Continuous iteration of dynamical maps

A precise meaning is given to the notion of continuous iteration of a mapping. Usual discrete iterations are extended into a dynamical flow which is a homotopy of them all. The continuous iterate reveals that a dynamic map is formed by independent component modes evolving without interference with each other. An application to turbulent flow suggests that the velocity field assumes nonseparable values. © 1998 American Institute of Physics.

Absolutely Continuous Spectrum for Parabolic Flows/Maps

This work is devoted to creating an abstract framework for the study of certain spectral properties of parabolic systems. Specifically, we determine under which general conditions to expect the presence of absolutely continuous spectral measures. We use these general conditions to derive results for spectral properties of time-changes of unipotent flows on homogeneous spaces of semisimple groups regarding absolutely continuous spectrum as well as maximal spectral type; the time-changes of the horocycle flow are special cases of this general category of flows. In addition we use the general conditions to derive spectral results for twisted horocycle flows and to rederive spectral results for skew products over translations and Furstenberg transformations.

Experience mapping : producing spatially continuous environment representations using RatSLAM

RatSLAM is a system for vision-based Simultaneous Localisation and Mapping (SLAM) inspired by models of the rodent hippocampus. The system can produce stable representations of large complex environments during robot experiments in both indoor and outdoor environments. These representations are both topological and metric in nature, and can involve multiple representations of the same place as well as discontinuities. In this paper we describe a new technique known as experience mapping that can be used online with the RatSLAM system to produce world representations known as experience maps. These maps group together multiple place representations and are spatially continuous. A number of experiments have been conducted in simulation and a real world office environment. These experiments demonstrate the high degree to which experience maps are representative of the spatial arrangement of the environment.

Career-path analysis using optimal matching and self-organizing maps

This paper is devoted to the analysis of career paths and employability. The state-of-the-art on this topic is rather poor in methodologies. Some authors propose distances well adapted to the data, but are limiting their analysis to hierarchical clustering. Other authors apply sophisticated methods, but only after paying the price of transforming the categorical data into continuous, via a factorial analysis. The latter approach has an important drawback since it makes a linear assumption on the data. We propose a new methodology, inspired from biology and adapted to career paths, combining optimal matching and self-organizing maps. A complete study on real-life data will illustrate our proposal.

Vision-only autonomous navigation using topometric maps

This paper presents a mapping and navigation system for a mobile robot, which uses vision as its sole sensor modality. The system enables the robot to navigate autonomously, plan paths and avoid obstacles using a vision based topometric map of its environment. The map consists of a globally-consistent pose-graph with a local 3D point cloud attached to each of its nodes. These point clouds are used for direction independent loop closure and to dynamically generate 2D metric maps for locally optimal path planning. Using this locally semi-continuous metric space, the robot performs shortest path planning instead of following the nodes of the graph --- as is done with most other vision-only navigation approaches. The system exploits the local accuracy of visual odometry in creating local metric maps, and uses pose graph SLAM, visual appearance-based place recognition and point clouds registration to create the topometric map. The ability of the framework to sustain vision-only navigation is validated experimentally, and the system is provided as open-source software.

Dynamic recrystallisation during hot working of Zr-2 center dot 5Nb: Characterisation using processing maps

The characteristics of the hot deformation of Zr-2.5Nb (wt-%) in the temperature range 650-950 degrees C and in the strain rate range 0.001-100 s(-1) have been studied using hot compression testing. Two different preform microstructures: equiaxed (alpha + beta) and beta transformed have been investigated. For this study, the approach of processing maps has been adopted and their interpretation carried out using the dynamic materials model. The efficiency of power dissipation given by [2m/(m + 1)], where m is the strain rate sensitivity, is plotted as a function of temperature and strain rate to obtain a processing map. A domain of dynamic recrystallisation has been identified in the maps of equiaxed (alpha + beta) and beta transformed preforms. In the case of equiaxed (alpha + beta), the stress-strain curves are steady state and the dynamic recrystallisation domain in the map occurs with a peak efficiency of 45% at 850 degrees C and 0.001 s(-1). On the other hand the beta transformed preform exhibits stress-strain curves with continuous flow softening. The corresponding processing map shows a domain of dynamic recrystallisation occurring by the shearing of alpha platelets followed by globularisation with a peak efficiency of 54% at 750 degrees C and 0.001 s(-1). The characteristics of dynamic recrystallisation are analysed on the basis of a simple model which considers the rates of nucleation and growth of recrystallised gains. Calculations show that these two rates are nearly equal and that the nucleation of dynamic recrystallisation is essentially controlled by mechanical recovery involving the cross-slip of screw dislocations. Analysis of flow instabilities using a continuum criterion revealed that Zi-2.5Nb exhibits flow localisation at temperatures lower than 700 degrees C and strain rates higher than 1 s(-1).

Characterization of hot deformation behaviour of Zr---2.5Nb---0.5Cu using processing maps

The characteristics of hot deformation of beta-quenched Zr-2.5Nb-0.5Cu in the temperature range 650-1050 degrees C and in the strain rate range 0.001-100 s(-1) have been studied using hot compression testing. For this study, the approach of processing maps has been adopted and their interpretation done using the Dynamic Materials Model. The efficiency of power dissipation given by [2m/(m + 1)], where m is strain rate sensitivity, is plotted as a function of temperature and strain rate to obtain a processing map. The processing map for Zr-2.5Nb-0.5Cu within (alpha + beta) phase field showed a domain of dynamic recrystallization, occurring by shearing of alpha-platelets followed by spheroidization, with a peak efficiency of 48% at 750 degrees C and 0.001 s(-1). The stress-strain curves in this domain had features of continuous flow softening and all these are similar to that in Zr-2.5Nb alloy. In the beta-phase field, a second domain with a peak efficiency of 47% occurred at 1050 degrees C and 0.001 s(-1) and this domain is correlated with the superplasticity of beta-phase. The beta-deformation characteristics of this alloy are similar to that observed in pure beta-zirconium with large grain size. Analysis of flow instabilities using a continuum criterion revealed that the Zr-2.5Nb-0.5Cu exhibits flow localization at temperatures higher than 800 degrees C and strain rates higher than about 30 s(-1) and that the addition of copper to Zr-2.5Nb reduces its susceptibility to flow instability, particularly in the (alpha + beta) phase field.

Fuzzy ARTMAP: A Neural Network Architecture for Incremental Supervised Learning of Analog Multidimensional Maps

A new neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors. The architecture, called Fuzzy ARTMAP, achieves a synthesis of fuzzy logic and Adaptive Resonance Theory (ART) neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and ART category choice, resonance, and learning. Fuzzy ARTMAP also realizes a new Minimax Learning Rule that conjointly minimizes predictive error and maximizes code compression, or generalization. This is achieved by a match tracking process that increases the ART vigilance parameter by the minimum amount needed to correct a predictive error. As a result, the system automatically learns a minimal number of recognition categories, or "hidden units", to met accuracy criteria. Category proliferation is prevented by normalizing input vectors at a preprocessing stage. A normalization procedure called complement coding leads to a symmetric theory in which the MIN operator (Λ) and the MAX operator (v) of fuzzy logic play complementary roles. Complement coding uses on-cells and off-cells to represent the input pattern, and preserves individual feature amplitudes while normalizing the total on-cell/off-cell vector. Learning is stable because all adaptive weights can only decrease in time. Decreasing weights correspond to increasing sizes of category "boxes". Smaller vigilance values lead to larger category boxes. Improved prediction is achieved by training the system several times using different orderings of the input set. This voting strategy can also be used to assign probability estimates to competing predictions given small, noisy, or incomplete training sets. Four classes of simulations illustrate Fuzzy ARTMAP performance as compared to benchmark back propagation and genetic algorithm systems. These simulations include (i) finding points inside vs. outside a circle; (ii) learning to tell two spirals apart; (iii) incremental approximation of a piecewise continuous function; and (iv) a letter recognition database. The Fuzzy ARTMAP system is also compared to Salzberg's NGE system and to Simpson's FMMC system.

Ecological Investigations with the Continuous Plankton Recorder: The Phytoplankton in the Southern North Sea. 1932-37.

1. The changes in the composition and distribution of the plankton of the southern North Sea have been investigated month by month, from June 1932 to December 1937; the present report deals with the phytoplankton. The survey was carried out by the Continuous Plankton Recorder, towed at a standard depth of 10 metres, by ships on regular steamship lines across the North Sea from Hull towards the Skagerrak, to Bremen and to Rotterdam, and later between London and Esbjerg. 2. The material and methods are described, together with a discussion on the validity of this type of survey and some comparison of its results with those obtained by other methods (pp. 76-86). 3. Particular attention has been paid to Rhizosolenia styliformis (pp. 92- 107), Biddulphia sinensis (pp. 108-115), Phaeocystis (pp. 149-153), and the Dinoflagellates (pp. 134-149); of these the first three are known to be of particular importance in relation to the herring fisheries. More generalised data are available for the principal diatoms other than R. styliformis and B. sinensis (pp. 116-134). 4. The main part of the work is an ecological study of the phytoplankton changes in time and space over the 5½ years. Each year is marked by some distinct variations in the abundance and the times of increase, maximum numbers and decline as recorded in the different forms. These variations in the annual cycles are compared on the different lines by a series of graphs arranged against a time scale of months, a set for each year being placed side by side (Plates I-XXI). More detailed studies by more frequent records were made in the autumns of 1934, 1935, 1936 and 1937 (cf. Figs. 3 and 4). The changes in spatial distribution are shown by a series of monthly maps arranged in a similar manner for each year (Plates XXII-LXIV). These intensive studies of the changes in time and space are also intended to form the basis for correlations with other features in the general ecology of the area (e. g. the zooplankton, hydrology, meteorology and fisheries) to be made in later publications. 5. Whilst each form has shown its own peculiar features, a trend towards a general increase in the phytoplankton as a whole has been observed during the period, although the years 1934 and 1936 have in some respects shown deviations and regressive features, and not all organisms have revealed the same trend. The possible relation of this gradual trend to other events observed in recent years in these and neighbouring waters is discussed (pp. 162-167). 6. The application of these results to the study of patchiness (pp. 154-158), inter-relationships in the plankton (pp. 159-160) and to water movements (pp. 160-162) is briefly discussed.

Analyzing laser plasma interferograms with a continuous wavelet transform ridge extraction technique: the method

Laser plasma interferograms are currently analyzed by extraction of the phase-shift map with fast Fourier transform (FFT) techniques [Appl. Opt. 18, 3101 (1985)]. This methodology works well when interferograms are only marginally affected by noise and reduction of fringe visibility, but it can fail to produce accurate phase-shift maps when low-quality images are dealt with. We present a novel procedure for a phase-shift map computation that makes extensive use of the ridge extraction in the continuous wavelet transform (CWT) framework. The CWT tool is flexible because of the wide adaptability of the analyzing basis, and it can be accurate because of the intrinsic noise reduction in the ridge extraction. A comparative analysis of the accuracy performances of them new tool and the FFT-based one shows that the CWT-based tool produces phase maps considerably less noisy and that it can better resolve local inhomogeneties. (C) 2001 Optical Society of America.

Conservation strategy maps: a tool to facilitate biodiversity action planning illustrated using the heath fritillary butterfly

1. The UK Biodiversity Action Plan (UKBAP) identifies invertebrate species in danger of national extinction. For many of these species, targets for recovery specify the number of populations that should exist by a specific future date but offer no procedure to plan strategically to achieve the target for any species. 2. Here we describe techniques based upon geographic information systems (GIS) that produce conservation strategy maps (CSM) to assist with achieving recovery targets based on all available and relevant information. 3. The heath fritillary Mellicta athalia is a UKBAP species used here to illustrate the use of CSM. A phase 1 habitat survey was used to identify habitat polygons across the county of Kent, UK. These were systematically filtered using relevant habitat, botanical and autecological data to identify seven types of polygon, including those with extant colonies or in the vicinity of extant colonies, areas managed for conservation but without colonies, and polygons that had the appropriate habitat structure and may therefore be suitable for reintroduction. 4. Five clusters of polygons of interest were found across the study area. The CSM of two of them are illustrated here: the Blean Wood complex, which contains the existing colonies of heath fritillary in Kent, and the Orlestone Forest complex, which offers opportunities for reintroduction. 5. Synthesis and applications. Although the CSM concept is illustrated here for the UK, we suggest that CSM could be part of species conservation programmes throughout the world. CSM are dynamic and should be stored in electronic format, preferably on the world-wide web, so that they can be easily viewed and updated. CSM can be used to illustrate opportunities and to develop strategies with scientists and non-scientists, enabling the engagement of all communities in a conservation programme. CSM for different years can be presented to illustrate the progress of a plan or to provide continuous feedback on how a field scenario develops.

Conservation strategy maps: a tool to facilitate biodiversity action planning illustrated using the heath fritillary butterfly

1. The UK Biodiversity Action Plan (UKBAP) identifies invertebrate species in danger of national extinction. For many of these species, targets for recovery specify the number of populations that should exist by a specific future date but offer no procedure to plan strategically to achieve the target for any species. 2. Here we describe techniques based upon geographic information systems (GIS) that produce conservation strategy maps (CSM) to assist with achieving recovery targets based on all available and relevant information. 3. The heath fritillary Mellicta athalia is a UKBAP species used here to illustrate the use of CSM. A phase 1 habitat survey was used to identify habitat polygons across the county of Kent, UK. These were systematically filtered using relevant habitat, botanical and autecological data to identify seven types of polygon, including those with extant colonies or in the vicinity of extant colonies, areas managed for conservation but without colonies, and polygons that had the appropriate habitat structure and may therefore be suitable for reintroduction. 4. Five clusters of polygons of interest were found across the study area. The CSM of two of them are illustrated here: the Blean Wood complex, which contains the existing colonies of heath fritillary in Kent, and the Orlestone Forest complex, which offers opportunities for reintroduction. 5. Synthesis and applications. Although the CSM concept is illustrated here for the UK, we suggest that CSM could be part of species conservation programmes throughout the world. CSM are dynamic and should be stored in electronic format, preferably on the world-wide web, so that they can be easily viewed and updated. CSM can be used to illustrate opportunities and to develop strategies with scientists and non-scientists, enabling the engagement of all communities in a conservation programme. CSM for different years can be presented to illustrate the progress of a plan or to provide continuous feedback on how a field scenario develops.

Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Df `` (f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d >= 2 and critical point c of order l > 1. As an application we prove that f exhibits exponential decay of geometry if and only if l <= 2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet-Eckmann condition. (C) 2009 Elsevier Masson SAS. All rights reserved.

Fibonacci bimodal maps

We introduce the Fibonacci bimodal maps on the interval and show that their two turning points are both in the same minimal invariant Cantor set. Two of these maps with the same orientation have the same kneading sequences and, among bimodal maps without central returns, they exhibit turning points with the strongest recurrence as possible.

Henon-like maps with arbitrary stationary combinatorics

We extend the renormalization operator introduced in [A. de Carvalho, M. Martens and M. Lyubich. Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669] from period-doubling Henon-like maps to Henon-like maps with arbitrary stationary combinatorics. We show that the renonnalization picture also holds in this case if the maps are taken to be strongly dissipative. We study infinitely renormalizable maps F and show that they have an invariant Cantor set O on which F acts like a p-adic adding machine for some p > 1. We then show, as for the period-doubling case in the work of de Carvalho, Martens and Lyubich [Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669], that the sequence of renormalizations has a universal form, but that the invariant Cantor set O is non-rigid. We also show that O cannot possess a continuous invariant line field.