Dr. StrangestuffOr: How I learned to stop programming and love

carbon foam

Jonathan W. MillsResearch Fellow and 2007Leverhulme Trust ProfessorUniversity of the West of EnglandBristol BS16 1QYUnited Kingdom

Associate ProfessorComputer ScienceIndiana UniversityBloomington, IN 47405United States of America

Visiting ResearcherThe Courant InstituteNew York UniversityNew York, NY 20002United States of America

Organization of This Talk

• The People• Digital vs. Analog Computers• The Extended Analog Computer (EAC)• Implementations of the EAC• A Few Applications• Protein Structure Prediction• Embedding Deutsch’s Problem in the EAC• New Kinds of Computers!

The People

Lee A. RubelRubel first described the extended analog computer (EAC) in 1993 to overcome limitations of Shannon’s general purpose analog computer (GPAC). Aside from some correspondence with Mills, it was his only publication about the EAC.

Lee A. Rubel (1928-1995)

Primary EAC Research Team

Bryce Himebaugh (left) designs the EACs that Mills (right)

uses to conduct real and gedanken computing experiments.

“Second String” EAC Research Team

This team performs “acoustic experiments” at Arcosanti, AZ.

Digital vs. Analog Computers

What Is a Computer?A computer is any physical object that can be

reconfigured to solve multiple problems, that is, to answer many

different questions.

(If it cannot be reconfigured, and can answer only one question, it is not

a computer according to this definition, but it may be an experiment.)

Algorithm (digital) compared to

Analogy (analog) From Mills, The Nature of the EAC, Physica D (2008)

Another View of the EAC Paradigm Analogy

Mills, The Nature of the EAC, Physica D (2008)

Feynman questioned an apparent limit of digital

computers (Algorithm):“It always bothers me that,

according to the laws [of physics] as we understand them today, it takes a [digital] computing machine an infinite number of

logical operations to figure out what goes on in no matter how tiny a volume of space, and no matter

how tiny a region of time.”

He also said, “There’s a lot of room at the bottom.”

Feynman was using the paradigm algorithm

But by following the paradigm analogy to its logical conclusion, the laws of physics as we

understand them comprise the “instruction set” of an EAC.

Bulk and minimally structured matter form its computational components.

The EAC takes advantage of Feynman’s “… room at the bottom.”

Computational Paths of algorithm and analogy

The Extended Analog Computer

(EAC)

Basic EAC Model

An extended analog computer implements an analogy, explicitly using physical laws and implicitly using mathematical principles to compute. It is implemented as a continuous-valued, inherently parallel, reconfigurable processor with two “instruction” classes:

solve-partial-differential-equation, and

compute-piecewise-linear-function.

Operating Principles

Physics MathematicsConservation Laws Abstract Objects mass, energy, charge, time, information variables, constants, metric spaces

Symmetries in Physical Law Operators translation in space, translation in time, arithmetic, inversion, ordinary and rotation in space, velocity (relativity), partial differentiation, substitution replacement of atoms and charge carriers

Pauli Exclusion Principle

Principles “pruning” principle prevents exponential limits, analytic continuation, extremely growth in number of states to be computed well-posed determinism (EWP),

quantum non-determinism (Q-box)

• Turing machine • Extended Analog Computer

• Algorithms • Analogies

• 1D von Neumann bottleneck • 2D/3D Non-von bottleneck• Inherently sequential • Inherently parallel• Fixed internal precision • Fixed external precision that increases temporally that increases spatially• Explicit pseudo-randomness • Implicit randomness

• Silicon, GaAs • Anything conductive• Transistors • Diodes, surfaces, solids• Increasingly error prone • Implicitly error tolerant as devices get smaller via structure and matter

Dualities

Liberation from von Neumann, Moore and Backus

• No von Neumann bottleneck (no CPU-cache-memory path)

• No “memory wall” (no computational memory)• Single EACs are inherently parallel (no internal CPU pipelines)

• Moore’s Law irrelevant (computational “devices” in sheet are atoms)

• EAC “CPU” is robust (no logic gates, transistors or memory cells)

• Multiple EACs are composed functionally (no side-effects)

• Scalable parallelism (may be multi-unit pipelines, MIMD, or mixed)

• “Software” is reusable (physical laws and given materials are invariant)

Digital 1D versus EAC 2D Bottlenecks

Digital multi-core processorExtended Analog Computer

The Benefit of Noise

Electromagnetic interference in the EAC can create a noisy gradient when small currents are input. It generates sequences of random numbers, which digital computers cannot produce (they compute pseudo-random numbers). Noise is useful in some applications (Monte Carlo methods; simulated annealing, genetic algorithms).

Pauli Pruning

The Pauli Exclusion Principle means that natural computers do not have to compute all possible states to obtain a result. The drawback is that the output,

although it may be completely accurate, is probabilistic and not certain. This phenomenon has been observed in the output of Lukasiewicz logic

arrays.

“Envelope” of possible paths Probable paths An actual path

Inherent Fault Tolerance

The sheets are fault tolerant because current flows adaptively in conductive materials, as this experiment demonstrates.

The LLAs are error-reducing, resisting errors due to their structure as binary trees.(An Information-theoretic Analysis of Lukasiewicz Logic Arrays, Montante, 1994)

Implementations of the EAC

Early EACs

1995

“Sponge Bob,” September 2004 to present

(can be manipulated over the web athttp://cgi.cs.indiana.edu/~bhimebau/ea

c.cgi)

“Sponge Bob Marley,” a 3D Jell-O® EAC

Prototype for injection molded & laser-polymerized 3D processors

USB Carbon Foam EAC with Digital Host

October 2005 to present

EAC Architecture Block Diagram

Host Data Is Converted to Continuous EAC Inputs

Once “inside” the interface, computation is continuous

EAC Results Discretized and Sent Back to the Host

Recurrent computations “inside” the interface remain continuous

A Few Applications

Three Ways to Configure the EAC

• Design an EAC configuration by inspection, using similar properties in each system to create an analogy

• Use an evolutionary algorithm, such as Particle Swarm Optimization, to evolve the configuration in a high-order dimensional space

• Use sensor feedback and simulated annealing to freeze a minimal result out of an “energy space;” this may be combined with either of the first two techniques

Silicon Retina: Alternative to Mead & Koch

ring diode

analog

inputs

conductive

sheet

sensor/processor

Lukasiewicz

logic arrays

(LLAs)

analog

outputs

digital LLA address bus

digital LLA configuration bus

Originally built in 1995, this design established structure for recent EACs

It also established a fundamental application technique: sense (or generate) and recognize, which

is useful for many problems other than vision

Nortel, Canada : Fast DDoS Detector

This simplified model learned an “alphabet” of router traffic patterns to spot DDoS attacks

Siemens, People’s Republic of China:

Ordinary Differential Equations

The intended application integrates an ODE to model a system that the EAC retina “watches” to yield intelligent and adaptive feedback control.

Protein Structure Prediction

Too Complicated!

Ricin, a simple toxic lectin

Back to Organic Chem 101

Valine (hydrophobic)Asparagine (hydrophilic)

Start by Modeling Coarse Spatial Structure

Valine (hydrophobic)

Rotation Models are “Slices”

Each pair is a spatial slice of the “shape” along the backbone of a protein. How do their sidechains interact to model the protein’s folded structure?

Add Another EAC Level to Model van der Waals Forces

Two levels interact through Lukasiewicz logic functions to reach an energy minimum between parts of protein. Scalability of EAC allows it to “zoom” in or out to model atoms, molecular

groups or side chains.

Behavior Can Be Observed As 2D Map of Slice

Attract Attract Repel

Structure Prediction Needs More Layers

This EAC architecture was named “The Torte” after the rich European layer cake, due its alternating layers of conductive sheets and Lukasiewicz logic functions.

Particle Swarm Using EAC Outputs Evolves Low-Energy Structure

Particle Swarm Optimization Process

1. Initialize population in hyperspace.2. Evaluate fitness of individual particles.

3. Modify velocities based on previous best and global (or neighborhood) best.

4. Terminate on some condition.5. Go to step 2.

Features of Particle Swarm Optimization

• Population initialized by assigning random positions and velocities; potential solutions are then flown through hyperspace (think of a swarm of bees whose center of mass seeks the global optimum, although all bees contribute to it, no one “bee” may be at the optimal point).

• Each particle (“bee”) keeps track of its best (highest fitness) position in hyperspace.– This is called “pbest” for an individual particle– It is called “gbest” for the best in the population– It is called “lbest” for the best in a defined neighborhood

• At each time step, each particle (“bee”) stochastically accelerates toward its pbest and gbest (or lbest—good for protein folding).

• When the center of mass does not vary within some epsilon over a pre-determined number of iterations, a set of particle properties (“the bee swarm”) has been found that defines the potential global optimum.

PSO Velocity Update Equations

• Global version:

( ) ( )ididid

idgdidididiid

vxx

xpRandcxprandcvwv

+=

−+−+= ()() 21

Where d is the dimension, c1 and c2 are positive constants, rand and Rand are random functions, and w is the inertia weight. For neighborhood version, change pgd to pld.

PSO has been found to work very well with the EAC

Manual Demonstration of PSO

Final Native Conformation of Artificial Protein

Embedding Deutsch’s Problem in the EAC

Joint work with Cristian Calude, University of Auckland, NZ

Deutsch’s Problem

Quantum Solution

Classical Solution in Complex Plane

The “black box” for f(x) is never seen by the user. Instead one of the four “embedding function boxes” is provided, upon which only a single measurement may be made. Do classical functions exist that emulate Deutsch’s solution with quantum superposition? Yes.

Classical Solution with Lukasiewicz Logic

f(x) balancedf(x) balanced f(x) constant

Classical Solution with Conductive Sheet

f(x) constant f(x) constant

Classical Solution with Conductive Sheet

f(x) balanced f(x) balanced

New Kinds of Computers!

Model of Hybrid Classical-Quantum Computer

This computer might be able to crack codes faster than a digital computer, although it would be slower than a quantum computer.

Graphenes have potential to build hybrid classical-quantum

computers• Easily integrated with silicon substrates • Continuous and multi-valued (no ADCs at low precision)• Sheet resistance easily adjusted• Other sheet properties can be varied locally• Quantum properties (hybrid quantum-classical architectures)• Optical, mechanical and chemical sensor inputs• Large-scale structures fabricated suited to EACs• 3D layered devices already demonstrated

Example Graphene Hybrid Classical-Quantum EAC

Thank you!