In any case, the point of this whole entry is that catalytic converters are a relatively easy part of your car to steal. They contain precious metals like platinum, palladium etc. and when mined for the metals can fetch $50 to $100. Replacing them, of course, costs more than a thousand dollars usually. There is nothing you can do to avoid such theft except avoiding parking in desolate lots. When parking in public areas make sure you park at a location that is visible to pedestrian or vehicular traffic. Such visibility maybe a deterrent. Park close to mall entrances if malls do not have police cars driving around the lot or surveillance cameras. Comprehensive insurance is a good idea, as long as the deductible is low enough that you don’t end up paying the whole amount. Park inside a garage where possible. If you have any other ideas about how to reduce the chances of such theft, let me know.

Here are some pictures from the trip.

Kavita and I walked around Lake Raleigh in the NCSU campus. Here Kavita discovered a treasure of mulberry trees lining the lake. She was so excited, she started to eat the mulberry fruit within 3 seconds of the discovery, without giving me a chance to think through the implications of eating some wild berry off of a wild tree. She enjoyed them so thoroughly that I was tempted to try it out, and it was, indeed, sweet. Later, we went to the DH Hill library (the main NCSU library). I wanted to show Kavita the Digital Medial Lab at the NCSU library. We also tried the long-distance wireless talking device on the lawns outside the library. This is a pair of pink stone (or cement) blocks with a concave piece gouged out of each and made to fact each other, with about a 100 feet between them.

I came back home and double-checked to make sure that we had not ingested something crazy and found out that what we ate was, most likely, morus rubra (red mulberry). Here is the wikipedia link to mulberry.

Click on the picture to go to the rest of the album.

Here is my approach and my solution to the problem. This solution has not been verified by Mau or anyone else, and there is a chance that I am missing some aspect of rigor required to make the proof watertight and, thus, self-verifying.

Approach

The space of all nxm matrices can be divided into a disjoint set of matrices that completely span the space. This disjoint set comprises
- matrices which have no row with all n numbers
- matrices which have exactly one row that contains all n numbers
- matrices which have exactly two rows that contain all the n numbers
… so on till
- matrices which have exactly n-1 rows that contain all the n numbers
- matrices which have each of the n rows containing all the n numbers

Now we can solve the problem for each subset that makes up the disjoint set that spans the space of mxn matrices, and add up the individual results. Interestingly, working backwards makes more sense to me. So let’s look at the subset of matrices which have all the n numbers in each of the n nows. There is no candidate matrix here that fails our criterion. All matrices will satisfy the criterion. Let’s call the set of matrices that satisfy the criterion, the set S and those that fail the criterion the set F. Therefore no matrix in this subset adds to F.

Next, let’s look at the subset of matrices which have all the n numbers in exactly n-1 rows. The remaining row, whatever be the number or numbers it carries, will cause the matrix to satisfy the criterion. Therefore no matrix in this subset adds to F.

Next, let’s look at the subset of matrices which have all the n numbers in exactly n-2 rows. The remaining 2 rows, will cause the overall matrix to fail, if they have no more than 1 number in them. That is they remaining two rows must be full of only one number. If a second number exists in either of the two rows, the matrix satisfies our criterion.

And so on.

So, the number of matrices in F is a sum of the following product over all values of i:
(how many ways can we select n-i rows)(how many ways can all n unique numbers show up in each of those selected rows)(how many ways can the remaining i rows contain, at most, i-1 unique numbers)

Solution

Basically, out of all possible matrices with n rows and m cols such that each element is an integer between 1 and n (both included), I try to figure out the number of matrices which do NOT satisfy the condition we are after, i.e., for these matrices you CANNOT select n elements, one on each row, such that the n elements are the n unique numbers, 1 through n. Call this set of matrices, which fail the condition, F (for fail). We are trying to find how many elements are in the set F.

The final answer for the number of matrices the satisfy the criteion, therefore, will be n^(n.m) - |F|, where |F| represents the cardinality of F, that is, the number of elements in set F.

To get to |F|, my line of thinking was:

F =
matrices for which there are, at most, n-1 unique numbers in the n rows
+ matrices for which there are, at most, n-2 unique numbers in n-1 rows and all n numbers in the remaining 1 row
+ matrices for which there are n-3 unique numbers in n-2 rows and all n numbers in the remaining 2 rows + … etc.

By ensuring that all the n numbers show up in the remaining x rows we are making sure that the matrix that satisfies a given term in the above summation does not satisfy the the previous term, and thus avoids being double counted.

Substituting terms,

As a summation, this can be written as

Here is how to understand each term in the summation above:
is the number ways can you choose n-i rows
is the number ways can you choose the n-i-1 numbers that will go into the selected n-i rows
is the number of ways can those (n-i).m elements in those n-i rows be filled with the chosen (n-i-1) numbers
is the number of ways we can guarantee that the remaining i rows each contain all the n elements.

Here are some video snippets of the event.

 

 



 

Two girls (whose names I will provide as soon as I can find out) did an awesome job singing the kriti, “Vande Vasudevam”.

 

Kavita’s music teacher, Mrs. Anuradha (in the center in the video) along with other participants (Left to Right: Mrs. Jyothi Sadhu, Mrs. Srikanthi Gunturi, Mrs. Anuradha Chivukula, Mrs. Lakshmi Putcha and Mr. Subramanyam Darbha) sang the 7 main compositions by Sri Annamacharya, called Saptagiri Kirtanas. They were supported by, Mr. Kalyan Sundar on the veena, Mr. Vikram Raj Kumar on the violin (Vikram is an NC State student) and Master Arjun Raghavan who did a splendid job playing the mridangam.

 



 

Kavita and friends (Left to Right: Mrs. Sumana Nanduri, Mrs. Kavita Krishna, Mrs. Usha Jayanthi, Mrs. Lakshmi Karra and Mrs. Uma Gorti) singing some kirtanas.

 

Vijay Vadali: Akka told my friends and me about your website.”You have made imagination turn real”. Some of my friends are so inspired by the pics of your house that they now are drawing inspiration. Wonderful pictures.

Anil’s Response: Thank you (also for bringing to my notice the problems with the previous guestbook)

March 22, 2005 - 08:22 PM

Venkat Moncompu: Hi Anil, It’s by far the most well created website by a working individual that I have come across in the recent times. The pains taken to keep it chronologically and meticulously organised, speaks for the enthusiasm and effort that does go into such an excellent website. One of your picture - that of the cyclist in motion - fascinated me since I’v been always wanting to take one such picture at high shutter speed. Have read about the techniques in photography books but never tried it. Looking forward to meeting you in early october.. till then. cheers, Venkat

Anil’s Response: I’ll tell you more about how to take such pics the next time we meet which I suppose would be this April!

December 22, 2004 - 08:22 PM

Saurabh Mishra: Awesome job anil!! Very well organized and excellent collection of poems, pics, thoughts and just everything else. Keep up the good work. Best wishes to you and Kavita for the wedding. -Saurabh

Anil’s Response: Thank you

March 22, 2005 - 08:22 PM

Prashant Kaushal Hi Anil, Congratulations for maintainig such a wonderful site. Good Job!. Also, CK’s pictures were great. Cheers, Prashant.

Anil’s Response: Thank you, CK’s pictures are usually great!

March 22, 2005 - 08:22 PM

Meenakshi Chandrasekar: anil!! ur poems are awesome!!the website on the whole is great! meenu

Anil’s Response: Thank you Meenu. Keep in touch!

March 22, 2005 - 08:22 PM

Giridhar Appaji Nag: Anil, surfed over here from Samya’s site. Good to read your poems again.

Anil’s Response: Thank you and your webpage inspires me. Good stuff.

March 22, 2005 - 08:22 PM

Babji Gudapati: Good work Anil. Keep it up. Picures are very good and your sketch work is excellent.

Anil’s Response: Thank you for your kind words!

March 22, 2005 - 08:22 PM

Amit Juneja: Great website, Anil. It was nice to put the tips for parents’ visit to the US. Of course, great sketches and paintings. And what is mango dal? Next time we meet, you are cooking this for us!

Anil’s Response: Most certainly we shall make mango dal the next time we meet!

Anil Krishna: The guestbook items posted March 22, 2005 are actually collected over a period of about a year or so prior to that date. The reason they all show up on the same date in this guestbook is because I moved these entries from my previous guestbook which did not have the date information

However, the show never really managed to significantly challenge my expectations from a play. There were moments where it was inspiring, but most of it was a drag. The storyline, whatever little there was of it, was linear, going through each character’s circumstances and personalities one by one. There was hardly any complex, thought-provoking, interaction between the characters. The ballad, called the “The I Love You Song”, where one of the contestants remembers her mother who is in far-away India, seeking enlightenment, is powerful. Another sequence that I liked was one where a contestant, who, before spelling a word, always writes it on the floor using his “magical” right foot, does it in super slow motion. The sequence starts off at normal speed, ramps up in speed to a frenzy, and then slows down to a low frequency stupor, before rebounding to normal. The songs were not awe-inspiring, in general, and some dialogues bordered on being vulgar.

The stage and props remained quite static throughout, with not much in terms of visual impact. The literary impact, which must have been the main motivation behind making this a play, instead of letting it stay in the book that it originates from, was not terribly impressive either. I am sure I did not get all the subtle jokes, but before I denigrate myself too much, let me add that I did not want to go the show having done any homework. I went there to be entertained; if I did not catch all the subtle jokes, maybe they were too subtle. There was one piece of clever wordplay, where “what” is spelled by taking the w from a word where w is silent, h is taken from a word in which h is silent and so on. Such a “what” is never heard, claimed the contestant. Clever, but such cleverness would do just as well staying in a book. The theatre is supposed to be a feast for the eye and the ear, thought-provoking and awe-inspiring. This play does not manage to consistently meet such criteria, although it grazes those thresholds once in a while. There were some members from the audience who participate in the early stages of the spelling bee, providing some opportunity for seemingly impromptu, but potentially well-rehearsed, jokes, before their pre-planned elimination. Some of the commentary and references were from surprisingly recent political events. Participation by some members of the audience and this sensitivity to current news indicates that the script for the play lends itself to some modification and improvization.

Reviews I have read online were surprisingly positive, even rave, about the show. This is a small-budget production; maybe my expecting it to be comparable to the few other plays I have seen - “Phantom of the Opera”, “42nd Street” and “Annie Get Your Gun” - was wrong. However, even then, given that the tickets were priced just as any regular show would be ($21 to $70), I just did not guess that it would be a low-budget production. I am glad we did not buy more expensive tickets. I feel that plays are over-priced in the US. Except for one of the contestants walking into the audience throwing candy, most of the action was on the stage, which stayed pretty much unchanged as well. I do not see why I needed to go there in person to watch this show, when I could have probably seen it clearer, and, for less, on a DVD, feeling just as involved.