Building a Culture in Research

This article stems from various aspects of research that has caught my attention, while being a graduate student at IIT Bombay. Although, India is a country with diverse culture and ancient history (dating back to vedic era), its involvement in research is still in the nascent stages. In recent years, there has been a series of strong reforms in the direction of lifting India's research output.  The manifold increase in the budgetary allocation for science and technology is a fitting example to this fact. However, scientific research cannot be progressive unless a research culture is introduced.

The Oxford  Learner's  dictionary defines the word culture as the beliefs and attitudes about something that people in a particular group or organization share. In a scientific context, research culture would mean a value system that is shared by the research community. It is a scenario where individuals work single-minded towards achieving a collective goal. ISRO's Mangalyan mission is an excellent instance where this has been demonstrated.The emphasis here was on collaborative exploration by setting aside social, regional  and language differences. No scientific advancement is possible without a sense of collective commitment and responsibility. Each scientist in that sense is accountable for the millions of taxpayers, to whom her/his services are to be delivered.

The culture of research is supported on three pillars - viz. academic institutions, industry and government agencies. Academic institutions have a major role in fostering scientific temperament through active engagement of its student community - UG, PG and PhD. Faculty members should facilitate exchange of ideas within the hierarchy of students as well as across departments. The academic environment needs to be shaped such that it encourages risk taking, allows experimentation, and accommodates failures. For instance, there can be provisions where the student is free to start a venture after completing a minimum number of credit.

Innovation is a constant companion to research. Especially this is very much true in engineering. Being an applied science, engineers try to find solutions to various problems that is of concern to the world around. In present times, it is further possible to convert the innovation to a venture and collaborate with other innovators in the area. A simple scheme to instil an innovation mindset is to encourage open discussions and pitching avenues. Apart from core subjects, engineers need to develop an open mindset to other subjects. Soft skills will be key for building successful research collaborations in the future. These include inter-personal skills as well as self management principles.

The foundations of research culture should be laid on integrity as well as social-responsibility. Ethics and values are pivotal to inculcate a holistic education, and this is more so important in research. In fact, the current educational culture of just accumulating information, needs to change.

Directing Creativity with Education

The system of education and upbringing should be to manifest the underlying creativity in oneself.

Anonymous

 
  Living in a community that gives tremendous importance to education, is it not required on questioning what benefits it brings forth?  On one side, education has given mankind numerous contributions in the form of progress in science, technology, economic development, management, space exploration, and to some extend reality. Reflecting on the present state of our education system, one might even see the entry of women in many fields that was only a dream in the past. In India, any child below 14 years of age is eligible for free primary education.  In a way, our schools have turned out to be laboratories of sprouting creativity. Oh! but what is meant by creativity on the first hand.

The word creativity generates a sense of positive vibes in many of us. Creativity can be best described by its three characteristic features - it is effortless, it happens with a giving attitude, it is ever joyous. Recall, any instant in your daily life, where these three streams congregate. Watch for a day and discover what activates the creative energies in you. Everybody has one, only one has to search it inside and not on the outside. The purpose of education is to formalize (I would like to call it manifest though) the inherent creative energy flow in oneself. This journey of life is to enter into one's inner dimension and bring out that joy of creativity. The touch of pen, or the movement of the vocal chords or the expressions on a face becomes the instrument of this divine energy. It is time we start this journey, and for those who are already in the midst, let you be the light to direct the others.

Turning ones thoughts into creative endeavors

Everyone needs to have a goal to move forth. Set your goal on revealing this inner lamp, so that it might serve many co-passengers with you . Leave out the set backs by smoothening your skill to learn.  Experience the change in you, brought forth by your attitude. Remember, it is the most valuable word in English and also the most valuable tool in ones life.

 A thought leads to an action, an action into a habit, a habit into a character, and character decides your destiny

-Stay Blessed

Elements in the pedagogy for the future IoT revolution

The internet of things is going to transform the way we perceive the objective world. The world is getting more and more connected with multiple devices available.  This post is a reflection on my recent encounter with the the use cases of the Internet of Things (IoTs) in education and academia There a pressing need for us to invest on the human resources for developing the current IoT. If there is lot of potential in IoT, then the need to train our younger generations is also high.

The IoT mania is more hyped than reality. In reality, we are not trying to do something that is entirely new. But IoT is just another way of getting things done in a smarter, simplified and user friendly manner. The whole jargon blinds us of many things that we can/have fundamentally deal/dealt with. For instance, has anyone thought about the number of multimedia content that gets transferred across the internet and the cloud. Is there that theoretical "infinite" storage that is available to us to store this on the clouds? Here comes the savior in the form of Wavelet and Time-Frequency transforms. A fundamental theory that has developed more than a 50 years back, comes into action in a beautiful coincidence to solve a Big Data issue. Looking at the various layers of the communication stack in the current, IoT can back on a huge legacy network if it gets focused on the specific constraints. The IoT is going to make access to every possible sensed data at any place. In a nutshell, it becomes an all pervasive network.

The key drivers in IoT is surely the ability to handle data. Are we prepared for that ? Some key anticipations in the industry goes in the areas of low power, storage and integration of the hardware software peripherals. The answers to all these are open as of today. The 50 billion or the a trillion devices by 2020 .. how can one possibly give a network address to each of these.

If the technologists claim it to be the next biggest revolution after the industrial revolution in the early 18th century, then we better get ready. - the earlier the better. There are a variety of starter kits for students to pick up early. Specifically, there needs to be training in the following aspects : sensing, networking and actuation. An undergraduate IoT lab facility is strongly required.


Navigate to IoT Lab.

Switch or Stay

One thing that is often reiterated, is that one should keep up to the pace of the world around. If you stay, you will miss somethings, but there is always an advantage in switching. Consider this classical example called the "Monty Hall" problem in probability theory:

The "Monty Hall" problem relates to a popular TV show, where the participant of the game is allowed to win a Bentley (most expensive car!) or has to be satisfied with a goat (most sort after domestic animal!). The problem is stated as a conversation between Monty and the participant Mr. P

Monty : Welcome, Mr P to this game. Before we begin let me explain. You can see 3 closed doors,     behind one of the doors is the most priced Bentley, and behind the others are the useful goats. Choose one and you will be prized with the gift behind the door. You can either go with a shiny, new expensive Bentley or be satisfied with the goat. So are you ready?

Mr. P  : Okay let me choose Door __ .

Monty : Okay let us see if the luck supports you. (Pause) Maybe I can give you another chance. I shall open a second door and see if you want to change the choice.

Monty opens a second door and shows that it is a goat.

Monty :  Do you wish to stay or switch?

Think that you are Mr. P and write your choice... Stay or Switch!

Figure showing the illustration of the Monty Hall Problem. (Drawn using MetaMoji Note App)

Solution : Mr. P would wish to switch in order to win the Bentley. The reasoning is as follows.

We contrast the chance of winning on switching vs the chance of winning on staying with the previous decision

$\mathbb{P} (win|switch) = \mathbb{P}(I = G, III = B) = \frac 23$ and $\mathbb{P} (win|stay) = \mathbb{P}(I = B, III = G) = \frac 13$.

The chances of winning is more while one switches. The solution to the problem seems to be very counter intuitive. Hence this is regarded as a good example problem for learning elementary probability.

Physical Layer Security Using Energy Harvesting Models

This article has appeared in the Technical Article Board of ECE Department, SSET - June 2016

Abstract

A point to point communication with a receiver and a single transmitter is the system under study. We consider the security aspect at the physical layer of the wireless communication transmission in the presence of an eavesdropper. A combination of techniques involving the channel state information(CSI) and energy harvesting information(EHI) is used to ensure the security. The experimentation is performed using the NI USRP 2920 hardware.

Extended Abstract

ireless communication systems consists of a transmitter and many distributed receivers. The eavesdropper is an unintended node that tries to know what the wireless transmitter sends. The eavesdropper can cause security hazards to the intended receiver by causing leakage of the message and causing intentional manipulations. These manipulations can in turn, lead to wrong message being delivered. The wireless physical layer is the lowermost level of the 7 layer OSI (Open System Interconnection) model. In many existing systems the security aspects are dealt mostly at the link layer and the network layer. These schemes have their drawbacks like, complex cryptographic cyphering, power consumption, hardware cost to name a few. Physical  layer security is destined to be the future, where systems can be implemented in low battery power devices using improved simplicity. 

The physical layer security is dealt with the help of the CSI information available at the transmitter and receiver[1]. The CSI information is independent at the eavesdropper and receiver. This helps us to manipulate the order of the interleaving bits. The scheme of the interleaver requires that the channel state observed by the receiver and the eavesdropper are both independent. This prompts us to look for methods that are statistically independent with the users, but at the same time observable. In this context we try to provide a scheme that is a combination of the CSI and the proposed scheme of Energy Harvesting Information.

Courtesy : https://arxiv.org/pdf/1505.07929.pdf
Fig 1: Communication and Security Model

Harvested Energy Model 

We consider the case of a device that is capable of harvesting/collecting renewable energy from sources such as solar, wind, piezo, etc. In general as energy impinges on the photo sensors(in the case of a solar panel) some part is lost in the conversion process to electrical energy. Thus, the harvested energy at any given time is high or low, ie a Bernouli random process. Depending on the position of the device the amount of energy harvested (say in a block interval) is an independent sequence. So the interleaving pattern can be made a function of the random energy harvested.

Fig 2 : The Block diagram of the OFDM scheme using the Energy Harvesting Information (EHI)

The schematic for the physical layer security using the OFDM scheme is described. The channel is estimated and used as an input to the interleaver along with the energy harvesting input. The combined inputs fed to the interleaver will allow for an improvement in the security and decoding performance. The system has been tested under the USRP test condition with the the eavesdropper being placed in a separation. Initially channel measurements are performed using perfect channel knowledge. Later it is modified to the case where in the absence of the perfect channel state information, an estimation is performed at both the transmitter and receiver.

Reference

[1] H. Li, X. Wang and Y. Zou, "Dynamic Subcarrier Coordinate Interleaving for Eavesdropping Prevention in OFDM Systems," in IEEE Communications Letters, vol. 18, no. 6, pp. 1059-1062, June 2014

[2] Universally near-optimal online power control for energy harvesting nodes
D Shaviv, A Özgür - arXiv preprint arXiv:1511.00353, 2015

This is joint work with a M.Tech student at the Wireless Communication Lab, SSET

Qualifying vs Quantifying

In this article we look into the duality of the two words, quality and quantity. The nature around us provides a good witness to make this duality precise. All the objects in the eyes of an observer are the same in the elements of composition while they are different in their nature, form and properties. The quality of an 'Engineering' product sets a standard whereas its quantity is only and (measuring) analysis tool.

Courtesy : http://thoughtprocess101.wordpress.com

It is often retold that Quality matters more than the Quantity. The reason for such a statement is recognized to be the connection and the duality of the two terms. The process of measurement comes into play, while one quantifies, whereas qualifying would require certain inferences or analysis from the measure. Look at the question "How old are you?". When this question is asked many of us has certain inherent doubts. But one knows that age is just another number. Look at this perspective into the matter. Can you think about it from the "half filled" angle of the age being a quantity that describes your physical strength, attitude, responsibility, or the like. The point being emphasized here is that quantification only leads to a sense of comparison, while qualifying brings around a sense of positive security(which in fact is the truth).

How do you measure your food habits? Is it dependent on the quality, quantity or both? Unless a desirable quality is derived from the measure being performed the exercise of measurement seems to be fruitless. In Engineering and Scientific study this stands out to a great extent. A sense of scientific enquiry, begins from the limited nature of our measuring tools, while the ability to draw useful interpretations (if not conclusions) would extend the possibility to expand our domain of knowledge.

Is the Nyquist sampling rate a fundamental limiting rate in sampling ?

This post is an assessment of the key assumptions of the  conventional sampling paradigm.

The conventional sampling process applies to Bandlimited signals, or in other words, signal spreads in the time axis. The process assumes taking evenly spread samples of the signal at a spacing depending on the maximum frequency component of the signal.

We analyze the question, if localization of information is allowed , will the Nyquist rate be sub-optimal. For instance, consider the signal and its sampling method:

The Transformed View - Part I

During my travel during the last few days, a lot of discussions happened about the KTU and its impact on the technical education. Many people from the teaching community feel that it is a ill-planned set up and exists only in news and hype. Let us not build a discussion here, but take some useful positives from the idea of unifying the local universities.

Many philosophers agree to the fact that the universe exists on a absolute "truth" and everything that we deal with are just its manifestation. Even the partitions that we build on religion, science, arts or any such streams actually are the same. In a united approach we see them as one. The learning in one stream does not in any way contradict the other.

Imagine you are in front of a white board and are gazing at it. Now you look the same screen with a yellow glass. The entire screen now becomes yellow. In reality the screen has remained white, and only the glass had made a difference. So are the different things that happen around us. Let us take this discussion to the subject of signal processing. Most of us are familiar with the natural time domain for the electrical signal. We are also aware that the power line signal that provides electricity has a sinusoidal fundamental frequency. We express the same thing here in different viewpoint. One viewpoint is the time and the other is the frequency. Nature imposes duality in the time-frequency, which brings about a conflict. Engineering solutions are nothing but a compromise on this duality. We shall build some interesting compromises in part II of this post.

Dynamic Programming Decision Making

All of us set certain goals and try to achieve them. What is the best way to keep track if you have taken the right decision?  Here is a quick method to keep track of your progress. Consider that you set a goal today, and you are trying to optimize all the actions in order to reduce the total cost. The cost here can be due to time, money, effort, social costs and others.

The idea is to incorporate a method to reach the optimum in a step by step manner that uses only the local information. We query that : "If I assume that I am optimal in the future, what action needs to be taken today to ensure a global optimum". This leads us to the answer that, the best way is to determine the best that you can do today, with the assumption that from tomorrow we are going to be optimal. This seems to be very suited to our current practice also. While we drive a car we put the gear to the right speed, so that we can endure the local roads and the nearby traffic. The goal might be distant but we always have to act optimally to reach there.  While spending we ensure that the basic needs for today is met. The savings also are done accordingly. Take the simple game of tic-tac-toe, here we are trying to see the local information in the game and trying to win or in most situations stop the opponent from winning !

Courtesy : http://experimental.designforfun.com

This approach of dynamic policy is widely employed in control systems and  communication. There are two things that we consider in this optimization problem, one is the value or the cost that is incurred due to our decision (actions)  and the second is the policy that we have come up with. So remember at the beginning of each day try to see that you are going to be optimum for 'today', because tomorrow will "take care for itself".

[Topic Courtesy :  Introduction to Stochastic Optimization, IITB]

On Decisions and Learning (Part II)

In the previous post, we have seen how the space and time constraints can affect the decision  making.  In this part, we extend the model to one of practical interest. Such a model should be robust across space and time variations. In effect we cover up the space and time and replace them by agents/players who affect our decision process. To illustrate with an example we take the case of a boy in say, Brazil and a similar aged boy in India. It is more probable that the Brazilian boy latches himself to football and the Indian boy would choose cricket with higher probability.

                     

The agents here is a representation of the culture and tradition - hence depends on the space. There can be agents representing time as well. For instance the decision on taking an umbrella before leaving the home depends on whether it is the rainy season or not. Rain is the agent here and hence represents time. Thus agents are the physical representation of the time-space (real) parameters. Another aspect of agents is that, there are certain agents that aid to the decision with more weight than certain other. Now there are decisions taken in accordance with logic, past experience, and predictions. Each of them has a correspondence with time - present, past and the future.

The process of making the decision can be summed up as \( f : (A_1,A_2, \cdots, A_k) \rightarrow  \mathcal{D} \). Here \(A|_1^k\) are the agents to be considered while taking the decision and the set \(\mathcal{D}  = d_1,d_2, \cdots, d_n\) are the decision choices. This model lacks the past learning that has been accumulated over time. To explain the learning in decision making, we can take the example of the man going out while it is raining (Agent = Rain). The man does not take the umbrella, and gets wet (Decision : No Umbrella). The next time he goes out in the rain he is reminded by the fact that he has got wet (which assumes a cost). Now it is possible to assign a cost of for the decision taken over a action set. Assume that the decision maker has learnt the decision taken over a set of agents till time \(T\). Now the system is opened and the learned costs are considered while taking the decision.

On Decisions and Learning (Part I)

An inquisitive mind always seeks the answer to this question, is the thing that I decide right? Has the trained mind in me educated enough to reach the "right" decision.

Decision making is a ever happening process in the world around us. Decisions may be taken for important as well as less important topics. The rightness of a decision is always debatable and often has a subjective element. So how does one take a decision, what elements are included in the process, and how the decision affects others. The three questions here has a strong theory in statistics. Let us parse each of them and look it in detail.

How does one take a decision?

Decision is a selection of a particular choice, from the given set of available choices. A decision may be prompted by a situation, which is both depending on space and time. So, deriving cues from the situation, any decision should particularly abide by time and space. Let us see a little example. Identically aged people live in a city and a village. Both fell ill (almost in the same time), and was taken to a doctor. The doctor in the city gave medicines in the form of tablets, while the doctor in the village asked the man to collect some herbs from the garden and have them. One can tell that space is the prominent factor in this example. The doctors decision complies with the locally available medicines. One may also expect in a closer analysis, that the domain of the doctor also plays a significant role in decision making. For this discussion we can avoid this possibility.

Now consider another example where time is the decision driver. A boy injured his knee while playing in the evening . Seeing the bleeding his parents took him to the local clinic for first aid. Imagine the same situation happening in the night. At this time, the parents have no access to the clinic, so they prefer to give whatever first aid is at home and later take up to the doctor if required. Time (and to an extend space) played the crucial role in this example.

We try to introduce some modelling. Consider a situation and \(n\) possible choices. A particular choice has to be picked. If one were to derive ideas from the examples presented, the decision \(D(S,t)\) is a function of the location and the time. Generally, space and time functions are difficult to generalize. So we somehow, avoid these by introducing a probability matrix over the choice. The simplification seems good, but did we handle the reality efficiently? Not really isn't it! What we did was to look into the decisions taken by us in the past and presented a distribution over those choices. From the point of view of an analyzer, this seems to be good. While the model seems to blind the decision makers view? One way to handle this is to bring in some dependence of space-time. The model should be robust to analyze and useful for the decision maker.

I leave this at a point for the reader to ponder a little :

Image Courtesy : olivergearing.com

Most of us act more or less according to this Importance vs Urgency model (logical planner!). We have a set of priority and the decision scheduling is performed by the urgency or the time requirement. Seems to convince why certain events require, us to wait in patience.

Get Puzzled!

As a continuation we will consider two more puzzle which motivates one or more applications in our day to day life.

Puzzle #1: A school  math teacher wants to teach geometry to her class 8 students. She collects 2 hemisphere shells and a cuboid, such that the cuboid can be inscribed inside the shell. She also bought paints -red and blue. One hemisphere was painted red, while only 80% of the second shell could be finished with the red paint.. So she decided to paint the remaining by blue paint. The teacher put the cuboid inside the sphere, and sees that all vertices fall on the red colour (assume that the shell is semi-transparent). Will her observation be true irrespective of the way she had painted.

The video solution of the puzzle above : - 

Solution:  If we consider the two hemispherical shells as a sphere, we understand that 10% of the sphere is painted in blue. Let us now denote, the vertices of the cube as \(v1\), \(v2\), \(v3\), \(v4\), \(v5\), \(v6\), \(v7\)  and \(v8\). The chance that a given vertex is placed in the blue part of the sphere, is given by:

\[\mathbb{P}(\cup_i v_i \in Blue)  = 0.1 \times 8 = 0.8\]

Thus, the chance that all eight vertices fall on the red part of the sphere \(= 0.2\). This means that there is at least one way of arranging the vertices such that all will fall on the red paint. The assertion made by the teacher is right.

(Courtesy : NIT Lecture, IITB)

Another one from geometry

Puzzle #2: A statistician is interested in this particular geometrical issue to find a spectrum allotment. An equilateral triangle is inscribed in a circle. The altitude of the equilateral triangle is 3/2 r. Find the chance (probability) that a chord chosen at random will intersect with the interior of the equilateral triangle. 

Try to work this out using more than one method. Is the answer you get the same in all cases?

Solution: 

Method 1 :  Each chord of the circle is uniquely defined by its center. We can place the chord's center inside the equilateral triangle area, so that it always falls inside the interior of the triangle. Thus the chance of choosing a chord which is in the interior of the triangle is

\(\mathbb{P}(\text{chord} \in \Delta) = \frac{\text{Area of } \Delta}{\text{Area of Circle}} = \frac{3\sqrt{3}}{4 \pi}\)

Method 2 :  Another method to express the probability is as follows; Fix one of the end points of the chord at the vertex of the equilateral triangle.. The chords that can fall in the interior will fall in the angle range \(\frac{\pi}{3} \leq \theta \leq \frac{2 \pi}{3}\) . Thus the probability of the event of interest

\(\mathbb{P}(\text{chord} \in \Delta) =  \frac{\pi/3}{\pi} = \frac 13\)

Method 3 : The chord is defined by its distance from the center of the circle.Thus the chords with distance from the center less than \(r/2\) can be classified as the interior of  the triangle. Thus the chance that the chord chosen at random will fall in the interior of the triangle is given as:

\(\mathbb{P}(\text{chord} \in \Delta) = \frac{r/2}{r} = \frac 12 \)


Notice the three distinct answers we obtained. Can you think of a good reason to justify this.

If we look into the situation more clearly it is evident that the notion of uniformly random chord is not well defined. In that case all 3 methods are right . Unless a fixed notion(reference) has been foretold, there is no clear solution. Such class of problems (challenges!) are called ill-posed .

(Courtesy : Introduction to Probability Theory, IITB )

The Balancing Act

Lets us start with a puzzle somewhat common place. A shopkeeper gets a stock of dozen cricket balls out of which one is a cork ball (kookaburra) and the remaining are rubber balls.  He is asked not to touch balls with hands (as it has to be used for the match), but is given a "pan" balance which will show either equal, less than, or larger than for the weights on the pans.

Find the minimum number of uses of the balance to find out the heavy ball.

Hint: 1 >> Separate the balls

The extension to this puzzle is interesting, Let us say that we want to find the odd ball (which can be  heavy/light) from the lot of 12 cricket balls. 

Guess how?

The interesting fact is that the odd ball can be determined with its weight in three measures. The idea is very similar to the source coding - Huffman coding. We can form a coding tree and verify it easily.

Let Left pan be represented as L and right pan as R.

The stepwise solution is as follows,

1. Divide the 12 balls into groups of three.
2. Weight 2 groups (of three balls) --> 1st measure. There are three possibilities 
• L=R then discard both the group
• L>R , call case A
• L<R , call case B
3. (If case A or case B happened) In the cases L>R and L<R, replace the right set by any of the untouched group. --> 2nd measure Then, 
• L=R, then the balls removed from the right pan is the odd group and follows the case in the previous measure. (ie, if case A-- light, case B -- heavy)
• L!=R, the the case which happened in the previous measure follows(ie, if case A-- heavy, case B -- light)
4. From the odd group determined from 3, take any two balls and do the measure;  --> 3rd measure
• if L=R, the  odd ball is the unmeasured ball and follows the same weight as in point 3.
• if L!=R, then the odd ball is one which follows the case in point 3.

The reader now can try to generalize this for \(m\) measurements