956,669 research outputs found
Quantum Computing of Poincare Recurrences and Periodic Orbits
Quantum algorithms are built enabling to find Poincar\'e recurrence times and
periodic orbits of classical dynamical systems. It is shown that exponential
gain compared to classical algorithms can be reached for a restricted class of
systems. Quadratic gain can be achieved for a larger set of dynamical systems.
The simplest cases can be implemented with small number of qubits.Comment: revtex, 5 pages, research at Quantware MIPS Center (see
http://www.quantware.ups-tlse.fr); minor changes and references adde
Improving information filtering via network manipulation
Recommender system is a very promising way to address the problem of
overabundant information for online users. Though the information filtering for
the online commercial systems received much attention recently, almost all of
the previous works are dedicated to design new algorithms and consider the
user-item bipartite networks as given and constant information. However, many
problems for recommender systems such as the cold-start problem (i.e. low
recommendation accuracy for the small degree items) are actually due to the
limitation of the underlying user-item bipartite networks. In this letter, we
propose a strategy to enhance the performance of the already existing
recommendation algorithms by directly manipulating the user-item bipartite
networks, namely adding some virtual connections to the networks. Numerical
analyses on two benchmark data sets, MovieLens and Netflix, show that our
method can remarkably improve the recommendation performance. Specifically, it
not only improve the recommendations accuracy (especially for the small degree
items), but also help the recommender systems generate more diverse and novel
recommendations.Comment: 6 pages, 5 figure
Pseudo-High-Order Symplectic Integrators
Symplectic N-body integrators are widely used to study problems in celestial
mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2
and 6 substeps per timestep, respectively. The number of substeps increases
rapidly with order in timestep, rendering higher-order methods impractical.
However, symplectic integrators are often applied to systems in which
perturbations between bodies are a small factor of the force due to a dominant
central mass. In this case, it is possible to create optimized symplectic
algorithms that require fewer substeps per timestep. This is achieved by only
considering error terms of order epsilon, and neglecting those of order
epsilon^2, epsilon^3 etc. Here we devise symplectic algorithms with 4 and 6
substeps per step which effectively behave as 4th and 6th-order integrators
when epsilon is small. These algorithms are more efficient than the usual 2nd
and 4th-order methods when applied to planetary systems.Comment: 14 pages, 5 figures. Accepted for publication in the Astronomical
Journa
Preemption of State Wildlife Law in Alaska: Where, When, and Why
This report describes how parameter estimation can be performed in linear DAE systems. Both time domain and frequency domain identification are examined. The results are exemplified on a small system. A potential application for the algorithms is to make parameter estimation in models generated by a modeling language like Modelica
Analysis of the accuracy and convergence of equation-free projection to a slow manifold
In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis, and A. Zagaris, Projecting to a
Slow Manifold: Singularly Perturbed Systems and Legacy Codes, SIAM J. Appl.
Dyn. Syst. 4 (2005) 711-732], we developed a class of iterative algorithms
within the context of equation-free methods to approximate low-dimensional,
attracting, slow manifolds in systems of differential equations with multiple
time scales. For user-specified values of a finite number of the observables,
the m-th member of the class of algorithms (m = 0, 1, ...) finds iteratively an
approximation of the appropriate zero of the (m+1)-st time derivative of the
remaining variables and uses this root to approximate the location of the point
on the slow manifold corresponding to these values of the observables. This
article is the first of two articles in which the accuracy and convergence of
the iterative algorithms are analyzed. Here, we work directly with explicit
fast--slow systems, in which there is an explicit small parameter, epsilon,
measuring the separation of time scales. We show that, for each m = 0, 1, ...,
the fixed point of the iterative algorithm approximates the slow manifold up to
and including terms of O(epsilon^m). Moreover, for each m, we identify
explicitly the conditions under which the m-th iterative algorithm converges to
this fixed point. Finally, we show that when the iteration is unstable (or
converges slowly) it may be stabilized (or its convergence may be accelerated)
by application of the Recursive Projection Method. Alternatively, the
Newton-Krylov Generalized Minimal Residual Method may be used. In the
subsequent article, we will consider the accuracy and convergence of the
iterative algorithms for a broader class of systems-in which there need not be
an explicit small parameter-to which the algorithms also apply
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