A New year’s post!

Kumbakarna

Happy new year all Belated wishes and wishes still even if somebody moved your new year to a different date On Vishu day, (apparently) it is tradition to pick a random chapter in the Ramayana early in the morning, and whatever is read is said to have some impact on the reader’s life in the coming year. I tried it yesterday and the chapter I picked was about Vibheeshana’s confrontation with Ravana. It was quite serendipitous as the event has constantly been a source of confusion to me. To elaborate …..,

Vibheeshana

Two of Ravana’s brother are source of particular interest – Kumbakarna and Vibheeshana. Both, at some point advise Ravana against a war with Rama. However Vibheeshana is shouted at for this advise and  leaves Lanka to join forces with Rama and betrays many of Lanka’s secrets to Rama. He is later anointed King of Lanka after Ravana’s death. Kumbakarna makes the same advice but follows it up by comforting Ravana speaking of an assured victory despite knowing fully well what was in store for him. Kumbakarna is eventually killed in battle.

Kumbakarna’s actions are all too familiar. Actions like his are replicated in the Mahabharatha and is generally seen as the nobler of the two courses. Vibheeshana is often criticized for betraying his King and is commonly seen as an usurper and traitor. So then what is the confusion? Vibheeshana is (at the end of the epic) ordered by Lord Vishnu in the original form to guide people towards Dharma. He also becomes an immortal joining the ranks of Hanuman, Parasurama and Mahabali. What the _?

For those of us who are used to seeing the epics in black and white (no, not literally) – and thanks to Ramanand Sagar for this - this situation is confusing. What is correct here? Too often in life we are faced with similar situations. When and why is it ever right to be a snitch!! And the epics seem to be of no help here – both courses are shown as good and not against Dharma. All along, Valmiki continually praises the qualities of Vibheeshana – he is at no point portrayed as greedy or selfish. Instead, the descriptions are

“Vibheeshana spoke to powerful Ravana the words convinced of reason and which were very much beneficial. He, who could discriminate between good and evil things in the world, having sought the favour from his eldest (half-) brother by means of soothing words arranged in an order, spoke in consonance with place, time and purpose.”

I am not still fully clear why this action is considered correct. I am not at that level yet. But the original author clearly seems to think so. Feel free to read the original text and make sense of it. If you come by interesting commentaries, I would love to be notified.

The intention that drives your action is perhaps more important than the action itself. From a different perspective, this episode reinforces the idea that there is no distinct line between black and white in such situations.

I want to make a special note of this because it is very easy to get lost in the strongly polar natures of the main characters in the epics. The epics would seem to be of no practical use as situations or characters as seen in them would never happen in real life. In fact however, there is a large trove of such useful tips and indicators buried within them. Many answers are here. So take a closer look.

References and Further reading:

• Vibheeshana on Wikipedia
• Kumbakarna on Wikipedia
• Yudha Kanda of Valmiki’s Ramayana

Note: Nope, this is no longer going to be an exclusively tech blog. There is enough boring content on the net already. Time for some arbit content. Sure there’s enough of that too, but the world could always use more

On Tigers, diffusion and chaos

Tiger

RT @sanchan89 Always good to know that my mojo is still intact after 4 years Take a look http://bit.ly/bGv5su

So, after quite a while, I tried sketching again. And it came out pretty neat, I suppose. But then, I want this to be a tech blog, right?

We humans, have a somewhat dull skin[1]. It is completely bereft of any fur[2] and any pattern to be had on are to be painfully tattooed. Look, on the other hand , at the pervasive presence of spacial patterns on animal coats and flora. Most commonly seen in plants are the rosette patterns, and self replicating branching systems. Mammals and fishes are so much richer – their fur coats come with stripes, spots, rosettes, bands, blocks, combination of these  and in the case of some sea shells – Serpenski triangle! Even in animal behavior, there is so much elegance – if you have not seen the movements of large schools of fish or birds in flight, you have a serious problem and you should consult a psychotherapist. Even the inanimate desert sands are beautifully patterned with near parallel curves.

Spacial patterns collage

It makes us think, doesn’t it? How are these patterns formed?

If every skin cell were to take on either black or white color with a uniformly random probability, then a zebra would look like white noise. Try imagining one with a coat like that. No probabilistic distribution is ever going to generate patterns as fantastic as those on every tiger. Does every cell, then, have a global spacial view of itself? Is it possible that a single cell knows that it is a part of the stripe across the head of the tiger, and therefore, it should take on a black pigmentation? That seems like something phenomenally complex for a single living cell to know.

Related problems in developmental biology are cell differentiation, and Morphogenesis. Every cell in an embryo is the same. Embryos are homogenous; and yet without a single central controller, cells in different areas of the embryo develop into different parts of the body. Some develop into the the heart and lungs and others into brain and legs.

The first explanation for this phenomenon was provided by the British Mathematician, code breaker, logician, computer scientist ( and during the later days of his life, a chemist )  Alan Turing in his paper titled ‘The Chemical basis of Morphogenesis” in 1951.  ( This paper has its own wiki page ) The paper described mechanisms; borrowing heavily from concepts of self-organisation, well known in physics; by which non-uniformity may arise from uniform homogeneous states, and outlined the reaction-diffusion theory of morphogenesis. Reaction–diffusion systems are mathematical models that describe how the concentration of one or more substances distributed in space changes under the influence of two processes: local chemical reactions in which the substances are converted into each other, and diffusion which causes the substances to spread out in space.

Independently, around the same time a Russian biophysicist Boris Belousov discovered a reaction-diffusion system, now called the Belousov-Zhabotinsky reaction. Where Turing had proposed mathematical models, here was already a demonstration of the self-organizing tendencies of the non linear systems which he had proposed. Here’s a video of a BZ cocktail evolving

From a uniformly homogeneous solution – spirals, spots and expanding rings are formed. And no two instances of the same experiment will get you the exact same results. The equations that govern these reactions are so expressive that you can actually come up with results that show stripes and hexagons! Try it out yourself in this applet.

These two works are considered by some as the founding work on chaos theory. In a nutshell, Chaos theory deals with highly nonlinear and usually self looped systems that despite being fully deterministic, are subject to abrupt and seemingly random change. It is clear in this case -  In spite of explicitly and deterministically defined rules, the reaction-diffusion yields a uniquely different result every time. The source of all this chaos is, well…, in the source itself. The non-linearity of the system greatly magnifies even immeasurably small changes in the initial state. So, the next time you round up a value from 0.506127 to 0.506, be warned! As a sidenote, the phrase “Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?“, is not a misunderstanding of chaos theory. It is in fact the title of the talk presented by Edward Lorenz at AAAS, 1972 on chaos theory. The title was the result of inferences from a run of the simulation he had built, when he changed one of the values of atmospheric conditions as stated above.

If you are interested in learning more about Chaos theory, there is a fantastic one hour program on BBC. No, it does not have equations ( well, maybe just one )

1. Well, thats not entirely true! We have fingerprints. And they are beautiful and unique, but not colorful or macro. Guess that still qualifies as dull.
2. This is interesting because, man is the only mammal; excluding those that are aquatic, that has no fur, check out the February 2010 edition of Scientific American

Further reading

• Design of diffusion-reaction systems
• Non linear chemical dynamics and pattern formation (comprehensive content)
• Publications page of the Max Plank Institute of Theoretical biology
• Secret life of Chaos on BBC

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• If you find my posts interesting, you can follow me via RSS here.
• Some of my shared items are here, in case you find it interesting.

Genetic Algorithms.., A Primer

It is Charles Darwin’s 200^th birthday. So I guess there must be loads of posts on GA, strewn across the Internet. Genetic Algorithms are special to me because they are the prime reason why I am doing whatever it is that I am doing.

This post is a light intro to Genetic Algorithms, sans its terms. Genetic Algorithms are delightfully simple. GA is an approximation algorithm, that is, they are used in situations where either the optimal solution is unnecessary or the complexity of the problem does not permit it. Sometimes, the Genetic Algorithm may produce the most optimal result also. Since examples are the best way to learn an algorithm, here’s the example problem we are to solve.

Balancing moments

Given to you is a configuration of balances as shown in the figure. The problem is to balance the configuration by adding weights on either side. You are provided with 10 weights measuring 1,2,3……10 kg each. Each weight is to be used exactly once. Thanks to GreatBG for this puzzle. His puzzles are always most entertaining. This can roughly be equated to the traveling salesperson problem. In the problem, the salesperson is to visit all cities (and comeback ), in such a sequence so as to minimize the total distance covered. The most naive solution is to try all possible sequences and see which one gives the minimum cost. For a map of n cities, that comes to n! combinations. A similar approach would work in our case also, but then, when the map or the number of weights is larger, the technique, takes so much more time. A more professional approach would be ruffle up your knowledge of elementary physics and reduce the problem to a set of linear equations and then solve them. Naaa.

Genetic Algorithms

My code, in C++, is here. Here’s the pseudo-code, sourced from wikipedia

1. Choose initial population
2. Evaluate the fitness of each individual in the population
3. Repeat until termination: (time limit or sufficient fitness achieved)
   1. Select best-ranking individuals to reproduce
   2. Breed new generation through crossover and/or mutation (genetic operations) and give birth to offspring
   3. Evaluate the individual fitnesses of the offspring
   4. Replace worst ranked part of population with offspring

Initializing the Population

The algorithm maintains a set of solutions. Not optimal solutions, just solutions. For example, in the case of the TSP, it may be a set of random ordering of the cities. In our problem, a set of random configuration of weights. In the program, I maintain the configuration as a string, where the weight alloted to each slot is represented by a character, with ‘A’ being 1, ‘B’ being 2 and so on. The weights are added bottom to top and left to right. One point to be noted here is that all solutions in the set must stick to the constraints of the problem. No city must be re-visited, no weight can be added twice.

Evaluating the Population

This is the key part of the algorithm. Once a way is found to evaluate each member of the ‘population’, the problem is half complete already. In our case, the “fitness” will be based on the resultant moment in the system. Therefore, best solution will have 0 fitness, the resultant moment in the system would be zero.

Until the required precision is obtained, or a maximum limit on the number of iterations is reached, we continue by doing the following opertions.

Crossover

This is where we actually begin to understand why it is called Genetic Algorithms in the first place. According to Darwin’s thery of Natural Selection, the best members of the population mate to produce better offsprings. Similarly, in our algorithms, the best solutions found so far mate with each other to (hopefully) produce a better solution. In code, this translates as the merging of substrings from different members, chosen from among the best solutions found so far. Point to be noted is that if done improperly, this could result in an offspring, that is not even a valid member of the population. It might violate the problems’ constraints. In TSP, and in this case, the same city/weight might get listed again, which cannot be allowed. So we use a special crossover method called, Partially Matched Crossover(PMX in code) which is beyond the scope of a primer.

Mutation

Some members of the population are randomly chosen to be mutated. Mutation is a process by which the offsprings get a trait that is inherited neither from the father nor the mother.While translating into code, this simply means swapping two characters within the string. You can choose more complex mutation techniques if desired. Again, the problem constraints must be satisfied. Mutation is required mainly to increase the variety of solutions in the population. Variety is very important.

Natural Selection and Elitism

Once these operations are done on the parents, a new generation of solutions are born. To make sure that the best solution in this generation is atleast as good as the best one in the previous generation, we introduce “elitism”. Normally, all the individuals in the previous generation are replaced by the members from the newer generation. But by having a non zero elitism value, a small portion of the best solutions from the previous generation survive on in the next generation.

Going by the paradigm of survival of the fittest, we now select the best solutions from the both the generations and these form the actual next generation. (My code is slightly varied. It does not use natural selection, the members of the younger generation simply replace all but the elite members of the elder population)

Local Maxima

Genetic Algorithms suffer from the problem that it might converge to a non-optimal solution. Consider that we are looking for the solution that is at the top of a mountain. It is possible that the population end up on an elevated hill, far away form the mountain. This is possible if the various values are not tuned properly. The algorithm will not get out of this situation by itself. the best way to go in this kind of a scenario is to simply start again.

People, Blogs, Conferences and Applications

• Illinois Genetic Algorithm Laboratory (Home of David Goldberg, the father of Genetic Algorithms )
• Genetic Argonaut ( Watch this blog for the latest updates in the field )
• GA and ART, evolving Mona-Lisa
• NEAT users group. (Highly active Yahoo! group, NEAT , that uses GA to train ANNs )
• Evolving Gaits
• GECCO ( the most impactful conference in all of computer Science )
• A formal and free treatment of Genetic Algorithms (ebook)
  
• Sanjeev (me), my poster on Dynamic Difficulty Adaptation in Games using GA has been accepted at ICFDG 09. Watch this blog for updates on that.

Game AI Development Event at Kurukshetra 09

College of Engineering, Guindy is organizing a game AI development event this time at  Kurukshetra, the annual International Techno-Management festival.

Kurukshetra 09

We wanted the event to reflect the current trends in the Game AI development industry. It is left to the participants to be the judge of to what extent the main goal is accomplished. The trends seem to be

• Player specific content
• A move away from hard-coded-rules based opponents.

We chose Lunar Lander to be the test game for both problem statements. Why? Lunar Lander was one of the earliest games to use Vector Graphics. But that’s not the reason why. Lunar Lander is simple, to code and to play. And.., it seemed to offer scope for hacking both problem statements. And now to the problem statements.

The First problem statement is a challenge to create a player that plays the Lunar Lander. You could try a rule based approach and try coding it. And you may succeed too. But I’ll bet the easier way out is to make your player learn how to handle the Lander. There are many situations where a rule based approach would fail. Consider the case of a car racing game, a rule based approach may satisfy the initial requirements of the game. Your racer may successfully out-race the human player, but it wouldn’t do well on tracks you, as its programmer would not have seen.  Because your AI doesn’t know how to ‘drive’. Well, that’s the motivation for this problem statement.

The second problem statement is with regards to content creation. Simple games such as Lunar Lander, I think deserve to engage the player for longer than 3 levels. The content of the game is very simple. It involves very little graphics. Is it possible to use modern / not-so-modern techniques to generate an infinite set of levels?? Theoretically, yes. Further, would these levels, ‘engage’ the player as much as hand-crafted levels would? It is definitely worth a try.

Well, if you are a Game AI developer PRO, and all this seems, well, ‘childish’ to you,  or in case you disagree with what we have identified as the current trend in the industry, try the third problem statement. If you have any innovative ideas on game AI, an implementation of your concept is most welcome. Although, we are not intending to accept any text-book based search algorithms. Even slightly modified but better versions are accepted.

This is the link to the event’s page. Please go through the problem statements again. This is the first time we are attempting such an event. Your comments and suggestions are welcomed. They would be most invaluable to making this a more successful event in the next editions of Kurukshetra. Have fun, Merry Christmas and Happy New Year!!!