Shannon Entropy Index Research Articles

Analysis and Modeling of Urban Land Cover Change in Setúbal and Sesimbra, Portugal

The expansion of cities entails the abandonment of forest and agricultural lands, and these lands’ conversion into urban areas, which results in substantial impacts on ecosystems. Monitoring these changes and planning urban development can be successfully achieved using multitemporal remotely sensed data, spatial metrics, and modeling. In this paper, urban land use change analysis and modeling was carried out for the Concelhos of Setúbal and Sesimbra in Portugal. An existing land cover map for the year 1990, together with two derived land cover maps from multispectral satellite images for the years 2000 and 2006, were utilized using an object-oriented classification approach. Classification accuracy assessment revealed satisfactory results that fulfilled minimum standard accuracy levels. Urban land use dynamics, in terms of both patterns and quantities, were studied using selected landscape metrics and the Shannon Entropy index. Results show that urban areas increased by 91.11% between 1990 and 2006. In contrast, the change was only 6.34% between 2000 and 2006. The entropy value was 0.73 for both municipalities in 1990, indicating a high rate of urban sprawl in the area. In 2006, this value, for both Sesimbra and Setúbal, reached almost 0.90. This is demonstrative of a tendency toward intensive urban sprawl. Urban land use change for the year 2020 was modeled using a Cellular Automata based approach. The predictive power of the model was successfully validated using Kappa variations. Projected land cover changes show a growing tendency in urban land use, which might threaten areas that are currently reserved for natural parks and agricultural lands.

Household Asset Portfolio Diversification: Evidence from the Household, Income and Labour Dynamics in Australia (Hilda) Survey

This paper examines the impact of demographic, socioeconomic and risk aversion factors on diversification in Australian household asset portfolios using Wave 6 of the HILDA Survey. Household assets are categorised as home and other property, superannuation, equity and cash investment, business assets, bank accounts, life insurance, trust funds and collectibles. The characteristics examined include family structure and composition, the source and level of income, age, gender and attitudes towards financial risk taking. The diversification measures comprise a naive index, a Hirschman-Herfindahl concentration index, a Shannon entropy index, absolute and relative benchmark indexes and a market asset share index. Tobit models are used to identify the source and magnitude of the factors associated with diversification. The results indicate that Australian household portfolios have very low levels of asset diversification and that the factors analysed exert a major impact. Importantly, the behaviour observed in household portfolios appears to bear little relation to the central predictions of classic portfolio theory.

Relations between Shannon entropy and genome order index in segmenting DNA sequences

Shannon entropy H and genome order index S are used in segmenting DNA sequences. Zhang [Phys. Rev. E 72, 041917 (2005)] found that the two schemes are equivalent when a DNA sequence is converted to a binary sequence of S (strong H bond) and W (weak H bond). They left the mathematical proof to mathematicians who are interested in this issue. In this paper, a possible mathematical explanation is given. Moreover, we find that Chargaff parity rule 2 is the necessary condition of the equivalence, and the equivalence disappears when a DNA sequence is regarded as a four-symbol sequence. At last, we propose that S-2(-H) may be related to species evolution.

Assessing forest fragmentation in northeastern region (NER) of India using landscape matrices

Abstract Northeastern region (NER) of India, one of the largest reserves of forests in India has so far been studied with a view to map the distribution of species or modeling the disturbance regimes and richness analysis. The present study focuses on the importance of regional level studies where the entire NER which is under the threat of forest fragmentation and degradation, is been assessed. In the present study, six historical data sets generated from remote sensing data (1972, 1982, 1987, 1989, 1993 and 1999) are used to assess forest cover loss, shape index and entropy to the degree of forest fragmentation over a multi-decadal period. The assessments have been carried out in the open (40–10% canopy density) and close (>40% canopy density) forest cover classes. The range of shape index and deviation from the actual mean in open forest and closed forest were computed separately. The patches among two categories were further analyzed based on patch area into six classes; ranging from 500 km2. This also indicates variability of the forest patches. It is noteworthy that patches of area within 1–10 km2 and 10–50 km2 have been severely fragmented. This loss could be attributed to the shifting cultivation practice where the patches of moderate size are cultivated by group of families. The present study could give an insight to the patch configuration and composition in terms of shape index and the Shannon's entropy index.

The Changing Structure of Ethnic Diversity and Segregation in England, 1991–2001

Using data from the 1991 and 2001 Censuses, I examine patterns of ethnic diversity and segregation in England's metropolitan regions. Diversity is measured using the Shannon entropy index and segregation is measured using the Theil index. Both indices can be decomposed into contributions due to region, district, and ward, which may indicate the processes responsible for patterns of ethnic diversity and segregation. The results show that ethnic diversity increased from 0.533 in 1991 to 0.731 in 2001. Between 1991 and 2001 the share of diversity contributed by Inner London and the West Midlands declined and the share contributed by Outer London and the Outer Metropolitan Area rose. Decomposition of total diversity shows that regional and district differences in ethnic diversity increased between 1991 and 2001 but differences between wards declined in importance. Within-ward diversity contributed more than 75% of total diversity at each census. Between 1991 and 2001 there was a slight increase in the overall level of segregation. Decomposition of total segregation into between-district and within-district components for each region shows that the contribution of within-district segregation to total segregation fell between 1991 and 2001. However, the contribution of between-district segregation to total segregation remained important and increased significantly in Inner London. Across the area investigated wards have on average become more ethnically diverse but there remain significant differences in diversity and segregation between regions and districts.

Comparing probability measures using possibility theory: A notion of relative peakedness

Deciding whether one probability distribution is more informative (in the sense of representing a less indeterminate situation) than another one is typically done using well-established information measures such as, e.g., the Shannon entropy or other dispersion indices. In contrast, the relative specificity of possibility distributions is evaluated by means of fuzzy set inclusion. In this paper, we propose a technique for comparing probability distributions from the point of view of their relative dispersion without resorting to a numerical index. A natural partial ordering in terms of relative “peakedness” of probability functions is proposed which is closely related to order-1 stochastic dominance. There is also a close connection between this ordering on probability distributions and the standard specificity ordering on possibility distributions that can be derived by means of a known probability–possibility transformation. The paper proposes a direct proof showing that the (total) preordering on probability measures defined by probabilistic entropy refines the (partial) ordering defined by possibilistic specificity. This result, also valid for other dispersion indices, is discussed against the background of related work in statistics, mathematics (inequalities on convex functions), and the social sciences. Finally, an application of the possibilistic specificity ordering in the field of machine learning or, more specifically, the induction of decision forests is proposed.

Towards a unifying approach to diversity measures: Bridging the gap between the Shannon entropy and Rao's quadratic index

The diversity of a species assemblage has been studied extensively for many decades in relation to its possible connection with ecosystem functioning and organization. In this view most diversity measures, such as Shannon's entropy, rely upon information theory as a basis for the quantification of diversity. Also, traditional diversity measures are computed using species relative abundances and cannot account for the ecological differences between species. Rao first proposed a diversity index, termed quadratic diversity ( Q) that incorporates both species relative abundances and pairwise distances between species. Quadratic diversity is traditionally defined as the expected distance between two randomly selected individuals. In this paper, we show that quadratic diversity can be interpreted as the expected conflict among the species of a given assemblage. From this unusual interpretation, it naturally follows that Rao's Q can be related to the Shannon entropy through a generalized version of the Tsallis parametric entropy.

Fisheries biodiversity conservation and sustainable tourism in Mauritius

This paper addresses the sustainability of the tourism sector from the perspective of a Small Island Developing State (SIDS), Mauritius. In this respect, the relationship between tourist earnings and fisheries biodiversity is examined. We begin, in the first place, by tracking and analyzing the evolution of fisheries biodiversity, a catalyst of the island's tourism, through the computation of Shannon's entropy index applied to 20 categories of fish experimented over a period of 25 years. In the second stage, this index is introduced, along with other control variables, in a regression equation to ascertain its potential impact on the value added of the tourism sector. Our empirical findings based on 25 years of observations undeniably reveal that fisheries biodiversity does play a major role in enhancing the revenue generated by the tourism sector. Hence, it is vital to promote biodiversity conservation, at least within the fisheries sector, to sustain economic progress; more so, given that tourism constitutes a major pillar of the economy of Mauritius and which is expected to grow even further.

Changes in Holdridge Life Zone diversity in the Xinjiang Uygur Autonomous Region (XUAR) of China over the past 40 years

The Holdridge Life Zone model, Shannon's Entropy Index and Simpson's Diversity Index were used to study the dynamics of vegetation distribution over the past 40 years in the Xinjiang Uygur Autonomous Region (XUAR), China. The results indicated that Holdridge Life Zone diversity was highest in the 1960s, dramatically decreased in the 1970s, and then gradually increased in the 1980s and 1990s. From the 1970s, the environment in XUAR seemed to be increasing in stability, as characterized by a reduction in the number of days of sandy dust storm activity in the 1990s, and an increase in temperature and precipitation leading to an increase in water flow in some rivers. It is possible that both changes in human activities and positive climate change contributed to the Holdridge Life Zone diversity dynamics and more stable environment in XUAR.

Entropy and scintillation analysis of acoustical beam propagation through ocean internal waves

Parabolic equation numerical simulations of waveguide acoustical beam propagation in an ocean of Garrett–Munk internal waves are used to examine the range evolution of beam properties such as beamwidth (both spectral and spatial), Shannon entropy, and scintillation index, as a function of beam angle. Simulations are carried out at 250- and 125-Hz acoustic frequencies. The ray trajectories associated with these beams are predominantly chaotic or exponentially sensitive to initial conditions and/or medium perturbations. At long range near saturation, the finite-frequency beams show a constant rate of change of Shannon entropy with range, independent of acoustic frequency. This full-wave rate of entropy is of the same order of magnitude as the average rate of entropy for the ray trajectories associated with this beam. Finite-range Lyapunov exponents provide the estimates of ray entropy rate or Kolmogorov–Siani entropy. The correspondence between full-wave and ray entropies suggests a full-wave manifestation of ray chaos, but only once statistical saturation is obtained. In spite of this correspondence, the simulated acoustical beams expand diffusively not exponentially (or explosively).