1,386 research outputs found
Towards the cohomology of moduli spaces of higher genus stable maps
We prove that the orbifold desingularization of the moduli space of stable
maps of genus g = 1 recently constructed by Vakil and Zinger has vanishing
rational cohomology groups in odd degree k < 10.Comment: Preliminary version, comments are welcom
Quantum cohomology of moduli spaces of genus zero stable curves
We investigate the (small) quantum cohomology ring of the moduli spaces of
stable n-pointed curves of genus 0. In particular, we determine an explicit
presentation in the case n=5 and we outline a computational approach to the
case n=6.Comment: Reference adde
Exploring NK Fitness Landscapes Using Imitative Learning
The idea that a group of cooperating agents can solve problems more
efficiently than when those agents work independently is hardly controversial,
despite our obliviousness of the conditions that make cooperation a successful
problem solving strategy. Here we investigate the performance of a group of
agents in locating the global maxima of NK fitness landscapes with varying
degrees of ruggedness. Cooperation is taken into account through imitative
learning and the broadcasting of messages informing on the fitness of each
agent. We find a trade-off between the group size and the frequency of
imitation: for rugged landscapes, too much imitation or too large a group yield
a performance poorer than that of independent agents. By decreasing the
diversity of the group, imitative learning may lead to duplication of work and
hence to a decrease of its effective size. However, when the parameters are set
to optimal values the cooperative group substantially outperforms the
independent agents
Imitative learning as a connector of collective brains
The notion that cooperation can aid a group of agents to solve problems more
efficiently than if those agents worked in isolation is prevalent, despite the
little quantitative groundwork to support it. Here we consider a primordial
form of cooperation -- imitative learning -- that allows an effective exchange
of information between agents, which are viewed as the processing units of a
social intelligence system or collective brain. In particular, we use
agent-based simulations to study the performance of a group of agents in
solving a cryptarithmetic problem. An agent can either perform local random
moves to explore the solution space of the problem or imitate a model agent --
the best performing agent in its influence network. There is a complex
trade-off between the number of agents N and the imitation probability p, and
for the optimal balance between these parameters we observe a thirtyfold
diminution in the computational cost to find the solution of the
cryptarithmetic problem as compared with the independent search. If those
parameters are chosen far from the optimal setting, however, then imitative
learning can impair greatly the performance of the group. The observed
maladaptation of imitative learning for large N offers an alternative
explanation for the group size of social animals
The collapse of ecosystem engineer populations
Humans are the ultimate ecosystem engineers who have profoundly transformed
the world's landscapes in order to enhance their survival. Somewhat
paradoxically, however, sometimes the unforeseen effect of this ecosystem
engineering is the very collapse of the population it intended to protect. Here
we use a spatial version of a standard population dynamics model of ecosystem
engineers to study the colonization of unexplored virgin territories by a small
settlement of engineers. We find that during the expansion phase the population
density reaches values much higher than those the environment can support in
the equilibrium situation. When the colonization front reaches the boundary of
the available space, the population density plunges sharply and attains its
equilibrium value. The collapse takes place without warning and happens just
after the population reaches its peak number. We conclude that overpopulation
and the consequent collapse of an expanding population of ecosystem engineers
is a natural consequence of the nonlinear feedback between the population and
environment variables
Social interaction as a heuristic for combinatorial optimization problems
We investigate the performance of a variant of Axelrod's model for
dissemination of culture - the Adaptive Culture Heuristic (ACH) - on solving an
NP-Complete optimization problem, namely, the classification of binary input
patterns of size by a Boolean Binary Perceptron. In this heuristic,
agents, characterized by binary strings of length which represent possible
solutions to the optimization problem, are fixed at the sites of a square
lattice and interact with their nearest neighbors only. The interactions are
such that the agents' strings (or cultures) become more similar to the low-cost
strings of their neighbors resulting in the dissemination of these strings
across the lattice. Eventually the dynamics freezes into a homogeneous
absorbing configuration in which all agents exhibit identical solutions to the
optimization problem. We find through extensive simulations that the
probability of finding the optimal solution is a function of the reduced
variable so that the number of agents must increase with the fourth
power of the problem size, , to guarantee a fixed probability
of success. In this case, we find that the relaxation time to reach an
absorbing configuration scales with which can be interpreted as the
overall computational cost of the ACH to find an optimal set of weights for a
Boolean Binary Perceptron, given a fixed probability of success
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