The Son, Daughter and Father Arc

The Ones

The light and the dark. The destruction and construction.
Too much dark or light will be undoing of the life as we understand it.

You’re the chosen one

Stay on Course, and you’ll do it again for the galaxy, you’ll bring balance! to the galaxy!

But beware, your heart!


Taylor Swift… A filament of the dying conuntry music?

I’m sure you’ve seen all these photos of TS your whole life. ( I assume you’re  a swiftie! )
This post is about the gradual change in her music from late 2000’s era to late 2010’s  era.
Has country music fallen prey to the showbiz aspect? Stellar Videos, awesome graphics but usual music. The one that has lost it’s charm? Has she too?











Oscillatory Neurocomputers with Dynamic Connectivity

TA: Sandip G Lashkare
Satyam Mohla n' Krishna Subramani
150010028, 150020008
***Stage I Completed (Oct 28)

MNIST Digit Classification using Oscillatory Networks


When someone mentions the name of a known person we immediately recall her face and possibly many other traits. This is because we possess the so-called associative memory.

Tasks, which are deemed computationally hard, such as pattern recognition, or speech recognition amongst others, can be successfully performed. The main inspiration such a computing architecture is the insight that the brain processes information generating patterns of transient neuronal activity excited by input sensory signals.

The two fundamental components that a neural network, capable of associative memory needs, are neurons and synapses, namely connections between neurons. Ideally, both components should be of nanoscale dimensions and consume/dissipate little energy so that a scale-up of such circuit to the number density of a typical human brain (consisting of about 1010 synapses/cm2) could be feasible. While one could envision an electronic version of the first component relatively easily, an electronic synapse is not so straightforward to make. The reason is that the latter needs to be flexible (”plastic”) according to the type of signal it receives, its strength has to depend on the dynamical history of the system, and it needs to store a continuous set of values (analog element).

We use Kuramoto’s model to illustrate the idea and to prove that such a neurocomputer has oscillatory associative properties. We demonstrate by simulation the behavior and evolution of the non-linear dynamical neural network, both spatially and temporally.




Neurons that fire dance together, wire together.


The phenomenon of synchronization pervades everyday experience. Some examples are hardly surprising, like the synchronization of the front and back wheels of a bicycle, as they are highly coupled as compared to synchronization in circadian rhythms observed in animals, and even in the subtle synchronization of the heartbeat to music.
Associative memory- the ability to correlate different memories to the same factor event is a fundamental property is not just limited to humans but it is shared by many species in the animal kingdom. Arguably the most famous example of this are experiments conducted on dogs by Pavlov whereby salivation of the dog’s mouth is first set by the sight of food. Then, if the sight of food is accompanied by a sound (e.g., the tone of a bell) over a certain period of time, the dog learns to associate the sound with the food, and salvation can be triggered by the sound alone, without the intervention of vision.
Today there is mounting evidence that the periodic and synchronized neuronal firing has a necessary role in neural information processing, especially in associative memory formation, visual perception and olfaction. The interactions of many excitatory and inhibitory neurons are
responsible for the rhythmic behavior. However, most of the today’s focus in neural networks is on neurons having equilibrium dynamics, modeled as neurons having a non-linear function with varying weights which in principle can model any transfer function. There is no temporal behavior.

Oscillatory Neurocomputers, unlike conventional von-Neumann Machines, rely on their auto-associative memory to recall the output when presented with a corrupt input (Pattern Recognition).


Fig. 1: We treat the cortex as being a network of weakly connected autonomous oscillators q1,..,qn forced by the thalamic input a(t).


Neurocomputing is a recently introduced, bioinspired computational paradigm that exhibits state-of-the-art performance for processing empirical data. There are still classes of computational problems, such as data classification and pattern recognition, where conventional digital computers perform very poorly compared to the elementary skill of human intelligence. For these applications, it is expected that neurocomputing characterized by a massive parallelism could lead to significant advances.
Among various neural networks, the most promising are oscillatory neural networks (ONN) because they take into account the rhythmic behavior of the brain. Arrays of weakly coupled oscillators represent a promising approach to unconventional computation. It has been proved that oscillator arrays can implement computational tasks such as pattern recognition and associative memory by exploiting their natural attitude to synchronization.
In these oscillator arrays, data information is commonly encoded in the relative phase differences achieved at synchronization, which makes computation robust against the intrinsic noise of circuit implementation.

To demonstrate our concept, we have chosen the widely studied Kuramoto oscillator. The model of this dynamical system is modeled by the Kuramoto’s dynamical equation. We now demonstrate by simulation, the capability of our single nonlinear dynamical node to identify corrupted digits (pattern recognition). The primary architecture used is that of a Hopfield-Grosberg paradigm, which is a kind of Recurrent Neural Network (RNN) Architecture.
Unlike conventional neural networks which work on backpropagation (training data), a Hopfield Network is a Dynamical System.


Fig 2.: Conventional neurocomputer having n neurons (circles) would have n2 connections (squares). An oscillatory neurocomputer with dynamic connectivity imposed by the external input (large circle) needs only n connections.


Through adjustment of its internal parameters (connection weighs), it leads to the system evolving from the input state(Corrupted Image) to the output state(Image pattern stored in memory) leading to identification. Addition of Oscillatory behavior leads to cycle attractors as opposed to fixed point attractors in a conventional Hopfield Networks.  Each oscillator plays an active role in the synchronization of coupled nonlinear oscillators is a common natural phenomenon. The coupling is typically the resulting synchronized state.



Fig 3: The Corrupted image to be resolved- Digit 1 and Digit 2


Broadly, the method followed is as follows :

  • In the initialization phase, the network is initialized with the fundamental states (stored patterns) and the corrupt image to be recognized is fed to the system in the form of connection weights. The system is evolved & directed by the energy minimisation feature of Kuramoto’s ODE

    leading the system to converge to the state corresponding to the corrupted image.


    Fig 4: Phase State of the ONN after being initialized with the corrupted image of 1. ONN is of 60 neurons (6×10)


  • In the recognition phase, the Hebbian Learning rule is introduced and the weights are set as per this HL equation. Now the system is in the corrupt image state and the system is again left to evolve to, the state which is closest to the corrupt image, thus giving the output as the uncorrupted image.h1
    Fig 5: Energy-State Diagram of the ONN for different convergent states
    (Note that in our case the states are namely ‘digit 0’ and ‘digit 1’ respectively.)


Simulation Results:

The time evolution of the ONN is shown above.

 The time evolution of the ONN is shown above. 



We have verified through numerical simulations the pattern recognition behavior of an interconnected oscillatory neural network using units (referred to here as oscillatory neurons) performing simple nonlinear transformations in parallel, underlining the feature of associative memory. Our brain also recalls memories in a similar fashion. Thus, the above architecture works very well for Pattern Recall and Recognition type problems, as minimal training (in our case, just one sample) is needed.  It is believed that a new generation of computers will employ these principles of the human brain for faster computation.

Future Direction:

We in the latter half of the project also extend the analysis to comment on the hardware implementation of the said network.

We also plan to bring in the writer’s newfound interest in spintronics in using an emerging class of highly nonlinear, nanoscopic, and ultra-broadband, low power wave oscillators, a spintronic oscillator as the hardware basis for an implementation of the architecture. *#

Ideas related to spintronic oscillator:

* Based on a paper by Julia Grover on 
Neuromorphic computing with nanoscale spintronic oscillators,
Nature 547, 428–431  doi:10.1038/nature23011

# A nature news article on the same
Applied physics: A new spin on nanoscale computing
Frank Hoppensteadt, Nature 547, 407–408 (27 July 2017) doi:10.1038/547407a


1. Hoppensteadt, F. C. & Izhikevich, E. M. Oscillatory neurocomputers with dynamic connectivity. Phys. Rev. Lett. 82, 2983–2986 (1999).

2. Nikonov, D. E. Coupled-oscillator associative memory array operation for pattern recognition. IEEE J. Explor. Solid-State Comput. Devices Circuits 1, 85–93 (2015).

3. Hoppensteadt, F. C. & Izhikevich, E. M. Synchronization of MEMS resonators and mechanical neurocomputing. IEEE Trans. Circuits Syst. -l Fundam. Theory Appl. 48, (2001).

4. F. C. Hoppensteadt & E. M. Izhikevich. Weakly Connected Neural Networks. Applied Mathematical Sciences 126 (Springer, 1997).

5. Robler, A. Runge-kutta methods for the strong approximation of solutions of stochastic differential equations. SIAM J. Numer. Anal. 48, (2010).

6. Roy, K., Sharad, M., Fan, D. & Yogendra, K. Brain-inspired computing with spin torque devices. Des. Autom. Test Eur. Conf. Exhib. (DATE), 2014 1–6 (2014). doi:10.7873/DATE.2014.245

7. Yogendra, K., Fan, D. & Roy, K. Coupled spin torque nano oscillators for low power neural computation. IEEE Trans. Magn. 51, 4003909 (2015).

8. Calayir, V. & Pileggi, L. Device requirements and technology-driven architecture optimization for analog neurocomputing. IEEE J. Emerg. Sel. Top. Circuits Syst. 5, (2015).

9. Aoyagi, T. Network of neural oscillators for retrieving phase information. Phys. Rev. Lett. 74, (1995).

10. P. Peretto. An Introduction to the Modeling of Neural Networks (Cambridge University Press, Cambridge, 1992).

11. Engel, A. K., Fries, P. & Singer, W. Dynamic predictions: oscillations and synchrony in top-down processing. Nat. Rev. Neurosci. 2, 704–716 (2001).

12. Gross, J. Dynamic imaging of coherent sources: studying neural interactions in the human brain. Proc. Natl Acad. Sci. USA 98, 694–699 (2001).

13. Laughlin, S. B. & Sejnowski, T. J. Communication in neuronal networks. Science (80-. ). 301, 1870–1874 (2003).




**Updates by PI**

Nice Work!

Add some immediate checks

1) Explore the frequency range
2) Addition of noise(how much will make the network fail to recognise pattern) on the sinusoid
3) Fixing couple of oscillators or all with same frequency
4) If any one oscillator fails(doesn’t work)

Couple of options for us to explore and choose one for stage 2.

1) The one we suggested.
2) Solve intricate problems using ONN Without weak coupling assumption You can check multiple papers here:
3) To replicate the results using experimental RRAM oscillator data (non-sinusoidal)

Finally, Comment on the difficulty in overall implementation. e.g. assumptions made(validity of those), hardware issues, amount of post-processing required if any, impact of your work.









ये दिल, ना होता बेचारा !

ये दिल, ना होता बेचारा
कदम, न होते आवारा
जो खूबसूरत कोई अपना हमसफ़र होता
ओ ओ ओ ये दिल, न होता बेचारा …
अरे सुना, जब से ज़माने हैं बहार के
हम भी, आये हैं राही बनके प्यार के
कोई न कोई तो बुलायेगा
पड़े हैं हम भी राहों में
ये दिल, न होता बेचारा …
अरे (माना, उसको नहीं मैं पहचानता
बंदा, उसका पता भी नहीं जानता आ आ
मिलना लिखा है तो आयेगा
पड़े हैं हम भी राहों में
ये दिल, ना होता बेचारा …
अरे (उसकी, धुन में पड़ेगा दुख झेलना
सीखा, हा हा, हमने भी पत्थरों से खेलना)
सूरत कभी तो दिखायेगा
पड़े हैं हम भी राहों में
ये दिल, ना होता बेचारा .

A classic gem. Evergreen.

Star Wars: Grey Jedi & Obi’s Sass


Droid: General, there is an incoming ship.
Grievous: Scan it.
Droid: We're detecting high levels of *sass on board.
Grievous: *slams fist Kenobi!



The FORCE PRIESTESSES were a form of shape-shifter beings, and would mutate their forms to manifest as Serenity, Joy, Anger, Confusion, and Sadness.Serenity, Joy, Anger, Confusion, and Sadness.



Star Wars The Clone Wars: Quotes…

The best show of my growing childhood. Asking dad to allow us (me and my brother) to watch the show back in '08 late at night, and the hurriedness with which we used to finish our all dinner and chores, before the show began. Oh! I seriously miss those days. A show, important part of my life, an inspiration. This show was really a class apart.

Season One



  1. Ambush: “Great leaders inspire greatness in others.”
  2. Rising Malevolence: “Belief is not a matter of choice, but conviction.”
  3. Shadow of Malevolence: “Easy is the path to wisdom for those not blinded by ego.”
  4. Destroy Malevolence: “A plan is only as good as those who see it through.”
  5. Rookies: “The best confidence builder is experience.”
  6. Downfall of a Droid: “Trust in your friends, and they’ll have reason to trust in you.”
  7. Duel of the Droids: “You hold onto your friends by keeping your heart a little softer than you head.”
  8. Bombad Jedi: “Heroes are made by the times.”
  9. Cloak of Darkness: “Ignore your instincts at your peril.”
  10. Lair of Grievous: “Most powerful is he who controls his own power.”
  11. Dooku Captured: “The winding path to peace is always a worthy one, regardless of how many turns it takes.”
  12. The Gungan General: “Fail with honor rather than succeed with fraud.”
  13. Jedi Crash: “Greed and fear of loss are the roots that lead to the tree of evil.”
  14. Defenders of Peace: “When surrounded by war, one must eventually choose a side.”
  15. Trespass: “Arrogance diminishes wisdom.”
  16. The Hidden Enemy: “Truth enlightens the mind, but won’t always bring happiness to your heart.”
  17. Blue Shadow Virus: “Fear is a disease; hope is its only cure.”
  18. Mystery of a Thousand Moons: “A single chance is a galaxy of hope.”
  19. Storm Over Ryloth: “It is a rough road that leads to the heights of greatness.”
  20. Innocents of Ryloth: “The costs of war can never be truly accounted for.”
  21. Liberty on Ryloth: “Compromise is a virtue to be cultivated, not a weakness to be despised.”
  22. Hostage Crisis: “A secret shared is a trust formed.”



Season Two




  1. Holocron Heist: “A lesson learned is a lesson earned.”
  2. Cargo of Doom: “Overconfidence is the most dangerous form of carelessness.”
  3. Children of the Force: “The first step to correcting a mistake is patience.”
  4. Senate Spy: “A true heart should never be doubted.”
  5. Landing at Point Rain: “Believe in yourself or no one else will.”
  6. Weapons Factory: “No gift is more precious than trust.”
  7. Legacy of Terror: “Sometimes, accepting help is harder than offering it.”
  8. Brain Invaders: “Attachment is not compassion”
  9. Grievous Intrigue: “For everything you gain, you lose something else.”
  10. The Deserter: “It is the quest for honor that makes one honorable.”
  11. Lightsaber Lost: “Easy isn’t always simple.”
  12. The Mandalore Plot: “If you ignore the past, you jeopardize your future.”
  13. Voyage of Temptation: “Fear not for the future, weep not for the past.”
  14. Duchess of Mandalore: “In war, truth is the first casualty.”
  15. Senate Murders: “Searching for the truth is easy. Accepting the truth is hard.”
  16. Cat and Mouse: “A wise leader knows when to follow.”
  17. Bounty Hunters: “Courage makes heroes, but trust builds friendship.”
  18. The Zillo Beast: “Choose what is right, not what is easy”
  19. The Zillo Beast Strikes Back: “The most dangerous beast is the beast within.”
  20. Death Trap: “Who my father was matters less than my memory of him.”
  21. R2 Come Home: “Adversity is friendship’s truest test.”
  22. Lethal Trackdown: “Revenge is a confession of pain.”



Season Three



  1. Clone Cadets: “Brothers in arms are brothers for life.”
  2. ARC Troopers: “Fighting a war tests a soldier’s skills, defending his home tests a soldier’s heart.”
  3. Supply Lines: “Where there’s a will, there’s a way.”
  4. Sphere of Influence: “A child stolen is a lost hope.”
  5. Corruption: “The challenge of hope is to overcome corruption.”
  6. The Academy: “Those who enforce the law must obey the law.”
  7. Assassin: “The future has many paths — choose wisely.”
  8. Evil Plans: “A failure in planning is a plan for failure.”
  9. Hunt for Ziro: “Love comes in all shapes and sizes.”
  10. Heroes on Both Sides: “Fear is a great motivator.”
  11. Pursuit of Peace: “Truth can strike down the specter of fear”
  12. Nightsisters: “The swiftest path to destruction is through vengeance.”
  13. Monster: “Evil is not born, it is taught.”
  14. Witches of the Mist: “The path to evil may bring great power, but not loyalty.”
  15. Overlords: “Balance is found in the one who faces his guilt.”
  16. Altar of Mortis: “He who surrenders hope, surrenders life.”
  17. Ghosts of Mortis: “He who seeks to control fate shall never find peace.”
  18. The Citadel: “Adaptation is the key to survival.”
  19. Counterattack: “Anything that can go wrong will.”
  20. Citadel Rescue: “Without honor, victory is hollow.”
  21. Padawan Lost: “Without humility, courage is a dangerous game.”
  22. Wookiee Hunt: “A great student is what the teacher hopes to be.”



Season Four



  1. Water wars: “When destiny calls, the chosen have no choice.”
  2. Gungan Attack: “Only through fire is a strong sword forged.”
  3. Prisoners: “Crowns are inherited, kingdoms are earned.”
  4. Shadow Warrior: “Who a person truly is cannot be seen with the eye.”
  5. Mercy Mission: “Understanding is honoring the truth beneath the surface.”
  6. Nomad Droids: “Who’s the more foolish, the fool or the fool who follows him?”
  7. Darkness on Umbara: “The first step toward loyalty is trust.”
  8. The General: “The path of ignorance is guided by fear.”
  9. Plan of Dissent: “The wise man leads, the strong man follows.”
  10. Carnage of Krell: Our actions define our legacy.”
  11. Kidnapped: “Where we are going always reflects where we came from.”
  12. Slaves of the Republic: “Those who enslave others inevitably become slaves themselves.”
  13. Escape from Kadavo: “Great hope can come from small sacrifices.”
  14. A Friend in Need: “Friendship shows us who we really are.”
  15. Deception: “All warfare is based on deception.”
  16. Friends and Enemies: “Keep your friends close, but keep your enemies closer.”
  17. The Box: “The strong survive, the noble overcome.”
  18. Crisis on Naboo: “Trust is the greatest of gifts, but it must be earned.”
  19. Massacre: “One must let go of the past to hold onto the future.”
  20. Bounty: “Who we are never changes, who we think we are does.”
  21. Brothers: “A fallen enemy may rise again, but the reconciled one is truly vanquished.”
  22. Revenge: “The enemy of my enemy is my friend.”



Season Five



  1. Revival: “Strength in character can defeat strength in numbers.”
  2. A War on Two Fronts: “Fear is a malleable weapon.”
  3. Front Runners: “To seek something is to believe in its possibility.”
  4. The Soft War: “Struggles often begin and end with the truth.”
  5. Tipping Points: “Disobedience is a demand for change.”
  6. The Gathering: “He who faces himself, finds himself.”
  7. A Test of Strength: “The young are often underestimated.”
  8. Bound for Rescue: “When we rescue others, we rescue ourselves.”
  9. A Necessary Bond: “Choose your enemies wisely, as they may be your last hope.”
  10. Secret Weapons: “Humility is the only defense against humiliation.”
  11. A Sunny Day in the Void: “When all seems hopeless, a true hero gives hope.”
  12. Missing in Action: “A soldier’s most powerful weapon is courage.”
  13. Point of No Return: “You must trust in others or success is impossible.”
  14. Eminence: “One vision can have many interpretations.”
  15. Shades of Reason: “Alliances can stall true intentions.”
  16. The Lawless: “Morality separates heroes from villains.”
  17. Sabotage: “Sometimes even the smallest doubt can shake the greatest belief.”
  18. The Jedi who knew too much: “Courage begins by trusting oneself.”
  19. To catch a Jedi: “Never become desperate enough to trust the untrustworthy.”
  20. The Wrong Jedi: Never give up hope, no matter how dark things seem.”


May the Force be with you!


Monstrous Moonshine. And Maths, obviously…

Math.  The dreaded word.

Everyone seems to hate math. For its unintuitive! It’s like, math doesn’t give a damn what we think is possible, or what we think is absurd. Math does exactly what it wants to do, because that’s all it can do. We may not always understand it, but sometimes, once in a blue moon, we get a peek behind the curtain. Once every few hundred years, we can prove that cicada mating rituals are related to weather on Mars, and briefly glimpse the universe in its true glory.

But what if math is not math, but really everything? What if physics is math? Like just maths?
Consider Monstrous Moonshine.




Pretty, Isn’t it?

Monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group M and modular functions, in particular, the j function. (*Wiki)

Professor Richard Borcherds of Cambridge University was awarded [August 1998] the Fields Medal, the mathematicians’ equivalent of a Nobel Prize, for proving a highly abstruse result in number theory called the moonshine conjecture.

It seems it was given this name because it was based on a coincidence between a result in number theory and the number of symmetries in an exotic concept called the Monster object. It was thought so unlikely that two such distinct areas of mathematics should have anything in common that the conjecture was described as moonshine, and the name has stuck.

Professor Borcherds was quoted as saying, “I was over the moon when I proved the moonshine conjecture”, a nice conflation of two of the common evocations of the Moon in the language.

Moonshine originally meant the same as moonlight. In A Midsummer Night’s Dream, Snug asks whether the moon will shine the night they perform their play, and Bottom replies in a brief panic: “A calendar, a calendar! Look in the almanack; find out moonshine, find out moonshine!” It still has this literal meaning in poetical or elevated contexts but we no longer use it in that way in daily life, unlike the matching sunshine. Instead, it commonly means something insubstantial or unreal, and so foolish or visionary.

It is now known that lying behind monstrous moonshine is a vertex operator algebra called the moonshine module (or monster vertex algebra) constructed by Igor Frenkel, James Lepowsky, and Arne Meurman in 1988, having the monster group as symmetries. This vertex operator algebra is commonly interpreted as a structure underlying a two-dimensional conformal field theory, allowing physics to form a bridge between two mathematical areas.


This makes me wonder, what if physics is also a part of mathematics?

Read this paper on On a Final Theory of Mathematics and Physics.    Maybe it’s true! Worth a read.


Mathematicians Chase Moonshine’s Shadow-Scientific American




The IITian’s Dilemma…

Some Musings on Life:

There are only two tragedies in life: one is not getting what one wants, and the other is getting it,” said Oscar Wilde , the famous Irish playwright, novelist, essayist, and poet. We feel extremely sad when we fail to achieve something which we desire a lot. However, even those people who achieve their heart’s desire fail to live happily ever after as often shown in movies.

It is true that most students who desire to become an Engineer, wish to get into IIT to realize their dream. However, hardly one in a 100 realize their dream of getting into an IIT. Even those who get into IIT don’t get the choice branch and feel unhappy.

I had a colleague whose son got IIT-JEE (Advance) rank of around 200 a few years ago. Even he was unhappy because he could not get CSE (B Tech) in IIT Delhi and he had to accept the dual degree programme of CSE in IIT Delhi.

One of the greatest tragedies of all IITians is that they are too brilliant to fail in written examinations. Many of them get into IIM or do MBA/MS from a foreign university. They can easily get great jobs in corporate or government which ensures them a decent life and a respectable position in society.

However, this security of the job becomes their greatest hurdle when it comes to taking risks and become leader or an entrepreneur. Most IITians end up becoming just managers of top leaders. You would hardly see an IITian leading the country in politics, business or art. These top leadership positions go to such people who could not make it into an IIT.

If you list the top 100 most influential people of India, you would hardly find any IITian in the list.

Hence, if you are not an IITian, you must not be disappointed.

It is wisely said, “When God closes a door, he opens a window.”

Find out the window left open when your doors of IITs are closed.

There lies your path of success, happiness and glory.


(*Taken from a Quora Answer)