Guwahati Guwahati
s t n e t n co HOD...3 President...4 The Editior...5 MATRIX...6 Department Picnic...7 Placements...9 Batch of 2013...10
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2 International Statistics Year 2013 A Welcome Note...11 Credit Scoring...12
TECH COLUMN
Graph Databases....15 Natural Logarithm....17 Gravitational Red-Shift...18
INSIGHT
Ripples of life...20
Credits: Cover depicts an infinite tree symbolising the concept of infinity. Pictures of Statistical year supplied by Dr. Arabin Kr. Dey. Pictures of Kurua Island by Dr. P.A.S.S. Krishna. Magazine designed by Sourav Bikash.
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Dr. Bhaba Kr. Sar�a Head of the Depar��ent Depar��ent of Mathematics IIT Guwahati.
It gives me immense pleasure to learn that the third edition of Anatha, the magazine of MATRIX, is about to come out. The magazine has the potentiality of being a platform for intense intellectual and recreational activities of the members of MATRIX. The pages of Anantha can reflect the creativity of our students and their experiences in academic as well as in areas including training, recreational and extra-curricular activities. I am sure the forthcoming volume will be successful in stimulating more interest and interactions among the members of the association with diverse ideas in mathematics and computing. I will be very happy to see on the pages of the magazine write ups of alumni of the departmenton their experiences in the department during their study here as well as about their present experiences. I am sure such contributions would be of help to the members.Further,I wish to see the activities of the MATRIX with enhanced vigour and more enthusiasm in coming days. I congratulate the editorial team of Anantha for their efforts.
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Abhinav Yadav, BTech 4th Yr. President, MATRIX IIT Guwahati.
Here at MATRIX we continue our march towards professional and intellectual development, paving the road to the future. The keywords remain the same, opportunity, challenge, innovation, support and development but the efforts have increased manifold. The highly qualified and creative professors of our department with their midas touch produce winners. We are committed towards providing the students with ample opportunities to explore different ideas and fields of Mathematics and Computing. MATRIX values the fact that the college is the most important phase of a person’s life where he/she learns to work in a team, take responsibility and make critical decisions.The past year has been an eventful one. From tough courses and labs to fun filled parties, we have seen it all. Though not very old we have been able to establish ourselves as one of the best in the world. Credit goes to the undying spirit of the students. I would like to mention the tireless work of the previous and present executive councils of MATRIX, for bringing it where it is today. Last but not the least, I would like to thank our faculty advisor Dr. N Selvaraju and the chairman Dr. B. K. Sarma for their support and guidance which has been essential in the growth of MATRIX through the years.
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Sourav Bikash, BTech 2nd Yr. Publication Scretarďż˝, MATRIX. IIT Guwahati.
It has been a great pleasure to successfully publish this edition of Anantha.It was heartening to see the zeal and involvement of so many students. For many of us, it would be like strolling down the memory lane. Whereas for our new members, it would be a glimpse into the future. Anantha proves a serene canvas over which we wish to share our thoughts, experiences, achievements and vignettes of our lives with each other. This year we celebrate the International Year of Statistics. You can also have a glimpse at the beautiful pictures of Kurua Island, the sight for this year’s Department Picnic. This year MATRIX has been through many ups and downs. However, at the end of the day it feels great to live through them. I would like to express my gratitude to Dr. B.K.Sarma, Dr. A.K.Dey, Dr. N.Selvaraju and the MATRIX for helping me in this endeavour. Finally, I thank all my batchmates and my Department.
6 matrix 2012-13 MATRIX is the student body of the Mathematics Department of IIT Guwahati started in 2008. It is actively involved in promoting the career interests of the students. Over the past few years it has organized seminars, workshops and lectures on topics of mathematics and computing. It not only acts as an interface between the students and the teachers, but tries to increase the involvement of students in the department. It consists of an executive council headed by the Head of the Department. The current council members are: President - Abhinav Yadav Treasurer - Vipin Singhal Tech Secretary - Chirag Maheshwari Web Secretary - Amit Mittal External Affairs Secretary - Manan Bhutani Social Secretary - Devarshi Waghela Publication Secretary - Sourav Bikash Apart from promoting technical and intellectual growth of its membres, it takes interests in social activities such as organizing freshers’ interaction, department picnic, placement talks, alumni interaction etc. It also acts as a forum dicussing ideas and sharing knowledge. Contribution of the faculty and the students has made MATRIX a success and hopefully will continue to do so.
Manan Bhutani
Vipin Singhal
Chirag Maheshwari
7 departmental picnic One of the prominet social initiatives of MATRIX is the Department Picnic.
This year we went to a river island - Kurua, about 40 km upstream Brahmaputra from Guwahati.
(Photo credits: Dr P.A.S.S. Krishna)
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kurua
(photo credits: Dr. P.A.S.S. Krishna)
9 placement 2012-13 The department nurtures its students to be placed in the best companies of the world. The training given the faculty is of international standard making the students fit for a career in Investment Banking Financial and Business Analysis Market Research Data Analysis Quantitative and Financial Analysis Information Technology Research and Development. This years’ placement record has been quite promising. The following are the statistics: Facebook - 1 Goldman Sachs (Strategies) - 3 Goldman Sachs (Technical Analyst) - 2 Microsoft - 1 Directi - 1 Schlumberger - 1 EXL Service - 1 Adobe - 1 Flipkart - 1 Oracle Server Technologies - 1 Oracle Systems - 1 FICO - 2 Y Media Labs - 1 Capital IQ - 1 iRunway - 1 Virtusa - 1 Ericsson - 1 IBM GBS - 1 Innovaccer Management - 1 CA Technologies - 1 Total on-campus placement - 24/31 (77.41%) Highest package - 110,000 USD Highest domestic package - INR 28 LPA
Median Salary - 8.2 LPA Average Salary - 14.6 LPA
10 the batch 2013
Bachelor of Technology 2013
Master of Science 2013
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11 a welcome note Objective of Statistics can be projected in three dimensions; making sense of the data, to forecast and to address uncertainty. A famous statement which was popularized by Mark Twain, an American author and humorist : ``There are three kinds of lies: lies, damned lies, and statistics." A statement often used to pull the leg of Statistics lovers and here is my defence : Statistics gives some decision driven by the data and decision made by any statistical algorithm always carry some probability. It never says the event will occur, rather it always try to add an extra truth of "the approximate chance" of occuring the event. Florence Nightingale, a celebrated English social reformer and statistician : "(Statistics is) the most important science in the whole world, for upon it depends the practical application of every other science and of every art: the one science essential to all political and social administration, all education...." About the growing interest for Statistics, an editorial in Science by Marie Davidian and Thomas A. Louis offers the comment : ``This field will become ever more critical as academia, businesses, and governments rely increasingly on data-driven decisions, expanding the demand fo r statistics expertise." These data-driven decisions already have started, and they will undoubtedly increase. Hindrance for statistical application particularly for the researchers is the availability of irrelavant public data. Hal Varian, Google’s chief economist, made a nice comment regarding this issue : ``If left shoes (the data) are really cheap and you have a monopoly in right shoes (people with analytic capability to analyze that data, i.e., statisticians), you are in a really good position." Goal of this worldwide awareness campaign are to : (1) Increase public understanding of the power and impact of statistics on all aspects of society. (2) Nurture statistics as a profession. The year 2013 is International Statistics Year. It is start to assure the rise of statisticians. Nearly 1,700 organizations in 115 countries are combining energies to promote the International Year of Statistics, a worldwide initiative that will highlight the contributions of the statistics field to finding solutions to global challenges. Every moment and every snapshot of the world you explore is ultimately a number sitting between zero and one. That's amazing. ``This is your year. 2013. 0123, in a different order - random, maybe. This is the year of Statistics This is the year of the Statistician Stand up and count, stand up and be heard Raise your voice Live Reach out and make a difference." Dr Arabin Kr. Dey Assistant Professor Department of Mathematics IIT Guwahati
12 credit scoring (the scope of machine learning and statistics)
A bank is a major fnancial institution in the fnancial market. Its main source of revenue is interest on loans, paid by its borrowers. However, it does not imply that the more loans it grants, the higher its profit will be. It is because a bank is subject to credit risk in lending. Credit risk is the possibility of default by borrowers, also known as default risk. In competitive markets, interest rates charged by different banks are very close. Therefore, in order to survive in the financial markets, the bank must manage its credit risk well. Credit scoring is one of the effective tools to do so. It is a quantitative and objective tool to distinguish low default risk borrowers from the high risk ones.The basic idea is to develop a statistical or operational research based model connecting the borrowers' characteristics, such as gender, age, income, etc, with their default risk. The resulting models are known as scorecards or classiffiers. Making use of the credit scores, a bank can screen out bad loan applicants, improve pricing of default risk (i.e. charging higher interest rate from riskier borrowers, and vice versa), identify important factors associated with the default risk, and more importantly, avoid subjective judgments in the loan approval process. In short, credit scoring is beneficial to making credit-granting decisions.
Figure 1 We can define a cost matrix based on credit history and other factors and calculate the threshold value of repayment. Taking, Pr(repayment) >5/7 The given cost matrix identifies the magnitude of repaid loans with refused loans, identifying the opp-ortunity cost of foregoing good loans with the amount of profit they would bring. Using the German Data-set and applying logistic regression, we have very less numbers customers that satisfy the threshold of probability of repayment. However the result drastically changes if only significant independent variables are considered. We get approximately 76% success rate. This shows the importance of choosing independent variables in the data. Professionals started looking for alternative algorithms that can provide better accuracy regarding classification.
13 In fact, several machine learning techniques can be compared to check the improvement. Capturing the dependencies among the variables through proper structural learning is an important issue. Model performance depends largely on input variable selection. Extensive search is needed in this direction. Credit risk models are used by fnancial companies to evaluate in advance the insolvency risk caused by credits that enter into default. With this objective a mechanism is being proposed based on the key idea of writing the default probability in terms of the conditional distribution function of the time to default. The method is based on Cox's regression model. An empirical study, based on modified real data, illustrates this method. We will use the Credit Score for the German credit data that we have calculated previously as covariates in this method. cox’s regression methodology Classification Models merely predict the probability of default by customers; they tell us nothing about the time-to-default. Obviously, that (time-to-default) is valuable information to the lender. Thus, it is the most critical limitation of Classification Models in credit risk management. In this section, a semi-parametric approach to perform the study of PD is given. Here we use Cox's proportional hazards approach to model the conditional survival function S(t|x). The key in this method rests on the estimation of the cumulative conditional hazard function, A(j|x), using maximum likelihood. The objective is to build a conditional model for the individual PD(t|x), which is defined in terms of A(t|x). In order to describe PD_PHM, we define the following expressions relative to Cox's Regression Theory. The estimator of the conditional hazard rate function is defined as:
Under the assumptions of Proportional Hazards Model (PHM), we can define PD as,
where,
14 the results obtained from cox’s phm:
Default rates varying with maturity of loans for 3 different forecasting periods * By using the German credit data, we have observed the above plots. scope and summary: Calculation of dafault-rate is done based on semi-parametric method. Some parametric assumption for hazard function can be explored. We have assumed all borrowers are risky, or at-risk, which may not be the case in practice. Therefore alternative statistical model can be incorporated in the above set-up. * The variables treated here are the following: Y = maturity or loan lifetime. Here, maturity means time to default (T), when time is uncensored or time to withdrawal (C = 36 months), in any other case. Time was measured in months. X = scoring (credit ratio) observed for each debtor. Here X is an univariate endogenous measure of propensity to default. The closer to zero the better the credit behaviour. delta = default indicator (uncensoring indicator). This variable takes value 1 if loan defaults or 0 if not. Amanjot Singh BTech(Mathematics & Copmuting), 4th yr.
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15 graph databases Graph databases address one of the great macroscopic business trends of today: leveraging complex and dynamic relationships to generate insight and competitive advantage. Whether we want to understand relationships between customers, elements in a telephone or datacentre network, entertainment producers and consumers, or genes and proteins, the ability to understand and analyse vast graphs of highly-connected data will be a key factor in the determining which companies outperform their competitors over the coming decade. These data storage technologies are also known as NOSQL; a cheeky acronym for Not Only SQL, or more confrontationally, No to SQL. What’s remarkable about this renaissance of graph data and graph thinking is that graph theory itself is not new. Graph theory was pioneered by Euler in the 18th century, and has been actively researched and improved since then. However, it is only in the last few years that graph theory and graph thinking have been applied to information management. This increased focus on graph is driven by the massive commercial successes of companies such as Facebook, Google and Twitter, all of whom have centred their business models on their own proprietary graph technologies. Historically, most enterprise-level Web apps could be run atop a relational database. The NOSQL movement has arisen in response to the needs of an emerging class of applications that must easily store and process data which is bigger in volume, changes more rapidly, and is more structurally varied that can be dealt with by traditional RDBMS deployments. acid v/s base: In the relational database world, we’re all familiar with ACID transactions. Atomic: all operations in a transaction succeed or every operation is rolled back Consistent: on transaction completion, the database is structurally sound Isolated: transactions do not contend with one another; they are moderated and appear to run sequentially Durable: the results of a transaction are permanent, even in case of failures In the NOSQL world, ACID transactions have gone out of fashion. The term BASE has arisen as a popular way of describing the properties of a more optimistic storage strategy. Basic Availability: the store appears to work most of the time Soft-state: stores don’t have to be write-consistent Eventual consistency: stores exhibit consistency at some later point; e.g. lazily at read time productive analysis: One of the most appealing aspects of the graph data model is its intuitiveness. People without any background in data modelling – which is to say, relational modelling – easily grasp the graph approach. The typical “whiteboard” or “back of the napkin” representation of a data problem is a graph. More often than not such representations can be directly translated into a graph data model. One of the most important contributions of graphs to informatics is how they make data modelling and data interrelationships available to the layperson.
16 the property graph model: While there are numerous kinds of graphs, most have settled on the property graph as its graph model. The main abstractions in a property graph are nodes, relationships and properties. -
Nodes are placeholders for properties. Relationships connect nodes; they are always connected and directed. In addition every relationship has a label and can also house properties; these add semantic clarity to connections between nodes. These simple primitives are all that is needed to create sophisticated and semantically rich models. the cypher query language: In Neo4j the language Cypher is the primary means of accessing the database. Other graph databases have other means of querying data. A quick view of Cypher will enable us to explore more interesting graph query scenarios. A reasonably simple query is made up of START, MATCH and RETURN clauses. START: specifies one or more starting points in the graph MATCH: this is the specification by example part; we “draw” the data we are interested in, using round brackets for nodes and ‘->’ or ‘<-‘ signs for relationships RETURN: specifies which nodes, relationships and properties in the matched data should be returned to the client Here’s an example of a Cypher query that uses these three clauses to find plays written by Shakespeare: START bard=node:authors(‘ firstname:”William” AND lastname:”Shakespeare” ’) MATCH (bard) – [:WROTE] -> (plays) RETURN plays Reasons for Choosing a Graph Database: 1. “Minutes to milliseconds” performance. Using index-free adjacency, a graph database turns complex joins into fast graph traversals. 2. Drastically-accelerated development cycles. The graph data model reduces the impedance mismatch that has plagued software development for decades. 3. Extreme business responsiveness. The schema-free nature of a graph allows it to evolve, reducing risk and time to market. common use cases: Some of the most common graph database use cases: 1. Social networks 2. Recommendation engines 3. Geospatial problems; like Euler solved the Seven Bridges of Konigsberg problem 4. Master data management 5. Network management 6. Access control and authorization Kumar Harsha BTech (Mathematics & Computing), 2nd yr.
17 natural logarithms In a seminar talk delivered on 29-03-2013 in Department of Mathematics, Prof. S. Pattanayak had asked the following question: How to calculate natural logarithms without using log table and what is the idea behind it? I have tried to give an answer to this question. The definition of natural logarithms is given by:
Take, x=1+t. Then,
or, now using the geometric expansion of 1/1+t , we get:
Using this equation, we can evaluate the aaproximate value of ln b numerically, by substituting b-1 for b. This is assuming the fact that the value of the last integral is negligible. Rohit Madhukar Patne MSc. (Mathematics & Computing), 2nd Yr.
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space-time curvature distortion
The theory of general relativity predicts that gravity distorts the geometry of space-time. One of the ways to experimentally verify the presence of space-time curvature is to observe stars near the limb of the Sun during a total solar eclipse. During such a solar eclipse, stars can be seen in the sky due to darkness that ensues. It has been verified that the known position of stars changes slightly when these stars are found near the limb of the Sun. Figure 1 shows the path of the photons coming from the star that is behind the sun and so should not be observable. The trajectory of the photons is bent due to the curvature of space time near the solar surface caused by the gravity of the Sun. This beam of light can be observed on the Earth during a total solar eclipse and its apparent position is slightly shifted. The measurement of such shifts confirms the presence of space time curvature by the general theory of relativity.
Figure 1 There exists other observational proof of space time curvature. For example, a distant quasar that is found behind another less distant galaxy is seen as four distinct images in the astronomical object called the Einsteinâ&#x20AC;&#x2122;s cross (see figure 2). The central galaxy acts as what is called a gravitational lens by bending the light coming from the distant quasar. If for instance, both the lensing and the distant galaxy were spherical and perfectly aligned, the image of the quasar would be a circular disk seen around the central galaxy.
19 Some galaxies are lensed by other galaxies for which their position is slightly offset from the line of sight. Thus the curvature of space time caused by astronomical objects such as galaxies and black holes can therefore distort astronomical observations.
Figure 2 References: 1. An Introduction to Stellar Astrophysics, Francis LeBlanc, Wiley 2. The Origin of Stars , M.D.Smith, World scientific
Sourav Bikash BTech(Mathematics & Computing), 2nd Yr.
20 ripples of life Is life's journey like a placid pond which is soothing, comforting and fulfilling these days ? Small tensions, career graphs, life's ups and downs, obsessive materialistic rat race have a rippling effect on your minds. Nobody knows what is in store for us in our future. Surprisingly the unknown future haunts us. But our modesty and moderate lifestyle can certainly ease out our tensions, worries and anxieties. Enjoying simple joys gifted to us by nature, giving back to the world more than what one has received, socializing, sharing thoughts and time with friends, following basic courtesies and virtues certainly have a healing and therapeutic effect on our lives. To build an aura of positivity around us is in our hands. loving, nurturing and preserving the bounties of nature and various facets of life, is the best way to positive living. Society is a reflection of our ethics and moral values. If we are clean and upright so shall it slowly reflect around us. It needs perseverance, determination and a gritty will to constantly motivate oneself and take along others who touch our lives. Good virtues do not come naturally but have to be constantly practiced. It is like scaling up a mountain step by step. Breaking barriers of mistrust and cynicism and going back to the serene innocence of a child is the need of the hour. Let us listen to our beckoning soul to bask in the sunlight of a happy, simple, and contented life for a certainly "better" tomorrow. Devarshi Waghela BTech (Mathematics & Computing), 2nd Yr.