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I wonder how this song found itself a way to the drains! I remember listening to this audio in All India Radio chalachithraganangal program during childhood. It is a little slow but I have enjoyed the rhythm. Never seen this video before. Now, the video brings more nostalgia about those paddy fields and picturesque Kerala, my home land. Missing Kerala!
Hope you guys enjoy this music. (For information the music is in malayalam)
It appears that, both the LDF and UDF have overcome the usual uneasiness in coming out with the candidate lists to the coming Loksabha elections. Quite strangely, LDF candidate selection meetings turned out to be much like the usual UDF fights. LDF known for their discipline and ideologies, had to face a lot of mudslinging exercise, not only from opponents, but as well from their allies. However, largely, their candidate list showed some sense of vibrancy by fielding young and cheerful candidates. After all, people need their MPs to talk and present their woes; more importantly present and represent them well in the Parliament. Personally, I am not too inclined and happy with these Ponnani episode. Nor am I happy with these religious mongers having a big say in these elections. Sadly, the sense of reality hastens that, even the religious outfits have their agendas waiting to be exploited by one of these two fronts, namely LDF and UDFs.
Now, what do we have from the UDF list? Quite frankly, all but two are hopeless. Among the UDF list, I would like Shashi Tharoor to get elected, even though he will have to sweat it out from Thiruvananthapuram. I am not enthused by the religious agenda dominated constituencies like Ponnani and Malappuram, partly because I am ignorant of the real scene there and partly because of my uneasiness in mixing religion and politics. In the remaining 16 seats, I would rather prefer LDF candidates to win, simply because the opponent candidates stay no chance of being effective representatives. Congress has been lacking smart leaders. Their usual choices are drawn from the pool of factions and castes. LDF, in spite of all their hodgepodge alliances, fielded some decent candidates. It will not be easy, I reckon even for LDF, because the unpleasantness among allies and even within the members of major party CPI(M) is looming large. Going by the corruption history and ability to stand up and speak, many of the LDF nominees deserve to get elected over the UDF counterparts. For sure, I would really think Shashi tharoor is an appropriate candidate to represent Kerala. If elected he can perhaps be a very vocal MP for not only Thiruvananthapuram, but Kerala as a whole. To be honest UDF inspite of the minor opposition from within Congress party, got a good candidate to contest from the state. You can argue that he is not a big wig politician, but he knows more about India and is an exemplary policy maker, which will help in the parliament.
As a footnote, it is appalling that Rajdeep Sardesai cant even say the word Thiruvanathapuram, not in one, but four or five trials. Quite pity that, a leading national reporter cant get this right. I don’t mind a little change in accent, but he seem to care little to get the name correct. Horrible. At least a sense of respect? Anyway, their credibility tag is lost long ago, with their sensational reporting. Sad thing is that, they seem to continuously relish on that ideology. And they are sort of ridiculing Mallika Sarabhai, by asking something like “You, urban English speaking candidate fielding from Ahmadabad?” It was (and still is) so stupid a question that, Mallika replied in Gujarati to create more splines and wrinkles on their face (Suhasini Hyder the other news anchor in this case). Weren’t they expecting it? Or do they think that, everything in this world revolve around their concept of Indianness? Being a broadcast medium one thing is that, they can say any nonsense, but being responsible is entirely another. Over the years, Rajdeep who had been such a fine journalist, now all confined to being one among the many, new era sensationalizing breed. It saddens people like me, who had enjoyed their good piece of reporting; all when sensibility prevailed! She is standing in an election from a constituency where she lives. How ignorant are these urban news reporters on her ability to speak her mother tongue? They fielded similar question to Shashi tharoor as well. For their information, he can speak Malayalam, pretty decently.
Oh boy! Didn’t this five foot five inches little big fella make us feel a little better today? Didn’t those back foot cover drives served our eyes as little soothing gels? Didnt the rolling of the leather ball deflected from middle of that MRF stickered famous bat, on to a lush green turfs to the boundary boards of the beautiful Hamilton cricket ground, fetched moisture to our eyes, even while gluing to the live stream on the LCD screen, all in the darkness of the midnight hours? I had stayed awake into the wee hours of a cold Lausanne night, to see his masterful show in the first innings of first test at Hamilton. As Mark Richardson commentating remarked, the innings of Tendulkar had been an absolute batting clinic. There were quite a few stamp shots of class, which included a few front foot cover drives, couple of back foot cover drives, the cut shots and the impeccable straight drive which separated the trace of the ball epsilon inches away from the stumps at the non striker’s position.
C.5 (Concentration of the Chromatic Number – Spencer and Shamir). Consider a graph on vertices. The chromatic number of a graph , denoted by , is the smallest number of colors needed to color all vertices so that no two vertices which are joined by an edge have the same color. Consider the standard ensemble of random graphs on vertices with parameter : to sample from this ensemble, pick vertices and connect each of the ordered pairs of vertices independently from all other connections with probability . Show that for this ensemble
My solution is as folllows: (PDF typeset as single file is available here. Look for problem 3)
Let is a random graph with vertices. If is the probability that a given edge is in . The probability space be . Let be a filter on the set of all such random graphs. We can define a Martingale as follows:
and is the Chromatic number of . Chromatic number changes at most by one , when the information about the new edge comes in. Clearly, satisfies the conditions for Azuma’s inequality.
is a Martingale, with ). Let . Clearly
Now we can use the Azuma’s inequality on to get,
Since , the result
Here is an interesting riddle on random matrices.
(Rank of Random Binary Matrix). Let denote the number of binary matrices of dimension and rank , so that by symmetry . This is a repost of the solution that I have arrived at (certainly not the first!) and submitted as part of a homework (9) problem from the doctoral course Modern coding theory (by Rudiger Urbanke) at EPFL. The sumbitted solution in PDF is available here.
Rank of a matrix is essentially the number of nonzero rows when the matrix is expressed in echelon form. So, we just need to compute the ways these matrices can be created with non zero rows. Since the elements of the matrix are binary (from ), we can simply do a counting.
It is trivial to compute for and . For , only all zero matrix possible, and only one such matrix exist. Hence . For , since , no matrix exist, which means .
Now we consider . How many ways? We have non zero rows of the matrix, which means all rows must be nonzero. Without loss of generality, for counting, we could assume that, the rows are ordered. The last row ( row can be be done in , since there anything other than all vector (of size ) is allowed. On -th row, anything other than that of row is allowed. There are ways here. -th row can have anything except any linear combination of the rows and . This is nothing but . Row then have and so on. In all, Following the same procedure, we can have a total of
ways. For , we can construct a rank matrix of size in any of the following ways:
- Take a rank matrix of size and add an independent row.
- Take a rank matrix of size and add a dependent row.
For every matrix,
ways. (Essentially avoid all possible linear combinations of existing rows). Using the second (item 2 above) method, we can have and
different ways a rank matrix can be formed. Where,the first term () is when the all zero row is picked as the new row. In ways we can pick any one of the exisiting row as a dependent (new row). In general for we can have combination of existing rows out of in different ways to make a dependent (new) row.
So using (1) and (2) we get,
Putting everything together,
In this post, I tried (for the first time) to write something in Malayalam, my mother tongue. My dear English only readers, please excuse! The pleasure of writing something in mother tongue is different. Sadly and regrettably, I seem to have forgotten some of the alphabets of Malayalam. I feel ashamed.
മലയാളത്തിലെഴുതാന് ഇപ്പോള് വളരെ എളുപ്പമായി. പണ്ട് ഞാന് മലയാളം LaTex malayalam ഉപയോഗിച്ചിരുന്നതോര്ക്കുന്നു (In 2000 or so, it was. Now, latex omega is pretty nice and easy too, especially while LaTexing). കുറച്ചതികം ബുദ്ധിമുട്ടിയാണ് അന്ന് കുറച്ചു വരികളെഴുതാന് കഴിഞ്ഞത്. എന്നാല് ഇപ്പോള് എത്രയോ എളുപ്പമാണ് (all thanks to Google Transliteration). എന്തായാലും വേര്ഡ്പ്രെസ്സില് ഒന്ന് എഴുതി നോക്കാമെന്ന് വച്ചു.
കഴിഞ്ഞ രണ്ട് ദിവസ്സമായി ഞാന് കേരളത്തിലെ രാഷ്ട്രിയ സംഭവ വികാസങ്ങള് നിരീക്ഷിക്കുകയായിരുന്നു. ഇവിടെ യുറോപ്പില് ഇന്റര്നെറ്റ് വഴി കിട്ടുന്ന വാര്ത്തകള് മാത്രമാണ് ഒരു മാര്ഗം. പ്രധാനമായും വാര്ത്തകളെല്ലാം വരുന്ന ലോകസഭ തെരഞ്ഞെടുപ്പ് സ്ഥാനാര്ത്തികളെ ചുറ്റിപറ്റിയുളളതായിരുന്നു. സി പി ഐ എം, സി പി ഐ തമ്മില് പൊന്നാനി സീറ്റ് സ്ഥാനാര്ഥി നിര്ണ്ണയം ചൊല്ലിയുള്ള വിവാദം ഒരു പക്ഷേ അനാവശ്യമായിരുന്നു. സി പി ഐ സെക്രടറി വെളിയം ഭാര്ഗവന് തീര്ത്തും നിര്ഭാഗ്യകരമായ രീതിയിലാണ് പത്ര സമ്മേളനം നടത്തിയത്. ഒരു മുന്നണിയില് പ്രവര്ത്തിക്കുമ്പോള് ചില അഭിപ്രായ വിത്യസങ്ങളൊക്കെ ഉണ്ടാകുന്നതു സ്വാഭാവികം. പക്ഷേ അത് ജനങ്ങളുടെയും പ്രവര്ത്തകരുടെയും മുന്നില് അവതരിപ്പിക്കുമ്പോള് കുറച്ചു പക്വതയൊക്കെ ആകാമായിരുന്നു. ഇത് കോണ്ഗ്രസിലെ അടിപിടി പോലെയുള്ള ഒന്നായി മാറ്റിയതിനു വെളിയത്തിന്റെ കൊള്ളരുതായ്മ്മയായി മാത്രമേ കാണാന് കഴിയു. ഇതില് ഏറ്റവും വിചിത്രം പൊന്നാനി സി പി ഐയുടെ കൊട്ടയോന്നുമല്ല. മിക്കവാറും തോക്കാറുള്ള മുസ്ലിം പ്രാധിനിത്യം അത്യധികമുള്ള ഒരു മണ്ഡലം,അതില് ഒരു പൊതു സമ്മതനെ അങ്ങീകരിക്കാന് ചേര്ന്ന ഒരു മീറ്റിങ്ങില് തങ്ങളുടെ ആഗ്രഹം അതെ പടി സാധിയ്ക്കാതത്തിന്റെ പേരില് ഒരു പത്ര സമ്മേളനം നടത്തി ശകാര വര്ഷം ചൊരിഞ്ഞ് വെളിയം അദ്ദേഹത്തിന്റെ ഉള്ള വിലയും ഇല്ലാതാക്കി. ഒരു കണക്കിന് ഭര്ദ്ദനും വെളിയവും ഏകദേശം ഒരേ പോലെയുള്ള മൂക്കിന്റെ അറ്റത്ത് ദേഷ്യം ഒട്ടിച്ച രണ്ടു നേതാക്കള്. നിര്ഭാഗ്യവശാല് രണ്ടുപേരും ഒരേ പാര്ട്ടിയില്. അതോ ഭാഗ്യവശാലോ?
Inkscape has come off age. Creating vector graphics has now become pretty cool with inkscape. I too tried to make one. The one I tried is an egg. Afterall, I am convinced that egg is first and then chicken (I mean on eating preference). The drawing is not that stellar neat, but then, I am a novice when it comes to inkscape. This simply is my first drawing and I will be excused, Won’t I? I am posting the scalable vector graphics (svg) file, just in case a random enthusiastic reader find it useful to make it better!
The inkscape source file (svg) is available from this link;
Wondering why I created this figure? Well, I was trying to illustrate the P versus NP. My idea was to say the yellow yolk is P and white outer one surrounding the yolk would represent NP. Anyway that is for another post!
I am caught with a little trouble to figure out an easier way to set up and solve a summation of a function of several variables. I just realized that Mathematica doesnt allow me to add a constraint in the summation operation. My problem is that, the summation should be performed over the ordered partition set of a number.
An example, will illustrate the problem definition a lot better. Suppose I want to compute the sum of a function of variables over all variables such that, the sum of the index variables always equal to a constant .
Clearly, the indices here runs over all the ordered partitions of the number . Since is not that big a number, we can simply write these partitions by hand and somehow get the job done. Let us say denote the ordered partitions and unordered partitions of the number by and respectively.
. The ordered partition will have the permutations of each of these on the three positions! So and are different sets of whereas, they are considered as one in . The summation needs to be carried over the ordered partition list . Since both and grow pretty big with even modest , the job of manual summation is not that appealing. I really hoped mathematica to aid me here. Unfortunately, I don’t see a way out here, other than the painful individual partition sum. Anyway, for the curious reader, the sum I attempt are of the following types:
typical values for is and is around . If any enthused reader finds a way/trick, I will be happy to sponsor a coffee 🙂 (Sorry at this recession time, nothing more 😦 sadly…).
In fact, the first one is easy (Interestingly, I just found a way, while typesetting the blog). I can do a differential with respect to and then scale it to get the requisite sum. It can be written as follows:
Second one is the trouble maker 😦
Oh man! power of a coffee. As I am typing this on a moody Lausanne swiss weather, here comes the trick. I just made a coffee and that seemed to have worked. I guess I can apply a similar trick to the second one too. Basically, we can split them into two expressions and then write each as differential versions of a multinomial sum. Here it is:
Amazingly, we can simplify both to get a simple looking expression. I am glad! Here is what I finally got:
Dont these terrorists and such insane folks have no other job? They are much more than a migraine now. What was considered to be a never ever target has now become the soft target of these terrorists. The latest dastardly attack on the touring Sri Lankan cricketers, near the Lahore stadium in Pakistan make us all the more worried about Pakistan. The horrific memories of Mumbai incident on 26/21/2008 are still ringing and now in the backdrop here is one which happened in the place it originated. I am hurt and saddened to see and hear these incidents happening again and again. By all means, these attacks are well planned operations and surely must have a background which cant be beyond the know hows of supporters and the territorial government. Will this be a wake up call to eliminate the terror network. They say cricket is a religion. Which religion? Fanatics from all religion made a mess in the name of cricket and otherwise. It is time for the entire population of Pakistan to come out in public and express a solidarity and say, “you terrorists made a mess of this world and you have no support from us, whatsoever”. Same pledge should be made by everyone in India, Srilanka and even Bangladesh. Terrorism cannot be justified, whether it is internal or external. This applies to not only to Jihadis, but also to folks like Ram sena and LTTE. All the doctrines which insists killing innocent section of population are of the same colour and they don’t deserve a piece of sympathy. The troubles of our times is getting worsened, ever so deeply. I am lost to get a feel of these fanatics. All these youth armed with AK47 should have been pillars of building a nation; alas! these very promising prodigies are sadly dragged, into those filthy cause in the name of religion and ethnic freedom! Terrible.
I feel sorry for Sri lanka who went ahead to express solidarity to a nation which was deprived of cricket by every other nation including India. They were promised express security! yet, in the end caught in the fallacy. Same sympathy to Pakistan normal folks who, to their innocence are denied of watching an international cricket game in their land. Now is the time to stand up and say, strongly against the doctrines which advocates terror. Act now, please…. Humanity is in danger at the hands of these cruel terrorists. Nurturing a wicked terrorist to kill your enemy can bite you back. So, never do that.