22,743 research outputs found
Field Theory on a Supersymmetric Lattice
A lattice-type regularization of the supersymmetric field theories on a
supersphere is constructed by approximating the ring of scalar superfields by
an integer-valued sequence of finite dimensional rings of supermatrices and by
using the differencial calculus of non-commutative geometry. The regulated
theory involves only finite number of degrees of freedom and is manifestly
supersymmetric.Comment: 31 pages, LaTe
Differentiable Genetic Programming
We introduce the use of high order automatic differentiation, implemented via
the algebra of truncated Taylor polynomials, in genetic programming. Using the
Cartesian Genetic Programming encoding we obtain a high-order Taylor
representation of the program output that is then used to back-propagate errors
during learning. The resulting machine learning framework is called
differentiable Cartesian Genetic Programming (dCGP). In the context of symbolic
regression, dCGP offers a new approach to the long unsolved problem of constant
representation in GP expressions. On several problems of increasing complexity
we find that dCGP is able to find the exact form of the symbolic expression as
well as the constants values. We also demonstrate the use of dCGP to solve a
large class of differential equations and to find prime integrals of dynamical
systems, presenting, in both cases, results that confirm the efficacy of our
approach
Efficient numerical solution of the time fractional diffusion equation by mapping from its Brownian counterpart
The solution of a Caputo time fractional diffusion equation of order
is expressed in terms of the solution of a corresponding integer
order diffusion equation. We demonstrate a linear time mapping between these
solutions that allows for accelerated computation of the solution of the
fractional order problem. In the context of an -point finite difference time
discretisation, the mapping allows for an improvement in time computational
complexity from to , given a
precomputation of . The mapping is applied
successfully to the least-squares fitting of a fractional advection diffusion
model for the current in a time-of-flight experiment, resulting in a
computational speed up in the range of one to three orders of magnitude for
realistic problem sizes.Comment: 9 pages, 5 figures; added references for section
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