Fountain spouts

Today I sculpted the spouts for the fountain on my back porch. The white boards under each are scaffolds supporting them until the dry at which time I will remove, glaze, and fire them. The firing should cause them to shrink so then I will be able to mortar them back into position.

Bed stain

Stained the bed today (not what you're thinking!). Almost done with this project! It's taken way too long.

Bed

I haven't been posting house progress for a while. My night-time project for the last week has been construction of a bed with a little bit of a floating cloud theme. I laminated four 4x8 sheets of maple plywood together and then cut out circles of various radii.


After Alex's sanding for many hours...


Here's the rough-cut end table before I cut out the circles...

Molecular model transfer function

Today I got around to trying out a simplified molecular version of the gate model that will replace my hyperbolic function.



The kinetics are all arbitrary for the model, but the shape of the transfer function looks even better than the made-up model from before. There's an almost perfectly linear section in the middle -- it looks more made-up than my made-up model! This is assuming that all three reactions have the same strength. Next, I need reasonable terms for the three reaction rates.

More parameter space of "standing" circuit

Using the parameter space maps made last time, I've set the "standing" circuit into a place where it has a nearly symmetric bi-stable steady-state at p1 =0.25 and p2=0.50.



The following is the derivative at a given concentration of standing. This dy/dt vs y plot (I don't know if there is a correct name for this find of plot) shows that there are two stable steady states at the zero crossings -5, and +5. There's also the unstable point near zero. It is not exactly at zero because the gate model functions do not cross at zero as seen below.






Now I continue the analysis with the "tired" half of the circuit. I'm interested in the response of "tired" when the "standing" input reaches 0, the point at which the tired circuit will charge fully.



Charging of the tired circuit when standing is 0 and tired starts at its steady-state value of -5


So, "tired" reaches 0 (the point at which the gate 5 is going to be fully on) within about 20 time units when standing = 0.

The following is a sampling of the parameter space for p1 and p2 given "standing" = 0. The steady-state value of tired changes as a function of p1, so for each graph I've started "tired" off at the appropriate steady-state and then watch the evolution when "standing" = 0. This demonstrates that I can delay both the onset of tired (when it hits zero) and how high tired gets at steady-state by adjusting these two parameters.


Next up, I put the circuit back together again...

Parameter space of "standing" circuit

I've been working on decomposing the traveling pulse circuit in order to understanding the parameter space. Today I've worked on the isolated "standing" circuit.



There's two parts. The "pull down" gate that is constantly trying to pull the system to a negative value against the action of the resistor which is trying to pull it to zero. The ratio of the pull down gate (1) to the resistor (RNAase) determines the steady-state level when the feedback gate 3 is not active. The RNAase resistor must be common to all nodes so I treat it as a fixed parameter; I picked the value 0.01 out of thin air for it.

For the following graphs, I pick different starting conditions for "standing" and let this circuit evolve. Each colored trace in the chart is one run of the circuit. Note that there are two steady states. One is about 28 and the other is about -1. If the "standing" value falls below about -0.5 then it goes to the low steady-state and above that it goes high. I like this chart in comparison to typical transform function plots because it lets you see both the kinetics and the steady-states in one place.


Here's the same chart but zoomed in around the origin so you can see that the critical point is about -0.5 which is determined by the gate model.

I varied the two parameters over a range and plotted the parameter space result (best viewed on large monitor).


From top to bottom p1 is increasing. From left to right p2 is increasing. Increasing p2 shifts the steady-state of the "standing" state upwards and thereby separates the two states more dramatically. As p1 is increased -- moving from top to bottom -- both the top and bottom steady-states shift downwards but the bottom one seems to move faster. In the lower left, the two states blur into each other and are poorly defined. So, in general you'd like to push p2 and p1 fairly high but this comes at the cost of slowing down the approach to steady-state as they are pushed further away. When the other half of the circuit is added, p2 value will have to be smaller than p5, so that will determine the upper bound of p2.

My conversation with Alpha

I tried out Wolfram's Alpha this morning. First, something technical and mathematical as it suggests:

Where are the tidal phase singularities?
> Wolfram|Alpha isn't sure what to do with your input. ...

The same search on Google not only brings up links to maps but also brings up the scanned and OCR pages from Winfree's book -- via Google books -- where I got the phrase! Google is amazing.


Why should I use wolfram alpha?
> Wolfram|Alpha isn't sure what to do with your input.

The same search on Google came up with the pages on Wolfram's own site and many more reviews.


Why is Stephen Wolfram so cocky?
> Wolfram|Alpha isn't sure what to do with your input. ... person: Stephen Wolfram ... chemical element: element Wolfram

Tungsten (according to Wiki) is also called "Wolfram" which is why it has the the chemical symbol "W", but nowhere on Wolfram's summary page about Tungsten does it mention this. If you do this same search on Google the first hit is a Slashdot article about the outrageous TOS on alpha that's only *16 hours* old! Google continues to amaze.


How big of an ego does Stephen Wolfram have?
> Wolfram|Alpha isn't sure what to do with your input. ...

The same search on Google returns all kinds of hits from book reviews and whatnot complaining about his inflated ego.


All joking aside, I did like its stock summary page (one of its suggested searches). When you do ask it about something it knows does present a very well formatted result with lots of good technical information. But the TOS is absurd.