91,317 research outputs found
Landscape and flux for quantifying global stability and dynamics of game theory
Game theory has been widely applied to many areas including economics,
biology and social sciences. However, it is still challenging to quantify the
global stability and global dynamics of the game theory. We developed a
landscape and flux framework to quantify the global stability and global
dynamics of the game theory. As an example, we investigated the models of
three-strategy games: a special replicator-mutator game, the repeated prison
dilemma model. In this model, one stable state, two stable states and limit
cycle can emerge under different parameters. The repeated Prisoner's Dilemma
system has Hopf bifurcation transitions from one stable state to limit cycle
state, and then to another one stable state or two stable states, or vice
versa. We explored the global stability of the repeated Prisoner's Dilemma
system and the kinetic paths between the basins of attractor. The paths are
irreversible due to the non-zero flux. One can explain the game for and
.Comment: 25 pages, 15 figure
K-nearest Neighbor Search by Random Projection Forests
K-nearest neighbor (kNN) search has wide applications in many areas,
including data mining, machine learning, statistics and many applied domains.
Inspired by the success of ensemble methods and the flexibility of tree-based
methodology, we propose random projection forests (rpForests), for kNN search.
rpForests finds kNNs by aggregating results from an ensemble of random
projection trees with each constructed recursively through a series of
carefully chosen random projections. rpForests achieves a remarkable accuracy
in terms of fast decay in the missing rate of kNNs and that of discrepancy in
the kNN distances. rpForests has a very low computational complexity. The
ensemble nature of rpForests makes it easily run in parallel on multicore or
clustered computers; the running time is expected to be nearly inversely
proportional to the number of cores or machines. We give theoretical insights
by showing the exponential decay of the probability that neighboring points
would be separated by ensemble random projection trees when the ensemble size
increases. Our theory can be used to refine the choice of random projections in
the growth of trees, and experiments show that the effect is remarkable.Comment: 15 pages, 4 figures, 2018 IEEE Big Data Conferenc
Elastic and non-linear stiffness of graphene: a simple approach
The recent experiment [Science \textbf{321}, 385 (2008)] on the Young's
modulus and third-order elastic stiffness of graphene are well explained in a
very simple approach, where the graphene is described by a simplified system
and the force constant for the non-linear interaction is estimated from the
Tersoff-Brenner potential.Comment: 4 pages, 4 figure
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