2,344 research outputs found
Sampling and Reconstruction of Spatial Signals
Digital processing of signals f may start from sampling on a discrete set Γ, f →(f(ϒη))ϒηεΓ. The sampling theory is one of the most basic and fascinating topics in applied mathematics and in engineering sciences. The most well known form is the uniform sampling theorem for band-limited/wavelet signals, that gives a framework for converting analog signals into sequences of numbers. Over the past decade, the sampling theory has undergone a strong revival and the standard sampling paradigm is extended to non-bandlimited signals including signals in reproducing kernel spaces (RKSs), signals with finite rate of innovation (FRI) and sparse signals, and to nontraditional sampling methods, such as phaseless sampling. In this dissertation, we first consider the sampling and Galerkin reconstruction in a reproducing kernel space. The fidelity measure of perceptual signals, such as acoustic and visual signals, might not be well measured by least squares. In the first part of this dissertation, we introduce a fidelity measure depending on a given sampling scheme and propose a Galerkin method in Banach space setting for signal reconstruction. We show that the proposed Galerkin method provides a quasi-optimal approximation, and the corresponding Galerkin equations could be solved by an iterative approximation-projection algorithm in a reproducing kernel subspace of Lp. A spatially distributed network contains a large amount of agents with limited sensing, data processing, and communication capabilities. Recent technological advances have opened up possibilities to deploy spatially distributed networks for signal sampling and reconstruction. We introduce a graph structure for a distributed sampling and reconstruction system by coupling agents in a spatially distributed network with innovative positions of signals. We split a distributed sampling and reconstruction system into a family of overlapping smaller subsystems, and we show that the stability of the sensing matrix holds if and only if its quasi-restrictions to those subsystems have l_2 uniform stability. This new stability criterion could be pivotal for the design of a robust distributed sampling and reconstruction system against supplement, replacement and impairment of agents, as we only need to check the uniform stability of affected subsystems. We also propose an exponentially convergent distributed algorithm for signal reconstruction, that provides a suboptimal approximation to the original signal in the presence of bounded sampling noises. Phase retrieval (Phaseless Sampling and Reconstruction) arises in various fields of science and engineering. It consists of reconstructing a signal of interest from its magnitude measurements. Sampling in shift-invariant spaces is a realistic model for signals with smooth spectrum. We consider phaseless sampling and reconstruction of real-valued signals in a shift-invariant space from their magnitude measurements on the whole Euclidean space and from their phaseless samples taken on a discrete set with finite sampling density. We find an equivalence between nonseparability of signals in a shift-invariant space and their phase retrievability with phaseless samples taken on the whole Euclidean space. We also introduce an undirected graph to a signal and use connectivity of the graph to characterize the nonseparability of high-dimensional signals. Under the local complement property assumption on a shift-invariant space, we find a discrete set with finite sampling density such that signals in shift-invariant spaces, that are determined by their magnitude measurements on the whole Euclidean space, can be reconstructed in a stable way from their phaseless samples taken on that discrete set. We also propose a reconstruction algorithm which provides a suboptimal approximation to the original signal when its noisy phaseless samples are available only
Anatomical curve identification
Methods for capturing images in three dimensions are now widely available, with stereo-photogrammetry and laser scanning being two common approaches. In anatomical studies, a number of landmarks are usually identified manually from each of these images and these form the basis of subsequent statistical analysis. However, landmarks express only a very small proportion of the information available from the images. Anatomically defined curves have the advantage of providing a much richer expression of shape. This is explored in the context of identifying the boundary of breasts from an image of the female torso and the boundary of the lips from a facial image. The curves of interest are characterised by ridges or valleys. Key issues in estimation are the ability to navigate across the anatomical surface in three-dimensions, the ability to recognise the relevant boundary and the need to assess the evidence for the presence of the surface feature of interest. The first issue is addressed by the use of principal curves, as an extension of principal components, the second by suitable assessment of curvature and the third by change-point detection. P-spline smoothing is used as an integral part of the methods but adaptations are made to the specific anatomical features of interest. After estimation of the boundary curves, the intermediate surfaces of the anatomical feature of interest can be characterised by surface interpolation. This allows shape variation to be explored using standard methods such as principal components. These tools are applied to a collection of images of women where one breast has been reconstructed after mastectomy and where interest lies in shape differences between the reconstructed and unreconstructed breasts. They are also applied to a collection of lip images where possible differences in shape between males and females are of interest
Implicit reconstructions of thin leaf surfaces from large, noisy point clouds
Thin surfaces, such as the leaves of a plant, pose a significant challenge
for implicit surface reconstruction techniques, which typically assume a
closed, orientable surface. We show that by approximately interpolating a point
cloud of the surface (augmented with off-surface points) and restricting the
evaluation of the interpolant to a tight domain around the point cloud, we need
only require an orientable surface for the reconstruction. We use polyharmonic
smoothing splines to fit approximate interpolants to noisy data, and a
partition of unity method with an octree-like strategy for choosing subdomains.
This method enables us to interpolate an N-point dataset in O(N) operations. We
present results for point clouds of capsicum and tomato plants, scanned with a
handheld device. An important outcome of the work is that sufficiently smooth
leaf surfaces are generated that are amenable for droplet spreading
simulations
From spline wavelet to sampling theory on circulant graphs and beyond– conceiving sparsity in graph signal processing
Graph Signal Processing (GSP), as the field concerned with the extension of classical signal processing concepts to the graph domain, is still at the beginning on the path toward providing a generalized theory of signal processing. As such, this thesis aspires to conceive the theory of sparse representations on graphs by traversing the cornerstones of wavelet and sampling theory on graphs.
Beginning with the novel topic of graph spline wavelet theory, we introduce families of spline and e-spline wavelets, and associated filterbanks on circulant graphs, which lever- age an inherent vanishing moment property of circulant graph Laplacian matrices (and their parameterized generalizations), for the reproduction and annihilation of (exponen- tial) polynomial signals. Further, these families are shown to provide a stepping stone to generalized graph wavelet designs with adaptive (annihilation) properties. Circulant graphs, which serve as building blocks, facilitate intuitively equivalent signal processing concepts and operations, such that insights can be leveraged for and extended to more complex scenarios, including arbitrary undirected graphs, time-varying graphs, as well as associated signals with space- and time-variant properties, all the while retaining the focus on inducing sparse representations.
Further, we shift from sparsity-inducing to sparsity-leveraging theory and present a novel sampling and graph coarsening framework for (wavelet-)sparse graph signals, inspired by Finite Rate of Innovation (FRI) theory and directly building upon (graph) spline wavelet theory. At its core, the introduced Graph-FRI-framework states that any K-sparse signal residing on the vertices of a circulant graph can be sampled and perfectly reconstructed from its dimensionality-reduced graph spectral representation of minimum size 2K, while the structure of an associated coarsened graph is simultaneously inferred. Extensions to arbitrary graphs can be enforced via suitable approximation schemes.
Eventually, gained insights are unified in a graph-based image approximation framework which further leverages graph partitioning and re-labelling techniques for a maximally sparse graph wavelet representation.Open Acces
The Panchromatic High-Resolution Spectroscopic Survey of Local Group Star Clusters - I. General Data Reduction Procedures for the VLT/X-shooter UVB and VIS arm
Our dataset contains spectroscopic observations of 29 globular clusters in
the Magellanic Clouds and the Milky Way performed with VLT/X-shooter. Here we
present detailed data reduction procedures for the VLT/X-shooter UVB and VIS
arm. These are not restricted to our particular dataset, but are generally
applicable to different kinds of X-shooter data without major limitation on the
astronomical object of interest. ESO's X-shooter pipeline (v1.5.0) performs
well and reliably for the wavelength calibration and the associated
rectification procedure, yet we find several weaknesses in the reduction
cascade that are addressed with additional calibration steps, such as bad pixel
interpolation, flat fielding, and slit illumination corrections. Furthermore,
the instrumental PSF is analytically modeled and used to reconstruct flux
losses at slit transit and for optimally extracting point sources. Regular
observations of spectrophotometric standard stars allow us to detect
instrumental variability, which needs to be understood if a reliable absolute
flux calibration is desired. A cascade of additional custom calibration steps
is presented that allows for an absolute flux calibration uncertainty of less
than ten percent under virtually every observational setup provided that the
signal-to-noise ratio is sufficiently high. The optimal extraction increases
the signal-to-noise ratio typically by a factor of 1.5, while simultaneously
correcting for resulting flux losses. The wavelength calibration is found to be
accurate to an uncertainty level of approximately 0.02 Angstrom. We find that
most of the X-shooter systematics can be reliably modeled and corrected for.
This offers the possibility of comparing observations on different nights and
with different telescope pointings and instrumental setups, thereby
facilitating a robust statistical analysis of large datasets.Comment: 22 pages, 18 figures, Accepted for publication in Astronomy &
Astrophysics; V2 contains a minor change in the abstract. We note that we did
not test X-shooter pipeline versions 2.0 or later. V3 contains an updated
referenc
Tissue-scale, patient-specific modeling and simulation of prostate cancer growth
Programa Oficial de Doutoramento en Enxeñaría Civil . 5011V01[Abstract]
Prostate cancer is a major health problem among aging men worldwide. This pathology
is easier to cure in its early stages, when it is still organ-confined. However, it hardly
ever produces any symptom until it becomes excessively large or has invaded other
tissues. Hence, the current approach to combat prostate cancer is a combination of
prevention and regular screening for early detection. Indeed, most cases of prostate
cancer are diagnosed and treated when it is localized within the organ. Despite the wealth
of accumulated knowledge on the biological basis and clinical management of the disease,
we lack a comprehensive theoretical model into which we can organize and understand
the abundance of data on prostate cancer. Additionally, the standard clinical practice
in oncology is largely based on statistical patterns, which is not sufficiently accurate to
individualize the diagnosis, prediction of prognosis, treatment, and follow-up.
Recently, mathematical modeling and simulation of cancer and their treatments have
enabled the prediction of clinical outcomes and the design of optimal therapies on a
patient-specific basis. This new trend in medical research has been termed mathematical
oncology. Prostate cancer is an ideal candidate to benefit from this technology for several
reasons. First, patient-specific clinical approaches may contribute to reduce the rates of
overtreatment and undertreatment of prostate cancer. Multiparametric magnetic resonance
is increasingly used to monitor and diagnose this disease. This imaging technology can
provide abundant information to build a patient-specific mathematical model of prostate
cancer growth. Moreover, the prostate is a sufficiently small organ to pursue tissue-scale
predictive simulations. Prostate cancer growth can also be estimated using the serum
concentration of a biomarker known as the prostate specific antigen. Additionally, some
prostate cancer patients do not receive any treatment but are clinically monitored and
periodically imaged, which opens the door to in vivo model validation. The advent of
versatile and powerful technologies in computational mechanics permits to address the
challenges posed by the prostate anatomy and the resolution of the mathematical models.
Finally, mathematical oncology technologies can guide the future research on prostate
cancer, e.g., proposing new treatment strategies or unveiling mechanisms involved in
tumor growth. Therefore, the aim of this thesis is to provide a computational framework for the tissuescale,
patient-specific modeling and simulation of organ-confined PCa growth within
the context of mathematical oncology. We present a model for localized prostate cancer
growth that reproduces the growth patterns of the disease observed in experimental
and clinical studies. To capture the coupled dynamics of healthy and tumoral tissue,
we use the phase-field method together with reaction-diffusion equations for nutrient
consumption and prostate specific antigen production. We leverage this model to run the
first tissue-scale, patient-specific simulations of prostate cancer growth over the organ
anatomy extracted from medical images. Our results show similar tumor progression as
observed in clinical practice.
We leverage isogeometric analysis to handle the nonlinearity of our set of equations,
as well as the complex anatomy of the prostate and the intricate tumoral morphologies.
We further advocate dynamical mesh adaptivity to speed up calculations, rationalize
computational resources, and facilitate simulation in a clinically relevant time. We
present a set of efficient algorithms to accommodate local h-refinement and h-coarsening
of hierarchical splines in isogeometric analysis. Our methods are based on Bézier
projection, which we extend to hierarchical spline spaces. We also introduce a balance
parameter to control the overlapping of basis functions across the levels of the hierarchy,
leading to improved numerical conditioning. Our simulations of cancer growth show
remarkable accuracy with very few degrees of freedom in comparison to the uniform
mesh that the same simulation would require.
Finally, we study the interaction between prostate cancer and benign prostatic hyperplasia,
another common prostate pathology that causes the organ to gradually enlarge. In
particular, we investigate why tumors originating in larger prostates present favorable
pathological features. We perform a qualitative simulation study by extending our
mathematical model of prostate cancer growth to include the equations of mechanical
equilibrium and the coupling terms between them and tumor dynamics. We assume that
the deformation of the prostate is a quasistatic phenomenon and we model prostatic tissue
as a linear elastic, heterogeneous, isotropic material. This model is calibrated by studying
the deformation caused by either disease independently. Our simulations show that a
history of benign prostatic hyperplasia creates mechanical stress fields in the prostate that
hamper prostatic tumor growth and limit its invasiveness.[Resumen]
El cáncer de próstata es un gran problema de salud en hombres de edad avanzada en
todo el mundo. Esta patología es más fácil de curar en sus estadios iniciales, cuando
aún es órgano-confinada. Sin embargo, casi nunca produce ningún síntoma hasta que es
demasiado grande o ha invadido otros tejidos. Por tanto, el enfoque actual para combatir
el cáncer de próstata es una combinación de prevención y exámenes rutinarios para una
detección precoz. De hecho, la mayoría de casos de cáncer de próstata son diagnosticados
y tratados cuando aún está localizado dentro del órgano. A pesar de la riqueza del
conocimiento acumulado sobre las bases biológicas y la gestión clínica de la enfermedad,
carecemos de un modelo teórico completo en el que podamos organizar y comprender
la enorme cantidad de datos existentes sobre el cáncer de próstata. Además, la práctica
clínica estándar en oncología está basada en gran medida en patrones estadísticos, lo
cual no es suficientemente preciso para individualizar el diagnóstico, la predicción de la
prognosis, el tratamiento y el seguimiento.
Recientemente, la modelización y la simulación matemáticas del cáncer y sus tratamientos
han permitido predecir resultados clínicos y el diseño de terapias óptimas de
forma personalizada. Esta nueva corriente de investigación médica se ha denominado
oncología matemática. El cáncer de próstata es un candidato ideal para beneficiarse de
esta tecnología por varios motivos. En primer lugar, un enfoque clínico personalizado
podría contribuir a reducir las tasas de tratamiento excesivo o insuficiente de cáncer de
próstata. La resonancia magnética multiparamétrica se usa cada vez más para monitorizar
y diagnosticar esta enfermedad. Esta tecnología de imagen puede proporcionar abundante
información para construir un modelo matemático de crecimiento de cáncer de próstata
personalizado. Además, la próstata es un órgano suficientemente pequeño para perseguir
la realización de simulaciones predictivas a escala tisular. El crecimiento del cáncer de
próstata también se puede estimar usando la concentración en sangre de un biomarcador
conocido como el antígeno prostático específico. Adicionalmente, algunos pacientes de
cáncer de próstata no reciben tratamiento pero son monitorizados clínicamente y se les
toman imágenes médicas periódicamente, lo que abre la puerta a la validación in vivo de
modelos. El desarrollo de tecnologías versátiles y potentes en mecánica computacional permite hacer frente a los retos derivados de la anatomía prostática y la resolución de los
modelos matemáticos. Finalmente, las tecnologías de oncología matemática pueden guiar
las investigaciones futuras sobre cáncer de próstata, por ejemplo, proponiendo nuevas
estrategias de tratamiento o descubriendo mecanismos involucrados en el crecimiento
tumoral.
Por tanto, el objeto de esta tesis es proporcionar un marco computacional para la modelización
y simulación del crecimiento del cáncer de próstata órgano-confinado de
forma personalizada y a escala tisular dentro del contexto de la oncología matemática.
Presentamos un modelo de crecimiento de cáncer de próstata localizado que reproduce
los patrones de crecimiento de la enfermedad observados en estudios experimentales y
clínicos. Para capturar las dinámicas acopladas de los tejidos sano y tumoral, usamos el
método de campo de fase junto con ecuaciones de reacción-difusión para el consumo
de nutriente y la producción de antígeno prostático específico. Empleamos este modelo
para realizar las primeras simulaciones personalizadas a escala tisular del crecimiento de
cáncer de próstata sobre la anatomía del órgano extraída de imágenes médicas. Nuestros
resultados muestran una progresión tumoral similar a la observada en la práctica clínica.
Utilizamos el análisis isogeométrico para resolver la no-linealidad de nuestro sistema de
ecuaciones, así como la compleja anatomía de la próstata y las intricadas morfologías
tumorales. Adicionalmente, proponemos el uso de adaptatividad dinámica de malla para
acelerar los cálculos, racionalizar los recursos computacionales y facilitar la simulación en
un tiempo clínicamente relevante. Presentamos un conjunto de algoritmos eficientes para
introducir el refinamiento y el engrosado locales tipo h en análisis isogeométrico. Nuestros
métodos están basados en la proyección de Bézier, que extendemos a los espacios de
splines jerárquicas. También introducimos un parámetro de balance para controlar la
superposición de funciones de base a través de los niveles de la jerarquía, lo cual conduce
a un condicionamiento numérico mejorado. Nuestras simulaciones de crecimiento de
cáncer muestran una notable precisión con muy pocos grados de libertad en comparación
con la malla uniforme que la misma simulación requeriría.
Finalmente, estudiamos la interacción entre el cáncer de próstata y la hiperplasia benigna
de próstata, otra patología prostática común que hace crecer al órgano gradualmente. En
particular, investigamos por qué los tumores que se originan en próstatas más grandes
presentan características patológicas favorables. Realizamos un estudio de simulación
cualitativo extendiendo nuestro modelo matemático de crecimiento de cáncer de próstata
para incluir las ecuaciones de equilibrio mecánico y los términos de acoplamiento entre
estas y la dinámica tumoral. Asumimos que la deformación de la próstata es un fenómeno
cuasiestático y modelamos el tejido prostático como un material elástico lineal, heterogéneo
e isotrópico. Este modelo es calibrado estudiando la deformación causada por
cada enfermedad independientemente. Nuestras simulaciones muestran que un historial
de hiperplasia benigna de próstata crea campos de tensión mecánica en la próstata que
obstaculizan el crecimiento del cáncer de próstata y limitan su invasividad.[Resumo]
O cancro de próstata é un gran problema de saúde en homes de idade avanzada en todo
o mundo. Esta patoloxía é máis fácil de curar nos seus estadios iniciais, cando aínda
é órgano-confinada. Porén, case nunca produce ningún síntoma ata que é demasiado
grande ou ten invadido outros tecidos. Polo tanto, o enfoque actual para combater o
cancro de próstata é unha combinación de prevención e exames rutinarios para unha
detección precoz. De feito, a maioría de casos de cancro de próstata son diagnosticados e
tratados cando aínda está localizado dentro do órgano. Malia a riqueza do coñecemento
acumulado sobre as bases biolóxicas e a xestión clínica da doenza, carecemos dun modelo
teórico completo no que podamos organizar e comprender a enorme cantidade de datos
existentes sobre o cancro de próstata. Ademais, a práctica clínica estándar en oncoloxía
está baseada en gran medida en patróns estatísticos, o cal non é suficientemente preciso
para individualizar a diagnose, a predición da prognose, o tratamento e o seguimento.
Recentemente, a modelización e a simulación matemáticas do cancro e os seus tratamentos
permitiron predicir resultados clínicos e o deseño de terapias óptimas de forma
personalizada. Esta nova corrente de investigación médica denomínase oncoloxía matemática.
O cancro de próstata é un candidato ideal para beneficiarse desta tecnoloxía por
varios motivos. En primeiro lugar, un enfoque clínico personalizado podería contribuír a
reducir as taxas de tratamento excesivo ou insuficiente de cancro de próstata. A resonancia
magnética multiparamétrica úsase cada vez máis para monitorizar e diagnosticar esta
enfermidade. Esta tecnoloxía de imaxe pode proporcionar abundante información para
construír un modelo matemático de crecemento de cancro de próstata personalizado.
Ademais, a próstata é un órgano suficientemente pequeno para perseguir a realización
de simulacións preditivas a escala tisular. O crecemento do cancro de próstata tamén
se pode estimar usando a concentración en sangue dun biomarcador coñecido como o
antíxeno prostático específico. Adicionalmente, algúns pacientes de cancro de próstata
non reciben tratamento pero son monitorizados clinicamente e se lles toman imaxes
médicas periodicamente, o que abre a porta á validación in vivo de modelos. O desenvolvemento
de tecnoloxías versátiles e potentes en mecánica computacional permite facer
fronte aos retos derivados da anatomía prostática e a resolución dos modelos matemáticos. Finalmente, as tecnoloxías de oncoloxía matemática poden guiar as investigacións futuras
sobre cancro de próstata, por exemplo, propoñendo novas estratexias de tratamento ou
descubrindo mecanismos involucrados no crecemento tumoral.
Polo tanto, o obxecto desta tese é proporcionar un marco computacional para a modelización
e simulación do crecemento do cancro de próstata órgano-confinado de forma
personalizada e a escala tisular dentro do contexto da oncoloxía matemática. Presentamos
un modelo de crecemento de cancro de próstata localizado que reproduce os patróns de
crecemento da enfermidade observados en estudos experimentais e clínicos. Para capturar
as dinámicas acopladas dos tecidos san e tumoral, usamos o método de campo de fase
xunto con ecuacións de reacción-difusión para o consumo de nutriente e a produción
de antíxeno prostático específico. Empregamos este modelo para realizar as primeiras
simulacións personalizadas a escala tisular do crecemento de cancro de próstata sobre
a anatomía do órgano extraída de imaxes médicas. Os nosos resultados amosan unha
progresión tumoral similar á observada na práctica clínica.
Utilizamos a análise isoxeométrica para resolver a non-linealidade do noso sistema
de ecuacións, así como a complexa anatomía da próstata e as intricadas morfoloxías
tumorais. Adicionalmente, propoñemos o uso de adaptatividade dinámica de malla para
acelerar os cálculos, racionalizar os recursos computacionais e facilitar a simulación nun
tempo clinicamente relevante. Presentamos un conxunto de algoritmos eficientes para
introducir o refinamento e o engrosado locais tipo h en análise isoxeométrica. Os nosos
métodos están baseados na proxección de Bézier, que estendemos aos espazos de splines
xerárquicas. Tamén introducimos un parámetro de balance para controlar a superposición
de funcións de base a través dos niveis da xerarquía, o cal conduce a un condicionamento
numérico mellorado. As nosas simulacións de crecemento de cancro amosan unha notable
precisión con moi poucos graos de liberdade en comparación coa malla uniforme que a
mesma simulación requiriría.
Finalmente, estudamos a interacción entre o cancro de próstata e a hiperplasia benigna
de próstata, outra patoloxía prostática común que fai crecer ao órgano gradualmente. En
particular, investigamos por que os tumores que se orixinan en próstatas máis grandes
presentan características patolóxicas favorables. Realizamos un estudo de simulación
cualitativo estendendo o noso modelo matemático de crecemento de cancro de próstata
para incluír as ecuacións de equilibrio mecánico e os termos de acoplamento entre estas e
a dinámica tumoral. Asumimos que a deformación da próstata é un fenómeno cuasiestático
e modelamos o tecido prostático como un material elástico lineal, heteroxéneo e
isotrópico. Este modelo é calibrado estudando a deformación causada por cada enfermidade
independientemente. As nosas simulacións amosan que un historial de hiperplasia
benigna de próstata crea campos de tensión mecánica na próstata que obstaculizan o
crecemento do cancro de próstata e limitan a súa invasividade
The Data Big Bang and the Expanding Digital Universe: High-Dimensional, Complex and Massive Data Sets in an Inflationary Epoch
Recent and forthcoming advances in instrumentation, and giant new surveys,
are creating astronomical data sets that are not amenable to the methods of
analysis familiar to astronomers. Traditional methods are often inadequate not
merely because of the size in bytes of the data sets, but also because of the
complexity of modern data sets. Mathematical limitations of familiar algorithms
and techniques in dealing with such data sets create a critical need for new
paradigms for the representation, analysis and scientific visualization (as
opposed to illustrative visualization) of heterogeneous, multiresolution data
across application domains. Some of the problems presented by the new data sets
have been addressed by other disciplines such as applied mathematics,
statistics and machine learning and have been utilized by other sciences such
as space-based geosciences. Unfortunately, valuable results pertaining to these
problems are mostly to be found only in publications outside of astronomy. Here
we offer brief overviews of a number of concepts, techniques and developments,
some "old" and some new. These are generally unknown to most of the
astronomical community, but are vital to the analysis and visualization of
complex datasets and images. In order for astronomers to take advantage of the
richness and complexity of the new era of data, and to be able to identify,
adopt, and apply new solutions, the astronomical community needs a certain
degree of awareness and understanding of the new concepts. One of the goals of
this paper is to help bridge the gap between applied mathematics, artificial
intelligence and computer science on the one side and astronomy on the other.Comment: 24 pages, 8 Figures, 1 Table. Accepted for publication: "Advances in
Astronomy, special issue "Robotic Astronomy
Recommended from our members
Computational Engineering
This Workshop treated a variety of finite element methods and applications in computational engineering and expanded their mathematical foundation in engineering analysis. Among the 53 participants were mathematicians and engineers with focus on mixed and nonstandard finite element schemes and their applications
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