TY - GEN A1 - Wolf, Thomas T1 - Positions in the Game of Go as Complex Systems N2 - The paper gathers evidence showing different dimensions of the game of Go: the continuous and discrete nature of the game and different types of relations between state variables happening on ultra local, local, regional, and global scales. Based on these observations a new continuous local model for describing a board position is introduced. This includes the identification of the basic variables describing a board position and the formulation and solution of a dynamical system for their computation. To be usable as a static evaluation function for a game playing program at least group-wide (regional)aspects will have to be incorporated. T3 - ZIB-Report - 10-19 KW - Computer Go KW - static evaluation KW - discrete dynamical systems Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11823 SN - 1438-0064 ER - TY - GEN A1 - Bouchareb, Adel A1 - Clément, Gérard A1 - Chen, Chiang-Mei A1 - Wolf, Thomas A1 - Gal'tsov, Dmitri V. A1 - Scherbluk, Nikolai G. T1 - G_2 generating technique for minimal D=5 supergravity and black rings N2 - A solution generating technique is developed for $D=5$ minimal supergravity with two commuting Killing vectors based on the $G_2$ U-duality arising in the reduction of the theory to three dimensions. The target space of the corresponding 3-dimensional sigma-model is the coset $G_{2(2)}/(SL(2,R)\times SL(2,R))$. Its isometries constitute the set of solution generating symmetries. These include two electric and two magnetic Harrison transformations with the corresponding two pairs of gauge transformations, three $SL(2,R) \; S$-duality transformations, and the three gravitational scale, gauge and Ehlers transformations (altogether 14). We construct a representation of the coset in terms of $7\times 7$ matrices realizing the automorphisms of split octonions. Generating a new solution amounts to transforming the coset matrices by one-parametric subgroups of $G_{2(2)}$ and subsequently solving the dualization equations. Using this formalism we derive a new charged black ring solution with two independent parameters of rotation. T3 - ZIB-Report - 10-14 KW - supergravity KW - black rings KW - Killing vectors KW - duality Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11732 SN - 1438-0064 ER - TY - GEN A1 - Wolf, Thomas T1 - Merging solutions of non-linear algebraic systems N2 - In solving large polynomial algebraic systems that are too big for standard Gröbner basis techniques one way to make progress is to introduce case distinctions. This divide and conquer technique can be beneficial if the algorithms and computer programs know how to take advantage of inequalities. A further hurdle is the form of the resulting general solutions which often have unnecessarily many branches. In this paper we discuss a procedure to merge solutions by dropping inequalities which are associated with them and, if necessary, by re-parametrizing solutions. In the appendix the usefulness of the procedure is demonstrated in the classification of quadratic Hamiltonians with a Lie-Poisson bracket $e(3)$. This application required the solution of algebraic systems with over 200 unknowns, 450 equations and between 5000 and 9000 terms. T3 - ZIB-Report - 10-13 KW - computer algebra KW - polynomial systems KW - Lie-Poisson brackets KW - quadratic Hamiltonians Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11769 SN - 1438-0064 ER - TY - GEN A1 - Wolf, Thomas T1 - A Dynamical Systems Approach for Static Evaluation in Go N2 - In the paper arguments are given why the concept of static evaluation (SE) has the potential to be a useful extension to Monte Carlo tree search. A new concept of modeling SE through a dynamical system is introduced and strengths and weaknesses are discussed. The general suitability of this approach is demonstrated. A Remark: Among users of the Internet Go server KGS the abbreviation SE is used for 'Score Estimator'. Although different from 'Static Evaluation' a score estimator is easily obtained from static evaluation by adding up probabilities of chains to be alive at the end of the game or points to be owned by White or Black T3 - ZIB-Report - 10-15 KW - discrete dynamical systems KW - Computer Go KW - static evaluation Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11771 SN - 1438-0064 ER - TY - GEN A1 - Hussin, V. A1 - Kiselev, A. V. A1 - Krutov, A.O. A1 - Wolf, Thomas T1 - N=2 supersymmetric a=4-KdV hierarchy derived via Gardner's deformation of Kaup-Boussinesq equation N2 - We consider the problem of constructing Gardner's deformations for the $N{=}2$ supersymmetric $a{=}4$--\/Korteweg\/--\/de Vries equation; such deformations yield recurrence relations between the super\/-\/Hamiltonians of the hierarchy. We prove the non\/-\/existence %P.~Mathieu's Open problem on constructing for of supersymmetry\/-\/invariant %Gardner's deformations that %solutions, retract to Gardner's formulas for the KdV equation %whenever it is assumed that, under the %respective component reduction. % in the $N{=}2$ super\/-\/field. the solutions . At the same time, we propose a two\/-\/step scheme for the recursive production of the integrals of motion for the $N{=}2$,\ $a{=}4$--\/SKdV. First, we find a new Gardner's deformation of the Kaup\/--\/Boussinesq equation, which is contained in the bosonic limit of the super\/-\/%$N{=}2$,\ $a{=}4$--\/SKdV hierarchy. This yields the recurrence relation between the Hamiltonians of the limit, whence we determine the bosonic super\/- /Hamiltonians of the full $N{=}2$, $a{=}4$--\/SKdV hierarchy. T3 - ZIB-Report - 10-16 KW - Korteweg-de Vries equation KW - Kaup-Boussinesq equation KW - supersymmetry KW - Gardner's deformations KW - bi-Hamilltonian hierarchies Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11787 SN - 1438-0064 ER - TY - GEN A1 - Kiselev, A. V. A1 - Wolf, Thomas T1 - Classification of integrable super-systems using the SsTools environment N2 - A classification problem is proposed for supersymmetric %scaling\/-\/in\-va\-ri\-ant evolutionary PDE that satisfy the assumptions of nonlinearity, nondegeneracy, and homogeneity. Four classes of nonlinear coupled boson\/-\/fermion systems are discovered under the weighting assumption $|f|=|b|=|D_t|=\oh$. The syntax of the \Reduce\ package \SsTools, which was used for intermediate computations, and the applicability of its procedures to the calculus of super\/-\/PDE are described. T3 - ZIB-Report - 10-17 KW - Integrable super-systems KW - symmetries KW - recursions KW - classifiaction Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11792 SN - 1438-0064 ER - TY - GEN A1 - Wolf, Thomas A1 - Efimovskaya, Olya V. T1 - Classification of integrable quadratic Hamiltonians on e(3) N2 - Linear Poisson brackets on e(3) typical of rigid body dynamics are considered. All quadratic Hamiltonians of Kowalevski type having additional first integral of fourth degree are found. Quantum analogs of these Hamiltonians are listed. T3 - ZIB-Report - 10-18 KW - Linear Poisson brackets on e(3) KW - rigid body dynamics KW - Kowalevski type Hamiltonians KW - first integrals Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11807 SN - 1438-0064 ER - TY - JOUR A1 - Hussin, V. A1 - Kiselev, A. V. A1 - Krutov, A.O. A1 - Wolf, Thomas T1 - N=2 Supersymmetric a=4 - Korteweg-de Vries hierarchy derived via Gardner's deformation of Kaup-Bousinesq equation JF - Journal of Mathematical Physics Y1 - 2010 U6 - https://doi.org/10.1063/1.3447731 VL - 51 ER -