6,978 research outputs found
Deterministic continutation of stochastic metastable equilibria via Lyapunov equations and ellipsoids
Numerical continuation methods for deterministic dynamical systems have been
one of the most successful tools in applied dynamical systems theory.
Continuation techniques have been employed in all branches of the natural
sciences as well as in engineering to analyze ordinary, partial and delay
differential equations. Here we show that the deterministic continuation
algorithm for equilibrium points can be extended to track information about
metastable equilibrium points of stochastic differential equations (SDEs). We
stress that we do not develop a new technical tool but that we combine results
and methods from probability theory, dynamical systems, numerical analysis,
optimization and control theory into an algorithm that augments classical
equilibrium continuation methods. In particular, we use ellipsoids defining
regions of high concentration of sample paths. It is shown that these
ellipsoids and the distances between them can be efficiently calculated using
iterative methods that take advantage of the numerical continuation framework.
We apply our method to a bistable neural competition model and a classical
predator-prey system. Furthermore, we show how global assumptions on the flow
can be incorporated - if they are available - by relating numerical
continuation, Kramers' formula and Rayleigh iteration.Comment: 29 pages, 7 figures [Fig.7 reduced in quality due to arXiv size
restrictions]; v2 - added Section 9 on Kramers' formula, additional
computations, corrected typos, improved explanation
Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model
We present a parareal in time algorithm for the simulation of neutron
diffusion transient model. The method is made efficient by means of a coarse
solver defined with large time steps and steady control rods model. Using
finite element for the space discretization, our implementation provides a good
scalability of the algorithm. Numerical results show the efficiency of the
parareal method on large light water reactor transient model corresponding to
the Langenbuch-Maurer-Werner (LMW) benchmark [1]
Two-Stage Subspace Constrained Precoding in Massive MIMO Cellular Systems
We propose a subspace constrained precoding scheme that exploits the spatial
channel correlation structure in massive MIMO cellular systems to fully unleash
the tremendous gain provided by massive antenna array with reduced channel
state information (CSI) signaling overhead. The MIMO precoder at each base
station (BS) is partitioned into an inner precoder and a Transmit (Tx) subspace
control matrix. The inner precoder is adaptive to the local CSI at each BS for
spatial multiplexing gain. The Tx subspace control is adaptive to the channel
statistics for inter-cell interference mitigation and Quality of Service (QoS)
optimization. Specifically, the Tx subspace control is formulated as a QoS
optimization problem which involves an SINR chance constraint where the
probability of each user's SINR not satisfying a service requirement must not
exceed a given outage probability. Such chance constraint cannot be handled by
the existing methods due to the two stage precoding structure. To tackle this,
we propose a bi-convex approximation approach, which consists of three key
ingredients: random matrix theory, chance constrained optimization and
semidefinite relaxation. Then we propose an efficient algorithm to find the
optimal solution of the resulting bi-convex approximation problem. Simulations
show that the proposed design has significant gain over various baselines.Comment: 13 pages, accepted by IEEE Transactions on Wireless Communication
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