Did you know the story of blind men and an elephant? The question is: is
synchrony relevant for understanding the brain function? Perhaps, and perhaps
not! It depends on what data you examine and how you interpret it. But coherent
firing of neurons is often a significant phenomenon in the brain. For example,
in models of Parkinson's disease, there is an enhancement of coherence among
neuronal activity. If you trust that activity at the level of single neurons is
indeed important for brain function, then you must make a connection between
single neuron behavior and population behavior that might show coherence or
incoherence. Coupled oscillator theory comes handy in addressing this question.
Arthur Winfree made singular contribution to understanding dynamics of coupled
biological oscillators [The Geometry of Biological Time, 2nd Edition, Springer, 2000.
when each oscillator is treated as a phase variable. Using neuronal response
to isolated stimuli (phase response curves or PRCs), Bard Ermentrout
software book link], and
others advanced the understanding of synchrony among phase coupled oscillators.
In this research we use PRCs to systematically investigate how their shapes
(that emerge from the properties of single neurons) affect synchrony among coupled
Winfree's definition: (p. 591)
Entrainment = phase-locking at a common frequency,
Synchronization = phase-locking at a common frequency and with zero phase difference.
Noise is not noise is not noise. The brain is noisy, of course. But noise can enhance some phenomena, and it might also disrupt some phenomena. There are various attempts in the field in understanding how noise is generated, how noise affects a certain phenomenon, and how noise modifies neuronal behavior. In this research, we study how noise modifies single neuron behavior, as well as how noise affects synchronization between coupled neurons. We find that if the noise is of the type that suppresses neuronal firing, then (1) it could actually enhance coherence of neuronal output, and (2) it could disrupt synchronization of even identical neurons.
How do you find signal in noisy data? If that data is an event data, i.e. like
a sequence of spike times recorded from brain neurons, the first thing you
would try is using autocorrelation or cross-correlation methods which require you
to pool a large number of data points. Using a gazillion data points should
not be a choice, because the signal buried in short sequences of events would
be masked and overwhelmed by what the long sequence of events behaves like.
Moreover do you think that the brain keeps collecting events for an hour and do
the computation then? No! You must use brief sequences and process that data
and make a decision. Here we introduce a "phase function" to compute simple
correlations in a sequence of discrete events - this method can be used for
short or long sequences.
A popular method to visualize event data is using scattergrams that show the spread of points in a two-dimensional plane, and also show a possible relation between the horizontal and vertical axes variables. If there is no apparent linear relationship between the two variables, would you not still like to quantify the spread somehow? For example, if you find a Pearson coefficient of 0.4, then it might not mean anything except that there is no reliable linear relationship. Here we introduce a quantification of the entire scattergram based on the distribution of the density in the plane. It systematically computes a weighted sum of the clusters at various length scales, and provides a single number for clustering coefficient at a given length scale, as well as a distribution of such clustering density.
Next time you think of picking up an object from the table (a voluntary movement), think of basal ganglia. Basal ganglia are like a man-in-the-middle actively participating between your idea of a conscious movement and the actual movement. The movement may go wrong as in a number of movement disorders such as Parkinson's disease, Huntington's disease, and dystonia. Basal ganglia consists of neurons from a number of interconnected nuclei displaying various levels of decorrelations among their spike timing. [A review here]. The broader question is to figure out what these decorrelations mean to the normal and diseased brain function. For that you need to first get hold of the basic function of the neurons and their diversity present in each of these nuclei. Here our focus is to investigate the cell variety of an important nucleus, the globus pallidus neurons in slices, how to model their spiking behavior, and how this nucleus in consort with another important nucleus, the subthalamic nucleus (STN) generates rhythms and coherent patters.
Neurons behave a lot like little children. If you give them candy, they are too excited and jump around. If you take away their candy they are depressed. How about taking away their candy for now, and wait a while before you give them back just a little candy, not as much as they had earlier but a little less? Well, they might just be too happy, as happy as they were when they had loads of candy. Try it out!
We did exactly this kind of thing in some neuronal models by appropriately delaying a weak excitatory stimulus after first causing a depression with an inhibitory stimulus. Bingo, the neurons fired! We showed this experimentally as well. Finally we also showed that if such inhibition arrives randomly mixed with random excitation, which by itself would not have caused great activity, would now enhance the firing rate. Our posters document more interesting stuff.
Did you figure out where that annoying cricket was hiding last time when you were disturbed from your sleep? The reason why it is difficult to spot such sounds is because they are of high frequency. But if somebody was dragging a big table on the street, you know exactly from were to where they are dragging, and you might be able to tell, without looking, where exactly the sound is coming from. Low frequency sounds are detected by our auditory system taking advantage of the little (often microsecond) delay that our head size would introduce between the sound arrived at the two ears. This delay is encoded in the medial superior olive (MSO) neurons of the auditory pathway. The encoding involves enhancement of temporal integration of inputs arriving at these neurons. Our study focusses on certain currents that enhance such integration as well as modeling that shows how such enhancement occurs due to combination of arriving inputs.
Did you ever wonder how those dozen or two of young violinists performing Mozart's symphony No. 40 pull it off so perfectly? Or how those wonderful singers turned the air into magic in a choir? Well they are real examples of coherent behavior, or synchrony. Coherent behavior is also ubiquitous in nature and across sciences such as in flashing fireflies, coupled lasers, coupled magnetrons, Josephson junctions, coupled chemical reactions, coupled biological cells, and electronic oscillators. Simple mathematical models in the form of coupled oscillators serve quite well in understanding the basic principles of phase-locking. Arthur Winfree [book link here], Yoshiki Kuramoto [book link here], Steven Strogatz [book link here] and many others propelled this work enormously in the field. Our main focus is to address the role of communication delay between the oscillator units in the synchronization of them. We show that delay could cause oscillator death, and explore the implications of time delay in other phase-locked solutions.
We know how heat is transmitted from the sun to the earth. It's by radiation. We solved the big problem! Next, did you hear of blowing hot winds causing death? Yes, we know how heat is transmitted there. It's by convection or movement of fluids. Then we are left with the last battle ground: How does heat get transmitted from one end of a metal to another? The atoms do not flow from the hot end to the cold end. They have to transmit the vibrations from one to another via the coupling they might have between them. If the coupling enables a linear transmission, then an immediate transmission of heat might take place, i.e. it would take no time to feel the heat of stove when you stick a spoon in it. Obviously that is not the case. So a nonlinear transmission takes place that gives the heat a finite speed. Here we construct an oscillator model to study the head transfer. Good reviews: (i) J. Ford. The Fermi-Pasta-Ulam problem: Paradox turns discovery, Physics Reports 213:271-310, 1992. (link) (ii) G. Gallavotti (Ed.) The Fermi-Pasta-Ulam Problem: A Status Report, Lecture notes in physics, Vol. 728, Springer, 2008. (link)
"At 32 I spoke English which no body else understood. And hence I drew more
attention," laughs away Prof. Leo Esaki
on this Wednesday at the Lindau meeting. Prof. Esaki shared
Nobel prize in Physics in the year 1973 for his discovery of the "Esaki tunnel diode" while
working for his thesis in 1957 at the age of 32. Very soft spoken, Prof. Esaki
recollects the time when one of his important papers was rejected by Physical
Review, and advises the young scientists to work without losing heart on
failures. Here're his 5 DON'TS verbatim:
A list of "five don'ts" which anyone with an interest in realizing his or her creative potential should follow. Who knows, it might even help win a Nobel Prize.After Prof. Esaki's talk, the chairman of the morning made a gesture that his 5 don'ts should be of use to the youngsters and asked him to make his transparencies available. The copies were distributed in the afternoon. [51st meeting of Nobel Laureates in Lindau, Germany. June 25-28, 2001.]
Rule number one: Don't allow yourself to be trapped by your past experiences. If you allow yourself to get caught up in social conventions or circumstances, you will not notice the opportunity for a dramatic leap forward when it presents itself. Looking back at the history of the Nobel Prize, you will notice that most of the laureates have received the Nobel Prize for work they had done during their thirties. In my case I was 32 years old when I developed the "Esaki tunnel diode." The point that I am trying to make is that younger people are able to look at things with a clearer vision, one that is not clouded by social conventions and past history.
Rule number two: Don't allow yourself to become overly attached to any authority in your field -- the great professor perhaps. By becoming closely involved with the great professor, you risk losing sight of yourself and forfeiting the free spirit of youth. Although the great professor may be awarded the Nobel Prize, it is unlikely that his subordinates will ever receive it.
Rule number three: Don't hold on to what you don't need. The information-oriented society facilitates easy access to an enormous amount of information. The brain can be compared to a personal computer with an energy consumption of about 25 Watts. In terms of memory capacity or computing speed, the human brain has not really changed much since ancient times. Therefore, we must constantly be inputting and deleting information, and we should save only the truly vital and relevant information. As the president of a university, I have the opportunity to meet with many people and to exchange meishis (name cards) with them. I try to discard the name cards as soon as possible, so that I always have maximum memory space left. I'm kidding, of course.
Rule number four: Don't avoid confrontation. I myself became embroiled in some trouble with the company I was working for many years ago. At times, it is necessary to put yourself first and defend your own position. My point is that fighting is sometimes unavoidable for the sake of self-defense.
Rule number five: Don't forget your spirit of childhood curiosity. It is the vital component for imagination.
Having listed the five rules, let me say that they do not constitute the sufficient conditions for success. They are only suggested guidelines. Good Luck!