7. 77
Small NumbersSmall Numbers
Switching time for a transistor circuit.seconds10 9−
metres101.7 15−
× The size of the atomic nucleus of a lead atom.
metres0075.0 Average width of a single human hair.
Nanoscale microscopes focus at this scale.metres1050 9−
×
Switching time for a Josephson junction circuit.seconds10 11−
8. 88
A Zoom in and out of the UniverseA Zoom in and out of the Universe
http://www.youtube.com/watch?v=0fKBhvDjuy0
10. 1010
GeometryGeometry
A branch of mathematics concerned with questions of shape, size, relative
position of figures, and the properties of space.
Euclidean geometry
Algebraic geometry
Differential geometry
Fractal geometry
Spherical geometry
Hyperbolic geometry
Eucid’s Elements of Geometry (300 BC) is the second best-selling book of all
time!
11. 1111
The Chaotic PendulumThe Chaotic Pendulum
CHAOS: Unpredictable seemingly random behaviour.CHAOS: Unpredictable seemingly random behaviour.
Fractal patterns emerge from chaotic behaviour!Fractal patterns emerge from chaotic behaviour!
20. 2020
The Mobiüs BandThe Mobiüs Band
Question 1: What happens if you cut aQuestion 1: What happens if you cut a Mobiüs band in half?
Question 2: What happens if you cut it into thirds?
21. 2121
The Mobiüs BandThe Mobiüs Band
A mathematician confided
That a Mobiüs band is one-sided
And you’ll get quite a laugh
If you cut one in half
For it stays in one piece when divided!
22. 2222
The Klein BottleThe Klein Bottle
If you could join two Mobiüs bands together you
would get a Klein bottle, a four-dimensional object!
23. 2323
The MemristorThe Memristor
Memristor – the missing circuit element
In 1971, Leon Chua mathematically proved the existence of the memristor.
In 2008, HP Labs built first memristor – industry said to be worth $250 billion!
Fundamental circuit variable relationships.
Professor Leon Ong Chua.
25. 2525
Brain Inspired ComputingBrain Inspired Computing
IBM researchers have simulated a
virtual brain comparable in complexity to
that of a human. The power used in
gathering thousands of sensory inputs
and interpreting and storing the data is
estimated to run to about 25W.
According to IBMs own estimates, a
computer of comparable complexity
using current CMOS technology would
require in the order of 100MW of power.
The average brain has about 80 billion
neurons and trillions of synaptic
connections.
The average brain has about 80%
excitatory and 20% inhibitory
connections.
26. 2626
Towards the Zettascale SupercomputerTowards the Zettascale Supercomputer
Lynch S. & Borresen J., Binary half adder using oscillators, International Publication
Number, WO 2012/001372 A1, 1-57 (2012).
Lynch S. & Borresen J., Binary half adder and other logic circuits, UK Patent Number,
GB 2481717 A, 1-57 (2012).
Borresen J. & Lynch S., Oscillatory threshold logic, PLOS ONE, 7(11) 1-25 (2012).
A zettascale Josephson junction based supercomputer would
perform a thousand, million, million, million Floating Point
Operations (FLOPs) per second!
Half-adder input and output.
27. 2727
Set Reset (SR) flip-flop (Memory)
SR flip-flop schematic.
Input and output of a Fitzhugh-Nagumo
ODEs SR flip-flop.
The memory switches on ballistic
propagation. Simulation run in MATLAB®.
28. 2828
SupercomputersSupercomputers
June 2011: Japan’s K supercomputer
A peak performance of 8.16 Petaflops
and consumes nearly 10 MW.
12/11/12 – USA’s Titan
supercomputer achieved 17.59
petaflops beating IBM’s
BlueGene/Q.
Using superconducting Josephson junctions and
our invention, we believe it is possible to build a
zettascale supercomputer. One zettasecond is
equivalent to 32 trillion years!!!!
June 17, 2013 (China): Tianhe-2
- meaning Milky Way-2 -
operates at 33.86
petaflop/sec.
29. 2929
An Assay for Neuronal DegradationAn Assay for Neuronal Degradation
Growing neurons on chips and looking for cures to Alzheimer’s,
Parkinson’s disease and epilepsy, for example.
30. 30303030
Professor Mark Slevin (Professor in Cell Pathology – Alzheimer’s)
Dr Chris Murgatroyd (Molecular Biologist – STEM cells)
Dr Kirstie Andrews (Bio-engineering)
Measuring electrical activity of cultured electrogenic cells (e.g. neurons, heart, retina, muscle):
1. Patch clamp technique (intrusive).
2. Extracellular recording (non-intrusive).
3. Optical measuring using voltage sensitive or fluorescent dyes.
Neuronal Circuits: MMU GroupNeuronal Circuits: MMU Group
31. 31313131
MicroElectrode Array (or MEA) for In-Vitro Applications
Multi Channel Systems MCS GmbH, Reutlingen
Germany.
UK sourcing company:
Scientifica Limited (www.scientifica.uk.com)
33. 3333
Mathematical PuzzlesMathematical Puzzles
Problem 1: Suppose that you have two jugs. One holds exactly 9 litres
and the other exactly 4 litres. How do you get exactly 6 litres given a
plentiful supply of water? What is the minimum number of steps involved?
9 litres 4 litres Water tank
Problem 2: Obtain exactly 10 litres of fluid without throwing any fluid away.
19 litres 13 litres 7
litres
34. 3434
Maths Voted Best Overall CourseMaths Voted Best Overall Course
At MMU 2012At MMU 2012
