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The incoming pictures and videos from the civil war in Srilanka is making a mockery of what human lives and values should be. We are in 21st century and belong to what is perceived as a modern society. Yet, millions of people are caught between two ethnic ideologies in a small country in the foot hills of India, the largest multicultural, democratic country in the planet. What an irony! Well, I am not suggesting that India is freed of problems, but looking at the magnitude of the ethnic problem to its total size bemuses me. The LTTE who have used various despicable methods of terrorism over more than a quarter century in the name of a seemingly improbable Tamil Ealem goal has made the life of poor people, nothing less than hell furnace.  The Sri Lankan government on the other hand seems to be in no mood to stop the bloody battle before they see the end of the Veluppillai Prabhakaran

War has never solved any problem,irrespective of the goal it ever aspired to achieve. What it leaves instead is the loss of millions of innocent lives and an unrepairable, long lasting trauma. Children who are caught between ethnic rivalry and stupid power struggle are denied of a life. It is easy to blame one another for this mass misfortune of innocents. The LTTE, now in the brink of being annihilated are wounded and are further exploiting poor peopleas human shields to counter attack the more powerful army force. It is a battle of loss. Sadly, the loss is imposed on to their own people for no genuine fault of theirs. What kind of doctrine is it? People are forced to flee from their dear land in desperation, hoping against hope. Clearly, their supposed leaders and power points have made life hell than the promised dream land.

What  (and still is) needed was a political solution, not war. It is a shame that such a tiny country couldn’t arrive at a political situation.  If that had happened, we could have avoided one of the most shameful refugee crisis in modern era. LTTE is a terrorist organization which caused havoc not only in SriLanka, but they also made a mess in India by killing a promising youth leader Rajiv Gandhi. In the name of achieving a mirage, they let the downtrodden Tamils in the northern Srilanka to suffer.  It is easy to promulgate an ideology of creating a dreamland, but the price you pay is in the form of innocent lives. It would have been far better to become part of the existing political system to put forward their demands. It might sound so silly, but in a country as big as India, it worked. Millions of religions and sub castes with varied social classes lives without a civil crsis as big as the one faced in a tiny SriLanka. I hope Kashmir too learn from this hard lessons from SriLanka and get to a more peaceful dialogue path than weapon confrontation.

I may be a little naive to comment on this SriLankan struggle, since I am not really aware of the intricate issues between these ethnic groups. No matter what the extend of enmity exist, as an outsider I find it hard to chew these gross deaths and massive refugee crisis. Seeing the pictures of millions of refugees walking away from their little homes, children and old people included, make me sad. We cant do this in a modern society. What is worse is that, the actual ground realities may be much more heinous and gruesome than the few aired videos and pictures. Oh! God, if only we learned to live in harmony!

Now, when the war end, what next? Will those refugees get a life back? A generation is in danger. What is the UN doing? War! no more of that beasts please. We have had enough of trauma.

Here are two video documentary on this unfortunate ethnic trouble in the naturally beautiful island nation.

Todays IPG seminar had Fritz Eisenbrand (the Disctete Opt chair, Math department EPFL) talking about Diameter of Polyhedra:Limits of Abstraction. I don’t think I followed the topic too well, but this is a share of what I understood.

The topic is about a convex geometric problem on the diameter of a polyhedra. The question of whether the diameter of a polyhedron is polynomial or not seemed to be a longstanding open problem. The largest diameter ${\Delta_{u}(d,n)}$ of a ${d}$ dimensional polyhedron with ${n}$ facets has known upper and lower bounds.

${n-d+\lfloor d/5 \rfloor \le \Delta_{u}(d,n) \le n^{\log d +1}}$.

The lower bound is due to Klee and Walkup and upper bound to Kalai and Kleitman. These bounds also hold good for combinatorial abstractions of the 1-skeleton of non-degenerate polyhedra (Polyhedron here is called non-degenrate). What Fritz and his colleagues have done is to look into the gap between these known lower and upper bounds. Apparently, the gap is wide and they have made some progress to get a super linear lower bound ${\Delta_{u}(d,n) \le \Omega\left(n^{3/2}\right)}$ if ${d}$ is allowed to grow with ${n}$.

The way they showed this bound is by establishing the bound for the largest diemeter of a graph in a base abstraction family. Let us say, the abstraction family of connected graphs be denoted by ${\mathcal{B}_{d,n}}$.The largest diameter of a graph in ${\mathcal{B}_{d,n}}$ is denoted by ${D(d,n)}$. They find that,${D(d,n) =\Omega\left(n^{3/2}\right)}$ and then using the fact that ${\Delta_{u}(d,n) \le D(d,n)}$, they conclude the bound ${\Delta_{u}(d,n) \le \Omega\left(n^{3/2}\right)}$

I have not had a chance to see their paper yet. I must say, the proof was not all that within my grab during the talk. However it appeared that it is based on some layering and combinatorics. He said some applications to covering problem, in particular disjoint covering design which I didn’t follow that well. Sometimes I get the feeling that I am a little dumb to grasp these ideas during a talk. I wonder whether others understand it very well on a first shot presentation. I have put it in my agenda (among the millions of other papers to read) to see through this problem and proof, one day! His presentation was very clear and legible though.

…and it is Oracle! Quite a surprise! Thats the least I felt, when the news broke out stating that Oracle is buying Sun Microsystems. The once great and proud maker of some of the best servers and computing power houses is now leading to the hands of a software giant, largely focused on database solutions. There is no natural connection to the obvious eye But who knows? Oracle may be eying something big! I cant see a justification of spending 7.4Billion \$ to get hold of Java and MySQL alone. These are the big software solutions from Sun, apart from Solaris.  Anyway both these are open source software too. Afterall Sun is known for its champion make of servers right? Is it that Oracle feared an imminent acquisition by some other competitor, which might have distracted their lead? For a good amount of time the speculation was on whether IBM would still buy Sun. Then it was the Cisco, and the HP taking rounds as potential buyers. None of these materialized, but Oracle, the one choice with maximum entropy!

Would it be that, Oracle saw something big with Solaris? Are they eying on a solid operating system market? In any case, a decision to buy a company for 7.4Billion cant be for fun. Surely there got to be a plan, at least in theory!As someone opined in some article recently about possible consolidation of SAP and a possible buy over by one of he bigger fishes like IBM or HP. Now, that would take some shape too. Nothing can be ruled out at the moment. This is the sort of indication floating around.

Today, during the evening chat, Emmanuel Abbe threw an interesting question: Whether the sum of square roots of consecutive binomial coefficients converge to some closed form! That is, ${S(n)=\displaystyle \sum_{k=0}^{n}{\sqrt{\binom{n}{k}}}}$. We tried a few known combinatorics tweak, but no meaningful solution arrived. We were also wondering whether this has some asymptotic limit, but that too did not yield anything. A quick check on Mathematica wasn’t helpful either. Now the question is: Does this sum yield some closed form expression.

While playing with this sum in Mathematica, I found that for the sum of squares of binomial coefficients, there is a nice simple closed form.

${S_{2}(n)=\displaystyle \sum_{k=0}^{n}{{\binom{n}{k}}^{2}}=\binom{2n}{n}}$

I was toying with a proof. It turns out that, the proof is extremely simple and is a one line tweak of the Vandermonde identity ${\binom{p+q}{m}=\displaystyle \sum_{i=0}^{m}{\binom{p}{i}\binom{q}{m-i}}}$. Simply substitute ${p=q=m=n}$ and we have the results on table. The natural question then would be: Is there a generalization for ${ S_{r}(n)=\displaystyle \sum_{k=0}^{n}{{\binom{n}{k}}^{r}}}$ for any ${r\in \mathbb{N}_{\ge 1}}$. Ofcourse now for ${r=1,2}$ it is trivial.

Apparently, it turns out that, there is no closed form expression for a general (all) ${r}$. There are some interesting divisibility properties of these sums. An interesting account of that is addressed by Neil Calkin (Factors of sums of powers of binomial coefficients).

At the moment, I get a feeling that sum of fractional powers of binomial coefficients is not trivial. May be there is no closed form. May be not!

It was almost unthinkable that a single company would rule the EDA world. At least this is what I strongly perceived, a few years ago. Now, put the present dishes on the table and I see that, Synopsys is giving nightmares to all other EDA shops. While working with Synopsys, we always saw Cadence as the rival company to get floored on. All of that, was in the wish list and not many of us thought we could do that, ever so easily. Cadence was the obvious leader of EDA for many years and Synopsys strongly stood at the second position. Then there were the Mentors and the Magmas, at a fair distance down. Magma was the emerging company with a strong future predicted by many pundits within and outside the EDA world. It was imminent that Magma one day would give a stronger competition to both the big brothers Synopsys and Cadence. They may still be a force to reckon, but sadly they tried to act over smart and it all triggered a downfall. I am not sure whether their, rather peculiar sue attempt on Synopsys was wholly responsible for their slide. Definitely that may have had a role.

Now it appears that, the discounts offered by the EDA big fellows are giving more aches to smaller players. It is well known that the EDA tools are phenomenally expensive and the marketing always revolved around giving deals for bulk purchase of tools. What is more colourful is that the buyers offer to make the deal public in exchange of more discounts. The concept of primary EDA vendor was not that prevalent a few years ago. However, the trend these days is to grab that extra mileage by roping with leading semiconductor houses. It is a big win for both the buyer and seller. Synopsys for sure  is going to enjoy this. First they are among the very few making profit even in these difficult economy. They are perhaps the only one from EDA. Considering that the EDA market itself is only about 4 or 5Billion dollar market, the impact of a near 1.5billion dollar Synopsys doing too well is going to give more headache to other little fellows, in the coming days.

Cadence is literally having a plate of their own problems and now with the whole semiconductor market trying to minimize their R&D spending, it is double advantage for Synopsys; That too with newer friends adding to their primary EDA friends list. Magma is becoming more or less a prospective buying target than a rival. A few years ago, Synopsys had worries about a growing Magma. Now I wouldnt rule out a potential buy over by Synopsys itself, may be Cadence or Mentor Graphics!

Some people say that Synopsys is going to be the next Microsoft in EDA. Aart perhaps rightly said they want to be the Apple of EDA. I would prefer Aarts view here. Not just because Synopsys was my breadwinner for a while and not because I attended the same grad school as De geus, nor because of the well known fact that yours truly is an ardent fan of Aart de Geus. But because Synopsys is  well managed by a great management team with great work ethics. When the ratable (subscription) revenue/ licensing model was announced there were lot of eyebrows, but it was a long term vision and Synopsys is really reaping the fruits now.

Having said all these, like many of you, I am too worried by this single monopoly trend in EDA. We need smaller players in every market and we need more innovation. From Synopsys standpoint having less competition would yield relaxed days ahead, but for the market we need better products and superior innovation. We need Cadence to revive and at the same time companies to emerge to take position for the next Magma. At this stage, I am worried about Magma. Is Magma to follow the Avant! route to get merged with Synopsys?

Aart has aptly mentioned that “I understand that the entire world is under economic pressure,” he said. “When that happens, some will do better than others”. One thing for sure. Among all the EDA executives, Synopsys folks must be getting better sleep these days.

…High above the city, on a tall column, stood the statue of the Happy Prince.

Oscar Wilde‘s ‘The Happy prince‘ is one of the many stories that I have read during early school days. Remarkably, this is one of the few I still remember! I was barely able to read difficult English literature per se then, but still the story of Happy prince was within my grab. I don’t recollect whether I had understood all the words of Wilde, back then. This was at a time, when I was happily enjoying my schooling and life in my mother tongue Malayalam. Malayalam literature had its penchant style and aura, which is difficult to explain to non-Malayalam readers.  I was ‘at-home‘ when it came to reading the Malayalam literary works. Yet, I had thrived to learn English stories, albeit at a reduced speed. That whenever, I got a chance to read. Oscar Wilde was one of the rare English writers whose work, somewhat accidentally came to my reading list.  I was surrounded and enthralled by the works of great south American and Russian writers, otherwise. Partly, thanks to the communist influence in Kerala society, the translations of great Russian and south American books were far more available at ease  and at cheap rate (In fact I don’t remember buying anything, but all borrowed from various small local libraries around).

Coming back to the Happy prince, the story had indeed put a stamp in my memory as a child.  I may have been 10 years or so when I was ‘introduced to’ the ‘Happy prince’.  The subdued request of the prince to the little swallow was by heart to me. When the prince says ” Swallow, swallow little swallow…”, my heart seemed to have resonated at a lower pace.  As a child, I had never seen an European city, for that matter any great city including the ones in India, let alone city across the Atlantic. It was all in my mind, that I’d imagined a mythical model of such a city, a city of the happy prince!  I used to visualise the position of the Happy prince statue standing tall in the middle of a city. Did I ever imagine the enormity of a city as big as this? As a child it is difficult to fathom and relate the seriousness of people’s struggle, a statue could see.  For sure, I was touched and moved by his sorrows and pain.

The swallow represented a role model so to speak  when it comes to helping others. Subconsciously, the little swallow literally drenched my cheeks by living through that difficult winter.  Back then, I had never seen what it is to be a snowy winter, still, could feel the chill of that season, when the shivering swallow wholeheartedly fulfilled the Prince’s wishes. Years later, the words “…Swallow, Swallow, little Swallow. Stay with me one night longer” still linger my ears. Tears still beckons! Perhaps that story have had a deep influence to me since childhood, to an extend that I’ve never imagined. As a child, I wished if only the swallow could go to Egypt, but alas!

Now, I have accidentally come across that very same story in video form in youtube. That brought in a rewinding of years! I feel the same chill now, as a 10 year old that I had felt years ago. I had told this story to Nivedita a few times. I could see her expression when I uttered the prince’s humble request “…Swallow, Swallow, little Swallow. Stay with me one night longer” .. The impact of Oscar Wilde’s powerful writing tells a story in itself. Don’t they?

…High above the city, on a tall column, stood the statue of the Happy Prince.

The prince and the swallow still stays on.. in my memory…I really want to tell this story to many kids! The youtube video is commendable too.

I’ve finished reading the memoirs of Walter Rudin. It was a quick read for a few hours. His autobiography is titled The way I remember it, published by AMS in the history of mathematics series.  It wasn’t particularly interesting, to say the least. From a mathematician who wrote excellent books on functional analysis and several others,  I was expecting a much better story. Of course one cant write an imaginary story in an autobiography, but then the incidents in his life is pretty much the story of any European intellectual during the war days. The best I liked is the one from Karl Popper. However, I could connect many incidents from Rudin’s life, primarily because of the geography. There is a chapter on his days in Switzerland, which also touched upon Lausanne. That part for once enthused me! Was wondering how Lausanne would have been 70 years ago! If you are completely unaware of the life in Europe around the WW period, then this will give you a perspective.  Like many scientific minds of that era, he had a long route to the United States. He discusses the path and family traits of that journey, in a somehat uncomplicated language.

In his autobiography, Rudin has discussed some of his contributions to mathematics as well. That part appeared a little informative, but technical read. If you know his work already, you would connect it nicely.  I particularly liked the chapter on Function Theory in the Unit Ball of Cn.

In all, not a book I would recommend, unless you are a Walter Rudin fan and knows his contributions in much more detail. However, this may be a motivating read for a young school kid aspiring to be a mathematician. Why did I say that? I don’t know! Don’t ask me why either!

A very interesting report on the neuro socio development and progress of children from poorer background, is reported in the recent edition of The Economist. In the report they discuss the research study by Martha Farah of UPenn.  Their investigation came out with a worrisome conclusion that, children born with poorer socio economic background have a greater chance of becoming underachievers (read as under performers compared to their middle-class counterparts). The study is of course based on statistical inference and hence there ought to be scope for exceptions (Large deviation theory!). However, being a statistical method, we can well assume that the behaviour is true on the average (expectation). This is truly not a conclusion we would like to hear, but to me, it appears to be a careful study and its conclusion opens up the ramifications of the larger crisis faced by millions of people all over the world, especially from developing countries and Africa.

What these researchers did is to study the stress level suffered by a person over the span of his/her life. They combined various type of pressure (such as systolic and diastolic blood pressure) and formed an index, what they called allostatic load. They found that this index is on the higher range among people from poorer background than those from middle class. They also have found that, the duration of the poverty life of  a person is correlated with allostatic load.

The report appears to conclude that, stress is more or less the sole reason for spoiling the working memories of an individual. We could say that it is a little too strong a statement. Children under too much socio-economic stress tend to do badly in studies and that unfortunately carries on for ever. I am tempted to argue that, a socio-economic push, say by providing opportunities to such children will change the performance of an individual. After all, we know many instances of children born into poorer backgrounds scaled highs.  But if you read the report carefully, they are not refuting this either. What they simply say is that, on a relative scale, the impact of stress during early childhood is much more serious than what we perceived to be. Children of poor perform poorly in school and stay on that way and sadly, remain as poor (under achievers) adults. Clearly, the authors refer ‘poor’ adults as state of ‘under achieving’ compared to their counter parts from a middle class background. In that case, one can always argue on the definition. True, one doesn’t have to be a genius to do well in life. But, the larger picture however is clear. A poorer childhood may limit his/her potential.

It can be very easily mistaken for that, this report is derived from a non scientific study. I too was inclined to think in those lines when I read the title.  A careful reading however convinced me that, there could be genuine truth in  their argument. After all, the conclusion is not on a single individual, but on a collection.

I am sure the wider picture of this report may have a scientific explanation too.  Too much stress, at an earlier stage of life may prevent development of nerve cells. Bottom line is that, we simply do not want to take a risk. It isindeed very important that our children and future generations not to undergo that ill fate. We have a social responsibility to be aware of these and try to do a part to ease up the trouble, as much as we can.

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