1,533 research outputs found
Non-perturbative features of driven scattering systems
We investigate the scattering properties of one-dimensional, periodically and
non-periodically forced oscillators. The pattern of singularities of the
scattering function, in the periodic case, shows a characteristic hierarchical
structure where the number Nc of zeros of the solutions plays the role of an
order parameter marking the level of the observed self-similar structure. The
behavior is understood both in terms of the return map and of the intersections
pattern of the invariant manifolds of the outermost fixed points. In the
non-periodic case the scattering function does not provide a complete
development of the hierarchical structure. The singularities pattern of the
outgoing energy as a function of the driver amplitude is connected to the
arrangement of gaps in the fundamental regions. The survival probability
distribution of temporarily bound orbits is shown to decay asymptotically as a
power law. The "stickiness" of regular regions of phase space, given by KAM
surfaces and remnant of KAM curves, is responsible for this observation
Complex Networks and Symmetry I: A Review
In this review we establish various connections between complex networks and
symmetry. While special types of symmetries (e.g., automorphisms) are studied
in detail within discrete mathematics for particular classes of deterministic
graphs, the analysis of more general symmetries in real complex networks is far
less developed. We argue that real networks, as any entity characterized by
imperfections or errors, necessarily require a stochastic notion of invariance.
We therefore propose a definition of stochastic symmetry based on graph
ensembles and use it to review the main results of network theory from an
unusual perspective. The results discussed here and in a companion paper show
that stochastic symmetry highlights the most informative topological properties
of real networks, even in noisy situations unaccessible to exact techniques.Comment: Final accepted versio
Artificial Intelligence in geospatial analysis: applications of self-organizing maps in the context of geographic information science.
A thesis submitted in partial fulfillment of the requirements for the degree of Doctor in Information Management, specialization in Geographic Information SystemsThe size and dimensionality of available geospatial repositories increases every day, placing additional pressure on existing analysis tools, as they are expected to extract more knowledge from these databases. Most of these tools were created in a data poor environment and thus rarely address concerns of efficiency, dimensionality and automatic exploration. In addition, traditional statistical techniques present several assumptions that are not realistic in the geospatial data domain. An example of this is the statistical independence between observations required by most classical statistics methods, which conflicts with the well-known spatial dependence that exists in geospatial data.
Artificial intelligence and data mining methods constitute an alternative to explore and extract knowledge from geospatial data, which is less assumption dependent. In this thesis, we study the possible adaptation of existing general-purpose data mining tools to geospatial data analysis. The characteristics of geospatial datasets seems to be similar in many ways with other aspatial datasets for which several data mining tools have been used with success in the detection of patterns and relations. It seems, however that GIS-minded analysis and objectives require more than the results provided by these general tools and adaptations to meet the geographical information scientist‟s requirements are needed. Thus, we propose several geospatial applications based on a well-known data mining method, the self-organizing map (SOM), and analyse the adaptations required in each application to fulfil those objectives and needs. Three main fields of GIScience are covered in this thesis: cartographic representation; spatial clustering and knowledge discovery; and location optimization.(...
Chaotic and fractal properties of deterministic diffusion-reaction processes
We study the consequences of deterministic chaos for diffusion-controlled
reaction. As an example, we analyze a diffusive-reactive deterministic
multibaker and a parameter-dependent variation of it. We construct the
diffusive and the reactive modes of the models as eigenstates of the
Frobenius-Perron operator. The associated eigenvalues provide the dispersion
relations of diffusion and reaction and, hence, they determine the reaction
rate. For the simplest model we show explicitly that the reaction rate behaves
as phenomenologically expected for one-dimensional diffusion-controlled
reaction. Under parametric variation, we find that both the diffusion
coefficient and the reaction rate have fractal-like dependences on the system
parameter.Comment: 14 pages (revtex), 12 figures (postscript), to appear in CHAO
A Comprehensive Overview of Computational Nuclei Segmentation Methods in Digital Pathology
In the cancer diagnosis pipeline, digital pathology plays an instrumental
role in the identification, staging, and grading of malignant areas on biopsy
tissue specimens. High resolution histology images are subject to high variance
in appearance, sourcing either from the acquisition devices or the H\&E
staining process. Nuclei segmentation is an important task, as it detects the
nuclei cells over background tissue and gives rise to the topology, size, and
count of nuclei which are determinant factors for cancer detection. Yet, it is
a fairly time consuming task for pathologists, with reportedly high
subjectivity. Computer Aided Diagnosis (CAD) tools empowered by modern
Artificial Intelligence (AI) models enable the automation of nuclei
segmentation. This can reduce the subjectivity in analysis and reading time.
This paper provides an extensive review, beginning from earlier works use
traditional image processing techniques and reaching up to modern approaches
following the Deep Learning (DL) paradigm. Our review also focuses on the weak
supervision aspect of the problem, motivated by the fact that annotated data is
scarce. At the end, the advantages of different models and types of supervision
are thoroughly discussed. Furthermore, we try to extrapolate and envision how
future research lines will potentially be, so as to minimize the need for
labeled data while maintaining high performance. Future methods should
emphasize efficient and explainable models with a transparent underlying
process so that physicians can trust their output.Comment: 47 pages, 27 figures, 9 table
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