69 research outputs found
Fatgraph expansion for noncritical superstrings
We study the fatgraph expansion for the Complex Matrix Quantum Mechanics
(CMQM) with a Chern-Simons coupling. In the double-scaling limit this model is
believed to describe Type 0A superstrings in 1+1 dimensions in a Ramond-Ramond
electric field. With Euclidean time compactified, we show that the RR electric
field acts as a chemical potential for vortices living on the Feynman diagrams
of the CMQM. We interpret it as evidence that the CMQM Feynman diagrams
discretize the NSR formulation of the noncritical Type 0A superstring. We also
study T-duality for the CMQM diagrams and propose that a certain complex matrix
model is dual to the noncritical Type 0B superstring.Comment: 16 pages, 1 epsi figur
The difficulty of folding self-folding origami
Why is it difficult to refold a previously folded sheet of paper? We show
that even crease patterns with only one designed folding motion inevitably
contain an exponential number of `distractor' folding branches accessible from
a bifurcation at the flat state. Consequently, refolding a sheet requires
finding the ground state in a glassy energy landscape with an exponential
number of other attractors of higher energy, much like in models of protein
folding (Levinthal's paradox) and other NP-hard satisfiability (SAT) problems.
As in these problems, we find that refolding a sheet requires actuation at
multiple carefully chosen creases. We show that seeding successful folding in
this way can be understood in terms of sub-patterns that fold when cut out
(`folding islands'). Besides providing guidelines for the placement of active
hinges in origami applications, our results point to fundamental limits on the
programmability of energy landscapes in sheets.Comment: 8 pages, 5 figure
Learned multi-stability in mechanical networks
We contrast the distinct frameworks of materials design and physical learning
in creating elastic networks with desired stable states. In design, the desired
states are specified in advance and material parameters can be optimized on a
computer with this knowledge. In learning, the material physically experiences
the desired stable states in sequence, changing the material so as to stabilize
each additional state. We show that while designed states are stable in
networks of linear Hookean springs, sequential learning requires specific
non-linear elasticity. We find that such non-linearity stabilizes states in
which strain is zero in some springs and large in others, thus playing the role
of Bayesian priors used in sparse statistical regression. Our model shows how
specific material properties allow continuous learning of new functions through
deployment of the material itself
Learning without neurons in physical systems
Learning is traditionally studied in biological or computational systems. The
power of learning frameworks in solving hard inverse-problems provides an
appealing case for the development of `physical learning' in which physical
systems adopt desirable properties on their own without computational design.
It was recently realized that large classes of physical systems can physically
learn through local learning rules, autonomously adapting their parameters in
response to observed examples of use. We review recent work in the emerging
field of physical learning, describing theoretical and experimental advances in
areas ranging from molecular self-assembly to flow networks and mechanical
materials. Physical learning machines provide multiple practical advantages
over computer designed ones, in particular by not requiring an accurate model
of the system, and their ability to autonomously adapt to changing needs over
time. As theoretical constructs, physical learning machines afford a novel
perspective on how physical constraints modify abstract learning theory.Comment: 25 pages, 6 figure
- …