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The Bow Tie

left hand extended bow tie crop

Bow-tie or hourglass structure is a common architectural feature found in biological and technological networks. A bow-tie in a multi-layered structure occurs when intermediate layers have much fewer components than the input and output layers. Examples include metabolism where a handful of building blocks mediate between multiple input nutrients and multiple output biomass components, and signaling networks where information from numerous receptor types passes through a small set of signaling pathways to regulate multiple output genes. Little is known, however, about how bow-tie architectures evolve.

bow tie robb twk.

We find that bow-ties spontaneously evolve when two conditions are met: (i) the evolutionary goal is rank deficient, where the rank corresponds to the minimal number of input features on which the outputs depend, and (ii) The effects of mutations on interaction intensities between components are described by product rule – namely the mutated element is multiplied by a random number. 

bow tie w tendrils

Product-rule mutations are more biologically realistic than the commonly used sum-rule mutations that add a random number to the mutated element. These conditions robustly lead to bow-tie structures. The minimal width of the intermediate network layers (the waist or knot of the bow-tie) equals the rank of the evolutionary goal. These findings can help explain the presence of bow-ties in diverse biological systems, and can also be relevant for machine learning applications that employ multi-layered networks.

bow tie control sys twk


bow tie w seeds

Many biological systems show bow-tie architecture: a huge number of inputs are converted to a small number of intermediates, which then fan out to generate a huge number of outputs. Examples are metabolic and signaling networks. However, there is no explanation of how bow-ties evolve in biology. Here, we find that bow-ties spontaneously evolve when information in the evolutionary goal can be compressed, known in mathematics as a deficient goal rank. This rank is a number that determines the size of the narrowest part of the bow-tie in the network. This offers a first mechanism to understand a common architural principle of biological systems, and a way to quantitate the rank of goals under which they evolved. <source text>


The strength of the Bow-Tie is evident in its ability to handle a wide variety of environmental demands, both efficiently and quickly. However, it can suffer catastrophic breakdowns when the core building blocks and protocols (the knot) are hijacked by parasites. These parasites can use access to the core to radically accelerate growth and gain new flexibility/adaptability. Eventually, other critical processes are crowded out and the entire system collapses.  <source text>

righthand extended bow tie crop

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Index of First Lines: Two Centos

cento crushed tom

According to Wikipedia:

The Latin term cento derives from Greek κέντρων (gen. κέντρωνος), meaning “‘to plant slips’ (of trees)”. A later word in Greek, κέντρόνη, means “patchwork garment”. According to Hugh Gerard Evelyn-White, “A cento is therefore a poem composed of odd fragments”.

Cento is also a brand of canned tomatoes, allegedly Italian. I say allegedly because I read a book about olive oil, Extra Virginity, and in it, one thing the author, Tom Mueller, lays out in some detail is that most of the olive oil sold in supermarkets as Extra Virgin and Italian is in fact not Italian and not virgin.* Sometimes it’s not even olive oil, though, sometimes, it is bottled in Italy. I now suspect “Italian” tomatoes. Maybe they’re not Italian. Maybe they’re not even tomatoes. Are you confused yet?

I tried my hand at centos yesterday. I went to the bookcase where I keep all the poetry, and picked out Poems of Stephen Crane and Gerard Manley Hopkins: The Major Works. Both Crane and Hopkins are poets who influenced me in my teens and twenties, and who I still read. I flipped to the Index of First Lines, first in the Crane, then in the Hopkins, inputting the lines, cutting and pasting. Piecing out the patchwork. All first lines, no words omitted therefrom. Assembling centos is more like collaging or quilting than writing a poem. Maybe they’re not even poems; certainly not the poetic equivalent of extra virgin, but I enjoyed doing it and like the results.

Crane cento:

A Fine Song

A man went before a strange god,
A god in wrath, walking in the sky,
“Have you ever made a just man?”

Behold, from the land of the farther suns
The livid lightnings flashed in the clouds,
The trees in the garden rained flowers
Each small gleam was a voice
The wind that waves the blossoms sang.

Once, I saw the mountains angry,
Once, I knew a fine song.

Hopkins cento:

Noises Too Old To End

Although she be more white,
A silver scarce-call-silver gloss
As void as clouds that house and harbor none:
Break the box and shed the nard.

Confirmed beauty will not bear a stress.
Earnest, earthless, equal, attunable
A noise of falls I am possessed by,
Elected silence, sing to me.

Glory is a flame off exploit, so we say–
Hence sensual gross desires
Flaunt forth, then chevy on the air

Myself unholy, from myself unholy
My prayers must meet a brazen heaven,
On ear and ear two noises too old to end.

*According to Mueller, the term Extra Virgin is a misnomer, about as meaningful as “Natural” or “Free Range” on the label of  packaged chicken parts.


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Steal This Meme: Werner Herzog Inspires

werner happiness garamond

Google informs me that today is “International Day of Happiness.” Wikipedia informs me that the United Nations in June 2012 proclaimed March 20 International Day of Happiness. So today is the third IDOF. I find happiness by decree suspect, to say the least, but then I suspect “happiness” of being a meaningless abstraction.  Despite the fact that it’s enshrined in the Declaration of Independence, I think the “the pursuit of happiness” is akin to a snipe hunt. One can be happy; happiness can not be achieved.  Being happy is largely a gift of fate, a state of grace, if you have the grace, that is to say detachment, to accept it. Happiness is a conveniently intangible commodity rather like a mortgage derivative.

Werner Herzog makes me happy. John Lennon singing “Happiness is a warm gun yes it is” makes me happy. Bang bang shoot shoot.

Bonus “Happy” meme:

OLYMPUS DIGITAL CAMERAHappy, happy, happy…

Since the Werner Herzog Inspirationals Tumblr is not posting new memes, I’m creating my own, and as Clay Shirky, author of Here Comes Everybody, puts it, “The stupidest possible creative act is still a creative act.” Words to live by in the latter days of the Internet Age. Steal this meme.

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