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Software tools for stochastic programming: A Stochastic Programming Integrated Environment (SPInE)
SP models combine the paradigm of dynamic linear programming with
modelling of random parameters, providing optimal decisions which hedge
against future uncertainties. Advances in hardware as well as software
techniques and solution methods have made SP a viable optimisation tool.
We identify a growing need for modelling systems which support the creation
and investigation of SP problems. Our SPInE system integrates a number of
components which include a flexible modelling tool (based on stochastic
extensions of the algebraic modelling languages AMPL and MPL), stochastic
solvers, as well as special purpose scenario generators and database tools.
We introduce an asset/liability management model and illustrate how SPInE
can be used to create and process this model as a multistage SP application
Universal neural field computation
Turing machines and G\"odel numbers are important pillars of the theory of
computation. Thus, any computational architecture needs to show how it could
relate to Turing machines and how stable implementations of Turing computation
are possible. In this chapter, we implement universal Turing computation in a
neural field environment. To this end, we employ the canonical symbologram
representation of a Turing machine obtained from a G\"odel encoding of its
symbolic repertoire and generalized shifts. The resulting nonlinear dynamical
automaton (NDA) is a piecewise affine-linear map acting on the unit square that
is partitioned into rectangular domains. Instead of looking at point dynamics
in phase space, we then consider functional dynamics of probability
distributions functions (p.d.f.s) over phase space. This is generally described
by a Frobenius-Perron integral transformation that can be regarded as a neural
field equation over the unit square as feature space of a dynamic field theory
(DFT). Solving the Frobenius-Perron equation yields that uniform p.d.f.s with
rectangular support are mapped onto uniform p.d.f.s with rectangular support,
again. We call the resulting representation \emph{dynamic field automaton}.Comment: 21 pages; 6 figures. arXiv admin note: text overlap with
arXiv:1204.546
Analysis of Dynamic Task Allocation in Multi-Robot Systems
Dynamic task allocation is an essential requirement for multi-robot systems
operating in unknown dynamic environments. It allows robots to change their
behavior in response to environmental changes or actions of other robots in
order to improve overall system performance. Emergent coordination algorithms
for task allocation that use only local sensing and no direct communication
between robots are attractive because they are robust and scalable. However, a
lack of formal analysis tools makes emergent coordination algorithms difficult
to design. In this paper we present a mathematical model of a general dynamic
task allocation mechanism. Robots using this mechanism have to choose between
two types of task, and the goal is to achieve a desired task division in the
absence of explicit communication and global knowledge. Robots estimate the
state of the environment from repeated local observations and decide which task
to choose based on these observations. We model the robots and observations as
stochastic processes and study the dynamics of the collective behavior.
Specifically, we analyze the effect that the number of observations and the
choice of the decision function have on the performance of the system. The
mathematical models are validated in a multi-robot multi-foraging scenario. The
model's predictions agree very closely with experimental results from
sensor-based simulations.Comment: Preprint version of the paper published in International Journal of
Robotics, March 2006, Volume 25, pp. 225-24
Analysis of data processing systems
Mathematical simulation models and software monitoring of multiprogramming computer syste
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