25,986 research outputs found
An Adversarial Interpretation of Information-Theoretic Bounded Rationality
Recently, there has been a growing interest in modeling planning with
information constraints. Accordingly, an agent maximizes a regularized expected
utility known as the free energy, where the regularizer is given by the
information divergence from a prior to a posterior policy. While this approach
can be justified in various ways, including from statistical mechanics and
information theory, it is still unclear how it relates to decision-making
against adversarial environments. This connection has previously been suggested
in work relating the free energy to risk-sensitive control and to extensive
form games. Here, we show that a single-agent free energy optimization is
equivalent to a game between the agent and an imaginary adversary. The
adversary can, by paying an exponential penalty, generate costs that diminish
the decision maker's payoffs. It turns out that the optimal strategy of the
adversary consists in choosing costs so as to render the decision maker
indifferent among its choices, which is a definining property of a Nash
equilibrium, thus tightening the connection between free energy optimization
and game theory.Comment: 7 pages, 4 figures. Proceedings of AAAI-1
Individual heterogeneity generates explosive system network dynamics
Individual heterogeneity is a key characteristic of many real-world systems,
from organisms to humans. However its role in determining the system's
collective dynamics is typically not well understood. Here we study how
individual heterogeneity impacts the system network dynamics by comparing
linking mechanisms that favor similar or dissimilar individuals. We find that
this heterogeneity-based evolution can drive explosive network behavior and
dictates how a polarized population moves toward consensus. Our model shows
good agreement with data from both biological and social science domains. We
conclude that individual heterogeneity likely plays a key role in the
collective development of real-world networks and communities, and cannot be
ignored.Comment: 6 pages, 4 figure
Partition function of the Potts model on self-similar lattices as a dynamical system and multiple transitions
We present an analytic study of the Potts model partition function on two
different types of self-similar lattices of triangular shape with non integer
Hausdorff dimension. Both types of lattices analyzed here are interesting
examples of non-trivial thermodynamics in less than two dimensions. First, the
Sierpinski gasket is considered. It is shown that, by introducing suitable
geometric coefficients, it is possible to reduce the computation of the
partition function to a dynamical system, whose variables are directly
connected to (the arising of) frustration on macroscopic scales, and to
determine the possible phases of the system. The same method is then used to
analyse the Hanoi graph. Again, dynamical system theory provides a very elegant
way to determine the phase diagram of the system. Then, exploiting the analysis
of the basins of attractions of the corresponding dynamical systems, we
construct various examples of self-similar lattices with more than one critical
temperature. These multiple critical temperatures correspond to crossing phases
with different degrees of frustration.Comment: 16 pages, 12 figures, 1 table; title changed, references and
discussion on multiple transitions adde
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