When, on song, nothing looked more pleasing to the eye than Martin Crowe‘s batting. The news of his final battle with cancer and the eventual farewell  felt like a beam of sadness flown through my mind. A champion in many ways. RIP, Martin Crowe. Thanks for the memories.

I am eagerly looking forward to tomorrow. Can’t wait to see the president Obama, interviewing the great David Attenborough. Two icons! Very few people captured the imagination of our wonderful world, the way David had done. His work over the years, filled with amazing visuals, stories and truly remarkable insights about our planet and its species has influenced my perception about life in general. He is a global treasure. His contribution to science and education surely complimented the works of Darwin and others. Thank you sir for showing the many beautiful things around us and our planet.

Without guessing, you can imagine, why I keep every one of his available blue ray as such valuable possessions!

The BBC interview is expected to get telecasted tomorrow (28th June 2015) 2.30 PST time. How I wish tomorrow came sooner.

As he moves to the 90s, couldn’t stop sharing the old video tribute from BBC. Let him live for many more years and open our eyes more.

Saw this first up on my Facebook feed. Initially, I’d gushed away, but later decided to take a look at the details. Glad that, I did. This is a mini documentary on the life of a man named Paul Smith. The amazing thing is that, he has made some marvelous art work, out of a few keys from a type writer, yes, the grand old type writer. Born with a severe cerebral palsy, he finds a new way to take creativity to super human level. Some of his works are simply stunning. Oh man, do we crib for simple thing in life? As they say, when there is a will, there is a way! All I can say is that, this man can easily be its guard honor. A special man, a special artist. Take a bow, Paul. Life is Beautiful!

Slowly getting back to blog once again. Let me start with a few updated photos, all selfies with my new iMac! Blogging will be back shortly…

The great writer of our lifetime passed away. I was aware about his illness and ongoing treatment at Mexico city.  Yet, the news of his death brings in a cold wave splashing through my mind.  Sadly the end came all too sudden, especially that he had looked jovial last month on his birthday, when he turned 87. What an incredible literary giant Gabriel Marquez has been. With his death, a huge void will remain unfilled.  The surreal touch of his pen in bringing life, social culture, colors, politics, revolutionary romanticism and then beautifully transform all of them to our minds, at mythical proportions is something Marquez-sh. It was a privilege to share a timeline, albeit brief with this colossal literary figure. The Latin American writers always had a special place in my heart, the reasons are many. Marquez surely tops that line with Neruda and perhaps Miguel_de_Cervantes among the pantheons. RIP Gabo. We will miss you, but your memories and work will stay timeless.

As such, I cant tell much about the dynamics behind Google buying Boston Dynamics, but I am excited to hear this news. All I can say is that, there is still life for innovation! Knowing Google, they will do a good job with this new addition. We will have to wait and see the big day.

If you haven’t seen, you must watch the Cheetah Robot, the Usain Bolt equivalent in machine form:-)

With Scott in all smiles:-)

Sadly, the great man has left us. The world becomes a lesser place. Nelson Mandela, has been a remarkable symbol of  peace, determination and humility. A champion leader for humanity. Perhaps, no one since Mahatma Gandhi will have a legacy like Mandela. I vividly remember holding a placard in one of the  school day processions, with a message “Free Nelson Mandela”.  Little would I have known the true greatness of this man, back then… An absolute hero.

The most striking thing about Mandela to me, is the way he composed himself, after release from 27 years of prison. 27 long years.. think of it! 18 of that 27 years  in the isolated Robben Island. He held himself, dumped all vengeance against the very people who took away a golden slice of precious life. For the world, we had a great leader in him for years since then! His release could easily have turned into a bloodshed like never before, but he instead chose the path of peace. Talk about leadership. He is something beyond special.

I can feel the deafening feeling in South Africa and Africa in general, the world by and large too. What a sacrifice! Hope we can continue his legacy. BBC has this nice obituary on him. RIP.

If you have not seen this before, here is a must watch page from PBS.

So, the number has descended down from 70 million to a mortal 600! Expectedly, there is a new Polymath initiative to improve this further and who knows, perhaps 2 indeed is that number. Well, we are talking about the new result by James Maynard on the asymptotic gap between prime numbers.

Just to recap, the problem statement is as follows: If $p_n$ and $p_{n+1}$ are the $n$th and $(n+1)$th prime numbers (e.g., $p_1=2,p_2=3,p_3=5, \ldots$). On cursory counting, the gap $p_{n+1}-p_{n}$ appears to grow larger as $n$, but not necessarily, because there are these well known twin prime pairs such as $\left(3756801695685 \times 2^{666669} \pm 1 \right)$. Will this gap of $2$ stay good forever as $n \to \infty$? If not as low as $2$, will that be something low enough? i.e.,  How small can $G$ be, where

$G=\lim_{n \to \infty} \inf \left(p_{n+1}-p_{n}\right).$

Earlier this year, Zhang proved that $G$ is no more than $70$ million. That in a way proved that, the prime gap is bounded as we move along the number line. A bunch of mathematicians including Terrance tao worked further (polymath project on this) and improved that gap to as a few thousands. The latest result from Maynard brings in an independent proof for $G=600$. Maynard also claims that if the Elliott–Halberstam conjecture (See this nice blog post on prime tuple theory this by Terry Tao) is indeed true, then, $G=12$. Stunning!

What is stated here is just one avatar of the prime tuple theorem. More general results are also being discussed within the community. Terrance Tao again has this nicely articulated and maintains a polymath page for us. As an onlooker, I am as excited as many others to see this progress.

Sitting at 15th floor of the Hyatt regency in Dallas, with a night view of the city scrapers in the background, the only thing that flashes is nostalgia. The feeling of growing up, adoring and tirelessly following a true champion in Tendulkar. Suddenly, he is taking one last walk to the 22 yard strip, a test match at his home turf in Mumbai. It must be emotional for many and I for sure cannot hold my tears. It is only a retirement, but wait no. It has been our life in some ways.

Today may well be his last innings with cricket bat in a test match. Stamp of vintage Tendulkar was seen yesterday. Let us hope that he adds a few more of his straight drives and cover drives today.  Never have a farewell touched this close. He was not just a hero, but a pride and a part of my growing up. As he walks to the sunset of a glittering career, a part of me fades from the horizon as well.  The timeless thing of our life, prepares to turn the page! Oh dear life, we have crossed two decades!

Who would have thought, a 62 year old woman, successfully swimming non-stop against all odds through a turbulent ocean stream of no less than 110 odd miles, a stretch guarded by dangerous jellyfish and the likes of sharks. It is a daunting task and indeed hard to believe, but those who have seen Diana Nyad nearly making the cut in the last two attempts would know the type of steel her will is made of. Today, Diana Nyad has achieved her cherished dream by successfully swimming the strip from Havana (Cuba) to Key west coast in Florida. A feat she achieved by a non stop swimming of over 54 hours. This is no ordinary feat. An outstanding feat in every sense of the word and a great inspiration.

The three messages, she said after the tiring journey are gems. So apt, crisp and powerful.  “I have three messages,”  with her face visibly tired after being soaked many hours in the ocean, Ms Nyad said. “One is we should never, ever give up. Two is you never are too old to chase your dreams. Three is it looks like a solitary sport but it takes a team.”  Do we need a better inspiration than these words, every time we look for excuses?

And you know what, I share birth day with her!

News from Syria is looming a huge disaster. Seeing the video clips, of thousands of innocent people falling down to deadly chemical assault is a shame to humanity. It is making a mockery of what human and humanity should be. What a calamity! Are we all living in this very same world? Such a contrast!

Today is my B’day. Time flies, huh! Google has this nice doodle celebrating my co-birthday boy, the great augmentative French composer Claude Debussy. The doodle had the soundtrack from the famous composition Moonlight (aka Clair de Lune). Such a soothing track, first up on a day, a birth day for sure! I had woken up at about 5am to do some stuff and the first google search at 7am had all this refreshing melody and an awesome, animated doodle of the moonlit night!

Amar Bose, the name almost symbolizes high quality sound has passed away. Years ago, I had come across reading up something about the man who had inspired the making of something that I literally use everyday, the Bose Wave music system. A tiny box which uses crisp quality sound has been my favourite since 2006.

Bose’s life reflects a successful life of a passionate researcher who fearlessly chased his dream, produced a world-class product and organization. What amazes me is that, he managed to do all this, while still staying as a faculty, having involved in a good share of regular teaching activities and formal student advising (For starters, Alan Oppenheim was his student). It is widely known that he was a great motivator as well as an exceptional teacher, said to have enthralled audience anytime, anywhere. If this is of any indication, then we can imagine how great it would have been to be in one of his class.

I have read and heard many stories of him, about his experience with starting up of Bose corporation, interaction with his illustrious professor Yuk-Wing Lee (who was instrumental in motivating the young Bose in eventually starting up a company; It was he apparently who donated his life savings of $10,000 in 1950s to seed in the making of what is now a multi million corporation) and also the rather interesting and embarrassing event where he had to his first ever public/technical talk on Wiener’s (then recent) work to a celebrated audience which had included a certain Norbert Wiener himself. After knowing a bit about all the Wiener stories, I pause to think, how different an experience that would have been! Anyway, Bose’s legacy will easily stretch beyond mere Bose corporation and MIT. His life is a message of courage and pursuit of passion, if not anything else. RIP. For consecutive ($n$th and $n+1$th)primes $p_n$ and $p_{n+1}$, the asymptotic gap $\mathcal{G}= \lim_{n \to \infty}{\inf}\left({{p_{n+1}}-{p_{n}}}\right)$ has got a fresh renewal off late. The famous twin prime conjecture says $\mathcal{G}=2$, but that is still a conjecture and not a proof. Recently, Zhang proved that $\mathcal{G}$ is a finite number and a number definitely not bigger than $70,000,000$. It was hoped that one day, the mathematical community will find a number lower than this and perhaps even the holy grail mark of $\mathcal{G}=2$. Now what? Within a span of a month or so, the established gap of 70 million has improved to a thousand odd number and is still on a path of decent. Still some distance to the ultimate mark of 2, but boy, does collaboration work? Ever since the now famous breakthrough from Zhang touched the broad light (I had scribed my little thoughts on that earlier!), Terrance Tao and his team steadily managed to improve the bound. Tao has already knitted a nice and detailed summary on the progress. As of last week, the proven gap was $12,006$, but now the updated gap could be as small as $5414$ (which is still under verification as per polymath8 project page). Let us hope that, they can go all he way to prove the twin prime conjecture, one day! It is interesting to read, from Tao’s blog (which any day is a treasure trove of many topics, thankfully written with a wider audience in mind) the several connections they made, including that to Elliott–Halberstam conjecture, for improving this fascinating distance between prime successors. It was a touching and inspiring one to read about that historic day when Nelson Mandela was released. Here is a photo from NY times . It is taken from Obama’s ongoing African leg tour. This particular one is apparently taken at Goree Island. For some reason, it feel pleasant to see this photo. The diary is an incredible read in itself. I don’t think we needed to be told about the perils of plastic. Enough is known and seen already. Among the many haunting stories, I distinctly remember the stories heard about animals and birds species being hit with the terminal trouble, after innocently consuming the plastic and other non-organic waste laregely left over by our actions. Those horrific stories that caught my attention were from cities of India, but I am sure that India is only a coincidence. It is sure to have happened or happens in many other parts of the world, especially the developing countries. Now, this documentary tells us how severe and grim the reality is. One of the remote island of our planet and its inhabitants too have to suffer for the callousness of our deeds. How unfair! Jack Eidt has this eye opener report on the plights of Albatross, caused by our own ignorance. At some point the great Federer run had to end. A 2nd round exit from Wimbledon is not what we are used to from the great champion. The last time, he had to bow this early, was more than 10 years ago and that tells the greatness of his journey. Even the great king, pistol Pete Sampras had to taste the sourness at this piece of grass. That way, it was not completely out of ordinary that this happened today, but I always loved to see master march on for this title; one more time, every time! The great man didn’t play all too badly today, but the Ukranian was full of confidence. Seeing the way Serhiy Stakhovsky served and stayed confident to go to the nets at Wimbledon, facing the 7 time champion was a sight that was reminiscent of foregone days . It was a pleasant sign to see some serve and volley show staged at Wimbledon. In that respect, as much pain I am with Federer’s exit, happy to take home, memory of a good match and feel for the star of the day. The 2012 Turing award goes to two cryptography pioneers Shafi Goldwasser and Silvio Micali. I don’t do much of cryptography (for that matter I never did anything serious on that front, besides doing some C programming to demonstrate RSA and later on some class project involving elliptic curve cryptography and mathematica programming at EPFL). But I always was fascinated by the topic of Cryptography, largely for the many interesting toy like, yet deeply thought provocative combinatorial as well as probabilistic problems it addressed. Several of these problems stay at the very intersection of CS theory and cryptography. One such classical problem that we all learned in graduate classes is the zero knowledge proof. The idea is pretty cute. In the most simple scenario, this involve two parties Alice and Bob, who don’t trust each other, but one of them (say Alice) have to convince the other (bob) that she has knowledge (say a mathematical proof) of something without really revealing it. The fact that it is not revealed explains why it is zero knowledge (Bob in the end never get to know what Alice know, but just gets convinced that she knows!). So, it will work more like an interactive protocol wherein a lot of questions are being asked by Bob, chosen randomly, depending on prior answers from Alice. Doing this way for long, can Alice convince Bob, with an overwhelmingly high probability, that she knows what was claimed? Such an interactive protocol constitute what is coined as a zero knowledge proof. An example would be a novel ATM machine where, you don’t have to enter the PIN (unlike the ones that we have), but you can still convince the machine that you know your correct PIN. Sound cool and yet thought provoking, right? Well, that is why I said it is cute and interesting. This zero knowledge interactive proof idea was first conceived by the new Turning award winners. The names didn’t strike me initially with the Turning award news, but after reading the details, it occurred to me that, I had read their classic paper , as part of my coursework at EPFL. A bit more formally stated, the two entities are namely a Prover and a Verifier. In the ATM example, the ATM machine is a verifier and you the user is a Prover. Prover knows the proof of a mathematical statement and verifier tries to verify whether the claim is indeed correct with high probability. The machinery of zero knowledge proof is that, if the prover is trying to trick, the verifier will be able to find that out as well, with high probability. There are many examples illustrating this beautiful idea. A classic example is the problem of helping a blind man in identifying whether two otherwise identical balls are of different colors? Can you convince him, without really telling which is which? Now there are variants of their original idea and myriads of practical significance have emerged or are still emerging. The ACM award page has pretty enthralling account of these two pioneers (Shafi and Micali). Now, here is an interesting family trivia. Shafi Goldwasser and her husband Nir Shavit together now keeps three Gödel Prize in their shelves, besides adding the Turing award aroma, now to their household! Through Anand Sarwate’s blog and this piece from Sergio Verdu, I came to know that the well known Information and Coding theorist Jim Massey has passed away. I don’t have any direct personal recollection of Massey, other than seeing him once at an Information theory workshop and also last year at the Marconi award ceremony at Irvine. The one thing I always remember (besides the Berlekamp Massey algorithm and transform decoding paper) is his notes at ETH. I have enormously benefited from his lecture notes on Cryptography when I was trying to learn the topic at EPFL. So lucid, crisp and intuitive were his scribes. How I always wished to sit in one of his live lectures! RIP! I am sure detailed writing on his life and work will appear at some point. I recall Rudi Urbanke once mentioned the early impact of Massey’s work (as a graduate student ?) on threshold decoding of convolutional code, having spurred interest in industry. Codex corporation (to which, he was a co-founder, I learned recently.) once wanted to implement it into their line modems. Not sure whether I have all the details intact here, but prior to the Viterbi algorithm, his threshold decoding scheme must have been a big hit in communication! To have industry interested in a graduate student work must be special, any day, anywhere! In his blog Sergio Verdu, has pointed to the IEEE oral history interview archive, which I happened to read last year almost same time. Info theory website has further details including the funeral info. If you have not seen this yet, a fascinating talk (Cryptography- Science or Magic) he did at MIT several years ago, is archived here. Boy! who did the speaker introduction? Another true connoisseur Peter Elias! First time, I saw a video of Elias. Almost all the deployed and successful communication strategies till date are half duplex (HD). That is, we don’t have simultaneous transmission and reception on the same frequency band, aka, full duplex (FD). For example, 802.11 WiFi uses a time switch (TDD) between transmit and receive mode. Both transmission and reception takes place over the same frequency band as well. A single antenna is (typically) used for both tx and rx in this case. It is always either transmit or receive (or none!) that happen at any given time. In the cellular world, such as LTE the popular scheme is to have the frequency slice shared (FDD). In that case the up-link (link from a cell phone to base station) takes place in a range of frequency band different from that on link receiving signal from base station, while both transmit and receive can take place simultaneously. In both TDD and FDD cases, there is no overlap between the transmit and receive signals at a given frequency at the same time. Let us posit this question. In a given frequency band, is it feasible at all to have simultaneous transmission and reception? One way of course is to find a domain where these two (transmit and receive) signals stay perfectly distinct. Say use some orthogonal codes. In theory yes, but there is an important practical hurdle here. It is the issue of the loudness (aka self interference) from own transmit signal! An analogy is like one tries to decipher a whisper coming from someone, while he/she is simultaneously shouting at top of his/her voice. In reality, the desired signal comes from a distant source after traveling through adverse medium/channel. More than anything else, the signal intensity level would have got severely degraded by the time signal arrives at the receiver unit. Well, let me put some numbers from a practical setup. In a (typical) WiFi scenario the incoming signal (from an AP) at your receiver antenna (of say tablet) may be around -70dBm, whereas, the power of (tablet PC’s) concurrent transmission power could be $20$ dBm! The task to fulfill the full duplex goal is really to recover the information from the relatively week signal in the presence of a self interference stronger by 80 to 90dB! In other words, we should hit a mechanism to suppress the self interference by 90dB! Getting a 90dB suppression is no easy, especially when we are constrained chip and board area to get deployed in portable devices! Traditional board layout tricks such as isolation, beam steering etc alone wouldn’t get us there. OK, now what? the reason I suddenly brought this up is largely due to the increased momentum this one is gathering off later in both academia as well as industry. It still has enormous challenges ahead. Realizing FD on the other hand will bring in enormous benefits. Historically, we always mulled over capacity and throughput, with the strong assumption that all resources in the lot are available. Say for a given channel bandwidth $W$, the capacity is $C(W)$ and throughput is so much and so on. The reality is that, in most cases, to have information exchange, we need two way communication and that means double resources. Spectrum being pricey and scarce, getting the full duplex can potentially get up to double fold in throughput and several other benefits along the way such as remedy to the hidden node problem in current 802.11 MAC access. Now 802.11 standards front, we have a new study group on high efficiency wireless (HEW). I believe HD can play a role there too. I am not prepared to discuss all the details involved here. Let me outline a rough problem formulation of FD. More general versions exists, but let me try with a simple case. Much more detailed formulation of the problem can be seen here and elsewhere. I kinda used the notations and problem statement from this. Let $y_{a}$ be the desired signal from a distant sender, arriving at the rx antenna. Simultaneously, a much high power signal $x$ is being sent . The signal $x$ is significantly higher power than $y_{a}$. Now, the signal $x$ leaks through some path $H$ and produce an interference $v_{a}$ at the receive antenna. In other words, the effective signal at the receiver antenna port is $z_a=x+y_a$. For sake of simplicity, let us assume that $H$ is modeled as a FIR filter. The sampled signal relationship can be then stated as follows. $z_{a}[n]=y_{a}[n]+\underbrace{\sum_{k=0}^{\infty}{H[m] x[n-m]}}_{\triangleq u_{a}[n]}$. Now here is the thing. We cannot simply pass the buck to digital domain and ask to recover the useful signal from powerful interference. Recall that, the A/D converter stands at the very interface of analog to digital partition. High power interference signal will severely saturate the A/D and result in irreversible clipping noise. So, first we must do a level of analog suppression of this interference and make sure that, the A/D is not saturated. Let us say, we go for an analog filter $C_{a}$ and do this job. Post analog cancellation using a filter $C_{a}[n]$ we will have, $\tilde{z}_{a}[n]=z_{a}[n]+\underbrace{\sum_{k=0}^{\infty}{C_{a}[m] x[n-m]}}_{\triangleq v_{a}[n]}$. The A/D signal transformation can be decomposed to the following form (using Bussgang theorem for instance). $\tilde{z}_{d}[n]=\mathcal{A} \tilde{z}_{a}[n]+q[n]$. Now, $\tilde{z}_{d}[n]={\mathcal{A}} z_{a}[n]+{\mathcal{A}} {\displaystyle \sum_{k=0}^{\infty}{H[m] x[n-m]}}$. If we do a digital cancellation at the A/D output state with a filter $C_{d}[n]$, we can have $\hat{z}_{d}[n]=\tilde{z}_{d}[n]+\sum_{k=0}^{\infty}{C_{d}[m] x[n-m]}$. Incorporating all these, we will have $\hat{z}_{d}[n]={\mathcal{A}} y_{a}[n]+ \displaystyle \sum_{m=0}^{\infty}{\left[\mathcal{A} \left(H[m]+C_{a}[m]\right)+C_{d}[m]\right] x[n-m]}+q[n]$. Now if we can adapt and find $C_{a}[n]$ and $C_{d}[n]$ such that $\mathcal{A} \left(H[m]+C_{a}[m]\right)+C_{d}[m] \rightarrow 0$, then we can hope to have a near perfect self noise cancellation and produce $\hat{z}_{d}[n]={\mathcal{A}} y_{a}[n]+q[n]$! So, in theory there is a way to do this, by a hybrid approach where in some correction is done in analog domain (before A/D) followed by a more easily realizable digital cancellation circuit. There are many more practical hurdles. Some of them are: 1. Performing correction/adaptation at RF frequency is not trivial 2. If we are to do this post mixer (after downconversion), then the LNA nonlinearity (and a potential saturation) will come into play 3. Channel/coupling path estimation error will degrade performance 4. Calibrating analog correction is a little more involved 5. A typical goal may be to have about 40dB suppression from analog correction and another 40dB from digital. 6. Digital and analog correction, calibration time should be reasonably fast, so as not to spoil the set goal of simultaneity! Some of the recent results, published are indeed promising. Some prototypes are also being developed. More general version involving multiple antennas’s are also being talked about. In that case, some beam forming can provide additional support. Let us hope that, with some more push and effort, we get to realize this one day into real world. Most of you may have been following this new prototype being developed and deployed by Google. I am talking about project Loon, an idea conceived by Google to help connect the few billion friends around the world who are still deprived of internet benefits. The idea at first may spell like fiction, but this one is for real. Already, some pilot projects are on the way, in New Zealand. Let us watch out for this to spread its wings in the coming months and years! Anyone remember the old Motorola/Iridium initiative? It scooped and failed for many a reasons, but the idea that time was to have the entire world voice connected, but project Loon is a bit more than that in intention, technology and economic viability. Besides, Loon is backed by a highly successful technology driven company. The goal in itself is to have pretty much every corner of the world to stay connected by internet, the holy grail of global networking. Whereas, Iridium needed sophisticated lower orbit satellites, project Loon can get the job done through a set of balloons equipped with wireless communication technologies. The number of balloons may be much larger than the number 66 or 70 satellites, but the latter is a lot less expensive and green than the failed initiative! So what goes into the making of project Loon? Logistic wise it needs deployment of enough number of helium powered balloons into the sky, the stratosphere layer of earth atmosphere to be precise. Why stratosphere? Because, the balloons will make use of the wind flow that prevail at stratosphere layers to steer and position it around a certain location locked to ground. The balloons are not quite stationary; they instead will move around, but on the average a certain number of balloons will stay put up in location range to provide a reasonable coverage for any given location. All the balloons are equipped with enough circuitry to perform necessary wireless communication networking jobs. The balloons are all the time connected (wireless that is) to neighboring balloons and some of them will talk to an available ground station terminals through which it will establish connection to the internet backbone and thus to rest of the connected world! The balloons may have varying shapes and orientation. The shape of the balloon and the wind pattern may come into the equation to steer them and stay around (or move around the earth) at the atmosphere. They may, not only move around the earth, but also can potentially move up and down in the stratosphere layers. Each of these balloons are of approximately 15 meters in diameter which will float at about 20 km altitude from earth surface. For record, this height is more than double the distance where we can spot the farthest cloud or for that matter the highest altitude where airplanes fly! The task involves gyration, ballon steering and of course quite a lot of wireless mesh networking as well as co-ordination prospects. At the user side, you will have specialized antenna (or antennas, depending on whether MIMO comes in) to talk to one of the balloons above your location and we are all set to go. When fully operational, everything else will be transparent! Pretty much the energy for operation at balloons all will come from solar energy. The other natural resource used is wind. Both are green and free and almost universal! I am very excited about the prospect of this coming off in full force in the near future. On the beneficiary side, one it will help reaching the far corners of our planet. More than that this may well serve as an inexpensive way for many billion folks to reap the benefits of internet and staying connected. Of all, the children of a lesser world can as well get to bite a share of a better world. Imagine a remote village school in Burundi or Bangladesh getting access to better educational tools through internet! Wouldn’t that be a beautiful? Corporations will make money, but when less privileged ones also benefit, that is something to cheer. In the end a model will sustain and everyone can have a share, monetary or otherwise. Check out more details at the project Loon page. The google+ page has more updates pouring in. In a lighter vein, what is the main downside of this everywhere connectedness? Here is a potential spoilsport scenario! You will agree with me here:-) One of my favorite cell phone app till date is the navigation utility Waze. The only downside that I’ve noticed is its hunger for power (It drains the phone battery in no time), but GPS in general hog battery anyway. In a car with some charging unit, it is not a killer drawback, but it is a negative thing anyway. Since this app has such nice user friendliness, coupled with ability to provide almost real time side information (through user assistance and online feeds) such as traffic situations, presence of police etc., makes this such a handy tool on the move. I was almost contemplating that this will be bought over by Google or a Facebook. Now what? It didn’t take too long! Waze is gobbled by Google, for a reported billion odd USD. I like Google maps too. Now, we have a chance to have all in one! Hopefully, a better one! Dr. Appanu Nambiar is someone I know personally. Being the father of a close friend of mine has surely helped me to know him from close quarters. He was a teacher and principal at various government institutions in Kerala. Upon retirement from professional life, he decided to contribute to the society by serving one of the most backward and ignored community in Waynad, Kerala, India. In 1997, he thus started a school named Pazhassiraja school, with the primary intention to provide education and skill development for the Adivasi children. Adivasi is a collective term referring to a tribal community which form a significant portion of the aboriginal population of India. We all at some stage have had the intention and good will to contribute to the society. Having a thought is one thing, but to commit yourself into realizing by working through all the nuances;that is an entirely different thing. Inspirational, but now we should read on and act. The history of his noble commitment goes like this. During the service as a principal at a neighboring college at Waynad, he happened to get a first hand glimpse of the plight the Adivasi community in Waynad go through. Without much financial or social support , he ventured his time and effort to help educating the children from the remote and an otherwise largely neglected section of society. The school follows a system more like the Gurukula tradition, where in the teachers (guru) and supporting staffs live along with children in the same premise. To really understand the level of commitment he was getting into, we must first know some background on the tribal community, their social setup and the geographical position of the school itself. Waynad is a beautiful place located at the southern tip of the Western ghatt mountain terrain in south India. Waynad belong to the state of Kerala in India. While Kerala is considered socially way forward compared to many other states in India, Waynad is unfortunately one of the more ignored ones among the province of Kerala, in terms of outreach of several reforms including education and health. The lack of social development reach to the tribal areas also meant that basic education options went missing for the children. As a consequence, generation after generation they are deprived of a good standard of living and livelihood. The hierarchy of this community is a bit more complicated than what we know from the outset. The adivasi tribes itself is classified into several sub-tribes or castes. The main ones are Adiyas, Kattunayakans, Kurichiyans,Kurumas,Ooralis, Paniyas and Uraali Kurumas. Some of them have slightly different physical characteristics (such as skin texture), but they are historically sectioned into different groups based on the profile of jobs they carried out. Each of these tribes follow social tradition and rituals of its own, while at the same time they collectively follow a generic form of social life including religious practice, marriage, art etc.,. Deforestation and general urbanization over the years meant that the traditional resources for these indigenous community is taken away. Instead of providing a needy hand, the society often found ways to exploit this tribe. For whatever reason, the tribal community has not yet been part of the mainstream society and that unfortunately spell disaster for their future. As always, the biggest casualty in any crisis are the children. For them as well as the generations there on to survive, first thing to do is to make them capable of making a decent livelihood. Nambiar’s initiative is also with that modest goal; to empower some of them to deal with the realities of world around them as they grow up to youth and beyond. When a stream of youth can stand to survive and deal with a decent social life, the next thing will be to pave the way for better education and living opportunities for their children and so on. In a streamlined system, a wagon can roll. But the first step is to survive this great initiative and that needs a lot of support from well wishers like us. Remember, the grand from government is extremely limited and the untimely arrival makes compound the agony. Relentless effort from the great man along with support from many kind hearted people and organizations have helped the cause reaching this far. Now it has come to a point where surviving itself hinges on generous support. The time is now. A failure here, not only will stop the good work done. There is also an increased danger looming where some of these youths may break into verge of alcoholism and anti social activities, once they lose the confidence of a viable future ahead. Remember, these are extremely vulnerable section of a population and they can be easily trapped, once let go. So, dear readers, if you plan to contribute to charity, please help this great cause. You can find the details on how to donate etc here. Any amount, however small it may be, will help its share. I am convinced why Einstein once supposedly remarked “My dear young boy, you have shown me that there is God in heaven”. I may have got the exact words quite not correct, but he is quoted something like this about the young genius of Yehudi Menuhin. Forget the literal reference, but the essence of Menuhin’s violin mastery is breathtaking. Here is that famous West meets East master piece by Yehudi Menuhin and the legendary pandit Ravi Shankar. Music can bring peace, cant it? Boy, how did this stuck accidentally, this afternoon? I am hearing this immortal piece, after a long long time! Wow, such a beautiful pleasantry musical. Dave Mathews band (DMB)’s famous Two step. The lyrics is a piece of gold too. Such priceless is life and love, Isn’t it? and this live show is simply captivating too…. The lyrics goes like this (courtesy ) Say, my love, I came to you with best intentions You laid down and gave to me just what I’m seeking Love,you drive me to distraction Hey my love do you believe that we might last a thousand years Or more if not for this, Our flesh and blood It ties you and me right up Tie me down Celebrate we will Because life is short but sweet for certain We’re climbing two by two To be sure these days continue These things we cannot change Hey, my love, you came to me like wine comes to this mouth Grown tired of water all the time You quench my heart and you quench my mind Celebrate we will Because life is short but Sweet for certain We’re climbing two by two To be sure these days continue The things we cannot Celebrate, you and me, climbing two by two, to be sure These days continue, things we cannot change Oh, my love I came to you With best intentions You laid down and gave to me Just what I’m seeking Celebrate we will Because life is short But sweet for certain We’re climbing two by two To be sure these days continue Things we cannot change… Things we cannot change During the past week, while at Hawaii for the IEEE 802.11 interim, I happened to glance this NY times article. The story is about a New Hampshire professor Yitang Zhang coming out with a recent proof on establishing a finite bound on the gap between prime numbers. While browsing the details, there are more details emerging as several pieces of blog and articles and reviews are being written (and some are still being written). Now, looks like the claim is more or less accepted by pundits in the field, and termed as a beautiful mathematical breakthrough. As an outsider sitting with curiosity, I feel nice to scratch the surface of this new finding. The subject surrounding this news is number theory, prime numbers to be precise. The question of interest is on the gap between adjacent prime numbers. We know that $2$ and $3$ are prime with a gap of $1$, but this is truly a special case and unique per definition. The gap between $3$ and $5$ is 2. Similarly $5$ and $7$ differ by $2$. One may have thought that, the gap between successive primes go up as we flee along the number line. Not quite. For example, we can see that there are a lot of pairs with a gap of 2. The easy ones are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139) and the list goes on. It was conjectured that there are infinitely many such pairs, but the proof of that is not quite as easy as yet! It is known that there are precisely $808,675,888,577,436$ below $10^{18}$, but infinity is still a lot far from $10^{18}$! An interesting quest was to really prove that there are infinitely many twin primes, but this still remain as an open conjecture. Now the new discovery by Zhang is not quite proving the twin conjecture, but a close relative of that. Twin conjectures are strictly about prime pairs separated by $2$. A related question is, how about prime pairs $p$ and $q$ which are separated by $k$ where $k$ could be a finite number. When $k=2$, then we have the special case of the classical twin prime case. Can we at least prove mathematically that there exists infinitely many primes such as $(p,q=p+k)$ for some$k\$. If so,  what is the smallest $k$ where this holds true? Zhang now has a proof that for $k$ as small as $70$ million. Mathematically, if we denote $p(n)$ is the $n$th prime, then the new claim says (stated crisply in the paper abstract),

$\lim_{n \to \infty} {} \left(p_{n+1}-p_{n}\right) <70 \times 10^{6}.$

$70$ million is still a large gap, but as Dorian Goldfeld says, is still finite and nothing compared to infinity! In future, it is not unlikely that  we may get to see this gap coming down and perhaps to the best case of $k=2$. Who knows?

The result is still interesting, even to general interesting folks like us. This kind of says that, the gap between prime numbers is worst case bounded by a finite number. If we really plot the prime numbers, then we will see a saturation like behavior!  Like many other things at asymptotic (for example, the eigenvalues of a large random matrices exhibit very interesting properties, when the size goes to infinity), things at infinity may exhibit some charm, after all!

The  paper is accessible here, but as expected the proof is hard (for me at least). Hopefully we will have some diluted explanation of its essence from experts in the coming days. Already,Terrence Tao had this sktech, a couple of weeks ago on his google+ feed. Over the last week or so, finer details on the new break through are still emerging. Terry Tao also has initiated an online Wiki collaboration in an effort to improve upon from this work (For experts that is, not for me!).

Congratulations Professor Zhang.

It is that time of the year and we have to be at Hawaii! This week being the IEEE 802 interim, I am hanging out at the Hilton Waikoloa resort in Big Island. Today morning, myself and my colleague Nihar went for a little swim at the clean Kahuna beach. A swim at the ocean after a long long time! The water here is not that cold like San Diego and that makes it pretty easy to swim. And the crystal clean water and soft sand beach makes the already good beach experience better. My family is joining this weekend and looking forward to more swim!

I leave you with some phone camera shots  from Hilton and the Hakuna beach.

I love Youtube.  Every day, more or less on the average, I ends up spending (or at times wasting) some time there. Today was no exception, yet I was pleasantly surprised to hit upon some video taped lectures of Richard Hamming. These are apparently recorded in 1995 and are on a wide variety of topics. I didn’t get to go through all of them, which hopefully I will do sometime. I particularly liked this one on Discrete Evolution. The depth of knowledge these folks have is immense. What is astonishing is their ability and skill on connecting their point of expertise to vast majority of physical analogies. Long live internet!

Couldn’t stop giggling seeing this. Nice composition here!

Some folks seriously believed Chechans are from Czechoslovakia! Swaziland neighbors Switzerland? If you thought that was funny, but not as much as Chechans and Czechoslovakia:-)

It was interesting reading up on this piece of remake; somewhat a historical remake so to speak. That classic Paul Allen and Bill Gates photo shot as young geeks in 1981, now have a complementary remake with a new, yet ‘older’ avatar!

Finally, I was there, but the 2 hour stunning drive from San Diego in the evening, through the picturesque terrain wast quite satisfying in the end. With the back injury backdrop, Federer was no where the fit champion he has been. The occasional graceful shots were in display last night, but by and large he was playing more from the shade than from the limelight. Nadal on the other hand was on the drive, even from the practice hit moments. The weather (as always) at Indian wells in the evening was superb and the atmosphere was blistering. The match unfortunately got over in less than 100 minutes. Always sad to see Federer losing this way, but then his legacy is not stemmed from a single match though. I wonder whether he will make it next year at 33. Hope he does!

A nice documentary on Aung San Suu Kyi  from BBC- The Choice. On the day of the great Gandhi‘s death Anniversary, I couldn’t have seen a better documentary than this. Another symbol of peace, in our generation. A symbol of resistance against a military dictatorship in the most Gandhian and peaceful way, much like Mandela elsewhere, Suu Kyi’s life is a message in itself. Gracious salute! We hear and talk about about great sacrifices, but this is beyond comparison!

On a nostalgic note, seeing the scenes in the documentary,the nostalgic days of punting at the Cam river in Cambridge comes to my mind. Punting along the calm Cam river (or stream) was such a relaxing experience! England is puritanical at times!

It was the last thing I would have ever imagined. Bertrand Russel in a Bollywood movie! Yes, apparently it did happen and this was in the year 1967. Anyway, it is only a cameo role and I am sure Russell didn’t see this any different from giving a TV interview. The posture he used in the movie looked akin to the way he sat during BBC interviews, all of which are now on Youtube. A very pleasant surprise to know this much anyway. The movie is Aman and Russel was acting as Russel himself , whom the hero (Rajendra Kumar) idolize.

Happened to see the highlights of the last test match of 1999  Wi-Aus test series at Sabina park! That great Brian Lara’s knock in 1999 at Sabina Park. Remember watching it late night live on TV. The final tense moments with Ambrose and then Walsh! And of course the Lara’s finishing drive.

One of my closest friend, Joshy Sebastian met with a tragic accident in Qatar and unfortunately left us for good. I am terrified in tears with that devastated feeling of emptiness. He was such a gem of a friend, ever since we met in middle school days.

Yesterday, a call from parents back home had this news. When they mentioned Joshy, my initial hope was that let it not be him, but unfortunately it came otherwise. I called another childhood friend with a glimmering hope that things wouldn’t be  as bad as I had feared. Sadly, there was nothing to hope for and it was all over. We just couldn’t utter a thing for a few seconds, just to console each other! It is tragic and the most unexpected.  How do I even scale such a loss? Sitting thousands of miles away, I suddenly felt numb and helpless. Memories rolled back, one by one, painted with pain all over. Oh dear, this is cruel!

After hearing this terrible news, I hardly could take an eye off his face etched in memory. I vividly remember the first day, a chubby boy transferring to our 6th grade class at MGM school; How soon we became good friends, and not before long the best pals around! Seated next to me, on the first day, he had given me a book sticker, which was a grand gift back then, for that matter anytime; Oh dear! How well I had cherished those moments? He would buy those caramel cookies and the groundnut  plaque with jaggery (kadala achu or chickey) from the little store across the road, break it into equal pieces and share with me. Those days, he was the one who had the chance to travel beyond territories, to the bigger towns, which many of us never could even think of during school days.  It may sound strange to fathom. We are talking about different times altogether, huh!  Joshy always would come back with stories to tell, a lot of them! Recently (about two months ago) when we spoke over phone , I had asked him, the movie buff he once was, whether he still watches all the new Malayalam movies. He sure did!

At high school, we were in different divisions, but during the breaks, we used to meet up; There he loved describing the movie plots and boy, did I love hearing those? Do I see those blue eyes brightening up while describing a script! Is it all real? Oh dear, how can he go this soon? Between him and another close friend we had pretty much all sources of Balamangalam, Balarama, Poompatta, Amar Chithra Katha and the Pico children books and many more. Memories keep coming, so do tears!

The middle and high school days are full of nostalgic memories of being together with him. And even the pre-degree days, the fun we all had! The gentle friend he always was, I hardly recollect him overly being angry, even on occasions when he looked pensive.

Once in UP school, we boys out of curiosity and partly spurred with the boyhood mischief, sneaked into a neighbourhood land and grabbed cinnamon skins (Karuvapatta). Without knowing what  it really was , we all munched pieces of it with thrill. Somehow the teachers came to know that. Back at school, post lunch was mayhem when the dreaded headmaster Father Chandi (fondly called Chandi Achan) himself barged into the class with his notorious chooral stick. He began asking who all had indulged into that mistake of crossing the school boarder. Joshy, sitting next to me was one of those honest guys who stood up first. After repeated probing, several heads started popping up. They were all beaten up heavily with Chooral; With each passing second, my feet would start rumbling more and more. The fact that I had decided not to stand up in the first place and the danger of getting a compounded punishment made me touch cold with all senses. Only about 5 or six boys were left sitting by then. Finally when Chandi Achan asked Joshy who among the remaining seated were with him there. The lone culprit remained in me, who was sitting next to him, was sure to get caught. But he chose not to and stood guard a friend he found in me! The greatness of a true friend at that young!  I’d asked him about that later on. He would just smile! It is that smile which comes to my mind even after years since I saw him last. When we spoke over phone, couple of months ago, we were hopeful to meet up sometime and now, a sense of void cutting through my breath.

Rest in peace dear friend. Thanks for the memories. It was such a privilege to be your friend. You will be missed and my heart will never be lighter without you. You were such a beautiful mind! Saying a good bye has never been this painful and how I wish I had a choice not to, but…

Looks like Mathematica 9 is released. I haven’t yet had a chance to take a look. Glancing through their release notes, a few interesting things I hope to try at some point are

– Signal Processing, which for some reason was fairly week on Mathematics till date, compared to Matlab for instance.
-The (random and social) network analysis tool is something I hope they made powerful.
-Integration with R.
-Time series, random process analysis new features and may be more.

Cary Huang and his collaborators made this stunning work showing  the scale of our Universe. We can get a gauge of a tiny measure Plank length to the grand size of observable Universe!. Work of these lads makes me speechless! It gives you a one shot view of various things.

Seeing this video, my daughter put us in a fix. Out of innocence, she asked us.  How big is the Universe? I said, we don’t even know precisely, how big it is. So far, the known size of observable Universe is so and so, I added. Then how come God knows all this, she probed. I followed: There are roughly two school of thoughts. One who believes that God created all these and the other who  believes that everything including the Universe evolved over time.

She was quick to say that she belongs to the second category. My wife was instant to claim the first the league affiliation. She asked what would I chose: Wife or daughter’s side!  Would rather evade that, I nodded . My kid wouldn’t let me escape that easily. Finally gave in and I said, I am more inclined to believe the second! She was all happy!

The one argument I was evading all along till today,  came all too sudden! I simply wanted them to figure it out and rationalize themselves in the years to come, without any parental influence or bias. But kids at times surprises us, don’t they? The profund words of Wordsworth lingered, The Child is the father of man! Truly!

I honestly think Bombay Jayashree and Michael Danna did a great job in creating this very soothing track for Life of Pi. However, this caught an unexpected plagiarism controversy while the Oscar nomination is on and a potential felicitation is ringing at the door.

The controversy is surrounding a portion of the lyrics of this track. Apparently, a couple of lines are taken or adapted from the very very famous Malayalam lullaby “Omana thingal kidavo… nalla komala thamara poovo….”, which almost all Malayalaee mothers recites to their babies at bedtime. The slow pace at which this being sung would draw even the crankiest of babies lulled into sleep. There is a sense of nostalgia and cultural belonging this song evokes to all Malayalees and in that sense it is not entirely surprising that a question being posed when a few of the lines of Life of Pi echoed resemblance to Irayimman Thampi‘s masterpiece. Some argue that the lines under dispute are literal translation of the original, from Malayalam to Tamil, but others refute with the claim that it is a common feeling any mother could have and Jayashree only scripted it in her own words. Whether a segment of the song was adapted from somewhere else, still a lot of work had to be done to make this to a wide awakening one and to something like an Oscar nomination. That way, it is touch unfair to simply brag the artists as copycats. At the same time, if there was a genuine adaptation pooled into the song, then it is only fair to respect and give credit to where it belongs. It is a bit sad that this had to be drawn to a public bashing. Getting an Oscar will be a real delight since that also will take Carnatic music trace to the world stage reaching to a broader audience, hitherto unheard of its rich and classical history.

Since we are on this subject, I thought it is a good time to read up a little on the history of the Omana thingal kidavo song. This song was supposedly written by the famous Travancore king Swathi Thirunal‘s uncle Irayimman Thampi. When Swathi Thirunal was born,  his maternal uncle himself a trained Carnatic musician composed this and was apparently sung by the mother Gowri Laksmi Bhai and the royal ladies to put the baby to sleep. The princely baby was all the more special since he was born after a prolonged wait at a time the Kingdom itself was at threat of being dissolved with the British empire having had no foreseeable replacement of a male successor to the King. Swathi Thirunal went on to become a famous King, who being  an ardent Carnatic music follower also produced several masterpieces, some of them are popular even today. Irayimman Thampi as well produced many more compositions including Karuna Cheyvan enthu thamasam.

Besides the rich and soothing music, the lyrics of Omana Thingal Kidavo are knitted with superlatives comparing the baby to the most wonderful things one can see in nature such as nectar in my sight or the bright and charming crescent moon. It doesn’t utter a word about the sleep, but just has many questions posed by the mother to baby as to which among the greatest wonders will match the priceless baby grandeur.  For any mother, none will match her baby and the lullaby carved into the minds of mothers of many generations. Whether they gave credit to Irayimman Thampi or not, the lullaby echoes in several hearts, even today.

Some interesting information on this composition is here. Further information on Irayimman Thampi and his contribution to Carnatic music is discussed by Dr. PP.Narayana Swamy. Renditions of some of the famous compositions can be heard here. A page on Swathi Thirunal is also maintained here. I am not sure whether it is the most comprehensive of his contribution, but has several useful links there.

A sad end to what looked like a promising and prodigious mind, complicated by many wizardly , perhaps at times turbulent actions and more so haste reactions from various corners of our society including the law enforcement offices. The news of Aaron Swart’s death at the young age of 26 is disturbing. The man, who at the age of 14 sparked into stardom by creating the now popular tool RSS for information subscription is no more! More than the wizardly invention, his name unfortunately caught into wider limelight perhaps through the MIT/JSTOR documents retrieving case.  He had later championed to several causes on free information access.  The right to free information in the internet era once again had caught the worldwide attention with that drive. It is difficult to keep side of this case, because it is strangled with multiple levels of complications involving the right to information, ethics, social stigma, law of the land, money, business,a wizardly mind and of course the turbulence of human mind!

I read his Uncle’s statement, “He looked at the world, and had a certain logic in his brain, and the world didn’t necessarily fit in with that logic, and that was sometimes difficult.” I couldn’t agree more to these words of Mr Wolf on Swartz. Don’t forget he was an ardent contributor to Wikipedia as well. Rest in peace Aaron!

Since most of us at home are hit by cold and feverishness from big bear and at Las vegas, the new year is largely spent at home, sipping hot tea, listening to some old songs, watching some movies and reading the book Land of a thousand Hills (Want to finish up reading that before office tomorrow!). Last night, we had a nice dinner pot lucking with  three other families!

I was scanning through the newspapers pages to get a glimpse of the new year celebrations across the globe. The Washington post has a few images of New year shots grabbed from across the world (the photo credits seem to be for Divyakant Solanki / European Pressphoto Agency). The following shot (form that list) captured my thoughts of a bright part of life in general. This one has two Indian girls enjoying the last sunset of 2012!

The other day, I saw a Facebook feed photo about Iran in the 1970s. It was a shot taken in some university/school in Tehran (This post on Iran of 1970s has some interesting thoughts).

It didn’t really surprise me, particularly because I have a second hand information about Iran, through a close friend whose parents had earlier immigrated to Tehran in the 70s for good. He also had his elder sister born there in the late 1970s. I remember, him describing stories told by his parents on the good days they had in Iran. They even had photo albums of his family with people on bikini etc. The point is that, the now prevailing restrictions in women’s cloth etc was not so, until a few decades ago. I have had a discussion on this very topic with a few Iranian colleagues who all seconded what I heard off! Quite a change of times, for now to digest!

Anyway, seeing that picture, my curiosity took wings to know Afghanistan would look in the 70s or may be the 60s. Incidentally, while on walk in the park, I bumped across to meet a neighbor friend who at the age of 5 or so, had migrated with his family to Poland and then to the United States on a cold winter  night in 1979. I posited this question to him about his recollection of the Afghanistan of yester years. His eyes were lit bright when he described some of the golden memories he had about his country. A sense of hope seemed to have been with him as a child, at least in retrospect when he portrayed those images! He later pointed me some pictures that he had came across on the internet, while on a nostalgic path. These pictures (some are here too. I don’t know much about the original rights holder of these pictures; just linking as I found on internet) portray a different Afghanistan than the one, majority of the world including myself, now know off as.

It is a complicated thing to discuss these topics because it is highly interlocked a subject messed up with religion, fundamentalism, society, culture, money , gender, huh, invasion,terrorism! you name it. One thing you can make out is that, both Iran and Afghanistan looked much modern and a better place to live (for their own people if not anyone else) than it is now. Alas! For a twist and tryst with time, things turned the other way. The net result is years og agony, hatred, war and of course that chopped the dreams of many generations.

Here is an image from Afghanistan in the 1960s!

One of the better ads, I have seen off late (Google search app). I couldn’t stop blushing when the kid says “You are so smart, dad!” and the dad is prepared for more and asks “did I ever tell you about Jupiter”!

I’m half way reading, what looks like a great memoir on Western Africa by a philanthropist Rosamond Halsey Carr. The book is titled Land of a Thousand Hills: My Life in Rwanda. Picked this from the 4S ranch library yesterday and I must say this is such a beautiful depiction of an otherwise ignored part of Africa, through the eye of a great philanthropist .

I will try to do a personal review of her book later, but a few things flashed my mind while traversing through the book. The biggest of course is the deadly genocide in 1994 which took place in Rwanda and Barundi. Back then, we were small and the magnitude of such an enormous ethnic clenching probably didn’t entirely register in our minds,reading the news from half the world away. Now, Rosamond’s book prompted me to think of the disasters of that great human tragedy; in the name of some misconceptions on ethnic difference, spurred by certain anti social elements as well as incompetent political leadership. Whatever the reason it may be, the biggest losers are the West African people. We cannot even gauge the extend of that horror since it still lingers through generations.

Rwanda and Barundi and the other western part of Africa may not top the list of go to places, but Rosamond’s takes us through her memory lane and describe how beautiful  those places used to look, before the colonization, civil and finally the holocaust hit them. Rwanda with the many hilly terrains is regarded as Africa’s Switzerland and it indeed looked so. If only we could reverse such tragedies! Alas, too late!

Now, Rosamond’s life itself is a great example of human sympathy towards a completely unprivileged part of an otherwise neglected corner of our earth. It is commendable that she, without any real social or material compulsion, decided on her on will, to make a living for a great cause for the African people. For a woman from a wealthy surroundings of New York to travel to that part of the planet with a great intention, struggles through the difficulties and finally fills joy to a lot of people is commendable. This brings joy and tears in our eyes.  I feel sad that I didn’t hear about her before. She will always have a place in my heart; Rwanda and west Africa are in my go to list as well!

There is a nice documentary on her life, “A Mother’s Love: Rosamond Carr & A Lifetime in Rwanda”,directed by Eamonn Gearon . I couldn’t find the full documentary in youtube or in PBS archive, but a short trailer is here. If you have not seen yet, I definitely recommend this one.

Since this is year end holiday time, I got a fair share of my time to read up on several random topics. Amidst the many sad out comings in the past couple of weeks starting from the shocking events from Newtown Connecticut elementary school shootout, then on had a few more disturbing news all over the world, particularly this one from the other side of globe. A rather non disturbing news is on the new claim on proving/establishing the  so called Ramanujan’s deathbed conjecture. I was doing a bit of follow up read up on this to first understand the premise of the problem in news.

OK, the subject deals with what is known as mock theta functions (Note: There is no credible Wikipedia entry to it and hence I cannot add one here. Also remember that this mock theta functions are not the same as Ramanujan’s theta functions; Just to not confuse these subtle mathematical terms!). These are not quite the Riemann Zeta functions, which are well known, but more similar to the Jacobi theta functions. The mathematical prodigy Srinivasa Ramanujan while on deathbed had shared some quick tidbits to the famous Cambridge mathematician (and I should say a hard core cricket enthusiasts! If you guys have not read his memoir A mathematician’s Apology already, step out and grab it soon. A fabulous quick read that!)  G.H.Hardy who was paying a visit to his now famous student. After their famous meet up (or may be during their meeting itself), somewhere in 1920, before his death, Ramanujan wrote a letter to Hardy in Cambridge in which he introduced as many as seventeen new functions. These functions, as per Ramanujan, had shared some distinct similarities with the theta functions (The Zeta functions were itself had been studied before before by mathematicians like Jacobi, Riemann and several others. Now of course the connection between Jacobi theta functions and Riemann Zeta functions is already established!).

The Jacobi theta function itself is pretty complicated to lesser mortals like us. It looks harmless for a starter, but the properties, its various avatars and connections to many real world applications is what makes it monstrous. And then there are also its generalized cousin Riemann Zeta functions $\zeta(n)=1+\frac{1}{2^{n}}+\frac{1}{3^{n}}+\ldots + \infty$, which as well, appear as a simple and elegant looking form for $n<3$ , for higher $n >2$ changes the form beyond what we can fathom (For example, it is not even known whether for larger $n$ such a number is transcendental!). I remember playing with (I think it was 2000 or 2001) a proof of  $\zeta(2)=\frac{\pi^2}{6}$  using some integral calculus in two variables, which again turns out to be rather well known as easy. There are other ways to prove as well for $n=2$, but it stops being that simplistic there!) Anyway, Jacobi’s theta function has the form $\theta(x,t)=\displaystyle \sum_{n=\infty}^{\infty}{\exp\left(i\pi t n^{2} + i2\pi n x\right)}$, which in words can be roughly stated as some form of elliptic form of exponentials.

Much like Fermat did for his famous last theorem, Ramanujan too didn’t give much hints beyond listing and stating that they are elegant. For example, he didn’t reveal where they come from or how to formulate them or for that matter what use having them. Like many of his other famous mathematical findings, Ramanjunan, a self taught genius, made a quick listing of these. Rest of the curiosity has enthralled and haunted the mathematical minds of coming generations, all over the world. A brilliant spark from the great genius helped to stir an intellectual stir for almost 10 years!

The latest is that, two Wisconsin mathematician, Ken Ono and University of Cologne professor Kathrin Bringmann came up with a framework explaining what mock theta functions are and how to derive them. They connect modular forms or more specifically the mass forms to Ramanujans’ functions. If you recall, the modular forms also played a big part in the proof of the other famous problem of this kind Fermat’s last theorem.

It will take  a while for me to understand (if at all I manage to digest it) all the details of this new claim. I must say, it is likely that I will fail to comprehend it in full . As always, I will be curious to read it up and grab as much as I can. As and Indian, the connection to India is always an interesting pursuit!

I leave you with a nice documentary video on Ramanjuan that I found in youtube. If you have not see this already, check this out. Pretty good documentary, unfortunately tarred by a lot of useless and unrelated comments.

This week has been filled with a lot of terrible news. First, the Tendulkar ODI retirement, the unfortunate and sudden demise of a young girl in New Delhi due to atrocity by a few reckless men and now Tony Greig’s untimely death making the day all the more sober.

Tony Greig was a pure excitement at cricket commentary. The energy he generates is simply stunning. He has been a top bracket cricket commentator since the 80s and the void that he leaves aside is going to be huge.

I first heard about Tony Greig (much before seeing him on TV) was while reading about a book on the English Australia test match rivalry where some match in the 1970s in which the former Aussie (again sadly demised) David Hookes’s hitting Tony, the then English captain, for five consecutive fours. It may not be a big thing in the modern era, but hitting something of that kind in the olden era is something I had fancied (even though I was not really born in that era, but growing up in the 80s and 90s, I had such fancies:-)). Both Hookes and Tony Greig somehow etched in my memory, so did Greg Chappell (the Aussie captain for that series). When David Hookes (also a future commentator, died during a freak bar incident) died, the mood was pensive too. Besides that reading, I didn’t have much know hows on Tony Greig’s days as a cricket player, except may be the fact that I was aware of he being part of the infamous Kerry Packer spin-off league and world series cricket.

What he did as a commentator  however is in clear memory. Some one remarked this on the other day, his now famous remark “What a player” on Tendulkar when he played that famous sandstorm knock in the late 1990s. I also remember many of his exciting comments in the India-Australia series in both 1998 as well as 2001, the finishing stages of the famous Calcutta test match comes to my mind where Glen McGrath walks in as the last man, until given out LBW. I don’t think any other commentator could have captured the finishing moments of the greatest test match of all time, as captivating as Tony Greig had done. Beside reading the game very well, the great thing about Tony Greig was that he was also a commentator who had understood the dynamics of cricket fans all over the world. Fans to an extend got what what they wanted and they could in some sense associate to him.

A few weeks back, I had read the sad news about his lung cancer diagnosis, but never realized that was this serious. He will be missed by fans all over the world, big time. Many a times I got the feeling that he has a special liking for Sri Lanka and its cricket! But I could be wrong. Whatever it is, he was loved all over the world. RIP Tony Greig! Thanks for the memories.

Ever since I heard the story of a young girl brutally raped in a moving bus in the capital city of my home country, I was restless and furious. It was not the first time, I’d read or heard about a rape story from India or for that matter from anywhere else. Time and again we hear these kind of brutalities and this happens and can happen any part of the world, not just the Taliban hit areas. Among the thousands of such incidents, only a few gets reported in public, a fraction of it gets to the mainstream news media and a smaller percentage reach us; And let us don’t forget, not many girls/women dare to say such incidents in public, with all the social pressure surrounding them.  Even in this modern society, woman and children largely have to live under the ego of a cruel world caricatured by sadism. It pains, it hurts and I am ashamed of myself not able to do anything to stop this suffering.

Think of this. A 23 year old medical student , an adult girl, is traveling with her male acquaintance in a capital city of the largest democracy in the world. Mind you, it is one of the most populous city in the world (with a population of 14 million. That means, there are a lot of folks around; For a comparison, this in count is more than that of a city like New York!) with all the central and state government establishments including the police administration in the vicinity! The girl and boy, to their innocence were lured to board a bus and to their misfortune, it turned out to be the wrong bus. What did the 6 wicked men in that bus do? They hit the boy on his head, dumped him on to the road; What happened then on is a mockery of what civilization should be.  In a moving bus the girl is brutally forced on by senseless men, one by one. All the while a helpess girl is being tortured, the bus moves around the city where police men patrol around, without noticing anything beyond normality. The girl in unconscious state is finally thrown out from the bus after all deed. She stays motionless for hours on the roadside before some medical help comes on her way. The police, government (both state and central) administration(s) turns first the blind eye, then a denial and eventually an eyewash damage control exercise.  Even after many days, the girl is battling for life. She has multiple organ damages, including intestine, liver and brain. When things got into dangerous situation, the government shifts her to another country, apparently a political move. Whether it is political or medical, the situation is grim! What a sorry state our society is in!

As usual, this news took people to streets. Naturally people are angry and they protests against the lackluster response from both state and central goverments. As always, some section tried to get some political milage out of this. Reality however is this. The biggest sufferers in cases like this are  the girl (in this case the boy too) and their families. They end up paying a very very high price for the recklessness of wickedness in our society. The elected government and its administration could have taken this as a last warning to engage a strong political and social change. Unfortunately, the leaders by and large miss the point. Few from the government dared to speak and whoever opened the mouth (like the President’s son) made a jock of  their senses. The mainstream media on the other hand is debating what punishment is ideal for the culprits, but the larger point should be: what are we doing as a society to prevent such atrocious incidents?

Praveen Swami has written this piece. Largely, I agree to his points. The solution to this social menace is not hinged on whether the culprits gets death penalty or not. Some may argue a Shariyath like law (arm for an arm, eye for eye or blood for blood method) is the way. Frankly, none of these post incident punishment alleviate this massive menace. The problem as Swami articulated here, is integrated in our social scheme of things. He rightly pointed the way the mass media, mainstream cinema and even the social stigma of son worshipping all directly or indirectly adding the bias to increasingly misogynic society of us. While the west also have cases of rape, the numbers are less because they have at some point in the past went through a political and social refinement, where the fundamental right of a woman to say no and a man to treat her no as a firm no. Again, this is not something that happened in Kandhahar or the tribal areas of Taliban hit Afghanistan, but the capital of the the largest boasted democracy in the world!

While the vast majority in any society will strongly condemn an act like rape, how many will respect the dignity of a woman travelling in any part of a country like India. Again, this problem may not be just India specific, but I have seen men’s colors even in buses in Kerala, a state socially way forward compared to the rest of India. As a matter of fact, you wont see woman in a bus after 7 PM in most part of Kerala too. The other parts of India may be even worse. The cities may be better off to stretch that 7PM mark to say 9PM, but thats it. Mumbai may be an exception, but even a city like Mumbai I wouldn’t count to be safe for woman. It will be a happy news if I hear otherwise. Bangalore, even with the celebrated success of modern life is unsafe for woman. I dont have the numbers, but during my stay there, I have heard far too many cases of woman employees getting assaulted, raped and at times murdered (Just do a google search on woman safety. You will hit through several of them). I am sure every city and small towns in India will have a gruesome shade of such a sad reality. No amount of police force can resolve this, in many cases they are the problem themselves, but things don’t stop even with them. It has to come from each one of us, from early stage to respect every one on their privacy and their right on individual freedom and choice. No one has the right to bulldoze on others, even morally, let alone physical. I don’t think the rape cases are mere act of sexual assault, they are deep rooted display of dominance of their hegemony. And in any case what sort of pleasure do men get after brutally injuring an innocent girl? These are beyond our senses. When will we as a society grow up to stand guard to our own sisters and mothers? Borrowing Bertrand Russell, “I long to alleviate this evil, but I cannot and hence I too suffer”.

Let us turn clock for a few years. Does anyone remember Aruna Shanbaug? Some may have forgotten, but she comes to my mind every now and then. I don’t know her, but ever since I heard about her (first time I heard was several years ago during the euthanasia debate) my bloodstream freezes at times. She is the living martyr of male recklessness. As a young nurse in a city hospital, she was brutally raped by a servant boy. Why? As a vengeance  for reporting a crime committed by the boy! Ever since then, she stay motionless, a life merely existing as a symbol of our social cowardliness. What punishment the culprit got is immaterial. The young woman, who was supposed to have soon got married to a doctor, sacrificed a good life for our social reckoning! Her case is largely forgotten. We got many new cases to ponder, but we failed to grow!

As I write this up, I just heard the news on NPR (yes, the news gets reported even in my KPBS car radio here in San Diego, while I was waiting for my daughter from the piano class) that the girl eventually succumb to injuries. She sacrificed her life. Just imagine, she was an aspiring medical student. She had a whole life of her choice had to be ahead. But for the callousness of few men, we had to see her go. What a shame! Aren’t we all responsible for this one way or the other?

Whether the insane gang of six stupid men gets death penalty or not is irrelevant. Our wicked society just threw our sister to the fire. The slow government acted ever slow and everyone in the administration will find a way to excuse themselves. The media will find another sensational story and latch on to it. Leaders like Abhijeet Mukharjee will again get re-elected (For record, a portion of the elected legislators in parliament and state assemblies are themselves criminals!). The family of the girl lost one of their own and we lost another beautiful life. Her homage made our lives less colorful. Didn’t it? If only we grow up and stand up to prevent yet another casualty like this beautiful girl. The grim reality is penned by the BBC reporter Soutik Biswas from Delhi. A serious introspection is needed and the time is now if it wasn’t earlier.

Rest in peace girl! Our hearts are heavier!

At the UN headquarters in New York, there is this picture. It draws you to numbness. Can a picture tell a story this powerful? Yes it does. This masterpiece from  the award winning Argentine photographer  Alejandro Kirchuk takes you deep down the perils of the wrecked disease Alzhemeirs. His full creations in the series titled “Never let you go” is archived online here.

Alzheimer’s disease is a very very complicated desease. One may ask, how about AIDS and cancer? They are dangerous too, but one thing which makes Alzheimer all the more different is its impact on the emotional and physical drain on the caretaker. At the later stage of this illness, the patient in the scene is devoid of any memory; He or she lose the sense of surroundings and at times fail to relate the partner for years and now serving as the caretaker.

Think of this. You suddenly arrive at a stage where you don’t even make sense of the surroundings, the loved one besides you? Your past is erased completely. Having to depend on others for even routine acts! How terrible a stage that can that be? Now think of the lucky patients who have the loved ones to take care of them. Think of those caretakers, who in majority are elderly people themselves struggling to cope with old age. The caretakers often ends up doing pretty much have to do a baby care like support to the patient, yet the patient  have no real sense of her/his association to the helping person.

I have seen some cases like this and I can understand the pains. Couple of Alzheimer cases had come across in my childhood, my neighbors etc. That time, I never had realized the name or its complexity, but this series of Kirchuk portraits took me back several years and I now relate how hard it must have been for the parties in my memory.

See one of Kirchuk’s portrait on Marcos. Marcos wordings goes like this “Tell me where she is going to be better than here. I treat her like a princess, here she has everything.” Sweet, isn’t it?, It takes our senses to numbness. It is not fiction. Thousands of people around the world, and some in our vicinity goes through this. Only the privileged few escapes from such difficulties! Life is priceless, isn’t it?

In the end, a fiercely fought battle, but I must say, the right choice is made in the end. To me, there is a sense of honesty when Obama speaks, if not anything else. As he admits not every of his opinion is agreeable to all (including me), but given the circumstances we are in, he did a good job as a president. He surely deserved a second term.

I will be hanging in at Indian wells this week for the IEEE September interim session. More on the IEEE 802.11 development later (may be at the weekend wrap up). First let me say, this place is hot (scorching at 100 plus degree Fahrenheit, most of the time) and yet this side is so stunning and beautiful. The hilly terrains are a treat to watch. The drive from San Diego to this place, a mere 70miles, but more than three quarter of it is is simply breathtaking.

The day  ended pretty late. Had the 802.11ah session running till 9.30 PM. What did we do after that? Well, when in Indian wells, should we miss a game of tennis? Certainly not. Nihar, myself and Carlos had an hour of tennis session at the Hyatt courts. These are by far the best courts I have ever played. True and good bounce, nicely maintained too. I heard when Federer and co comes for the Paribas open, they go for hits here! Just had a shower and now I am off to sleep. Need to wake up early as well.

A few snaps I took on the way are placed at the bottom. Hopefully, I get to capture a few more towards the weekend. There are tons of Palm spring photos in the web, but I like this one in particular.

Last week, had a chance to catch up with two pioneers at Irvine. The coding (among so many other things, trellis coded modulation came to light through his seminal thoughts) champion Gottfried Ungerboeck and the multi faceted public crypto (Diffie-Hellman fame among the so many other things he has done) fame Martin Hellman were gracious enough to join me for lunch. They were in town for this years Marconi award felicitation. For me, personally, it was whale of an opportunity to interact with these two connoisseurs. I didn’t have much time to interact with Ungerboeck when he was still employed at Broadcom, but the little time I spent with him last week gave an indication on how much I would have gained, had he stayed longer (or had I joined Broadcom earlier):-)

With the Crypto guru Martin Hellman

With the great Ungerboeck

The IEEE plenary (I was largely following only 802.11 variants, more specifically ac, af and ah alone) was here in downtown San Diego and was largely busy with that. Syria trouble, Rajesh Khanna’s passing away and the horrific theater shooting at Colarado were the other prominent news of this week.

At the IEEE front, 802.11ac draft 3.0 passed the motion. That is the main milestone in terms of ac progress. 802.11af also will have a first draft soon, which is good.

Rajesh Khanna, the super star of yesteryear passed away. I was never into serious Bollywood watching (especially while growing up), but heard many stories of how the young girls worshipped this Bollywood hero in his hay days, writing love letters with own blood etc. Recently, I’d met an Armanian born (now may be in the 50s) Piano teacher  who fondly recollected her teenage days worshipping the hot Indian hero. Well, if you think that is interesting, her mom, now a 90 year old grandma in silver has tears when she saw the Indianness in me; You know why? She was a Raj Kapoor fan!  Anyway, Rajesh Khanna (kaka as he is fondly known as)’s charm had crossed the boundary far lands away from Bombay.

I leave you with a nice view of the Coronardo island and San Diego bay from the Manchester Hyatt.

The news from Syria and the Colarado shooting made the week all the more disturbing.

This year’s Marconi foundation prize is being awarded to our company founder Henry Samueli. With last year’s price awarded to the other connoisseur Irwin Jacob (jointly with another stalwart Jack Wolf), now we have the two stellar communication company founders getting the prestigious award in consecutive years!. Feel proud to be part of the company he founded. Broadcom simply has a lot of vibrancy and part of this must surely be due to the champion founder. You can see the energy when Henry Samueli talk. I could feel a similar charm when Aart De Geus (founder and CEO of my earlier employer Synopsys) talks too.  Congratulations Dr. Samueli, we are proud of you.

I was following the world chess championship pretty closely, in spite of the weak media coverage on this. What a treat to wake up in the morning to learn that Anand stays on as the champion. It is an extra ordinary achievement! Gelfand played very well and it was neck and neck until the games progressed to the fast track mode.  Even there, it wasn’t that sunlight  separated the two great players, but in the end Anand had that little extra and that can make the difference at the highest stage. As always, staying at the top is a harder task than reaching there. Stupendous champion!  Anand successfully did that not just once, but now three in a row. Salute the champion!

It is a mind blowing journey that Anand, who almost without any serious chess legacy in Indian schools (unlike USSR where chess was built into the Soviet system among kids) walked up and then conquered the world stage. Now he has successfully defended three strong stalwarts themselves Kramnik, Topalov and now Gelfand, all arguments must cease. Way to go Anand. You made my day and likely that for many others too. Feel proud!

Memories roll back to 1995 when Anand was challenging Kasparov at the World trade center event. It was much hyped and spiced up then. I remember Anand winning the 9th game and then Kasparov hitting back, much in expected lines from the great Kasparov,  albeit to the disappointment of many Anand fans.  Almost 20 years on and we are in different stage and Anand remain calm, so does the champion in him.

The first mail  this morning (from Nihar Jindal)  brought this very sad news that Tom Cover has passed away. A giant in this field who contributed immensely to many flavours of Information theory will be missed. Everything he touched had class written all over, gracefulness, simplicity, elegance and all the more depth.

A tremendous loss! His legacy will continue.

Yesterday evening, during the dinner at a restaurant  at  Hawaii, I and my colleagues (Eric, Jun, Nihar and myself) along with a fellow colleague (Neycer) from Motorola were having some random ramblings. Somewhere in the course,came the topic on history of OFDM. It was indeed fascinating to trace the history. I did a bit of Googling later on and also traced some old notes from the discussion with Emre Telatar (who to me is a walking encylcopedia on several things). My information may not be too acurate, but roughly this is what I gathered after all the pile collection.

The origin of OFDM idea as such is largely attributed to Chang 1970.  Saltzberg had identified the problem of ISI and in came the notion of guard interval. Apparently, there is also a patent filed on this idea. The idea of cyclic prefix, the killer beauty which made OFDM ridiculously easy for equalization, was brought in by Peled and Ruiz in 1980. It was then Weinstein and Ebert who came up with the possibility of using FFT into OFDM. This traces back to the summer of 1971.

There are a few more interesting pre-work prior to these official OFDM milestones. Even though they are not really related, but hindlisht, we can still bring in similarities on how ideas shaped over time and different eras. For instance, the concept of parallel transmission was realized even in a product form in 1957 by a company Collins Radio Company. It was known as a Kineplex system. And the very idea of splitting to multiple carriers and power filling have signs of Gallager’s work and even waterfilling:-)

There is a Globecom paper which discusses all these. All these and may be more are neatly discussed there.

I am here in Hawaii this week for the IEEE plenary. The view from the Hilton in Waikoloa village is pretty enthralling…

Sadly, the journalist Anthony Shadid passed away all too sudden. It brought a bit of sudden stress on me, not because I know him anything beyond through his columns, but his very vey recent interview on NPR/KPBS radio is still reverberating in my ear and the death has become all too soon to cope with. A fantastic journalist as he always has been, he was often beyond that and largely the window of the middle east to the world, for sure to me. Through his reporting, I still feel as though I knew him very personally. His reflection from Libya, in spite of the horror he had to go through during the dictatorship has always been remarkable.

Now when I start my car to work, when the San Diego FM radio KPBS kicks on, the Terry Gross interview with Shadid on Fresh Air is still ringing. Boy, he was talking about tracing his ancestral village in Lebanon and so on. My mind transcend quickly to my mothers ancestral village in the serene riverside in Kerala. Rest in piece Shadid. Thanks for the sacrifices in reporting the middle east woes and sharing their pain.

While coming back from lunch, the office front desk TV had this breaking news from CNN. It said “Kodak exiting camera business”. Firs thought, I said, Huh!,and  I am sure many would have felt like what I did. Kodak’s case is really a case of getting footed in the analog world, when the world around had the technology transformed in digital way. A sad loss, but then in business there is no emotion!

Here is the BBC clip

The SODA 2012 paper by Dina Katabi, Piotr Indyk et al promises a relatively faster way to compute DFT of sparse signals. This is getting traction from outside the community too, after the MIT broadcast. The well know FFT originated from Gauss and laregely resurrected by Cooley and Tukey has the time complexity of  $\mathcal{O}(n\log n)$, which offers significant gains over the conventional DFT complexity of $\mathcal{O}\left(n^2\right)$ when the size $n$ is large.

If we really dissect the FFT complexity limits, it is already pretty good. With $n$ points to compute, the complexity will be proportional to $n$ and roughly, the per node complexity is $\log n$.

Now, what the new scheme promises is not a change in the order of complexity, but a clever way of simplifying the complexity depending on the inherent signal sparsity. When the signal is $k$ sparse (i.e.,  only $k$ among $n$ is significantly different from zero $0$ ), it is fanciful to ask whether we can indeed get to the complexity $\mathcal{O}(k \log n)$ and Katabi, Indyk et al have indeed reached there. Quite remarkable achievement this is, considering that the gain could be as good as the compressibility limit in most of the real world signals we deal today. Signals such as audio and video are the leading candidates in the practical signal signal processing world and they both are sparse in some transform basis. Recall that, the recent compressed sensing results for $k$ sparse signals showed the potential benefits of sparse signal processing and this new scheme will help to realize many things in a more meaningful way. One good thing with this is that this generalizes the conventional FFT. In that way, this is not just for sparse signals, but something which holds for any $k$ and in the limit when $k \to n$, the complexity is as good as the old mate FFT!

I want to try this out sometime for some communication problem that  I have in mind. At the moment, I am hopeful!

I wasn’t surprised at all with this. To be honest, I did expect this to happen, a long long ago, as early as 2006 or so. In 2009, I was seeing the writing on the wall. So, when my colleague sent the note yesterday afternoon, I was pointing him this blog to him!

Now then, Magma is now part of Synopsys. With Extreme-DA too in the kitty, Synopsys is clearly staying ahead in the EDA leadership. The Analog is where Cadence still have the thrust above them.

Quite shocked to hear the news of Peter Roebuck‘s sudden demise. An incredible cricket columnist Peter was and it was always a wonder to me, on how well he analyzes the games. The earliest recollection of his name to me was when I heard the story about he firing the greats Viv Richards and Joel Garner, the aftermath of which resulted inIan Botham changing the playing county from Somerset etc. Irrespective of his famous acrimony with the stars of that era, his cricketing analysis skill is unparallell. A huge loss to cricket, especially test cricket writing. Hard to think of a natural death for a Wisden award winning cricketer and a man known to be of such strong will, but never know. I hope it is not one of those David Hooke’s kind of story. A tremendous loss to cricket writing.

Come to think of it, I remember his recent article on Australia’s 21/9 collapse in the first test against the South Africans. If that was a tragedy, his death is an even bigger one. After all, cricket was just  a game, but death, boy!

Happened to see this youtube link, through a Facebook feed. Not sure how credible the information is, but interesting corner point. No harm in listening to an alternate view. Who knows, is it the truth or is it just another conspiracy?

Qaddafi for sure has done several horrible stuffs and no way a man to be worshiped, but the way he was publicly assassinated portray a sorry figure to civilized society. It is appalling that NATO had the freedom to do such barbaric acts to curt the end of another man who was criticized for similar acts to his own people.

Another stalwart, the founding father of Unix, C and in many ways one of the founding fathers of computing itself, Dennis Ritchie passed away. For me, Ritchie along with Kernigham was one of the first few names registered in mind, since learning computer programming. The first book I have ever seen on a programming language is this duo’s book on C. And boy wasn’t that most concise book in technology, every so compact and yet rich and clean!

Come to think of it, the impact of Ritchie to modern science and technology is enormous. He may not have been a very public figure, but his contributions indeed is the touchstone on the modern world, especially the information network world. Much of the internet, the Google, the iPhone’s and what more, almost everything we can think of runs on his stuffs or its variants. Quite remarkable.

I think the most apt summary of Ritchie’s contribution is heard from Brian Kernighan himself.  He said  “The tools that Dennis built -and their direct descendants – run pretty much everything today”

A Facebook feed (through a friend) led me to this nice article on Sachin Tendulkar. The title is “Point to Cover” and the author is Senantix. I liked the Bayesian view of Tendulkar’s performance. Quite simply true. Often, the short memory and incorrect assumptions lead to most of the controversies and criticisms against Tendulkar. As they say, Bayesian can never go wrong!

P(Sachin fails| crisis) = [P(crisis|Sachin fails) x P(Sachin fails)]/[P(crisis|Sachin fails)xP(Sachin fails)+P(crisis|Sachin does not fail)xP(Sachin does not fail)]

We all knew that this will be inevitable, but all of us were hoping that it will be delayed as much as possible. Sadly, that day we all feared has finally come and it was today. Steve Jobs, the ever so mercurial leader of our industry has finally lost his battle with cancer and passed away this evening. Thousands of pages have been written about him and on his contributions. More will follow in days to come as well, from every corner of this planet. Let me not go there. To me, he has been a symbol of a child who always followed his dream and to top it up, he had the trust and ability to see it through. People may say, he is not philanthropic, but that is not his title, nor did he claim to be one. What he showed us is that, it is what “you decide”, what you want to become and it is entirely up to you to follow it tirelessly and achieve it. That’s it, no more no less.  What others think and say is completely irrelevant, as long as you put the trust honestly into your mind.

Come to think of it, his life and work and the glory associated with the making of one of the largest valued company in the world all have a charm and special persona associated with. His 2005 Stanford commencement speech made him immortal and inspirational to wider circle of life all over the world. More than being a tech whizkid, he was a symbol of innovation. More than a manager or a programmer, where he stays above the rest is the clarity in product vision and leadership to drive it through. I have heard several stories from my friends and comrades on his passion to drive stuffs at all cost and at times at the risk of spoiling personal relationships. That single minded drive to realize something special everyday made him this special. More often than not, we could see the sense of honesty in every statements he made, whether it is in public forums or in personal remarks at interviews. No tantrums and no diplomacy hanging around, plain simple truth in blunt words.

The world has lost a leader, visionary and innovator. He did not invent a medicine for cancer or aids, but he had made many a mark in the lives of thousands of people around the world. For some, he was the man who championed behind the realization of many amazing products of everyday use (Myself a huge beneficiary of it directly and indirectly!) and for others, his life itself serves as a message to follow their own dreams and then enjoy a lovely and satisfying life.  Thank you Steve Jobs. You have made a stamp in many lives.

While driving back home this evening on  a dark and rainy day I had the Stanford speech in mind. My mind seem to have said. Thank you sir. The words “Stay hungry, Stay foolish” reverberated on. Immortal words! Along the same bay he is resting at peace!

Footnote: CNN money had this report published sometime ago. The level of scaling Apple achieved under his rein since the beginning of this century is stunning.

Courtesy: From CNN money report (See the link above)

No wonder and no dispute to this argument. It was quite apt when Túlio said ” Lionel Ritchie works all the time” in the movie Rio (see the official website here). Listening to this is a treat, all the time, all places. Simply beautiful!

It is kind of sad to see Federer loosing from a rather reaching to a comfortable position of winning the match. But it did happen in Wimbledon 1 months ago and now the very same thing happened in US open on Saturday. You may call it unlucky and some may say it is just aging. Hopefully he wins another grand-slam.

I woke up touch early (4am) to watch the final day of the fourth India-England test match at Oval. First, I checked cricinfo and wow, Tendulkar was still batting. After a series of troubles and time outs, I managed to find one video streaming link. He wasn’t at the imperial best, but all looked set for that 100th 100. Other than that momentary hope, there was not even a glimpse of hope in the test match result. Anyway, much like the millions (or billions) all across the globe, I waited to see that 100. But alas! On 91, yet again a 90s misfortune for Tendulkar. Out LBW, somewhat contentious, but not overly outrageous a decision by an umpire anyway. He wasn’t at his imperial best in this series, but he was looking good for one to make that 100th number. Now, we will have to wait again for more from the great man.

Now the England white wash over India in a 4 test match series. The BCCI and the much hopeless cricket administration is putting the nails on the test cricket coffin. What a pity! For them IPL is the cash cow. Everything else is just for time pass. When a lot of money is poured in, even the most respected commentators and ex test cricket players have swallowed tongues. No one will put a blame on preparation. An IPL soon after world cup have paid more than damage to Indian cricket. Half fit players for an all important test series? In the end, made a mockery of test cricket!

I was long curious about the origin of the name San Diego. I feel ashamed of myself if I don’t know a bit of history of the place where I stay. As far as history is concerned, to a decent extend, I was indeed aware about the history of California, including San Diego. But, I didn’t know where the name San Diego originated from. Thanks to this and a bunch of Google/Wikipedia hits, here I know why San Diego!

Here is the official explanation behind the name San Diego, at least per San Diego Historical Society.  The Spanish explorer Sebastian Vizcanio arrived San Diego from the Mexican coast of Acapulco . This was in the year 1602 and it took. He had departed Acapulco with four ships on May 5, 1602 and only three of them, his flagship ship being San Diego, made it to what is now known as San Diego bay.  Besides the flagship ship named San Diego, he had two other ships arrived at the bay. They are the San Tomás and the Tres Reyes. The exact date (as per history) of his arrival in San Diego bay is November 10, 1602. Acapulco found no qualms in naming the new coastal area by his flagship ship name and hence we now live in the beautiful San Diego and not San Thomas or Tres Reyes, huh! Apparently, there was another reason why Acapulco chose San Diego. It was to honor the Mission Basilica San Diego de Alcalá.

Windowing techniques have always offered confusion to me. The hardest one was to remember what is what and how they looked in frequency domain (the time domain view was something thankfully I recollect from the names). I hit upon this yet again while trying to map the theoretical spectrum to spectrum computed from discrete samples (for an OFDM modulated signal) and then to analog spectrum measured by an instrument (By the way, I figured out that, the closest discrete technique which maps to the spectrum computation in spectrum analyzer is the Danielle method, which for some reason is not there in Matlab!) . For ages, I was using the pwelch (now spectrum.pwelch) function (pwelch method to estimate the spectrum) to compute/plot the spectrum in Matlab. Usually, some windowing as well is used to adjust the mean square versus resolution.  What window function is more suitable is something that I’ve never mastered. These days, doing a Wikipedia search to find a temporary fix and then move on is the adopted, yet not entirely satisfying strategy. The frequency domain characteristic of the popular window functions are now in here for reference, thanks to Marcel Müller. Since I may need it once in a while, I’ll keep a copy here for my own selfish quick reference. If you ever need to grab a copy, please be aware that, the ownership of this is with them.

Just came across a neat little Google App for Meegenius to use with Google chrome. Quite cute and nice. Basically, a little story telling/book reading (with audio) app for small kids; Essentially, this is an add on to the Meegenius online book store/reading for kids while using Google Chrome as the browser. I am sure kids will have an enjoyable ride with this. I found it to be incredibly cute!

Well, if you are not really obsessed with Google chrome, then you can as well go direct to MeeGenius and read it there!

One thing I like (besides it being an absolute gem of  a search genie) about Google is their customized logos, usually marking the day in history. Today, on Pierre de Fermat’s b’day they setup a nice and cute logo. On the logo, the famous Fermat’s last theorem is pictured.  I think, it was in 1993 I first, heard of this famous problem when England born Oxford/Princeton mathematician Andrew Wiles unveiled the solution. In 1996 or so, there was this documentary telecast in BBC on Andrew Wiles and his journey to solving one of the greatest (if not greatest, one of the most talked about problem) problem in the history of mathematics. A high class documentary is archived in youtube. I am not sure whether it was BBC who made it originally. I see that some youtube link shows UTV.

Here is another piece of writing/blog on this subject (by Chloe Albanesius).

Happened to see a wonderful animation on the formation of human embryo and how a baby develops from almost nothing to the cute avatar!. First, I saw as it through a Facebook feed, but it is also there in you tube. I don’t know who the original creator of this nice animation is . Wonderful!

It was in 2006, I guess, I had written a mail to Mathworks on this topic. I did get an acknowledgment from them saying that they will incorporate this into the future version. I don’t see it yet. I wonder why! Anyway, here is the Email I had sent to them. Unfortunately, I couldn’t trace their Email reply since it was sent to my earlier official ID, which has changed! Hopefully, I will ping Mathworks  again and get this up.

I believe the theoretical BER under fading scenarios, provided by the ‘berfading’ function in Communication toolbox is not quite accurate, for frequency flat fading, when Doppler shift to be considered. Currently, for example, the berfading gives out the BER for Rayleigh (or Rice) fading channel, without considering the impact of Doppler spread. In the presence of  Doppler, there may be an irreducible error floor for certain modulation schemes, especially differential modulation schemes. There are theoretical results (not closed form) to reflect such impacts. Closer approximations of the average bit error probability are derived in closed form for some of the differential schemes (say DBPSK, DQPSK etc).

Just to illustrate the point, I am enclosing here, a snapshot of the comparative BER results. For DBPSK, the exact BER, considering maximum Doppler frequency, for a uniform scattering model (Jakes spectrum) can be better approximated to Pb=(0.5./(1+EbN0) ) .*(1+ (EbN0.*(1-besselj(0,2*pi*Ts*fd)) )); The simulation results closely match this result, as against the berfading  result “berfading(SNR,’dpsk’,M,1)”

The BER curves are shown in the figure, attached with. Blue curve is what Matlab ‘berfading’ gives. The pink (Pb_doppler_theory) is the approximate and more correct bound, for Jakes spectrum (See [1], [2], [3]). The latter result is in close unison with the simulation as well.It would be nice if Mathworks can modify (may be in the next release) berfading such that, the  theoretical BER expected take care of such fading characteristics (in this case Doppler). I am  using 2006b version of matlab. In this only Jakes spectrum can be compared. For other  spectrum (I read in the Mathworks website that other spectrums can be configured in later
versions of Matlab/toolboxes), appropriate modifications to be done.

[1] P. Y. Kam, Tight bounds on the bit-error probabilities of 2DPSK and 4DPSK in nonselective Rician fading,IEEE Trans. Commun., pp. 860-862, July 1998.
[2] P. Y. Kam, Bit error probabilities of MDPSK over the nonselective Rayleigh fading channel with diversity reception,IEEE Trans. Commun., pp. 220-224, Feb. 1991.
[3] M. K. Simon and M.-S. Alouini, Digital Communication over Fading Channels A Unified Approach to Performance Analysis, Wiley 2000.

The cricket world cup 2011 was at best boring, until yesterday. The Chinnaswami stadium in Bangalore, when all lights were alight, Ireland looking down the barrel at 111/5 with 26 overs to go, in search of the English target of 328, in came Kevin O’Brien. What stuck then onwards was sheer magic. Scintillating innings of power and conviction, which in the end sink the English hope. I cant imagine how berserk the Irish pubs in Dublin would have been last evening, post the most thrilling upsets in the world cup cricket history.

Come to think of it that Ireland has beaten a reasonably in form England by 3 wickets with 5 balls to spare. That too chasing a mammoth target of 328 for a win! If only they had beaten a relatively easy Bangladesh in the earlier match, this pool would have been very interesting. Honestly, the Ireland-Bangladesh match was played on a hopeless pitch, but that is no excuse.

Until yesterday, not many people would have given a chance to Ireland, in spite of the upset victory over Pakistan in the 2007 edition. No one had feared Kevin O’brien this much. But from now on, the teams will be aware of this massive threat, especially on flat tracks where one can hit through the line at will. Ireland is due to play India next in the very same ground. Not to forget that, the last match prior to this at the same venue produced a classic tie at 238, between England and India. So, game on?

For some reason, I really love the beginning scenes of the movie Tangled. The screen visualization and the audio are simple amazing. These days, I really relish seeing this again and again, especially the starting scene and the songs. Thanks Disney for such a wonderful movie!

For a generation of kids like me, growing up in the 80s and 90s in India, Anant Pai, popularly known as Uncle Pai was one of the most influential figure. Not because of his personality or the aura in public life, but the sheer creativity in transpiring the richness in the Hindu mythological stories to us in the form of children stories. The Amar Chitra Katha stories from him, not only had improved our knowledge on the many epic stories and its variants, but also brought the curiosity in the fairy tale world to young minds. It is with immense sadness I passed the day hearing his sad demise, last week.

The song from the animation movie tangled has become one of my favourite already. The movie is one surely one of my favourite as well. Here is the the youtube link. So beautiful.

I heard about the Indian agricultural minister Sharat Pawar making such an atrocious statement on the highly dangerous pesticide Endosulfan. According to him, Endosulfan is a good thing. Holy cow. What an insane statement!. Someone sitting in the ivory tower with the rich cricket administration under his tummy, may not have to be overly bothered by the hundreds and thousands of lives already ruined by a dangerous pesticide. A pesticide which is banned in pretty much all the developing countries, is enjoying 70% market share in the largest democracy in the world. That shows the will and responsibility of our government. Kerala is the first Indian state to ban this pesticide. Why wouldn’t they. Their state, the northern Kasargod district is the worst hit by the hazards of Endosulfan. Hundreds of people are still suffering from the genetic impact of the dangerous venom, Endosulfan.

According to this, Endosulfan export from India is worth 180 crores. The largest democracy in the world has no time and seriousness to protect its good majority of poor people. The Endosulfan tragedy is rated as the disaster whose magnitude is next only to the Bhopal gas tragedy. It is so sad that, the government is so sick in their drive on corporate responsibility.

Here is a video revelation of the nonsense pesticide that Sharat Pawar think is good. For him, the IPLs and the billions along with that is more precious than the millions of suffering elsewhere. Shameless.

It came as a shock, when I heard the demise of Rudi Ahlswede, first from here. He passed away in December 2009, just two months after the ITW in Dublin where he looked jovial as ever. Interestingly, I had lunch with him, in one of those ITW days and it was fun conversing him. A great loss to Applied math and Information theory in particular. With his demise a massive figure has been lost. Very sad indeed. Besides the large contribution to the field, the special thing which standout is his humility and the sense of respect to fellow researchers, and the occasional humour in light conversations. His lectures were very jovial and filled with the innocence of an enthused child.

For me, there has never been a second thought on what the best ever love poem and the poet are. It is the one and only Elizabeth Browning and her beautiful poem How do I love thee (See below. A beautiful reading by Helen Mirren is here in youtube).The Browning couple stands tall when it comes to some of the all time toppings in literary romantic poems. I remember my wife (then my fiancee) sharing a piece of Hindu Sunday literary supplement which had this poem. I have the sonnet etched back in my mind, even now!

How do I love thee? Let me count the ways.
I love thee to the depth and breadth and height
My soul can reach, when feeling out of sight
For the ends of Being and ideal Grace.
I love thee to the level of everyday’s
Most quiet need, by sun and candle-light.
I love thee freely, as men strive for Right;
I love thee purely, as they turn from Praise.
I love thee with a passion put to use
In my old griefs, and with my childhood’s faith.
I love thee with a love I seemed to lose
With my lost saints, — I love thee with the breath,
Smiles, tears, of all my life! — and, if God choose,
I shall but love thee better after death.

Ok, why did this pop up now? Well, in UK, apparently there was an opinion poll on the best one liner; the love one liner that is. Mind you, it is not the full fledged poem, or for that matter a full sonnet or stanza itself, just a one linear. Here are the 10 most popular according to the survey. Just ahead of the Valentines day, a good time pass! Happy reading and Happy Valentines day folks!

1. ‘ Whatever our souls are made of, his and mine are the same’ – Emily Bronte
2. ‘If you live to be a hundred, I want to live to be a hundred minus one day so I never have to live without you’ – A A Milne
3. ‘But soft! What light through yonder window breaks? It is the east and Juliet is the sun’ – Shakespeare ‘Romeo and Juliet’
4. He was my North, my South, my East and West, My working week and my Sunday rest, My noon, my midnight, my talk, my song; I thought that love would last forever: I was wrong’ – W.H. Auden
5. ‘You know you’re in love when you don’t want to fall asleep because reality is finally better than your dreams’ – Dr. Seuss
6. ‘ When you fall in love, it is a temporary madness. It erupts like an earthquake, and then it subsides. And when it subsides, you have to make a decision. You have to work out whether your roots are become so entwined together that it is inconceivable that you should ever part’ – ‘Captain Corelli’s Mandolin’
7. ‘Grow old along with me! The best is yet to be’ – Robert Browning
8. For you see, each day I love you more. Today more than yesterday and less than tomorrow’ – Rosemonde Gerard
9. ‘But to see her was to love her, love but her, and love her forever’ – Robert Burns
10. ‘I hope before long to press you in my arms and shall shower on you a million burning kisses as under the Equator’ – Napoleon Bonaparte’s 1796 dispatch to wife Josephine.

I am at aghast when these sort of things are happening in 21st century.  Zahra Bahrami was executed by the Iranian government! Where has the civilization gone? A large section of our world still hangs and hails the Neanderthal laws. So sick of these religion and cowardly laws being prevailed in many parts. Make a mockery of humanity.

I didn’t know much about Zahra Bahrami. Couple of years ago, I happened to see an Iranian protest in Lausanne down town. The mass then were protesting against the large scale rigging which took place in their country, during the general elections. Apparently, during a home protest the ruling government had arrested Zahra Bahrami, who held a dual citizen citizenship  of of Dutch-Iranian. A series of reports and news piece popped up everywhere in Internet, calling for a fair trial in the case.

Now, much to the world’s surprise the Iranian government hanged Zahra Bahrami for what many perceive as a fake case involving drug possession. Whatever be the truth, nothing justifies a government execution of this kind. In civilized society, there is no place for such barbaric acts. Shame!

Over the weekend, I watched the new animation movie from Walt Disney. It is the fairy tale story of Stuepnsil. A really nice movie. Quite different from many of the animation movies of the past.

So, Google is going to have Larry Page as CEO from April 4. Eric Schmidt is going to head the strategic drives.

What an epic clash this at the first round of Australian open, between the local boy Hewitt and Argentine Nalbandian. Who can forget the 2005 epic clash between Nalbandian and Hewitt? That day, Hewitt just had the luck to edge out Nalbandian. Come 2010, the excitement and clash was as good as 2005, just that the winning number changed sides. And this time, first round itself. What a great start for this Australian open!

A Nalbandian Nadal clash somewhere down the lane is likely. How will the two best friends in circuit clash there. I cant wait.

Tom Kailath is a genius when it come to presenting concepts. His talk at USC during the annual Viterbi lecture in 2011 was no exception. He talked about the connection between radiative transfer and how some of the results there beautifully connected to algorithms used in communications. As always, the master of many had a lot of stories to tell and it was mind blowing, to say the least.

So, things are going great for the high tech. Hopefully things will stay like this for a while. Intel just reported a strong 4th quarter result. Q4,10 to Q4,11 increase in revenue is 40%. Wow! The forecast is looking good too. Clearly, the tablet market is set to explode. The upbeat was reflective in the market as well. The good thing with big brother companies like Intel is that, they can take the market along. When they produce great results, it generally strengthens the health of the industry as a whole. When they take a hit, the impact is disastrous for the high tech houses and semiconductor industry in particular.

In recent times, I heard about these Somali pirates. Initially, I brushed aside as just another news piece. The repeated presence of their action in news papers prompted me to explore a bit about these characters. And guess what, there is some kind of history to their origin. As expected, Wikipedia has stuffed quite  a lot of details already.

Somali Pirates are without doubt, a threat to the world. But think about this. According to many reports, including that from a United Nations study, says that, this came as a result of the rest of the world (read, the rich trading nations)’s exploitation and illicit dumping of toxic wastes in the Somali waters. The toxication of their waters severely damaged the livelihood of majority of Somalians who largely relied on fishing to make a living. So, actually the locals were forced to take up piracy as a means to live. What a pity. Whom to blame?

Other than the title tag of being the founding father of Western Philosophy, the first thing I remember about Socrates is the saying “I know nothing about me, other than that I know nothing”.

It is quite amazing that, Socrates has never bothered to write books or manuscript. It is largeley due to the remarks and subsequent referencing through works of his illustrious students, we got to know something about the great thinker and philosopher. Without Plato, we probably wouldnt have got to know much about him.

And by the way, Steve Jobs had this to say about Socrates: “I would trade all my technology for an afternoon with Socrates” (Newsweek, 2001). See the Wikipedia link for details.

If this is true, then this has to be one of the heaviest buy in the communication industry. Atheros buy may well be a WLAN entry for Qualcomm. Fingers crossed!

I just caught hold of this bizarre news from a recent verdict by a lower court in India. A community serving NGO doctor is sentenced life term for some strange accusation. Dr.Binayak Sen, a Vellore medical college alumni (Vellore medical college is one of the premier medical school in India) is serving the poorest of poor in one of the north Indian state (Chathisgarg).

A friend of mine, asked me whether I know anything about IPNLMS. Honestly, I didnt even hear about this. He said it is something like progressive NLMS. We did a bit of googling and then found that it is somewhat a new adaptive scheme.

Well, IPNLMS stands for Improved Proportionate Normalized Least Mean Square scheme, which is a modified version of the well known NLMS technique used in adaptive filter theory. OK, the idea of IPNLMS as I understood is, as follows. Each of the coefficient (tap) is independently updated, where the adaptation step is proportional to the estimated filter coefficient. How is this helping?

I was off from computer and internet for a few days, during the year end holidays. The thrill of going through some of the scenic mountains and farm lands was simply freshening.  This morning, while scanning through some articles, I caught the attention of Ian Chappell’s piece on Ricky Ponting. Good read, but touch sad to see a sad end to Ponting this way. A master on his on merit truly deserve a better end to his amazing test career. But then, sport is cruel and unpredictable at times. I don’t know whether Ponting has the same resolve as Tendulkar, who by the way is still going strong as ever.

This topic may have been discussed and debated a thousand times. I remember seeing one such report, not so long ago in EE times. The Economist has just placed a new one as well. The title is ” Why doing a PhD is often a waste of time”. Pretty interesting nevertheless.  Anyway, I personally do not think that it is all waste. On the other hand there are a lot of things out to learn in the process. Eventually it is a matter of personal choice!

On the Christmas day, out of blue I bumped across an old archive of Robert Fanos’s interview (oral history). Beautiful one.

Henri Padé wrote his PhD thesis in 1867 at the École Normale Supérieure in Paris. The dissertation was on what we know today as the Pade approximant. Come to think if it today, it is really remarkable that 100 years ago, mathematicians had thought about function approximations using rational polynomials. Now it may appear all too simple, but without the aid of a serious computing machine, one would have to rely on the mathematical rigour on every small argument. In comparison, these days, we can quickly check the validity using some computer program before venturing into a formal proof.

Anyway, the sudden recollection of this French mathematician happened, as I was looking for a good curve fit for a problem I need as part of my work. I needed to minimize the maximum error than the average or squared error. I thought about Legendre polynomial fit, which gave me the minimum root mean squared error and Chebychev who minimized the worst case error. The order of the polynomial and the number of sample points seemed to have dependency. Pade approximant is a cool technique which reduces the polynomial order while using a rational polynomial. I am not too convinced about the statistical properties of this method. The data points I have at disposal may have some measurement error attributed. I need to investigate a bit more before taking a decision on the potential optimality for the given problem! Happy knowing this scheme though. In retrospect, I remember hearing it in my statistical signal processing books, but never paid any serious attention then! Silly.

Official call on the world cup soccer hosts for 2018 and 2022 came out couple of days ago. It is going to be the beautiful Russia in 2018 and the Arab land gets the lot for 2022. One in eastern Europe and the other truly middle east Asia. Both these announcements created ripples and expected controversies, but I personally liked both the choices. My liking is bound from the fact that, these are two new hosts and the world deserve it see a global event occurring in 4 year gap to be held at different countries. So much to see and so much to learn. Why restrict only to a selected few countries. Afterall, there are 8 and 12 years to prepare. Unless the country is seriously deprived of money, then go ahead. Qatar with oil reserve have no shortage of bucks. Russia will never have a dearth, looking at the sheer volume of natural resources they have.

One of the major criticism against Qatar was that, it is hot. So what?It is really glad to hear that Qatar is planning eco friendly stadiums for the super event to be held in 2022.

And the Worldcup 2018 bid by Russia in Zurich was a fabulous one.

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