3,435 research outputs found
Mathematical problems for complex networks
Copyright @ 2012 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy
is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics
Interception and deviation of near Earth objects via solar collector strategy
A solution to the asteroid deviation problem via a low-thrust strategy is proposed. This formulation makes use of the proximal motion equations and a semi-analytical solution of the Gauss planetary equations. The average of the variation of the orbital elements is computed, together with an approximate expression of their periodic evolution. The interception and the deflection phase are optimised together through a global search. The low-thrust transfer is preliminary designed with a shape based method; subsequently the solutions are locally refined through the Differential Dynamic Programming approach. A set of optimal solutions are presented for a deflection mission to Apophis, together with a representative trajectory to Apophis including the Earth escape
Trajectory optimization for the Hevelius-lunar microsatellite mission
In this paper trajectory optimisation for the Hevelius mission is presented. The Hevelius-Lunar Microsatellite Mission - is a multilander mission to the dark side of the Moon, supported by a relay microsatellite, orbiting on a Halo orbit around L2. Three landers, with miniaturized payloads, are transported by a carrier from a LEO to the surface of the Moon, where they perform a semi-hard landing with an airbag system. This paper will present the trajectory optimisation process, focusing, in particular, on the approach employed for Δv manoeuvre optimization. An introduction to the existing methods for trajectory optimization will be presented, subsequently it will be described how these methods have been exploited and originally combined in the Hevelius mission analysis and design
Controlled diffusion processes
This article gives an overview of the developments in controlled diffusion
processes, emphasizing key results regarding existence of optimal controls and
their characterization via dynamic programming for a variety of cost criteria
and structural assumptions. Stochastic maximum principle and control under
partial observations (equivalently, control of nonlinear filters) are also
discussed. Several other related topics are briefly sketched.Comment: Published at http://dx.doi.org/10.1214/154957805100000131 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Compressed matched filter for non-Gaussian noise
We consider estimation of a deterministic unknown parameter vector in a
linear model with non-Gaussian noise. In the Gaussian case, dimensionality
reduction via a linear matched filter provides a simple low dimensional
sufficient statistic which can be easily communicated and/or stored for future
inference. Such a statistic is usually unknown in the general non-Gaussian
case. Instead, we propose a hybrid matched filter coupled with a randomized
compressed sensing procedure, which together create a low dimensional
statistic. We also derive a complementary algorithm for robust reconstruction
given this statistic. Our recovery method is based on the fast iterative
shrinkage and thresholding algorithm which is used for outlier rejection given
the compressed data. We demonstrate the advantages of the proposed framework
using synthetic simulations
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