40,479 research outputs found
The unique continuation property for a nonlinear equation on trees
In this paper, we study the game p-Laplacian on a tree, that is, u(x) = α / 2 max y∈S(x) u(y) + min y∈S(x) u(y) + β m y∈S(x) u(y);here x is a vertex of the tree and S(x) is the set of successors of x. We study the family of the subsets of the tree that enjoy the unique continuation property, that is, subsets U such that u |U = 0 implies u ≡ 0.Fil: del Pezzo, Leandro Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Mosquera, Carolina Alejandra. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Rossi, Julio Daniel. Universidad de Alicante; España. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentin
Weiqi games as a tree: Zipf's law of openings and beyond
Weiqi is one of the most complex board games played by two persons. The
placement strategies adopted by Weiqi players are often used to analog the
philosophy of human wars. Contrary to the western chess, Weiqi games are less
studied by academics partially because Weiqi is popular only in East Asia,
especially in China, Japan and Korea. Here, we propose to construct a directed
tree using a database of extensive Weiqi games and perform a quantitative
analysis of the Weiqi tree. We find that the popularity distribution of Weiqi
openings with a same number of moves is distributed according to a power law
and the tail exponent increases with the number of moves. Intriguingly, the
superposition of the popularity distributions of Weiqi openings with the number
of moves no more than a given number also has a power-law tail in which the
tail exponent increases with the number of moves, and the superposed
distribution approaches to the Zipf law. These findings are the same as for
chess and support the conjecture that the popularity distribution of board game
openings follows the Zipf law with a universal exponent. We also find that the
distribution of out-degrees has a power-law form, the distribution of branching
ratios has a very complicated pattern, and the distribution of uniqueness
scores defined by the path lengths from the root vertex to the leaf vertices
exhibits a unimodal shape. Our work provides a promising direction for the
study of the decision making process of Weiqi playing from the angle of
directed branching tree.Comment: 6 Latex pages including 6 figure
Infinitary Classical Logic: Recursive Equations and Interactive Semantics
In this paper, we present an interactive semantics for derivations in an
infinitary extension of classical logic. The formulas of our language are
possibly infinitary trees labeled by propositional variables and logical
connectives. We show that in our setting every recursive formula equation has a
unique solution. As for derivations, we use an infinitary variant of
Tait-calculus to derive sequents. The interactive semantics for derivations
that we introduce in this article is presented as a debate (interaction tree)
between a test > (derivation candidate, Proponent) and an environment <<
not S >> (negation of a sequent, Opponent). We show a completeness theorem for
derivations that we call interactive completeness theorem: the interaction
between > (test) and > (environment) does not produce errors
(i.e., Proponent wins) just in case > comes from a syntactical derivation
of >.Comment: In Proceedings CL&C 2014, arXiv:1409.259
Existence, uniqueness and decay rates for evolution equations on trees
We study evolution equations governed by an averaging operator on a directed tree, showing existence and uniqueness of solutions. In addition we find conditions of the initial condition that allows us to find the asymptotic decay rate of the solutions as . It turns out that this decay rate is not uniform, it strongly depends on how the initial condition goes to zero as one goes down in the tree.Fil: del Pezzo, Leandro Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Mosquera, Carolina Alejandra. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Rossi, Julio Daniel. Universidad de Alicante; España. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentin
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