Influence of memory in deterministic walks in random media: Analytical calculation within a mean-field approximation

Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2, as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N >> 1) is just < n >=e=2.72... while in the mu=2 case, the mean number < n > of visited points grows proportionally to N(1/2). Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones.

Texture analysis using graphs generated by deterministic partially self-avoiding walks

Texture is one of the most important visual attributes for image analysis. It has been widely used in image analysis and pattern recognition. A partially self-avoiding deterministic walk has recently been proposed as an approach for texture analysis with promising results. This approach uses walkers (called tourists) to exploit the gray scale image contexts in several levels. Here, we present an approach to generate graphs out of the trajectories produced by the tourist walks. The generated graphs embody important characteristics related to tourist transitivity in the image. Computed from these graphs, the statistical position (degree mean) and dispersion (entropy of two vertices with the same degree) measures are used as texture descriptors. A comparison with traditional texture analysis methods is performed to illustrate the high performance of this novel approach. (C) 2011 Elsevier Ltd. All rights reserved.

Texture analysis based on maximum contrast walker

Recently, the deterministic tourist walk has emerged as a novel approach for texture analysis. This method employs a traveler visiting image pixels using a deterministic walk rule. Resulting trajectories provide clues about pixel interaction in the image that can be used for image classification and identification tasks. This paper proposes a new walk rule for the tourist which is based on contrast direction of a neighborhood. The yielded results using this approach are comparable with those from traditional texture analysis methods in the classification of a set of Brodatz textures and their rotated versions, thus confirming the potential of the method as a feasible texture analysis methodology. (C) 2010 Elsevier B.V. All rights reserved.

Anomalous diffusion in non-Markovian walks having amnestically induced persistence

We report numerically and analytically estimated values for the Hurst exponent for a recently proposed non-Markovian walk characterized by amnestically induced persistence. These results are consistent with earlier studies showing that log-periodic oscillations arise only for large memory losses of the recent past. We also report numerical estimates of the Hurst exponent for non-Markovian walks with diluted memory. Finally, we study walks with a fractal memory of the past for a Thue-Morse and Fibonacci memory patterns. These results are interpreted and discussed in the context of the necessary and sufficient conditions for the central limit theorem to hold.

Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems

Consider N sites randomly and uniformly distributed in a d-dimensional hypercube. A walker explores this disordered medium going to the nearest site, which has not been visited in the last mu (memory) steps. The walker trajectory is composed of a transient part and a periodic part (cycle). For one-dimensional systems, travelers can or cannot explore all available space, giving rise to a crossover between localized and extended regimes at the critical memory mu(1) = log(2) N. The deterministic rule can be softened to consider more realistic situations with the inclusion of a stochastic parameter T (temperature). In this case, the walker movement is driven by a probability density function parameterized by T and a cost function. The cost function increases as the distance between two sites and favors hops to closer sites. As the temperature increases, the walker can escape from cycles that are reminiscent of the deterministic nature and extend the exploration. Here, we report an analytical model and numerical studies of the influence of the temperature and the critical memory in the exploration of one-dimensional disordered systems.

Sudden onset of log-periodicity and superdiffusion in non-Markovian random walks with amnestically induced persistence: exact results

Random walks can undergo transitions from normal diffusion to anomalous diffusion as some relevant parameter varies, for instance the L,vy index in L,vy flights. Here we derive the Fokker-Planck equation for a two-parameter family of non-Markovian random walks with amnestically induced persistence. We investigate two distinct transitions: one order parameter quantifies log-periodicity and discrete scale invariance in the first moment of the propagator, whereas the second order parameter, known as the Hurst exponent, describes the growth of the second moment. We report numerical and analytical results for six critical exponents, which together completely characterize the properties of the transitions. We find that the critical exponents related to the diffusion-superdiffusion transition are identical in the positive feedback and negative feedback branches of the critical line, even though the former leads to classical superdiffusion whereas the latter gives rise to log-periodic superdiffusion.

Glow worms as a tourist attraction in Springbrook National Park: Visitor attitudes and economic issues

nsect-based tourism mainly caters to a niche market, but its popularity has been growing in recent years. Despite its popularity this form of tourism has remained under-researched and in a sense its contribution to the tourism industry has gone mostly unnoticed. This paper reports the results of a study undertaken on one form of popular insect-based tourism, namely glow worms. The study was undertaken in Springbrook National Park (Natural Bridge section) southeast Queensland, which has one of the largest glow worm colonies in Australia that attracts thousands of visitors each year. A study of this form of tourism is important and useful for several reasons. It is important to understand this hitherto under-studied tourism activity to determine the type of visitors, their socio-economic attributes, economic benefits to the local economy, visitors’ knowledge of glow worms, education imparted, visitor satisfaction of glow worm viewing and visitor attitudes for the introduction of a user fee system to view glow worms. An understanding of these issues could not only help to better manage this valuable biological resource, but can be used to develop the industry to cater to a growing number of visitors. Tourism in glow worms can potentially be used not only to educate the public on the threats affecting glow worms and their colonies, but could also be used to conserve them. Lessons learnt from glow worms as an attraction to Springbrook National Park can be used to better manage and further develop other existing and new glow worm sites in Australia and elsewhere for tourism. Furthermore, it could provide some guidance for the management and development of other forms of current insect-based tourism activities (eg. butterflies) and develop new tourism ventures based on species such as stick insects and jewel beetles for which Australia is well known (Reader’s Digest, 1997)

Visitor profiles and environmental attributes, especially of birds, attracting visitors to Lamington National Park: Tourist attitudes and economic issues

Uses a sample of 622 day and overnight visitors to the O’ Reilly’s/Green Mountains site of Lamington National Park, Queensland, Australia, to identify their socio-economic and other pertinent characteristics and the main reasons and attributes that attract them to the site. Particular attention is given to birds and their attributes as attractions. The primary economic injection accruing locally as a result of visits is examined and the difference that the presence of birds makes to local expenditure by visitors is explored. The extent of support for and objection to the introduction of a fee for entering Lamington National Park is estimated. The many suggestions received from visitors for environmental improvements at this site are discussed. It is suggested that unless a way can be found to regulate the number of visitors to this site and obtain extra funds to finance improvements at this site, the magnitude of many of these problems will grow. This will necessitate a fresh look at the desirability or otherwise for charging entry fees to Lamington National Park.

The effects of place of residence on tourist motivations: a revised case of the Urban Quadrangle of Minho

This study seeks to capture the underlying reasons for the travel decisions of residents of the Urban Quadrangle of Minho (composed of the municipalities of Barcelos, Braga, Guimarães, and Vila Nova de Famalicão). The aim of the research is three-fold. Firstly, the study identifies the push and pull motivational factors of residents of the Urban Quadrangle of Minho. Secondly, the study examines whether there are differences between the tourist motivations of residents of the four different municipalities of the Urban Quadrangle. Finally, the study investigates if there are any differences in the motivations of those who choose national and international destinations. The methodology comprises quantitative research based on questionnaires administered in 2012 to residents of the Urban Quadrangle of Minho. A principal component factor analysis is employed to identify six push and seven pull factors. The comparison of the mean scores of these factors across municipalities and across residents that choose national and international destinations reveals that the most valued and least valued factors are common to all four municipalities and both groups of residents (that choose national and international destinations).

The effects of place of residence on tourist motivations: the case of Urban Quadrangle of Minho

The aim of this preliminary study is three-fold. Firstly, the study identifies the push and pull motivational factors of residents of the Urban Quadrangle of Minho. Secondly, the study examines whether there are differences between the tourist motivations of residents of the four different municipalities. Finally, the study investigates if there are any differences in the motivations of those who choose national and international destinations.

Tourist motivation of the residents of the Urban Quadrilátero of Minho: a gender analysis

Women are increasingly active in the participation and consumption of tourism, representing a strong and unique market segment. Knowledge of the needs and preferences of female tourists represents a key success factor in the tourism industry. This preliminary study seeks to capture the underlying reasons for the travel decisions of the residents of the Urban Quadrilátero of Minho, investigating their tourist motivations from a gendered perspective. Insight on tourism motivation may be an important policy tool for tourism planners and managers in the development of products and marketing strategies. The empirical analysis is undertaken based on questionnaires administered in 2012 to residents of the Urban Quadrilátero of Minho. Preliminary results do not reveal significant gender differences in the importance that the local residents place on various tourism motivation factors.