20 research outputs found
Zipper logic
Zipper logic is a graph rewrite system, consisting in only local rewrites on
a class of zipper graphs. Connections with the chemlambda artificial chemistry
and with knot diagrammatics based computation are explored in the article.Comment: 16 pages, 24 colour figure
Chemical concrete machine
The chemical concrete machine is a graph rewriting system which uses only
local moves (rewrites), seen as chemical reactions involving molecules which
are graphs made up by 4 trivalent nodes. It is Turing complete, therefore it
might be used as a model of computation in algorithmic chemistry
GLC actors, artificial chemical connectomes, topological issues and knots
Based on graphic lambda calculus, we propose a program for a new model of
asynchronous distributed computing, inspired from Hewitt Actor Model, as well
as several investigation paths, concerning how one may graft lambda calculus
and knot diagrammatics
The Pure Virtual Braid Group Is Quadratic
If an augmented algebra K over Q is filtered by powers of its augmentation
ideal I, the associated graded algebra grK need not in general be quadratic:
although it is generated in degree 1, its relations may not be generated by
homogeneous relations of degree 2. In this paper we give a sufficient criterion
(called the PVH Criterion) for grK to be quadratic. When K is the group algebra
of a group G, quadraticity is known to be equivalent to the existence of a (not
necessarily homomorphic) universal finite type invariant for G. Thus the PVH
Criterion also implies the existence of such a universal finite type invariant
for the group G. We apply the PVH Criterion to the group algebra of the pure
virtual braid group (also known as the quasi-triangular group), and show that
the corresponding associated graded algebra is quadratic, and hence that these
groups have a (not necessarily homomorphic) universal finite type invariant.Comment: 53 pages, 15 figures. Some clarifications added and inaccuracies
corrected, reflecting suggestions made by the referee of the published
version of the pape
Non-Stationary Forward Flux Sampling
We present a new method, Non-Stationary Forward Flux Sampling, that allows
efficient simulation of rare events in both stationary and non-stationary
stochastic systems. The method uses stochastic branching and pruning to achieve
uniform sampling of trajectories in phase space and time, leading to accurate
estimates for time-dependent switching propensities and time-dependent phase
space probability densities. The method is suitable for equilibrium or
non-equilibrium systems, in or out of stationary state, including non-Markovian
or externally driven systems. We demonstrate the validity of the technique by
applying it to a one-dimensional barrier crossing problem that can be solved
exactly, and show its usefulness by applying it to the time-dependent switching
of a genetic toggle switch.Comment: 18 pages, 10 figure