11,899 research outputs found
Two Sets of Simple Formulae to Estimating Fractal Dimension of Irregular Boundaries
Irregular boundary lines can be characterized by fractal dimension, which
provides important information for spatial analysis of complex geographical
phenomena such as cities. However, it is difficult to calculate fractal
dimension of boundaries systematically when image data is limited. An
approximation estimation formulae of boundary dimension based on square is
widely applied in urban and ecological studies. However, the boundary dimension
is sometimes overestimated. This paper is devoted to developing a series of
practicable formulae for boundary dimension estimation using ideas from
fractals. A number of regular figures are employed as reference shapes, from
which the corresponding geometric measure relations are constructed; from these
measure relations, two sets of fractal dimension estimation formulae are
derived for describing fractal-like boundaries. Correspondingly, a group of
shape indexes can be defined. A finding is that different formulae have
different merits and spheres of application, and the second set of boundary
dimensions is a function of the shape indexes. Under condition of data
shortage, these formulae can be utilized to estimate boundary dimension values
rapidly. Moreover, the relationships between boundary dimension and shape
indexes are instructive to understand the association and differences between
characteristic scales and scaling. The formulae may be useful for the
pre-fractal studies in geography, geomorphology, ecology, landscape science,
and especially, urban science.Comment: 28 pages, 2 figures, 9 table
Theoretical Interpretations and Applications of Radial Basis Function Networks
Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains
Electro-Optic Effects in Colloidal Dispersion of Metal Nano-Rods in Dielectric Fluid
In modern transformation optics, one explores metamaterials with properties
that vary from point to point in space and time, suitable for applications in
devices such as an "optical invisibility cloak" and an "optical black hole". We
propose an approach to construct spatially varying and switchable metamaterials
that are based on colloidal dispersions of metal nano-rods (NRs) in dielectric
fluids, in which dielectrophoretic forces, originating in the electric field
gradients, create spatially varying configurations of aligned NRs. The electric
field controls orientation and concentration of NRs and thus modulates the
optical properties of the medium. Using gold (Au) NRs dispersed in toluene, we
demonstrate electrically induced change in refractive index on the order of
0.1.Comment: 27 pages, 23 figure
Data-driven Soft Sensors in the Process Industry
In the last two decades Soft Sensors established themselves as a valuable alternative to the traditional means for the acquisition of critical process variables, process monitoring and other tasks which are related to process control. This paper discusses characteristics of the process industry data which are critical for the development of data-driven Soft Sensors. These characteristics are common to a large number of process industry fields, like the chemical industry, bioprocess industry, steel industry, etc. The focus of this work is put on the data-driven Soft Sensors because of their growing popularity, already demonstrated usefulness and huge, though yet not completely realised, potential. A comprehensive selection of case studies covering the three most important Soft Sensor application fields, a general introduction to the most popular Soft Sensor modelling techniques as well as a discussion of some open issues in the Soft Sensor development and maintenance and their possible solutions are the main contributions of this work
Transient engine model for calibration using two-stage regression approach
Engine mapping is the process of empirically modelling engine behaviour
as a function of adjustable engine parameters, predicting the
output of the engine. The aim is to calibrate the electronic engine
controller to meet decreasing emission requirements and increasing
fuel economy demands. Modern engines have an increasing number
of control parameters that are having a dramatic impact on time and
e ort required to obtain optimal engine calibrations. These are further
complicated due to transient engine operating mode.
A new model-based transient calibration method has been built on the
application of hierarchical statistical modelling methods, and analysis
of repeated experiments for the application of engine mapping. The
methodology is based on two-stage regression approach, which organise
the engine data for the mapping process in sweeps. The introduction
of time-dependent covariates in the hierarchy of the modelling led
to the development of a new approach for the problem of transient
engine calibration.
This new approach for transient engine modelling is analysed using
a small designed data set for a throttle body inferred air
ow phenomenon.
The data collection for the model was performed on a
transient engine test bed as a part of this work, with sophisticated
software and hardware installed on it. Models and their associated
experimental design protocols have been identi ed that permits the
models capable of accurately predicting the desired response features
over the whole region of operability. Further, during the course of the work, the utility of multi-layer perceptron
(MLP) neural network based model for the multi-covariate
case has been demonstrated. The MLP neural network performs
slightly better than the radial basis function (RBF) model. The basis
of this comparison is made on assessing relevant model selection criteria,
as well as internal and external validation ts.
Finally, the general ability of the model was demonstrated through the
implementation of this methodology for use in the calibration process,
for populating the electronic engine control module lookup tables
Fast scalable visualization techniques for interactive billion-particle walkthrough
This research develops a comprehensive framework for interactive walkthrough involving one billion particles in an immersive virtual environment to enable interrogative visualization of large atomistic simulation data. As a mixture of scientific and engineering approaches, the framework is based on four key techniques: adaptive data compression based on space-filling curves, octree-based visibility and occlusion culling, predictive caching based on machine learning, and scalable data reduction based on parallel and distributed processing. In terms of parallel rendering, this system combines functional parallelism, data parallelism, and temporal parallelism to improve interactivity. The visualization framework will be applicable not only to material simulation, but also to computational biology, applied mathematics, mechanical engineering, and nanotechnology, etc
Spatial Signal Analysis based on Wave-Spectral Fractal Scaling: A Case of Urban Street Networks
For a long time, many methods are developed to make temporal signal analyses
based on time series. However, for geographical systems, spatial signal
analyses are as important as temporal signal analyses. Nonstationary spatial
and temporal processes are associated with nonlinearity, and cannot be
effectively analyzed by conventional analytical approaches. Fractal theory
provides a powerful tool for exploring complexity and is helpful for
spatio-temporal signal analysis. This paper is devoted to researching spatial
signals of geographical systems by means of wave-spectrum scaling. The traffic
networks of 10 Chinese cities are taken as cases for positive studies. Fast
Fourier transform and least squares regression analysis are employed to
calculate spectral exponents. The results show that the wave-spectral density
distribution of all these urban traffic networks follows scaling law, and the
spectral scaling exponents can be converted to fractal dimension values. Using
the fractal parameters, we can make spatial analyses for the geographical
signals. The analytical process can be generalized to temporal signal analyses.
The wave-spectrum scaling methods can be applied to both self-similar fractal
signals and self-affine fractal signals in the geographical world.Comment: 22 pages, 7 figures, 4 table
Quantum Loewner Evolution
What is the scaling limit of diffusion limited aggregation (DLA) in the
plane? This is an old and famously difficult question. One can generalize the
question in two ways: first, one may consider the {\em dielectric breakdown
model} -DBM, a generalization of DLA in which particle locations are
sampled from the -th power of harmonic measure, instead of harmonic
measure itself. Second, instead of restricting attention to deterministic
lattices, one may consider -DBM on random graphs known or believed to
converge in law to a Liouville quantum gravity (LQG) surface with parameter
.
In this generality, we propose a scaling limit candidate called quantum
Loewner evolution, QLE. QLE is defined in terms of the radial
Loewner equation like radial SLE, except that it is driven by a measure valued
diffusion derived from LQG rather than a multiple of a standard
Brownian motion. We formalize the dynamics of using an SPDE. For each
, there are two or three special values of for which
we establish the existence of a solution to these dynamics and explicitly
describe the stationary law of .
We also explain discrete versions of our construction that relate DLA to
loop-erased random walk and the Eden model to percolation. A certain
"reshuffling" trick (in which concentric annular regions are rotated randomly,
like slot machine reels) facilitates explicit calculation.
We propose QLE as a scaling limit for DLA on a random
spanning-tree-decorated planar map, and QLE as a scaling limit for the
Eden model on a random triangulation. We propose using QLE to endow
pure LQG with a distance function, by interpreting the region explored by a
branching variant of QLE, up to a fixed time, as a metric ball in a
random metric space.Comment: 132 pages, approximately 100 figures and computer simulation
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