942 research outputs found
Smart random walkers: the cost of knowing the path
In this work we study the problem of targeting signals in networks using
entropy information measurements to quantify the cost of targeting. We
introduce a penalization rule that imposes a restriction to the long paths and
therefore focus the signal to the target. By this scheme we go continuously
from fully random walkers to walkers biased to the target. We found that the
optimal degree of penalization is mainly determined by the topology of the
network. By analyzing several examples, we have found that a small amount of
penalization reduces considerably the typical walk length, and from this we
conclude that a network can be efficiently navigated with restricted
information.Comment: 9 pages, 11 figure
Memory and long-range correlations in chess games
In this paper we report the existence of long-range memory in the opening
moves of a chronologically ordered set of chess games using an extensive chess
database. We used two mapping rules to build discrete time series and analyzed
them using two methods for detecting long-range correlations; rescaled range
analysis and detrented fluctuation analysis. We found that long-range memory is
related to the level of the players. When the database is filtered according to
player levels we found differences in the persistence of the different subsets.
For high level players, correlations are stronger at long time scales; whereas
in intermediate and low level players they reach the maximum value at shorter
time scales. This can be interpreted as a signature of the different strategies
used by players with different levels of expertise. These results are robust
against the assignation rules and the method employed in the analysis of the
time series.Comment: 12 pages, 5 figures. Published in Physica
A study of memory effects in a chess database
A series of recent works studying a database of chronologically sorted chess
games --containing 1.4 million games played by humans between 1998 and 2007--
have shown that the popularity distribution of chess game-lines follows a
Zipf's law, and that time series inferred from the sequences of those
game-lines exhibit long-range memory effects. The presence of Zipf's law
together with long-range memory effects was observed in several systems,
however, the simultaneous emergence of these two phenomena were always studied
separately up to now. In this work, by making use of a variant of the
Yule-Simon preferential growth model, introduced by Cattuto et al., we provide
an explanation for the simultaneous emergence of Zipf's law and long-range
correlations memory effects in a chess database. We find that Cattuto's Model
(CM) is able to reproduce both, Zipf's law and the long-range correlations,
including size-dependent scaling of the Hurst exponent for the corresponding
time series. CM allows an explanation for the simultaneous emergence of these
two phenomena via a preferential growth dynamics, including a memory kernel, in
the popularity distribution of chess game-lines. This mechanism results in an
aging process in the chess game-line choice as the database grows. Moreover, we
find burstiness in the activity of subsets of the most active players, although
the aggregated activity of the pool of players displays inter-event times
without burstiness. We show that CM is not able to produce time series with
bursty behavior providing evidence that burstiness is not required for the
explanation of the long-range correlation effects in the chess database.Comment: 18 pages, 7 figure
Innovation and Nested Preferential Growth in Chess Playing Behavior
Complexity develops via the incorporation of innovative properties. Chess is
one of the most complex strategy games, where expert contenders exercise
decision making by imitating old games or introducing innovations. In this
work, we study innovation in chess by analyzing how different move sequences
are played at the population level. It is found that the probability of
exploring a new or innovative move decreases as a power law with the frequency
of the preceding move sequence. Chess players also exploit already known move
sequences according to their frequencies, following a preferential growth
mechanism. Furthermore, innovation in chess exhibits Heaps' law suggesting
similarities with the process of vocabulary growth. We propose a robust
generative mechanism based on nested Yule-Simon preferential growth processes
that reproduces the empirical observations. These results, supporting the
self-similar nature of innovations in chess are important in the context of
decision making in a competitive scenario, and extend the scope of relevant
findings recently discovered regarding the emergence of Zipf's law in chess.Comment: 8 pages, 4 figures, accepted for publication in Europhysics Letters
(EPL
Stability as a natural selection mechanism on interacting networks
Biological networks of interacting agents exhibit similar topological
properties for a wide range of scales, from cellular to ecological levels,
suggesting the existence of a common evolutionary origin. A general
evolutionary mechanism based on global stability has been proposed recently [J
I Perotti, O V Billoni, F A Tamarit, D R Chialvo, S A Cannas, Phys. Rev. Lett.
103, 108701 (2009)]. This mechanism is incorporated into a model of a growing
network of interacting agents in which each new agent's membership in the
network is determined by the agent's effect on the network's global stability.
We show that, out of this stability constraint, several topological properties
observed in biological networks emerge in a self organized manner. The
influence of the stability selection mechanism on the dynamics associated to
the resulting network is analyzed as well.Comment: 10 pages, 9 figure
Memory Kernel in the Expertise of Chess Players
In this work we investigate a mechanism for the emergence of long-range time correlations observed in a chronologically ordered database of chess games. We analyze a modified Yule-Simon preferential growth process proposed by Cattuto et al., which includes memory effects by means of a probabilistic kernel. According to the Hurst exponent of different constructed time series from the record of games, artificially generated databases from the model exhibit similar long-range correlations. In addition, the inter-event time frequency distribution is well reproduced by the model for realistic parameter values. In particular, we find the inter-event time distribution properties to be correlated with the expertise of the chess players through the memory kernel extension. Our work provides new information about the strategies implemented by players with different levels of expertise, showing an interesting example of how popularities and long-range correlations build together during a collective learning process
Continuous slice functional calculus in quaternionic Hilbert spaces
The aim of this work is to define a continuous functional calculus in
quaternionic Hilbert spaces, starting from basic issues regarding the notion of
spherical spectrum of a normal operator. As properties of the spherical
spectrum suggest, the class of continuous functions to consider in this setting
is the one of slice quaternionic functions. Slice functions generalize the
concept of slice regular function, which comprises power series with
quaternionic coefficients on one side and that can be seen as an effective
generalization to quaternions of holomorphic functions of one complex variable.
The notion of slice function allows to introduce suitable classes of real,
complex and quaternionic --algebras and to define, on each of these
--algebras, a functional calculus for quaternionic normal operators. In
particular, we establish several versions of the spectral map theorem. Some of
the results are proved also for unbounded operators. However, the mentioned
continuous functional calculi are defined only for bounded normal operators.
Some comments on the physical significance of our work are included.Comment: 71 pages, some references added. Accepted for publication in Reviews
in Mathematical Physic
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