20,965 research outputs found
A Dynamical Systems Approach for Static Evaluation in Go
In the paper arguments are given why the concept of static evaluation has the
potential to be a useful extension to Monte Carlo tree search. A new concept of
modeling static evaluation through a dynamical system is introduced and
strengths and weaknesses are discussed. The general suitability of this
approach is demonstrated.Comment: IEEE Transactions on Computational Intelligence and AI in Games, vol
3 (2011), no
The integration of systems of linear PDEs using conservation laws of syzygies
A new integration technique is presented for systems of linear partial
differential equations (PDEs) for which syzygies can be formulated that obey
conservation laws. These syzygies come for free as a by-product of the
differential Groebner Basis computation. Compared with the more obvious way of
integrating a single equation and substituting the result in other equations
the new technique integrates more than one equation at once and therefore
introduces temporarily fewer new functions of integration that in addition
depend on fewer variables. Especially for high order PDE systems in many
variables the conventional integration technique may lead to an explosion of
the number of functions of integration which is avoided with the new method. A
further benefit is that redundant free functions in the solution are either
prevented or that their number is at least reduced.Comment: 26 page
Size reduction and partial decoupling of systems of equations
A method is presented that reduces the number of terms of systems of linear
equations (algebraic, ordinary and partial differential equations). As a
byproduct these systems have a tendency to become partially decoupled and are
more likely to be factorizable or integrable. A variation of this method is
applicable to non-linear systems. Modifications to improve efficiency are given
and examples are shown. This procedure can be used in connection with the
computation of the radical of a differential ideal (differential Groebner
basis)
Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations
We construct new integrable coupled systems of N=1 supersymmetric equations
and present integrable fermionic extensions of the Burgers and Boussinesq
equations. Existence of infinitely many higher symmetries is demonstrated by
the presence of recursion operators. Various algebraic methods are applied to
the analysis of symmetries, conservation laws, recursion operators, and
Hamiltonian structures. A fermionic extension of the Burgers equation is
related with the Burgers flows on associative algebras. A Gardner's deformation
is found for the bosonic super-field dispersionless Boussinesq equation, and
unusual properties of a recursion operator for its Hamiltonian symmetries are
described. Also, we construct a three-parametric supersymmetric system that
incorporates the Boussinesq equation with dispersion and dissipation but never
retracts to it for any values of the parameters.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
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