14,856 research outputs found
Viscosity in the escape-rate formalism
We apply the escape-rate formalism to compute the shear viscosity in terms of
the chaotic properties of the underlying microscopic dynamics. A first passage
problem is set up for the escape of the Helfand moment associated with
viscosity out of an interval delimited by absorbing boundaries. At the
microscopic level of description, the absorbing boundaries generate a fractal
repeller. The fractal dimensions of this repeller are directly related to the
shear viscosity and the Lyapunov exponent, which allows us to compute its
values. We apply this method to the Bunimovich-Spohn minimal model of viscosity
which is composed of two hard disks in elastic collision on a torus. These
values are in excellent agreement with the values obtained by other methods
such as the Green-Kubo and Einstein-Helfand formulas.Comment: 16 pages, 16 figures (accepted in Phys. Rev. E; October 2003
On mining complex sequential data by means of FCA and pattern structures
Nowadays data sets are available in very complex and heterogeneous ways.
Mining of such data collections is essential to support many real-world
applications ranging from healthcare to marketing. In this work, we focus on
the analysis of "complex" sequential data by means of interesting sequential
patterns. We approach the problem using the elegant mathematical framework of
Formal Concept Analysis (FCA) and its extension based on "pattern structures".
Pattern structures are used for mining complex data (such as sequences or
graphs) and are based on a subsumption operation, which in our case is defined
with respect to the partial order on sequences. We show how pattern structures
along with projections (i.e., a data reduction of sequential structures), are
able to enumerate more meaningful patterns and increase the computing
efficiency of the approach. Finally, we show the applicability of the presented
method for discovering and analyzing interesting patient patterns from a French
healthcare data set on cancer. The quantitative and qualitative results (with
annotations and analysis from a physician) are reported in this use case which
is the main motivation for this work.
Keywords: data mining; formal concept analysis; pattern structures;
projections; sequences; sequential data.Comment: An accepted publication in International Journal of General Systems.
The paper is created in the wake of the conference on Concept Lattice and
their Applications (CLA'2013). 27 pages, 9 figures, 3 table
Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method
Quantum systems out of equilibrium are presently a subject of active
research, both in theoretical and experimental domains. In this work we
consider time-periodically modulated quantum systems which are in contact with
a stationary environment. Within the framework of a quantum master equation,
the asymptotic states of such systems are described by time-periodic density
operators. Resolution of these operators constitutes a non-trivial
computational task. To go beyond the current size limits, we use the quantum
trajectory method which unravels master equation for the density operator into
a set of stochastic processes for wave functions. The asymptotic density matrix
is calculated by performing a statistical sampling over the ensemble of quantum
trajectories, preceded by a long transient propagation. We follow the ideology
of event-driven programming and construct a new algorithmic realization of the
method. The algorithm is computationally efficient, allowing for long 'leaps'
forward in time, and is numerically exact in the sense that, being given the
list of uniformly distributed (on the unit interval) random numbers, , one could propagate a quantum trajectory (with 's
as norm thresholds) in a numerically exact way. %Since the quantum trajectory
method falls into the class of standard sampling problems, performance of the
algorithm %can be substantially improved by implementing it on a computer
cluster. By using a scalable -particle quantum model, we demonstrate that
the algorithm allows us to resolve the asymptotic density operator of the model
system with states on a regular-size computer cluster, thus reaching
the scale on which numerical studies of modulated Hamiltonian systems are
currently performed
An Overview of Moving Object Trajectory Compression Algorithms
Compression technology is an efficient way to reserve useful and valuable data as well as remove redundant and inessential data from datasets. With the development of RFID and GPS devices, more and more moving objects can be traced and their trajectories can be recorded. However, the exponential increase in the amount of such trajectory data has caused a series of problems in the storage, processing, and analysis of data. Therefore, moving object trajectory compression undoubtedly becomes one of the hotspots in moving object data mining. To provide an overview, we survey and summarize the development and trend of moving object compression and analyze typical moving object compression algorithms presented in recent years. In this paper, we firstly summarize the strategies and implementation processes of classical moving object compression algorithms. Secondly, the related definitions about moving objects and their trajectories are discussed. Thirdly, the validation criteria are introduced for evaluating the performance and efficiency of compression algorithms. Finally, some application scenarios are also summarized to point out the potential application in the future. It is hoped that this research will serve as the steppingstone for those interested in advancing moving objects mining
PRESS: A Novel Framework of Trajectory Compression in Road Networks
Location data becomes more and more important. In this paper, we focus on the
trajectory data, and propose a new framework, namely PRESS (Paralleled
Road-Network-Based Trajectory Compression), to effectively compress trajectory
data under road network constraints. Different from existing work, PRESS
proposes a novel representation for trajectories to separate the spatial
representation of a trajectory from the temporal representation, and proposes a
Hybrid Spatial Compression (HSC) algorithm and error Bounded Temporal
Compression (BTC) algorithm to compress the spatial and temporal information of
trajectories respectively. PRESS also supports common spatial-temporal queries
without fully decompressing the data. Through an extensive experimental study
on real trajectory dataset, PRESS significantly outperforms existing approaches
in terms of saving storage cost of trajectory data with bounded errors.Comment: 27 pages, 17 figure
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