Confessions of a research junkie (on squeezing the magic out of stuff)

As a researcher, your topic of interest has its magic.

You bond with your topic; get to know all there is to know about it, explore it from new perspectives, think about it day and night.

You get to the point where you know that what you know about your topic is known by less than a handful of the 6 billion people walking the planet.

You work on, looking for the break.

If it were that easy, someone else would have published it by now. So you toil on, working that new angle.

And then you hit the payload;

What a rush!

Sometimes it’s a deluge; other times it comes in sweet dribs; things gel out; you see the light. You OWN that topic.

It pushes you through the process of publishing your findings.

There is no magic left there. You move on. Find something else interesting. You hope, pray, work for the next rush.

Hopefully bigger; hopefully better.

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DARPA Math Challenges

These are good times for Artificial Intelligence research; DARPA (the Defense Advanced Research Projects Agency) has put out a request for proposals on 23 contemporary mathematical challenges that has the potential for changing the state of AI as we know it.

The challenges are:

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1

The Mathematics of the Brain.

2

The Dynamics of Networks.

3

Capture and Harness Stochasticity in Nature.

4

21st Century Fluids.

5

Biological Quantum Field Theory.

6

Computational Duality.

7

Occam’s Razor in Many Dimensions.

8

Beyond Convex Optimization.

9

What are the Physical Consequences of Perelman’s Proof of Thurston’s. Geometrization Theorem?

10

Algorithmic Origami and Biology.

11

Optimal Nanostructures.

12

The Mathematics of Quantum Computing, Algorithms, and Entanglement.

13

Creating a Game Theory that Scales.

14

An Information Theory for Virus Evolution.

15

The Geometry of Genome Space.

16

What are the Symmetries and Action Principles for Biology?

17

Geometric Langlands and Quantum Physics.

18

Arithmetic Langlands, Topology, and Geometry.

19

Settle the Riemann Hypothesis.

20

Computation at Scale.

21

Settle the Hodge Conjecture.

22

Settle the Smooth Poincare Conjecture in Dimension 4.

23

What are the Fundamental Laws of Biology?

I am partial to challenges 15 and 16 as they fall within areas of my doctoral research work. One result of this work is my paper detailing new perspectives on genotype-phenotype map geometries.

Challenges 3, 14, 20 and 23 also look very appealing. Please email me (dom_wilson at yahoo dot com) if you are looking for collaboration on any of the challenges.

Some ways you can go wrong with Evol. Comp. II

Misunderstanding Randomness

There are two aspects of randomness in Evolutionary computing that are frequently misunderstood . The first issues is the assumption that the effects of random mutations are always random. No that is not a typo, the effects of random mutation are usually not random but are coordinated into nonrandom distributions based on how genes map to their measured behavior (aka their phenotypes).

A good analogy to explain this concept is the bean machine. As explained in Wikipedia, the bean machine

Bean Machine

Bean Machine

was invented to demonstrate the law of error and the normal distribution. The machine consists of a vertical board with interleaved rows of pins. Balls, dropped from the top, bounce in random directions on hitting the pins. Not withstanding their random horizontal motions on descent, the balls settle at the bottom of the machine in an approximately normal distribution.

The second misunderstood aspect of randomness has to do with the way it is measured in populations. Some researchers measure the amount of diversity in a population by summing the variance of genetic (or allelic) values for all locations on genomes.Based on the evolutionary landscape this measure can overstate the search potential of a population. A population can be effectively converged (i.e. all of the genomes can have the same fitness and all can be searching the representation space the same way) without there being a low variance between their gene values.

I have a forthcoming  paper (accepted by IEEE Transactions on Evolutionary Computing) , which among other things, looks at preferred directions of motion due to random mutation as well as randomness in evolutionary populations. I will blog on this further when it is published.

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