facts and ending at the desired statement.


Google AdWords is one of the services advertisers use for online promotion of their content, brand, website, etc through certain defined keywords to achieve traffic or leads. It is a form of brief advertising copy with keywords that are displayed on Google web pages and partner websites (called publishers) after matching their content with the keywords. By matching relevant advertising content to the content on a publisher page, Adwords present an efficient way for an advertiser to increase traffic on their website without having to purchase advertising inventory on other sites. Advertisers usually pay for a click generated (cost per click), which is revenue to Adwords, which is shared with the publisher in a certain percentage. This helps not only the advertiser to pay for traffic which is real as Adwords employ a lot of methods to detect and minimise fraud clicks, but also helps publisher monetise its content which was previously less monetised or not monetised at all. Besides CPC (cost per click) advertising, Adwords offers CPM (cost per mile) advertising, site targeted advertising (exclusively for text, banner and rich media ads) and re-targeting. This type of online advertising can be targeted local, national and for international distribution. The text advertisements are generally short with 1 headline of 25 characters, 2 descriptive text lines of 35 characters each and the URL with 35 characters. The most useful feature of Google Adwords is that it enables advertisers to target the placement of their ads to any specific location, language and even IP address exclusions. The limitation to exclude IP address, or the ranges of addresses is 500. Advertisers get an option of a control panel wherein they can put keywords, domain names, topics, demographic preferences to target the sites of Google network for promotion. This is known as Site-Targeting. Another useful feature of Adwords is re-marketing wherein it allows advertisers to show the ads to the users who have already been to their site. This way the conversion rate gets high.

Digital Fingerprinting

Digital Fingerprinting Technology enables the content owner to exercise control on their copyrighted content by effectively identifying, tracking, monitoring and monetising it across distribution channels (web, broadcast, radio, streaming, etc.) by converting their content into a compact digital asset or impression by a known fingerprint algorithm. In a fingerprinting algorithm, a large data item (audio or video or any files) maps to a much shorter bit string, i.e. fingerprint of the file which uniquely identifies the original data for all practical purposes. Digital Fingerprints have contents’ characteristics and enough details to identify a content variant upon comparison. Fingerprinting algorithm is based on a variety of content properties (frame snippets, motion and music changes, the camera cuts, brightness level, object movements) which are used for creating a digital asset reference along with content metadata and storing it in the database repository. The system is smart enough to identify whenever any part of audio/video content coming from any distribution sources is compared even in cases of content modification (compression, aspect ratio changes, re-sampling, change in color, dimensions, format, bitrates, equalization) or content degradation (distortion due to conversion, loss in quality, blurring, cropping, addition of background noise etc.) Digital Fingerprinting Workflow: The process involves content owners register their content for fingerprinting and creating reference digital representation of the content which is used for future comparisons. The steps follows are: i) Extraction of unique characteristics- fingerprint of digital content and submission to rights, registry along with metadata of the file. ii) Identification of content - By comparing against fingerprints in the database to check for infringement. iii) Result - Based on comparison take appropriate action under agreed business rules (block, delete, authorize). Common Fingerprinting Algorithms: 1) Rabin's fingerprinting algorithm. 2) Cryptographic hash functions. Example: Audible Magic, one major digital fingerprinting company, works for huge content providers like NBC Universal, Sony Music and 20th Century Fox. This company claims that its CopySense technology can identify the source of a video clip within five seconds of playback and can identify an audio file within 10 seconds. The company also claims its software can recognize a piece of media which contains recorded off a movie theatre screen with a handheld camera. The identification is based on the perceptual characteristics of audio and video as described by the company. The system can see past transformative changes to audio and video files like transcoding among file formats, equalizing of audio, cropping of an image or even blurring of a picture for analysing it.

Data Mining

In simple words, data mining is defined as a process used to extract usable data from a larger set of any raw data. It implies analysing data patterns in large batches of data using one or more software. Data mining has applications in multiple fields, like science and research. As an application of data mining, businesses can learn more about their customers and develop more effective strategies related to various business functions and in turn leverage resources in a more optimal and insightful manner. This helps businesses be closer to their objective and make better decisions. Data mining involves effective data collection and warehousing as well as computer processing. For segmenting the data and evaluating the probability of future events, data mining uses sophisticated mathematical algorithms. Data mining is also known as Knowledge Discovery in Data (KDD).  Key features of data mining: • Automatic pattern predictions based on trend and behaviour analysis. • Prediction based on likely outcomes. • Creation of decision-oriented information. • Focus on large data sets and databases for analysis. • Clustering based on finding and visually documented groups of facts not previously known. The Data Mining Process: Technological Infrastructure Required: 1. Database Size: For creating a more powerful system more data is required to processed and maintained. 2. Query complexity: For querying or processing more complex queries and the greater the number of queries, the more powerful system is required. Uses: 1. Data mining techniques are useful in many research projects, including mathematics, cybernetics, genetics and marketing. 2. With data mining, a retailer could manage and use point-of-sale records of customer purchases to send targeted promotions based on an individual’s purchase history. The retailer could also develop products and promotions to appeal to specific customer segments based on mining demographic data from comment or warranty cards.

Bounce Rate

By definition, this means the number of single-page visits by visitors of your website. Bounce rate in terms of website traffic lets you know about the visitors who arrive on your website and leave without initiating any other action or event, like visiting a second page. He came, he saw and he went somewhere else. The visitor enters the website on the entrance page or the landing page. These visitors view only that single page and exit the site on that same page. For example, around 100 visitors read a particular news story yesterday, out of which 75 went to other pages while 25 did not. The bounce rate, thus, was 25%. Bounce rates are often used for measuring the performance of e-mails, websites, advertising campaigns, and particular landing pages. Bounce rate is measured in percentage. Bounce Rate Event tracking – Below are top visitor actions that can be identified as a bounce from your site and typically signal that the visitor’s expectations were not met. - Clicks the back button – The visitor landed on your website and clicked on ‘Back’ and was redirected to the previous page. Hence navigated away from your website. - Closes the browser – The visitor saw your page/website - either found or couldn’t for the information they were looking for and closed the browser. - Types a new URL – The visitor typed in a different URL from your website and was redirected to a different page. - Does nothing – The visitor chooses to stay on the site and does no further activity. Average session times out after 30min. - External link – The visitor clicks on a link to a page on an external website link. 2) Email Bounce Rate Bounce rate in terms of emails describes the percentage of email addresses in your subscriber list that didn’t receive your message. There are two types of email bounce - - Soft email bounce means that the intended email address is valid and has reached the recipient’s mail server. But it was temporarily rejected by the mail server due to reasons like - mailbox was full, a server was down etc. - Hard email bounce means that the intended email address in not valid or does not exist. And the message has been permanently rejected by the mail server.

Gantt Chart

A Gantt chart is a useful graphical tool which shows activities or tasks performed against time. It is also known as visual presentation of a project where the activities are broken down and displayed on a chart which makes it is easy to understand and interpret. A Gantt chart is a popular tool in project management. It basically drills down activities which need to be done by a fixed time period. It is commonly used for tracking project schedules. On the chart, tasks are shown on the vertical axis while the scheduled time-spend is laid out on the horizontal axis. Each task is represented by a bar that shows the time required for the project. The bar then represents or shows percentage of tasks that have been completed. It also shows dependencies, which simply means the interlinkages between various activities in the project.Understanding the interlinkage between activities is very important to monitor and Gantt charts help the project manager to do just that. It conveys the information about the completion of other activities in the project. This information is important because of the interlinkages between various activities and if one activity gets delayed it will have an impact on others. Gantt chart is a useful tool in planning and scheduling the projects. It keeps the management updated as to when the project will get completed. It also keeps the management informed about any additional resources that are required, and manage dependencies between tasks. They are commonly used in scheduling production processes, employee roster or scheduling, events scheduling, production processes, etc. Microsoft Excel can also be used to create Gantt charts apart from other independent software available in the market.  

Reference Price

Reference price is also known as competitive pricing, because here the product is sold just below the price of a competitor’s product. Reference price is the cost at which a manufacturer or a store owner sells a particular product, giving a hefty discount compared to its previously advertised price. Reference pricing, in simple terms, is known as that price which users compare with the price of a competitor’s product or the previously advertised price. Here the price of the product, which is more expensive, becomes the reference price for your product.Marketers generally induce buying behaviour in customers by putting goods and services at a huge discount compared to its original price. Human beings tend to compare the price of the product with the reference price, and if the new price is heavily discounted compared to the original price, it could trigger buying.Reference pricing is also part of psychological pricing, because it is the price of the product which buyers use as a reference while making a decision to buy the product. Usually reference price is also mentioned on the product so that consumers can compare the difference in rupee value terms.Let's understand reference price with the help of some examples. Big Bazaar, India's leading supermarket store, conducts a sale around Independence Day every year. Here the price is discounted heavily which leads to an increased sales volume. They also extend discounts to electronics like camera and mobile phones. The idea is to generate sales in that particular time frame. The consumers usually see the difference between discounted price and the original price or the reference price. Online shopping portals such as Flipkart and Amazon also run their big billion days or festive sales on particular days, where products are sold at a hefty discount.