Dynamical properties of a dissipative discontinuous map: A scaling investigation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Transition matrices characterizing a certain totally discontinuous map of the interval

We study a totally discontinuous interval map defined in [0,1] which is associated to a deformation of the shift map on two symbols 0−1. We define a sequence of transition matrices which characterizes the effect of the interval map on a family of partitions of the interval [0,1]. Recursive algorithms that build the sequence of matrices and their left and right eigenvectors are deduced. Moreover, we compute the Artin zeta function for the interval map.

Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing

Existence of multiple attractors and the nature of bifurcations in a discontinuous logistic map

We present the analytical investigations on a logistic map with a discontinuity at the centre. An explanation for the bifurcation phenomenon in discontinuous systems is presented. We establish that whenever the elements of an n-cycle (n > 1) approach the discontinuities of the nth iterate of the map, a bifurcation other than the usual period-doubling one takes place. The periods of the cycles decrease in an arithmetic progression, as the control parameter is varied. The system also shows the presence of multiple attractors. Our results are verified by numerical experiments as well.

A posteriori error estimates of discontinuous Galerkin methods for the Signorini problem

A reliable and efficient a posteriori error estimator is derived for a class of discontinuous Galerkin (DG) methods for the Signorini problem. A common property shared by many DG methods leads to a unified error analysis with the help of a constraint preserving enriching map. The error estimator of DG methods is comparable with the error estimator of the conforming methods. Numerical experiments illustrate the performance of the error estimator. (C) 2015 Elsevier B.V. All rights reserved.

Novel method to construct a quality map for phase unwrapping based on modulation and the phase gradient

A novel method to construct a quality map, called modulation-phase-gradient variance (MPGV), is proposed, based on modulation and the phase gradient. The MPGV map is successfully applied to two phase-unwrapping algorithms - the improved weighted least square and the quality-guided unwrapping algorithm. Both simulated and experimental data testify to the validity of our proposed quality map. Moreover, the unwrapped-phase results show that the new quality map can have higher reliability than the conventional phase-derivative variance quality map in helping to unwrap noisy, low-modulation, and/or discontinuous phase maps. (c) 2006 Society of Photo-Optical Instrumentation Engineers.

Novel method to construct a quality map for phase unwrapping based on modulation and the phase gradient

A novel method to construct a quality map, called modulation-phase-gradient variance (MPGV), is proposed, based on modulation and the phase gradient. The MPGV map is successfully applied to two phase-unwrapping algorithms - the improved weighted least square and the quality-guided unwrapping algorithm. Both simulated and experimental data testify to the validity of our proposed quality map. Moreover, the unwrapped-phase results show that the new quality map can have higher reliability than the conventional phase-derivative variance quality map in helping to unwrap noisy, low-modulation, and/or discontinuous phase maps. (c) 2006 Society of Photo-Optical Instrumentation Engineers.

Discontinuous epitopes of hepatitis B surface antigen derived from a filamentous phage peptide library.

The structure of the small hepatitis B virus surface antigen (HBsAg) was investigated by epitope mapping of four anti-HBsAg monoclonal antibodies (mAbs). Amino acid sequences of epitopes were derived from affinity-enrichment experiments (biopanning) using a filamentous phage peptide library. The library consists of 10(9) different clones bearing a 30-residue peptide fused to gene III. Sequence homologies between peptides obtained from panning the library against the antibodies and the native HBsAg sequence allowed for precise description of the binding regions. Three of four mAbs were found to bind to distinct discontinuous epitopes between amino acid residues 101 and 207 of HBsAg. The fourth mAb was demonstrated to bind to residues 121-124. The sequence data are supported by ELISA assays demonstrating the binding of the HBsAg-specific peptides on filamentous phage to mAbs. The sequence data were used to map the surface of HBsAg and to derive a topological model for the alpha-carbon trace of the 101-207 region of HBsAg. The approach should be useful for other proteins for which the crystal structure is not available but a representative set of mAbs can be obtained.

Combining ganglion cell topology and data of patients with glaucoma to determine a structure-function map

PURPOSE: To introduce techniques for deriving a map that relates visual field locations to optic nerve head (ONH) sectors and to use the techniques to derive a map relating Medmont perimetric data to data from the Heidelberg Retinal Tomograph. METHODS: Spearman correlation coefficients were calculated relating each visual field location (Medmont M700) to rim area and volume measures for 10 degrees ONH sectors (HRT III software) for 57 participants: 34 with glaucoma, 18 with suspected glaucoma, and 5 with ocular hypertension. Correlations were constrained to be anatomically plausible with a computational model of the axon growth of retinal ganglion cells (Algorithm GROW). GROW generated a map relating field locations to sectors of the ONH. The sector with the maximum statistically significant (P < 0.05) correlation coefficient within 40 degrees of the angle predicted by GROW for each location was computed. Before correlation, both functional and structural data were normalized by either normative data or the fellow eye in each participant. RESULTS: The model of axon growth produced a 24-2 map that is qualitatively similar to existing maps derived from empiric data. When GROW was used in conjunction with normative data, 31% of field locations exhibited a statistically significant relationship. This significance increased to 67% (z-test, z = 4.84; P < 0.001) when both field and rim area data were normalized with the fellow eye. CONCLUSIONS: A computational model of axon growth and normalizing data by the fellow eye can assist in constructing an anatomically plausible map connecting visual field data and sectoral ONH data.

Correlating eye gaze direction, depth and vehicle information on an interactive map for driver training

The over represented number of novice drivers involved in crashes is alarming. Driver training is one of the interventions aimed at mitigating the number of crashes that involve young drivers. Experienced drivers have better hazard perception ability compared to inexperienced drivers. Eye gaze patterns have been found to be an indicator of the driver's competency level. The aim of this paper is to develop an in-vehicle system which correlates information about the driver's gaze and vehicle dynamics, which is then used to assist driver trainers in assessing driving competency. This system allows visualization of the complete driving manoeuvre data on interactive maps. It uses an eye tracker and perspective projection algorithms to compute the depth of gaze and plots it on Google maps. This interactive map also features the trajectory of the vehicle and turn indicator usage. This system allows efficient and user friendly analysis of the driving task. It can be used by driver trainers and trainees to understand objectively the risks encountered during driving manoeuvres. This paper presents a prototype that plots the driver's eye gaze depth and direction on an interactive map along with the vehicle dynamics information. This prototype will be used in future to study the difference in gaze patterns in novice and experienced drivers prior to a certain manoeuvre.

The Brisbane media map : participatory design and authentic learning to link students and industry

The Brisbane Media Map is both an online resource and a tertiary-level authentic learning project. The Brisbane Media Map is an online database which provides a detailed overview of about 600 media industry organisations in Brisbane, Australia. In addition to providing contact details and synopses for each organisation’s profile, the Brisbane Media Map also includes supplementary information on current issues, trends, and individuals in the media and communication industry sectors. This resource is produced and updated annually by final-year undergraduate Media and Communication students. This article introduces the Brisbane Media Map, its functionality and systems design approach, as well as its alignment with key learning infrastructures. It examines authentic learning as the pedagogical framework underpinning the ongoing development work of the resource and highlights some synergies of this framework with participatory design principles. The Brisbane Media Map is a useful example of an authentic learning approach that successfully engages students of non-traditional and non-design areas of study in human-computer interaction, usability, and participatory design activities.

A distributed knowledge management infrastructure based on a Topic Map grid

Modern enterprise knowledge management systems typically require distributed approaches and the integration of numerous heterogeneous sources of information. A powerful foundation for these tasks can be Topic Maps, which not only provide a semantic net-like knowledge representation means and the possibility to use ontologies for modelling knowledge structures, but also offer concepts to link these knowledge structures with unstructured data stored in files, external documents etc. In this paper, we present the architecture and prototypical implementation of a Topic Map application infrastructure, the ‘Topic Grid’, which enables transparent, node-spanning access to different Topic Maps distributed in a network.