Mamta Rani Deals with Chaos

WHO? MAMTA RANI

WHAT? COMPUTER SCIENTIST

WHERE? CENTRAL UNIVERSITY OF RAJASTHAN, BANDAR SINDRI

Reported by Aashima Dogra

I was leaving Rajasthan and driving northwards to Haryana. Before leaving the colourful state behind, I was happy to spend one last night in the desert. I turned left from the superhighway NH8 and parked my van outside the massive campus of the brand new Central University of Rajasthan. The next morning, I would go inside the university and hopefully meet some scientists.

The CURAJ campus is still under construction but most of the ornate buildings are complete. The cream-coloured faculty buildings are pretty and huge, with plenty of parking area and large roads flanked by thorny bushes connecting them. The campus is being prepared for many more students than there are presently, so currently, it looks a little bit excessive and unused.

It’s still early days for the institution that has big plans for itself. You can see this on the faculties’ faces. When I first met Mamta at the Computer Science department that she is heading, she was frantically making her way across the large entrance hall, fit for a 5-star hotel, to a 10 o’clock exam that she was scheduled to supervise.  She could squeeze me in at noon, she said, giving me time to interview Hemlata on the other side of campus.

Later I turned up at her roomy office where she was busy delegating administrative duties and at the same time handling her laptop awkwardly with her left arm; her working arm was in plaster. Despite obvious difficulties, Mamta is calm, wise and straightforward. You can tell she works with computer algorithms by the way she responds to questions. She takes her time processing them and outputs an answer that is systematic and logical.

Perhaps, this is her way of dealing with the mounting pressure. Having been a researcher for sixteen years, she is now setting up the Computer Science department at CURAJ. Proposing courses, taking them through various boards and finally the University Grants Commission and Ministry of Human Resource and Development, takes time and involves lots of frustrating legal procedures.

Apart from this, Mamta finds herself under added pressure, much of which is easily avoidable. “Honestly, my main job here has been to set up the IT infrastructure for the university,” she laughs as we start talking about her role at the university.

“People in computer science are always overloaded in any academic organisation, it seems. Because they have to maintain and develop IT infrastructure for the university.” This should not ideally be the case, Mamta points out – “there is a provision of a separate cell and a system administrator and a group of people to handle that job. But in the initial phases of the organisation, it so happens that they are unable to appoint people and they ask the computer faculty to do the work.”

“People in computer science are always overloaded in any academic organisation. Because they have to maintain and develop IT infrastructure for the university.”

Of course, Mamta’s research has suffered as a result. She points out: “Job profile of all faculty needs to be at least 70% academic work and maximum 30% administrative tasks. I have to spend my time doing 20% academic work and 80% administrative.”

This is unfortunate because Mamta’s research is valuable to many scientific disciplines.  And there are very few people working in this area in India or abroad. So let me tell you all about it.

Making graphics of objects found in nature

A lot of the advanced application-based scientific research relies on computer models.

It is easier to see how a complex system will behave if you have a model of it on the computer. The back-end of these models is a computer algorithm – one that feeds on input of scientific values, processes this data based on an equation that is specific to the model and gives a result.

Maple and fern leaf generated with an iteration based computer model. Credit: Demko et al 1985

The result that Mamta is concerned with is computer graphics of natural objects. This is where Fractal Graphics and Chaos come in. “Traditional computer graphics can generate algorithms to visualise man-made objects like a building complex. But these linear algorithms are not efficient for modelling natural objects such as trees, waterfalls, rivers, mountains and society. So we need a special field to make algorithms for natural objects. Fractals are a tool for this.”

Graphics of a maple leaf and A fern leaf generated with an iteration based computer model. Credit: Demko et al 1985

Fractals are mathematically generated shapes that can model chaotic systems such as the shape of a galaxy, a fern leaf or human population growth pattern which is determined by ever-changing social events. These shapes are determined by increasing and decreasing values that have some kind of ratio between them.

The backbone of the processing that takes place is an iteration system or feedback system. Imagine a series of values. The algorithms work with one value; this is one-step. After this is done the algorithm processes the next value based on the result of the first iteration. And the process goes on for repeated values. These values might have some relationship between them. When we put them together what we get is a beautiful pattern that is a model for a natural system.

Revolutionising Modeling

Mamta has already made a mark in her field. Just like discovering a drug that treats multiple diseases instead of one, Mamta’s work has changed the paradigm of fractal models and taken the whole field to the next level.

“I must say the whole world was working on one-step iteration method.” But this changed after Mamta’s two-step iteration process was published in Chaos, Fractals and Solitons – “an Elsevier journal,” she stresses.

“When I started working in this area, I replaced the one-step iteration method with the two-step iteration method. Then the whole field got revolutionised. That has been my main contribution to the field.”

A fractal of a complex quadratic equation generated by Mamta using her 2 step iteration method

With the two-step iteration method, a lot more values can be incorporated into these fractal-making algorithms, and the models generated become more robust.

For example, consider an agricultural scientist working on hybrid plants by cross-breeding two different varieties. Before this experimental plant actually grows, the researcher is able to visualise the plant in a computer system. Of course, many visualisations of the plant need to be generated so that all the hybrid possibilities can be accounted for. The challenge is to identify the algorithm to generate all these possibilities. With a one-step iteration, visualisations for a certain number of plants can be created, beyond which the algorithm starts being inefficient.

However, when the two-step iteration method is applied, models of a much wider variety of plants can be generated for the agricultural scientist to work with. If ten types of plants were generated before, now, with Mamata’s two-step iteration, hundreds and thousands of plants can be generated.

The difference between one-step and two-step method

In one-step iteration process, we have an input on which we do some processing and get the output. For the next step, this output will work as an input.

One step iteration

In two-step, the idea is to combine the input and output in some ratio. Both input and output are numerical values, so we can combine them in many ways: we could take an average or-or we can apply some function like say input is x and output is y, and we take 1/3rd of x and 2/3rd of y and then add it, or we use only half of x and half of y.

Two step iteration.

“You can combine them in any ratio and the result of this combination will be the input for the next step or iteration. If we do not take any content of input but take output 100 percent, then you are back with is the one-step-method.”

So the one-step-iteration process is in fact just a subset of Mamta’s two-step-method.

Playing with Fractals

The Hindu ‘Trishul’ created by Mamta

While living in Bangalore, the so-called city of start-ups, I once heard someone say: “Everything and anything is possible in software.” I rarely see this motto put to practice, but in Mamta’s research papers this belief shines  right through.

Having grown up in a mountain village close to Rishikesh in Uttarakhand, Mamta went to university at the Gurukula Kangri Vishwavidyalaya in Haridwar. “The university follows a Gurukul-like culture. They want to focus the research on traditional Indian concepts.” This had a particular influence on Mamta’s research.

With fractal graphics, she created an algorithm to generate the Trishul – the Hindu trident representing the three fundamental forces or gods – Brahma the creator, Shiva the transformer and Vishnu the preserver.

This passion project was an extension, via the two-step iteration process, of  work done by Gordon Cooper, a South African scientist. “The original equation was given by Cooper. He called it the Carotid-Kundalini function because the equation generated some pictures which are alike to the Kundalini energy flow of our body [according to yoga theory]. He had obtained those pictures using the one-step method.”

A “superior” Carotid-Kundalini function generated by a team of Indian scientists developing on Cooper’s work Credit: Dimri et al

“We [Mamta and her PhD students] used his equation and applied our two-step method in this equation and we could generate many pictures using this. At some values, we could obtain the trident. We adjusted the equation so that we can get this trident.”

However, Mamta plans to go beyond explorative and recreational mathematics and graphics soon as she can get some respite from her administrative duties. “Up till now, my work has been more theoretical. It can be applied to only a few real problems. My plan is to take real problems and apply all these concepts to them.”

Population science is one area she is very keen on. “I have done scientific work which shows that population models can, in fact, be improved manifold. After that, nobody worked on it. I want to now collaborate with social scientists and understand how they analyse the data. And we can then apply my work on real problems of population prediction of 5 years, 10 years or 15 years in the future.”

“Go your own way, girls”

Mamta comes from a “mixed-type” family. Her father had high regard for higher education, being a university mathematics professor himself. But beyond education, their expectations for her were smaller than those she had for herself. “Being from a large family in a village, they were less excited about life after higher education. Everyone wanted me to get a job at a safe place, close to home. If I did this, I wouldn’t have reached here. So then you have to rebel.”

She has resisted the pressure to get married and settle down and start a family. “It will happen when it has to,” says the 39-year-old.

After her father pushed her in the direction of computer science, Mamta explored the software world in Mumbai for a while but soon lost interest in corporate life. She went on to teach at a long list of colleges, mainly in UP, did a stint as a scientist with the Malaysian government and finally found her place in CURAJ where she now runs the computer science show.

Specifically, in academia, Mamta says she has experienced no discrimination as a woman. But she agrees that there are obstacles posed by society as whole:  “I have struggled through these societal problems to come to this point.”

“I have experienced that when you are rising higher than your male colleagues, they try and stop you by pointing fingers in your personal life. In the start of my career, I also faced some discrimination for being a villager.”

“Most girls are fearful and feel shy. They need to overcome this and go their own way. Don’t bother with what people are saying.” With this attitude, Mamta goes through her day. She arrives in the morning, mentors budding computer scientists, performs administrative duties until 6 pm. After this, with her four PhD students, she works late into the night on her research.

“I have experienced that when you are rising higher than your male colleagues, they try and stop you by pointing fingers on your personal life.”

The university is practically in the middle of nowhere. I found it only on my way out of interior Rajasthan. While it was for me a nice, quiet camping site for a night, for Mamta it is not such a pleasant reality. I ask her how she travels home every night. “There is no public transport here. So I drive 22km back and forth everyday. And for women, it is not safe to travel after late working hours.”

What keeps Mamta going then? “I take the risks,” she says smiling.