quarterwave

Say you're climbing up a long staircase and the step height increases suddenly - then you'll bump into the next step. If the height were to go the other way i.e; decrease, then you'll put your foot down hard trying to place the next step. That change in step height is in fact a change in frequency, and you're forced to adjust your pace abruptly by adjusting the timing (phase) of your subsequent steps.

Is there a 'gentler' way to adjust the phase? Now say you're wearing some kind of spongy sandals that can take up the slack, so at every step you increasingly sense that the frequency has changed. This accumulation indicates that phase is mathematically the integral of instantaneous frequency with respect to time.

We now put this integral in a feedback loop. Then, if the staircase step height changes suddenly we use the slow accumulated phase to produce an error signal that gradually drives the frequency generator (in this case, our brain) to adjust the pace of our step till we get in lock-step.

The actual dynamics is more complicated, involving a non-linear frequency capture (which linearizes the system) and then the slower phase lock. You can see this in the waveforms in the original post.

I = mu_friction * Mass * grav_acc / (Turns_per_length * Area * Br_magnet)

Say Mass=0.1kg, coil at 600 turns per metre, hand-wave mu_friction=0.2, and a rare-earth retention Br=1Tesla, gives a current of 3A. Maybe more to chug along, would deplete a 2000mAh battery in about 30 minutes. Wire looks about 20 AWG, should get quite hot.

Example: Server generates a sine wave which gets displayed as a rolling chart waveform on the client. As client spins a knob to control the amplitude, the server-generated stream should change (sine wave is a trivial example, representative of more complex server-side computation).

Balki also introduced us to the mythical student HAROLD - Hypothetical Alert Reader Of Limitless Dedication, whom he had encountered in Schwinger's lectures.

Naively I'd expect image hashing to be like cross-correlation (non-linear) while password hashing can be done with shifts and modulo-2 (linear).

Alexander Graham Bell came up with the idea of increasing the capacity of telegraph lines by combining several 'dit-da-dit' streams at different pitches. He called it a 'harmonic telegraph'. The idea was that a mechanical arrangement of reeds tuned to different pitches would pluck out each stream of data. This insight eventually led to the invention of the telephone.

Finally, if 'orthogonal basis set' is difficult to understand, think of giving someone 'left/right' driving directions. An FFT would then (roughly) be the mathematical equivalent of 'driving directions' for a clip of music or speech.

The section on reverberation reminds me of Dr.Cooper at the cinema, conducting impulse response tests.

A 'predictive model' should say 'if you do X then you will end up with Y' - and the X cannot be adjusting some number. The X has to be stuff like 'building ETU's in West Africa', or 'canceling all flights',... A predictive model should be able to say 'don't bother canceling flights, it's no use - instead do this...'.

Note: I'm going to be teaching a course in Erlang programming next month where the homework assignment is epidemic modeling - 100K's of concurrent processes moving around, getting exposed to each other - that sort of stuff. Rather ambitious, but I feel it's a good use case for Erlang - a pandemic is a 'viral' chat application.

The kriti eventually led to the modern Carnatic concert format, in the early twentieth century. Where concerts once used to be night-long expositions of virtuosity in rural temple festivals, the modern concert became a brisk 2 hour affair that catered to urban schedules. A couple of 'heavy' abstract pieces, then a few kritis serving as anchor, rounded off with several light blitz pieces (usually scorned by the cognoscenti).

http://en.wikipedia.org/wiki/Nick_Holonyak

http://www.ecdc.europa.eu/en/healthtopics/documents/0905_pan...

Note the sharp jump as R_0 goes from sub-2 to over-2, which should not be surprising (hand wave about branch processes, light of a thousand suns, etc).

Over to someone better qualified to comment - is the present situation with Ebola taking us into a pandemic territory similar to 1918 H1N1?

tl, dr: One puzzler is that antenna radiation is frequency dependent, while that of Johnson noise in the microwave regime is flat with frequency. Then, considering detailed balance, how does an antenna matched to a terminated coax cable establish thermal equilibrium with space? What happens is that the 1/f^2 of the antenna pattern is cancelled by the f^2 (in the long-wavelength regime) of the Rayleigh-Jeans blackbody radiation formula.

Control: Yes, Tony?

Tony: If I may ask, how did you determine this sum of a 150,000 pounds a day?

Control: A very good question, Tony. You see, I simply took the figure that our American cousins have calculated using a supercomputer, and converted the currency.

Tony: That's very clever of you, Control.

Control: Thank you, Tony. It proves that what we lack by way of resources we make up for with good old British ingenuity.

mentions two theories why the 1918 flu pandemic ended (see section 'End of the pandemic').

I'm trying to understand the mutation theory. How come there is no 'watchmaker' situation here? Is it because a virus is simple enough that its replication is directly driven by thermodynamics, as opposed to more 'organized' forms of exploring the configuration space?

http://en.wikipedia.org/wiki/Binary_star#mediaviewer/File:Or...

OP: This is an amazing tool to learn the sensitivity of dynamical systems to initial conditions. Well done!

A logic chip like a microprocessor is designed for a particular supply voltage, if this voltage drops too much the logic circuitry will switch falsely. Say we had only a capacitor and we tried to power the logic chip with it. As the chip draws current the capacitor discharges - this is because current is movement of charge, so the charge (and energy) can come only by draining the capacitor. For an ideal capacitor the voltage is directly proportional to the charge across it, so as the charge drains the voltage falls. To hold the voltage constant we need to keep 'topping up' the capacitor with charge. This is what a voltage regulator does - it uses a negative feedback loop to sense the capacitor voltage and when that voltage falls the circuit provides just the right amount of charge 'juice' for the top-up.

As we take the foot off the clutch pedal in a car, the load gets engaged to the engine and if we sense a stall we press the gas pedal a bit. That's the imagery of a voltage regulator in action.

The capacitor plays a key role because the regulator feedback loop isn't very fast - one trouble with fast feedback circuits is chatter, or responding to every blip. Negative feedback circuits are designed to be more like ship wheels - they like to steer sedately and not respond to every excited cry from the mast. But what happens if a current blip arises because a logic circuit block turns on all at once (in response to some block of code)? That local current blip is provided by the capacitor, it acts like an ATM to provide local draws - but it still depends on the regulator to top it up.

In fact you can think of a battery as a capacitor that tops itself up via electrochemistry, it works as long as there are ions in the electrolyte. If instead of 'bandgap energy' we used the chemist's terminology of 'electrochemical potential difference', then the system similarity becomes evident.

I realized only much later that this was an obsessive approach, like buying chess books after losing early in one's first tournament. There was no sense of carpe diem, it was about owlishly building up a 10:1 advantage before closing in.

Ramanujan wrote to Hardy: "I am already a half starving man. To preserve my brains I want food and this is my first consideration. Any sympathetic letter from you will be helpful to me here to get a scholarship either from the university of from the government."

Returning to our world, a tenured university position could provide stability, while a contractual appointment to teach Linear Algebra I & II might end next year - and a journey by stagecoach to the next temporary appointment. In such a situation it may be simpler to write code for a living, while one 'dreamed a dream' on weekends.

The way it normally works, one figures out these answers during the M.A level itself. The trouble starts if one does not & keeps plodding on.

I apologize if this sounds dull & dreary, but I recently gave this advice to a nephew who wanted to study maths after an undergrad degree - he is now safely writing code for a salary & his parents are relieved. Have I stymied the next Ramanujan, perhaps out of a sense of sour grapes at my own inability to prove the Riemann Hypothesis? Both are possible, but unlikely.

It would cool to add a few images with periodicity. I expected the lake bed image to show some quasi-periodic lines, but couldn't make that out in the spectrum.

When we were in school our class was taken to see the film "Gandhi". Our usually noisy class sat stunned throughout. Thanks to Attenborough the hope of Einstein came true.

A time varying electromagnetic field is produced by moving charges (except for a minor distinction about steady currents). The direction of motion of the charges determines the polarization of the emitted field. Later on, when the field encounters matter it produces an identical motion of charges i.e; if originally an East-West charge motion produced a North-South field then a N-S field will induce an E-W motion among new charges which in turn re-emit N-S light. The original light and the re-emitted light interfere, the delay is what slows the light down, as noted by others. But you can see why the direction is the same.

Note: I suppose this picture is somehow tied to reciprocity of the Maxwell equations between sources and fields, I need to go look it up again.