# Udit Kumar

Student at Chandigarh University

Graph Theory

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 &quot;The Queen of Mathematics&quot;.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.

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&rsquo; 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&#39;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). &nbsp;Key features of data mining: &bull; Automatic pattern predictions based on trend and behaviour analysis. &bull; Prediction based on likely outcomes. &bull; Creation of decision-oriented information. &bull; Focus on large data sets and databases for analysis. &bull; 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&rsquo;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.

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