1,138 research outputs found
Elementary Derivative Tasks and Neural Net Multiscale Analysis of Tasks
Neural nets are known to be universal approximators. In particular, formal
neurons implementing wavelets have been shown to build nets able to approximate
any multidimensional task. Such very specialized formal neurons may be,
however, difficult to obtain biologically and/or industrially. In this paper we
relax the constraint of a strict ``Fourier analysis'' of tasks. Rather, we use
a finite number of more realistic formal neurons implementing elementary tasks
such as ``window'' or ``Mexican hat'' responses, with adjustable widths. This
is shown to provide a reasonably efficient, practical and robust,
multifrequency analysis. A training algorithm, optimizing the task with respect
to the widths of the responses, reveals two distinct training modes. The first
mode induces some of the formal neurons to become identical, hence promotes
``derivative tasks''. The other mode keeps the formal neurons distinct.Comment: latex neurondlt.tex, 7 files, 6 figures, 9 pages [SPhT-T01/064],
submitted to Phys. Rev.
Implementing a Class of Permutation Tests: The coin Package
The R package coin implements a unified approach to permutation tests providing a huge class of independence tests for nominal, ordered, numeric, and censored data as well as multivariate data at mixed scales. Based on a rich and flexible conceptual framework that embeds different permutation test procedures into a common theory, a computational framework is established in coin that likewise embeds the corresponding R functionality in a common S4 class structure with associated generic functions. As a consequence, the computational tools in coin inherit the flexibility of the underlying theory and conditional inference functions for important special cases can be set up easily. Conditional versions of classical tests---such as tests for location and scale problems in two or more samples, independence in two- or three-way contingency tables, or association problems for censored, ordered categorical or multivariate data---can easily be implemented as special cases using this computational toolbox by choosing appropriate transformations of the observations. The paper gives a detailed exposition of both the internal structure of the package and the provided user interfaces along with examples on how to extend the implemented functionality.
An extension of the satellite monitoring Liberty GPS system for the support requirements of transportation companies
In working out the performance principles introduced into the construction and functionality of a Satellite Monitoring Liberty GPS System for vehicles and its possibilities in offering services that improve the logistical processes for transportation companies
Artificial Neural Network Methods in Quantum Mechanics
In a previous article we have shown how one can employ Artificial Neural
Networks (ANNs) in order to solve non-homogeneous ordinary and partial
differential equations. In the present work we consider the solution of
eigenvalue problems for differential and integrodifferential operators, using
ANNs. We start by considering the Schr\"odinger equation for the Morse
potential that has an analytically known solution, to test the accuracy of the
method. We then proceed with the Schr\"odinger and the Dirac equations for a
muonic atom, as well as with a non-local Schr\"odinger integrodifferential
equation that models the system in the framework of the resonating
group method. In two dimensions we consider the well studied Henon-Heiles
Hamiltonian and in three dimensions the model problem of three coupled
anharmonic oscillators. The method in all of the treated cases proved to be
highly accurate, robust and efficient. Hence it is a promising tool for
tackling problems of higher complexity and dimensionality.Comment: Latex file, 29pages, 11 psfigs, submitted in CP
Neural network representation and learning of mappings and their derivatives
Discussed here are recent theorems proving that artificial neural networks are capable of approximating an arbitrary mapping and its derivatives as accurately as desired. This fact forms the basis for further results establishing the learnability of the desired approximations, using results from non-parametric statistics. These results have potential applications in robotics, chaotic dynamics, control, and sensitivity analysis. An example involving learning the transfer function and its derivatives for a chaotic map is discussed
Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition
Cylindrical algebraic decomposition(CAD) is a key tool in computational
algebraic geometry, particularly for quantifier elimination over real-closed
fields. When using CAD, there is often a choice for the ordering placed on the
variables. This can be important, with some problems infeasible with one
variable ordering but easy with another. Machine learning is the process of
fitting a computer model to a complex function based on properties learned from
measured data. In this paper we use machine learning (specifically a support
vector machine) to select between heuristics for choosing a variable ordering,
outperforming each of the separate heuristics.Comment: 16 page
Probability of local bifurcation type from a fixed point: A random matrix perspective
Results regarding probable bifurcations from fixed points are presented in
the context of general dynamical systems (real, random matrices), time-delay
dynamical systems (companion matrices), and a set of mappings known for their
properties as universal approximators (neural networks). The eigenvalue spectra
is considered both numerically and analytically using previous work of Edelman
et. al. Based upon the numerical evidence, various conjectures are presented.
The conclusion is that in many circumstances, most bifurcations from fixed
points of large dynamical systems will be due to complex eigenvalues.
Nevertheless, surprising situations are presented for which the aforementioned
conclusion is not general, e.g. real random matrices with Gaussian elements
with a large positive mean and finite variance.Comment: 21 pages, 19 figure
Infering Air Quality from Traffic Data using Transferable Neural Network Models
This work presents a neural network based model for inferring air quality from traffic measurements.
It is important to obtain information on air quality in urban environments in order to meet legislative and policy requirements. Measurement equipment tends to be expensive to purchase and maintain. Therefore, a model based approach capable of accurate determination of pollution levels is highly beneficial.
The objective of this study was to develop a neural network model to accurately infer pollution levels from existing data sources in Leicester, UK.
Neural Networks are models made of several highly interconnected processing elements. These elements process information by their dynamic state response to inputs. Problems which were not solvable by traditional algorithmic approaches frequently can be solved using neural networks.
This paper shows that using a simple neural network with traffic and meteorological data as inputs, the air quality can be estimated with a good level of generalisation and in near real-time.
By applying these models to links rather than nodes, this methodology can directly be used to inform traffic engineers and direct traffic management decisions towards enhancing local air quality and traffic management simultaneously.Universidad de Málaga. Campus de Excelencia Internacional AndalucĂa Tech
Neural parameters estimation for brain tumor growth modeling
Understanding the dynamics of brain tumor progression is essential for
optimal treatment planning. Cast in a mathematical formulation, it is typically
viewed as evaluation of a system of partial differential equations, wherein the
physiological processes that govern the growth of the tumor are considered. To
personalize the model, i.e. find a relevant set of parameters, with respect to
the tumor dynamics of a particular patient, the model is informed from
empirical data, e.g., medical images obtained from diagnostic modalities, such
as magnetic-resonance imaging. Existing model-observation coupling schemes
require a large number of forward integrations of the biophysical model and
rely on simplifying assumption on the functional form, linking the output of
the model with the image information. In this work, we propose a learning-based
technique for the estimation of tumor growth model parameters from medical
scans. The technique allows for explicit evaluation of the posterior
distribution of the parameters by sequentially training a mixture-density
network, relaxing the constraint on the functional form and reducing the number
of samples necessary to propagate through the forward model for the estimation.
We test the method on synthetic and real scans of rats injected with brain
tumors to calibrate the model and to predict tumor progression
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