"Despite the many great achievements of computers, no man-made computer can learn from its environment, adapt to its surroundings, spontaneously self-organize, and solve complex problems that require these abilities as well as a biological brain. These abilities arise from the fact that the brain is a complex system capable of emergent behavior, meaning that the system involves interactions between many units resulting in macroscale behavior that cannot be attributed to any individual unit.
Unfortunately, conventional fabrication methods used for today's computers cannot be used to realize complex systems to their full potential due to scaling limits—the methods simply cannot make small enough interconnected units.
Now in a new paper published in Nanotechnology, researchers at UCLA and the National Institute for Materials Science in Japan have developed a method to fabricate a self-organized complex device called an atomic switch network that is in many ways similar to a brain or other natural or cognitive computing device.
"Complex phenomena and self-organization—though ubiquitous in nature, social behavior, and the economy—have never been successfully used in conventional computers for prediction and modelling," James Gimzewski, Chemistry Professor at UCLA, told Phys.org. "The device we have created is capable of rapidly generating self-organization in a small chip with high speed. Furthermore, it bypasses the issue of exponential machine complexity required as a function of problem complexity as in today's computers. Our first steps form the basis for a new type of computation that is urgently needed in our ever increasingly connected world."...."
Water is fascinating, for many reasons. It takes more energy to heat than most substances. It's one of the few substances that expands when it freezes. It forms complicated patterns in its liquid state, which are just beginning to be understood. There are at least 18 kinds of ice, which exist at different temperatures and pressures. Snowflakes are endlessly subtle.
And ice can form cages that trap other molecules! Here you see the 3 main kinds.
They're called clathrate hydrates. There's a lot under the sea beds near the north and south pole - they contain huge amounts of methane. At some moments in the Earth's history they may have erupted explosively, causing rapid global warming.
But let's focus on the fun part: the geometry! Each of the 3 types of clathrate hydrates is an architectural masterpiece.
Type I consists of water molecules arranged in two types of cages: small and large. The small cage, shown in green, is dodecahedron. It's not a regular dodecahedron, but it still has 12 pentagonal sides. The large cage, shown in red, has 12 pentagons and 2 hexagons. The two kinds of cage fit together into a repeating pattern where each unit cell - each block in the pattern - has 46 water molecules.
Puzzle 1: This pattern is called the Weaire-Phelan structure. Why is it famous, and what does it have to do with the 2008 Olympics?
You can see little balls in the cages. These stand for molecules that can get trapped in the cages. They're politely called guests. The type I clathrate often holds carbon dioxide or methane as a guest.
Type II is again made of two types of cages – small and large. The small cage is again a dodecahedron. The large cage, shown in blue, has 12 pentagons and 6 hexagons. These fit together to form a unit cell with 136 water molecules.
The type II clathrate tends to hold oxygen or nitrogen as a guest.
Type H is the rarest and most complicated kind of clathrate hydrate. It's built from three types of cages: small, medium and huge. The small cage is again a dodecahedron, shown in green. The medium cage - shown in yellow - has 3 squares, 6 pentagons and 3 hexagons as faces. The huge cage - shown in orange - has 12 pentagons and 8 hexagons. The cages fit together to form a unit cell with 34 water molecules.
The type H clathrate is only possible when there are two different guest gas molecules - one small and one very large, like butane - to make it stable. People think there are lots of type H clathrates in the Gulf of Mexico, where there are lots of heavy hydrocarbons in the sea bottom.
Puzzle 2: how many cages of each kind are there in the type I clathrate hydrate?
Puzzle 3: how many cages of each kind are there in the type II?
Puzzle 4: how many cages of each kind are there in the type H?
These last puzzles are easier than they sound. But here's one that's a bit different:
Puzzle 5: the medium cage in the type H clathrate - shown in yellow - has 3 squares, 6 pentagons and 3 hexagons as faces. Which of these numbers are adjustable? For example: could we have a convex polyhedron with a different number of squares, but the same number of pentagons and hexagons?
The picture is from here:
• Timothy A. Strobel, Keith C. Hester, Carolyn A. Koh, Amadeu K. Sum, E. Dendy Sloan Jr., Properties of the clathrates of hydrogen and developments in their applicability for hydrogen storage, Chemical Physics Letters 478 (27 August 2009), 97–109.
The Chinese gene editing of human embyros does not appear to have been using the latest techniques for maximum accuracy. CRISPR-Cas9 is a powerful new tool for editing the genome. For researchers around the world, the CRISPR-Cas9 technique is an exciting in...
"As Christopher Voigt explains it, his lab at the Massachusetts Institute of Technology has been “working on new experimental and theoretical methods to push the scale of genetic engineering, with the ultimate objective of genome design.” It’s genetic engineering on a genomic scale, with the expectation for major advances in agriculture, materials, chemicals, and medicine.
As they’ve gone along, Voigt’s group has also been assembling the toolbox needed for anyone to begin considering genetic engineering projects in a very big way. In one of his latest papers, published in Molecular Systems Biology in November, Voigt and Alex Nielsen describe what’s possible when multi-input CRISPR/Cas genetic circuits are linked to the regulatory networks within E. coli host cells.
Category theory is a branch of math that puts processes on an equal footing with things - unlike set theory, where everything is fundamentally a thing. Can we use category theory to help understand the complex processes that underlie biology and ecology?
I believe so, and I'm hoping this is a good way for fancy-schmancy mathematicians like me to help the world. But it will take a while. I think we should start by seeing what category theory has to say about some related subjects that are better understood: chemistry, electrical engineering, classical mechanics, and the like.
We're having a workshop about this next week - and to organize our thoughts we've been writing some blog articles. Check 'em out!
• John Baez, Categorical foundations of network theory - an introduction to the workshop and what it's about. https://johncarlosbaez.wordpress.com/2015/04/04/categorical-foundations-of-network-theory/
• David Spivak, A networked world.
• Eugene Lerman, Networks of dynamical systems.
• Tobias Fritz, Resource convertibility - an introduction to the mathematics of 'resources'.
• John Baez, Categories in control - about my paper with Jason Erbele on using categories to study signal flow diagrams in control theory.
• John Baez, A compositional framework for passive linear networks - about my paper with Brendan Fong on using categories to study electrical circuit diagrams.
• John Baez, Decorated cospans - about Brendan Fong's paper providing mathematical infrastructure for the study of networks.
• John Baez and Brendan Fong, Cospans, wiring diagrams, and the behavioral approach - an attempt to reflect on how our work connects to that of David Spivak.
• Brendan Fong, Resource theories - about Brendan's new paper with Hugo Nava-Kopp on resource theories.
• John Baez, PROPs for linear systems - about Simon Wadsley and Nick Woods' generalization of a result in my paper with Jason Erbele, describing categories where the morphisms are linear maps.
The picture, by the way, was drawn by Federica Ferraris and appears in this book:
• John Baez and Jacob Biamonte, Quantum techniques for stochastic physics, http://math.ucr.edu/home/baez/stoch_stable.pdf
It's about Petri nets and reaction networks - two kinds of networks that appear in chemistry and population biology.
Bad news for psychology -- only 39 of 100 published findings were replicated in a recent coordinated effort. Nature News : An ambitious effort to replicate 100 research findings in psychology ended last week — and the data look worrying. Results posted onli...
In a world first, Chinese scientists have reported editing the genomes of human embryos . The results are published in the online journal Protein and Cell and confirm widespread rumours that such experiments had been conducted—rumours that sparked a high-p...
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