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In recent days, examination of medical images had been carried out using a number of image processing tools, specifically implemented for such purposes. This proposed work is based on a hybrid image processing technique focuses on extracting the tumour section from the brain Magnetic-Resonance-Image (MRI) recorded with various MR sequences. The proposed technique aims to identify the best possible image processing methodology for brain MRI investigation and subsequently to extract the tumour section for clinical setting. For exploring the proposed technique, most popular Radiopedia database, BraTS 2015 dataset is primarily considered for the assessment and later, real time clinical brain MRI slices are investigated. The proposed work implements Shannon Entropy (SE) objective function assisted with Social Group Optimization (SGO) algorithm to enhance the image. The results produced by SGO are compared with the other heuristic approaches like the Firefly-Algorithm (FA), Bat-Algorithm (BA) and Differential-Evolution (DE). Then Distance-Regularized-Level-Set (DRLS) segmentation technique is performed for extracting the tumour part from the enhanced slices. Further, the segmentation comparison of DRLS against traditional Active-Contour (AC) is also adopted for the evaluation. This integrated approach offers better picture-similarity-measures (PSM) compared with the alternatives. [ABSTRACT FROM AUTHOR]

Phonocardiogram (PCG) recordings contain valuable information about the functioning and state of the heart that is useful in the diagnosis of cardiovascular diseases. The first heart sound (S1) and the second heart sound (S2), produced by the closing of the atrioventricular valves and the closing of the semilunar valves, respectively, are the fundamental sounds of the heart. The similarity in morphology and duration of these heart sounds and their superposition in the frequency domain makes it difficult to use them in computer systems to provide an automatic diagnosis. Therefore, in this paper, we analyzed these heart sounds in the intrinsic mode functions (IMF) domain, which were issued from two time-frequency decomposition techniques, the empirical mode decomposition (EMD) and the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), with the aim of retrieving useful information on an expanded basis. The decomposition of PCG recordings into IMF allows representing the fundamental cardiac sounds in many oscillating components, increasing thus the observability of the system. Moreover, the time-frequency representation of PCG recordings could provide valuable information to automatically detect heart sounds and diagnose pathologies from characteristic patterns of these heart sounds in the IMF. The analysis was made through the variance and Shannon's entropy of the heart sounds, observed in time windows located among different IMF. In addition, we determined the frequencies ranges of the IMF from the decomposition of the PCG recordings using both techniques. Given that the frequency content of S1 and S2 is different but overlap each other, and the duration of these sounds are also different, these heart sounds were represented in different IMF with different variances and entropies, in both techniques, but the ICEEMDAN offers a more consistent decomposition of S1 and S2 (they were concentrated in IMF 4-6). The decomposition of PCG signals into IMF has allowed us to identify the frequency components of the IMF in which these sounds are found. [ABSTRACT FROM AUTHOR]

In this paper, we develop a kernel adaptive filter for quaternion data, using stochastic information gradient (SIG) cost function based on the information theoretic learning (ITL) approach. The new algorithm (QKSIG) is useful for quaternion-based kernel applications of nonlinear filtering. Adaptive filtering in quaterion domain intrinsically incorporates component-wise real valued cross-correlation or the coupling within the dimensions of the quaternion input. We apply generalized Hamilton-real (GHR) calculus that is applicable to quaternion Hilbert space for evaluating the cost function gradient. The QKSIG algorithm minimizes Shannon's entropy of the error between the filter output and desired response and minimizes the divergence between the joint densities of input-desired and input-output pairs. The SIG technique reduces the computational complexity of the error entropy estimation. Here, ITL with SIG approach is applied to quaternion adaptive filtering for three different reasons. First, it reduces the algorithm computational complexity compared to our previous work quaternion kernel minimum error entropy algorithm (QKMEE). Second, it improves the filtering performance by considering the coupling within the dimensions of the quaternion input. Third, it performs better in biased or non-Gaussian signal and noise environments due to ITL approach. We present convergence analysis and steady-state performance analysis results of the new algorithm (QKSIG). Simulation results are used to show the behavior of the new algorithm QKSIG in quaternion non-Gaussian signal and noise environments compared to the existing ones such as quadruple real-valued kernel stochastic information gradient (KSIG) and quaternion kernel LMS (QKLMS) algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we produce a new of continuous distribution based on [0,1] Truncated Lomax distribution, is called [0,1] Truncated Lomax – Uniform distribution. The cumulative distribution function, the rth moment, the mean, the variance, the skewness, the kurtosis, the median, the characteristic function, the reliability function, the hazared rate function, the quantile function, the Shannon entropy function and Relative entropy function has been derived for the distribution. We know that the an element fails when it exceeds the stress of the corresponding strength. therefor, the [0,1] Truncated Lomax-Uniform strength – stress model with different parameters has also been derived here. Finally, we proposed a study in Estimation for parameters of [0,1] Truncated Lomax – Uniform distribution by using maximum likelihood estimation method and we used simulation to generate random variables to take four experiments for the default values of three real parameters with samples sizes (n = 30, 60, 90, 120) and sample iteration (S = 1000). [ABSTRACT FROM AUTHOR]

Chennai is one of the most densely populated cities in India facing challenges in shifting the city to metropolitan or mega city in the last two decades with continuing agglomeration. To model the growth of Chennai city, we have used cellular automata-based urban growth models based on the historical datasets. In the present study, urban growth of Chennai Metropolitan Area (CMA) was predicted for the year 2017 based on 2010 and 2013 dataset and Chennai city master plan using neural-network-coupled agent-based cellular automata (NNACA) model. Eight different agents of urbanization including transportation, hotspots, and industries were used in the prediction modeling. On validating the 2017 predicted outputs, NNACA model with hotspots proved to be better (hits: 498.52 km2) than that of without hotspots (hits: 488.31 km2). Out of the total eight agents of urbanization, the most influencing agent of urbanization of 2017 was identified to be the neighborhood of 'Existing built-up of 2013' using 'sensitivity analysis'. Further, the urban sprawl of CMA for 2010, 2013 and 2017 was measured through Shannon's entropy. The study area was divided into five directional and distance-based zones with the State Secretariat as the center. Entropy values suggest the need for more careful planning for further development in the southern region of CMA which has undergone congested urban growth while urbanization is dispersed in the northern part of the study region which can be thought for future urban developments. [ABSTRACT FROM AUTHOR]

Let H be a hypergraph with n vertices. Suppose that d1,d2,...,dn are degrees of the vertices of H . The t-th graph entropy based on degrees of H is defined as I d t (H) = − ∑ i = 1 n ( d i t ∑ j = 1 n d j t log d i t ∑ j = 1 n d j t ) = log ( ∑ i = 1 n d i t ) − ∑ i = 1 n ( d i t ∑ j = 1 n d j t log d i t) , where t is a real number and the logarithm is taken to the base two. In this paper we obtain upper and lower bounds of I d t (H) for t = 1, when H is among all uniform supertrees, unicyclic uniform hypergraphs and bicyclic uniform hypergraphs, respectively. [ABSTRACT FROM AUTHOR]

Brain tumor is one of the harsh diseases among human community and is usually diagnosed with medical imaging procedures. Computed-Tomography (CT) and Magnetic-Resonance-Image (MRI) are the regularly used non-invasive methods to acquire brain abnormalities for medical study. Due to its importance, a significant quantity of image assessment and decision-making procedures exist in literature. This article proposes a two-stage image assessment tool to examine brain MR images acquired using the Flair and DW modalities. The combination of the Social-Group-Optimization (SGO) and Shannon's-Entropy (SE) supported multi-thresholding is implemented to pre-processing the input images. The image post-processing includes several procedures, such as Active Contour (AC), Watershed and region-growing segmentation, to extract the tumor section. Finally, a classifier system is implemented using ANFIS to categorize the tumor under analysis into benign and malignant. Experimental investigation was executed using benchmark datasets, like ISLES and BRATS, and also clinical MR images obtained with Flair/DW modality. The outcome of this study confirms that AC offers enhanced results compared with other segmentation procedures considered in this article. The ANFIS classifier obtained an accuracy of 94.51% on the used ISLES and real clinical images. [ABSTRACT FROM AUTHOR]

Flooding is one of the main natural hazards in Northern Europe and several areas of the Northern Boreal Hemisphere, where during intense rainfall events, several river basins are affected by a fast water level rise that may cause severe damage to human lives and properties. For these reasons, the development of flood models to identify susceptible areas is essential for decision-makers. Geographic Information Systems (GIS) are currently accurate and valuable support tools for defining flood susceptibility maps at different spatial scales. In this study, the prediction accuracy of different GIS-based procedures in the identification of flooding susceptibility is tested and compared. These procedures include the frequency ratio, a combination of the frequency ratio and logistic regression, a combination of the frequency ratio and Shannon's entropy index, and the statistical index. Ten conditioning parameters of flooding susceptibility are considered: elevation, slope, curvature, land use, Topographic Wetness Index, Stream Power Index, hydrogeology, stream distance, flow direction and average annual rainfall. The comparison analysis is carried out by applying these methods to the study area of Devon County in Southwest England. A total of 225 flood events are used to define the models. For model validation, 1000 randomly selected training and testing sub-datasets have been used in the definition of the receiver operating characteristic (ROC) curves. The results show that the procedure based on the statistical index provides the highest accuracy and reliability in flood susceptibility predictions. [ABSTRACT FROM AUTHOR]

The Remote Sensing (R/S) and Geographical Information System (GIS) play a vital role to evaluate and study the urban expansion pattern. In this study, the Chennai city was selected to perform the urban sprawl study. Five different periods of satellite imageries for the time elapsed between 1994 and 2016 were used. The main aim of this paper was to identify the urban sprawl of Chennai as a patterning process. The extended areas of urban in the period of 1994, 2001, 2006, 2011 and 2016 were extracted by the sub-pixel classification method from the satellite imageries. Furthermore, Shannon's entropy index was used for assessing urban expansion. The findings of this study proved that Chennai city has sprawled by urban expansion during the period between 1994 and 2016. Likewise, the dispersion rate of urban sprawl for the periods of 1994, 2001, 2006, 2011 and 2016 were 0.671, 0.679, 0.688, 0.693 and 0.695 respectively. Consequently, this uncontrolled dispersed urban development had resulted in the study area losses their green space. [ABSTRACT FROM AUTHOR]

A very recent proposal of a set of entropy measures for spatial data, based on building pairs of realizations, allows to split the data heterogeneity that is usually assessed via Shannon's entropy into two components: spatial mutual information, identifying the role of space, and spatial residual entropy, measuring heterogeneity due to other sources. A further decomposition into partial terms deeply investigates the role of space at specific distance ranges. The present work proposes improvements to the method and adds relevant results proving that the new set of spatial entropies satisfies a list of desirable properties. We extend the methodology to sets of realizations greater than pairs. We also show that the approach is more general, better performing and more interpretable than the most popular proposals in the literature, thanks to the property of additivity and a new way of computing entropy that explicitly discards the order within sets. A novel procedure for building the necessary quantities for computations is also provided. A comparative study illustrates the superior performance of the new set of measures over representative spatial configurations. Practical questions are answered by means of a case study on land use data. [ABSTRACT FROM AUTHOR]

With the realisation of the substantial changes made by Homo sapiens on earth dynamics; initiated a proposal of geological time scale ahead of the Holocene named as the Anthropocene, i.e., the Human Age. The conditions of the Anthropocene have redacted in a way by the optical modes of analysis; being made through data interpretation, changes experienced through satellite imagery, the consistent updating of climatic change, and the altered man–environment relationship across ages. Urban spatial areas have expanded in an accelerated speed during the last few decades, and rates of urban population growth are higher than the overall growth in most cities because urban areas are the locus of economic activity and transportation nodes. The study focuses on the increasing burden on the metropolitan cities like Delhi National Capital Region (NCR) of India—thereby inducing analogous effects over the suburban conurbation through ceaseless outgrowths. These patterns of urban densification and internal modifications are of major concern to sustainable development because they represent the physical manifestations of a range of social, economic, cultural, and political dimensions associated with urban dynamics. Considering the altered man–environment relationship; this paper deals with the urban assessment of Ghaziabad for the years—2001, 2006, 2011, and 2015. It further focuses on the directional change of the region as a suburb of NCR in context with buffer zone analysis and Shannon's entropy approach. [ABSTRACT FROM AUTHOR]

So far, many methods have been proposed to classify items based on ABC analysis, but the results of these methods have had relatively low compliance with the principles of ABC. More precisely, collective value and sometimes the number of items belonging to each category in the methods provided do not meet the basic requirements of ABC called Pareto's principle. In this study, a number of hybrid methodologies including Shannon's entropy, TOPSIS (the technique for order preference by similarity to ideal solution) and goal programming are respectively used for determining the weight of criteria which are effective in the inventory items classification, calculations of each item value and its classification based on Pareto's principle. To this end, the value of each item as well as classification of inventory items is calculated based on Pareto's principle. The performance of the proposed method is evaluated through (1) statistical analysis, (2) checking the percentage of similarity with other methods and (3) comparison with another method in terms of the number and value allocated to each class. The results confirm the capability of the listed method. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Four versions of Shannon's entropy were applied and analyzed in atoms and molecules. • Only two expressions proposed fulfills rigorously with the general properties of the entropy. • Negative values of Shannon's entropy have not physical meaning. Abstract In this letter, we analyzed some common expressions of Shannon's entropy used in the field of quantum chemistry. The expressions analyzed were defined in the position and momentum space, for our propose we used the first thirty-six atoms of the periodic table and a large set of molecules and only two of them fulfills with the general properties of the entropy. We compared the general trends obtained and discussed the reason about why the negative values of the continuous entropy in this field are unacceptable. [ABSTRACT FROM AUTHOR]

In recent years, technological advances have motivated industries, companies and even governments to look for an improved alignment between strategic objectives and technology management, preferably through the application of structured and flexible approaches that use techniques such as technology roadmapping. There are a lot of studies that have presented various models, processes and frameworks to develop technology roadmap and more studies have developed roadmaps based on these contributions. Most of these studies have mentioned that the roadmapping process must be customized in every case. Accordingly, having a model or a framework that represents the most prominent findings of these studies in one view is so helpful for customizing the process. But there is no research that accumulates previous studies and achieving this purpose. This paper presents the outcomes of a Meta-synthesis review of technology roadmapping literature that was published between 1997 and 2016 (73 papers) and develops a framework from important roadmapping components which affected the roadmapping process and roadmaps. Finally, the components of the proposed framework have been evaluated by survey benefiting from experts' opinion and Shannon's entropy technique. [ABSTRACT FROM AUTHOR]

In recent years, drought has inflicted significant damage on agriculture and rural communities in Iran. Resilience is the capability of communities to handle and tolerate exterior pressures such as drought. The purpose of this study was to identify the indicators affecting social resilience against drought, determining the cause of reduction or increase of resilience in different regions. It also focuses on strategies for increasing resilience of rural communities through the provision of social services in Iran. The required information was collected using a questionnaire from five villages, including 237 villagers who were selected through snowball method. Shannon's entropy and COPRAS methods were employed to determine and classify the drought resilience. The results show that some indicators like modified irrigation methods and new methods of coping with drought have devoted the highest weight. Also, there is a significant relationship between resilience rating of villages with average age of the households and number of households in nonfarm job. Finally, absolute drought resilience of rural communities remained in moderate situation. Doing study in wider areas to coordinate the effective indicators in the matter and studying how empowerment of local communities by providing a variety of social services can be considered as a further research in the future. [ABSTRACT FROM AUTHOR]

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In this paper, we study the concomitants of dual generalized order statistics (and consequently generalized order statistics) when the parameters γ1,…,γn are assumed to be pairwise different from Huang–Kotz Farlie–Gumble–Morgenstern bivariate distribution. Some useful recurrence relations between single and product moments of concomitants are obtained. Moreover, Shannon’s entropy and the Fisher information number measures are derived. Finally, these measures are extensively studied for some well-known distributions such as exponential, Pareto and power distributions. The main motivation of the study of the concomitants of generalized order statistics (as an important practical kind to order the bivariate data) under this general framework is to enable researchers in different fields of statistics to use some of the important models contained in these generalized order statistics only under this general framework. These extended models are frequently used in the reliability theory, such as the progressive type-II censored order statistics.

The growth and development of rice crops primarily depend on appropriate soil water balance for which soil moisture is the key determinant. Soil moisture is a crucial parameter in the hydrological cycle, which has a vital role in optimal water management for sustainable agricultural growth as it has a significant impact on hydrological, ecological, and climatic processes. Thus, accurate estimation of soil moisture is important otherwise it will drastically reduce crop yields, intensifying the global food crisis. A novel soil moisture prediction model (SVM-COLGWO) that incorporates the Grey Wolf Optimizer (GWO) into Chebyshev chaotic maps and opposition-based learning to optimize the Support Vector Machine (SVM) model is proposed. The suggested model simultaneously increases the simulated model's accuracy while speeding up global convergence. To evaluate the proposed model, the prediction performance is compared with other hybrid and standalone models where the feasibility of the proposed model is validated through superior simulation results (MAE = 0.167, MSE = 0.179, RMSE = 0.423, MAPE = 0.162, and R 2 = 0.949) including Shannon's Entropy. Thus, based on accurate soil moisture simulation through the proposed model, irrigation can be effectively scheduled for sustainable rice growth. • Rice growth depends on appropriate soil water balance or soil moisture. • Soil moisture predicted using optimized support vector machine. • The model accelerates the global convergence speed and prediction accuracy. • The model provides better prediction results compared to other models. [ABSTRACT FROM AUTHOR]

Novel measures of symbol dominance (dC1 and dC2), symbol diversity (DC1 = N (1 − dC1) and DC2 = N (1 − dC2)), and information entropy (HC1 = log2 DC1 and HC2 = log2 DC2) are derived from Lorenz-consistent statistics that I had previously proposed to quantify dominance and diversity in ecology. Here, dC1 refers to the average absolute difference between the relative abundances of dominant and subordinate symbols, with its value being equivalent to the maximum vertical distance from the Lorenz curve to the 45-degree line of equiprobability; dC2 refers to the average absolute difference between all pairs of relative symbol abundances, with its value being equivalent to twice the area between the Lorenz curve and the 45-degree line of equiprobability; N is the number of different symbols or maximum expected diversity. These Lorenz-consistent statistics are compared with statistics based on Shannon’s entropy and Rényi’s second-order entropy to show that the former have better mathematical behavior than the latter. The use of dC1, DC1, and HC1 is particularly recommended, as only changes in the allocation of relative abundance between dominant (pd > 1/N) and subordinate (ps < 1/N) symbols are of real relevance for probability distributions to achieve the reference distribution (pi = 1/N) or to deviate from it.

Rainfall-induced floods often cause significant loss of life as well as damage to infrastructure and crops. Synthetic Aperture Radar (SAR) Earth Observation Satellites (EOS) can be used to determine the extent of flooding over large geographical areas. Unlike optical sensors, SAR instruments are suitable for cloudy weather conditions, making them suitable for flood detection and mapping during extreme weather events. In this study, we explore the application of the Normalized Difference Sigma-Naught Index (NDSI) and Shannon’s entropy of NDSI (SNDSI) of Sentinel-1 data for open water flooding detection, based on automatic thresholding and Bayesian probability. The proposed methodology was tested using the floods in Sofala province, Mozambique, caused by cyclone Idai on March 14–19 of 2019. Results show that thresholding of the NDSI Vertical Transmit-Horizontal Receive (VH) can produce results with Overall Accuracy above 90%, and Kappa higher than 0.6. Considerable performance improvements were obtained by our thresholding method over the entropy of NDSI, yielding results with Kappa of 0.70–0.77. Additionally, it was found that Weibull distribution can properly describe the properties of flooded pixels within the histogram of SNDSI, which allows us to generate a flood probability raster using a Bayesian approach. The final per-pixel flooding probability is useful to indicate certainty in the classification results. The SNDSI Bayesian model produced an AUC (Area Under the Receiver Operating Characteristic Curve) of 0.93–0.97, with cross-polarized data yielding the most accurate results.

Define Batna city, define its outlines and follow the spatio-temporal evolution is one of the complex problems. Urban sprawl, that rapid urbanization is the occupancy factor of soil changes, generally irreversible. His study in a medium-sized city is an important issue that requires monitoring and detailed analysis. Our approach includes the use of remotely sensed images to evaluate and qualify urban sprawl in Batna. For this purpose, we used a series of images in digital format for the years 1972, 1987, 2001 and 2013, acquired by multispectral sensors mounted on Landsat satellite platforms, for area which is the subject of experimentation, then supervised classification by Support Vector Machine (Radio Basis Function classifier RBFC) was utilized. The selection of the images available from Landsat archives was made so that their acquisition date is spread enough to better distinguish changes within the urban fabric. The results obtained confirm that urban area increased 173.32% between 1972 -1987, 55.62% between 1987 -2001 and 38.71% between 2001 -2013. Furthermore, Shannon’s entropy index shows that the city has a high level of sprawl along its urban expansion history.

The graph entropies inspired by Shannon’s entropy concept become the information-theoretic quantities for measuring the structural information of graphs and complex networks. In this paper, we continue studying some new properties of the graph entropies based on information functionals involving vertex degrees. We prove the monotonicity of the graph entropies with respect to the power exponent. Considering only the maximum and minimum degrees of the ( n , m ) -graph, we obtain some upper and lower bounds for the degree-based graph entropy. These bounds have different performances to restrict the degree-based graph entropy in different kinds of graphs. Moreover the degree-based graph entropy can be estimated by these bounds.

Shannon entropies for networks have been widely introduced. However, entropies for weighted graphs have been little investigated. Inspired by the work due to Eagle et al., we introduce the concept of graph entropy for special weighted graphs. Furthermore, we prove extremal properties by using elementary methods of classes of weighted graphs, and in particular, the one due to Bollobás and Erdös, which is also called the Randi´c weight. As a result, we derived statements on dendrimers that have been proven useful for applications. Finally, some open problems are presented.

In the present communication, we introduce a quantity which is called weighted ( α , β ) -norm entropy and discuss its some major properties with Shannon and other entropies in the literature. Corresponding to the proposed entropy, a new weighted directed divergence measure has been introduced and its validity is established. Further, we give the application of ( α , β ) -norm entropy in coding theory and a coding theorem analogous to the ordinary coding theorem for a noiseless channel has been proved. The theorem states that the proposed entropy is the lower bound of mean code word length. [ABSTRACT FROM AUTHOR]

In this article, we have introduced a new distribution named as Weibull-Lomax (T-X) distribution (WLD). Various mathematical properties of Weibull-Lomax distribution are obtained such as moments, survival, hazard rate function, limiting behaviour of its probability density and hazard rate functions. Quantile functions, mode, median and Shannon entropy are also obtained. The relations between WLD and Weibull, Exponential and the type I extreme value distributions are discussed by transformation. The estimation of model parameters have been done using maximum likelihood estimation (MLE) method. The shape of the distribution is discussed. Sufficient conditions for failure rate functions are derived. A simulation study is presented for performance of estimators. Finally an application of real data set is used to illustrate the flexibility of the new model. [ABSTRACT FROM AUTHOR]

Land in the peri-urban interface is of vital importance as there is a lack of clarity in the planning and policies in this region whether they should be governed under the authority of rural administration. In general, these areas are frequently ignored as a specific area in the study of urbanization being neither pure urban nor pure rural. In this regard, an attempt has been taken to detect the spatio-temporal dynamics of sprawl, the nature of land transformation taken place in the identified peripheral settlements with high probability of urban development within the buffer zone of 2.5 km around the boundaries of the two major urban bodies of Malda i.e. English Bazar municipality an Old Malda municipality. The secondary data of Census of India of 2011and Landsat TM imageries (1987, 2003, 2011 and 2015) have been employed to detect the evolutionary process with the view to capture the urban land-use growth by Land Use–Land Cover classification. The result shows that the built-up area has increased around 30% over the course of 28 years span. Computations of Shannon’s Entropy, Urbanisation intensity index, built-up density have helped to explore the degree of transition taking place in each spatial unit under investigation. The spatial metrics with the gradient approach has revealed that beyond the buffer of 7 km from the city centre the increase of residential land uses is maximum which is characterised by a fragmented pattern with nearest entropy value to log N. The suitability analysis in search of most prospective future urban centre suggests the maximum distribution of urban units in the western front of the ULBs. [ABSTRACT FROM AUTHOR]

Image segmentation, the splitting of a multispectral and panchromatic image into groups of homogeneous pixels based on the region of interest(ROI), is a universal step for many advanced image processing and object recognition. Image segmentation essentially affects the overall performance of any automated image analysis system due to utmost importance of its quality. Image segmentation can be performed by recursively splitting the whole image or by merging together a large number of minute regions until a specified condition is satisfied. Thresholding is an old, simple and important method in gray scale image segmentation. In this paper, we have used Shannon’s entropy and proposed a new multilevel thresholding image segmentation method based on minimization of bi-entropy function. A smoothing technique based on weight value of the pixel within a w × w moving window is introduced to make the splitting result continuous and qualitative. The proposed algorithm takes full account of the spatial information and the gray information to decrease the computing quantity. Standard medical images, texture images, and remote sensing images are segmented in the experiment and compared with other related segmentation methods with different measures. Experimental results show that the proposed method can quickly converge with high computational efficiency. [ABSTRACT FROM AUTHOR]

Spatial expansion of cities appears to be unavoidable. Despite concern around landscape alterations caused by urban expansion, the understanding of the amounts and patterns of this phenomenon is sorely lacking. In this study, we quantified the current pattern of landscape fragmentation in the urban region (UR) of Milan and analysed the trend of urban sprawl over more than 50 years. The UR of Milan was spatially defined using a standardised and repeatable methodology that combines land-use and population density data. Fragmentation was assessed using the effective mesh size (meff). The trend of sprawl was monitored between 1954 and 2012 and over different areas to detect the magnitude (amount and direction) and patterns of changes. Results revealed a positive trend and a high degree of sprawl over the whole study area. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a quantity measure which is called (R, S)-norm entropy and discuss some of its major properties with Shannon’s and other entropies in the literature. Based on this (R, S)-norm entropy, we have proposed a new (R, S)-norm fuzzy information measure and discussed its validity and properties. Further, we have given its comparison with other fuzzy information measures to prove its effectiveness. Attribute weights play an important role in multiple-attribute decision-making problems. In the present communication, two methods of determining the attribute weights are introduced. First is the case when the information regarding attribute weights is incompletely known or completely unknown and second is when we have partial information about attribute weights. For the first case, the extension of ordinary entropy weight method is used to calculate attribute weights and minimum entropy principle method based on solving a linear programming model is used in the second case. Finally, two methods are explained through numerical examples. [ABSTRACT FROM AUTHOR]

Groups of animals (including humans) may show flexible grouping patterns, in which temporary aggregations or subgroups come together and split, changing composition over short temporal scales, (i.e. fission and fusion). A high degree of fission-fusion dynamics may constrain the regulation of social relationships, introducing uncertainty in interactions between group members. Here we use Shannon's entropy to quantify the predictability of subgroup composition for three species known to differ in the way their subgroups come together and split over time: spider monkeys (Ateles geoffroyi), chimpanzees (Pan troglodytes) and geladas (Theropithecus gelada). We formulate a random expectation of entropy that considers subgroup size variation and sample size, against which the observed entropy in subgroup composition can be compared. Using the theory of set partitioning, we also develop a method to estimate the number of subgroups that the group is likely to be divided into, based on the composition and size of single focal subgroups. Our results indicate that Shannon's entropy and the estimated number of subgroups present at a given time provide quantitative metrics of uncertainty in the social environment (within which social relationships must be regulated) for groups with different degrees of fission-fusion dynamics. These metrics also represent an indirect quantification of the cognitive challenges posed by socially dynamic environments. Overall, our novel methodological approach provides new insight for understanding the evolution of social complexity and the mechanisms to cope with the uncertainty that results from fission-fusion dynamics. [ABSTRACT FROM AUTHOR]

The logistic distribution and the S-shaped pattern of its cumulative distribution and quantile functions have been extensively used in many different spheres affecting human life. By far, the most well-known application of logistic distribution is in the logistic regression that is used for modeling categorical response variables. The exponentiated-exponential logistic distribution, a generalization of the logistic distribution, is obtained using the technique proposed by Alzaatreh et al. (2013) of mixing two distributions, hereafter called the EEL distribution. This distribution subsumes various types of logistic distribution. The structural analysis of the distribution in this paper includes limiting behavior, quantiles, moments, mode, skewness, kurtosis, order statistics, the large sample distributions of the sample maximum and the sample minimum, and the distribution of the sample median. For illustrative purposes, a real-life data set is considered as an application of the EEL distribution. [ABSTRACT FROM PUBLISHER]

In recent years, there has been an increasing proliferation of initiatives focusing on the concept of quality of life and well-being. At the centre of these studies there is the recognizing that the GDP offers only a partial perspective of factors affecting people's lives. Following this line of the research, this paper is aimed at computing the well-being efficiencies of a sample of Italian Province capital cities, using a methodological approach that combines data envelopment analysis (DEA) with Shannon's entropy formula. To avoid subjectivity in choosing a representative set of variables that proxy the phenomenon under study, we rely on the theoretical framework adopted by the Italian National Institute of Statistics (ISTAT) within the equitable and sustainable well-being (BES) project. The dashboard of indicators included in the analysis are related to the Ur-BES initiative, promoted by ISTAT to implement the BES framework at cities level. In a first step of the analysis, an immediate focus on separate dimensions of urban well-being is obtained by summarizing the plurality of available indicators through the building of composite indices. Next, the adopted integrated DEA-Shannon entropy approach has permitted to increase the discriminatory power of DEA procedure and attain a more reliable profiling of Italian Province capital cities well-being efficiencies. The results show a marked duality between the Northern and Southern cities, highlighting important differences in many aspects of human and ecosystem well-being. [ABSTRACT FROM AUTHOR]

The paper presents a new digital relaying for detection, classification and localization of faults on the hybrid transmission line consisting of an overhead line and an underground cable. The entropy principle together with fast discrete orthogonal S-transform (FDOST) represented by window dependent bases is utilized for feature extraction and the support vector machine (SVM) classifier model & support vector regression (SVR) model are employed for pattern recognitions to predict the types and locations of faults. After modelling and simulation of the transmission system in Electromagnetic Transient Program (EMTP) software, three phase fault current signals are recorded at one end of the line to extract entropy of FDOST coefficients from each of the three current signals of half cycle duration after fault initiation. The proposed relaying technique is tested on a single-junction and a multi-junction hybrid transmission lines under different fault conditions and is found fast and accurate independent of fault type, fault section, fault resistance, fault inception angle (FIA) and load angle. Another important aspect of the method is that it needs no prior identification of the faulty section for the estimation of fault location. The immunity of the proposed method to noise is also established by testing it with fault current signals impregnated with white Gaussian noise of level 30 dB signal to noise ratio (SNR). [ABSTRACT FROM AUTHOR]

In this research article we develop a new two parametric new generalized inaccuracy measure Iαβ(P:Q) and a new two parametric generalized average code-word length Iαβ (P). These measures are the generalizations of some familiar measures existing in the subjects of information and coding theory. Also we develop the noiseless coding theorems for discrete noiseless channel. (i.e., we find the lower and upper bounds of Iαβ(P) in terms of Iαβ (P:Q)). The mathematical results obtained in this research article are verified by using empirical data. Also the monotonic behavior of Iαβ (P:Q) and Iαβ (P) with respect to parameters α and β have been discussed. [ABSTRACT FROM AUTHOR]

In this article we develop a new additive information measure of order α and a new average code-word length and develop the noiseless coding theorems for discrete channel. Also we show that the measures defined in this communication are the generalizations of some well-known measures in the subject of coding and information theory. The results obtained in this article are verified by considering Huffman and Shannon-Fano coding schemes by taking an empirical data. The important properties of the new information measure have also been studied. [ABSTRACT FROM AUTHOR]

Entropy is widely employed in many applied sciences to measure the heterogeneity of observations. Recently, many attempts have been made to build entropy measures for spatial data, in order to capture the influence of space over the variable outcomes. The main limit of these developments is that all indices are computed conditional on a single distance and do not cover the whole spatial configuration of the phenomenon under study.Moreover, most of them do not satisfy the desirable additivity property between local and global spatial measures. This work reviews some recent developments, based on univariate distributions, and compares them to a newapproach which considers the properties of entropy measures linked to bivariate distributions. This perspective introduces substantial innovations. Firstly, Shannon's entropy may be decomposed into two terms: spatial mutual information, accounting for the role of space in determining the variable outcome, and spatial global residual entropy, summarizing the remaining heterogeneity carried by the variable itself. Secondly, these terms both satisfy the additivity property, being sums of partial entropies measuring what happens at different distance classes. The proposed indices are used for measuring the spatial entropy of a marked point pattern on rainforest tree species. The new entropy measures are shown to be more informative and to answer a wider set of questions than the current proposals of the literature. [ABSTRACT FROM AUTHOR]

The topological characterization of molecular structures will enrich the zeolite family and expand the possibility of developing highly active catalysts in the field of microporous materials. Because it would reduce the environmental issues associated with the industrial mass manufacturing of zeolites and prevent the high labor cost of designing novel structures. Theoretical chemists synthesized several nitrido-zeolites, including nitridosodalites (SOD), nitridophosphate-1 (NPO) and oxonitridophosphate-2 (NPT) with respect to their thermal stability characteristics. In QSPR and QSAR research, topological indices can be used to measure the physicochemical and biological properties of molecules. Utilizing graph-theoretical and Shannon's approaches, we determine the precise analytical expressions of various descriptors for zeolite NPT. Furthermore, we propose the predictive regression model to explore the potential energies such as electrostatic, dispersion and total energy for the selected dimensions of NPT zeolite framework. • Zeolites are acid catalysts that are widely used in petrochemistry, refining, adsorption, and solar energy conversion. • Molecular descriptors generate QSAPR model that can predict molecular structures physicochemical characteristics. • We computed zeolite NPT information entropies using different degree and degree sum-based descriptors. • Further, we propose the predictive regression model to explore the potential energies of large dimensions of NPT zeolite. [ABSTRACT FROM AUTHOR]

The inherent qualities of carbon nanosheets that come from their underlying molecular structure have drawn an enormous amount of interest from researchers. Molecular descriptors are commonly used graph-theoretic metrics to analyze the physicochemical properties of a molecule based on its molecular structure. Our current research validates the use of molecular descriptors in studying three recently developed carbon allotropes: pentagraphene, phagraphene, and phographene. These allotropes have significant thermal, dynamic, and mechanical stabilities that are comparable to graphene. General analytical expressions for both degree and neighborhood degree sum-based indices of these nanosheets are derived through the utilization of graph theoretical methods. Following a filtering process of the significant indices, regression models that accurately predict atomic density, specific heat capacity and total π -electron energy of carbon allotropes are developed. Additionally, Shannon entropy is introduced as an information index, which can be utilized for predictive studies in the future and as a tool for comparing structural complexity by incorporating topological index in its definition. [ABSTRACT FROM AUTHOR]

The rapid urbanization in Delhi-NCR has been inducing enormous anthropogenic pressure, result in degraded ecological infrastructure. Therefore, in the present study, the changing landscape pattern in Delhi's urban and peri-urban regions was investigated over the last five decades (1973–2020) using satellite remote sensing and landscape metrics to understand its trends and impacts on ecological infrastructure, especially on green cover space (UGS) that provide an opportunity to evaluate cities' sustainability. The study exhibits significant built-up growth in the peri-urban (516.9% growth; net growth 2407 km2) compared to Delhi urban (236.9%; 431.7 km2), with an overall decline in UGS (−14.3%; −168.60 km2). A large segment of UGS deterioration observed in the peri-urban (31.36%; −327.41 km2 loss) compared to Delhi urban, showed significant UGS recovery (120.25%; 158.81 km2 growth) during the later period. The landscape modeling and Shannon entropy-based study exhibited coalescence in Delhi urban (Hn ≤ 1.5) and dispersion in peri-urban (Hn > 2). The zonal analysis showed a significant dispersion in Panipat, Gurgaon, and Faridabad (Delhi NCR) with the establishment of major socio-economic development and population aggregation. The UGS availability and land consumption analysis highlighted the major hotspots of UGS decline in Gurgaon, Ghaziabad, and Shahdara, within Delhi urban, while in Jhajjar, Gurgaon, and Panipat in the peri-urban regions, having insufficient per capita green spaces (9 m2/person) and high land consumption (>85 m2/person). Moreover, recovery in UGSs (256% during 2014–2020) was observed in the Delhi urban. The study necessitates efficient functioning of the urban ecosystem for making the cities safe, resilient, and inclusive. • High urban growth (438.2%) in Delhi-NCR (1973–2020) with coalescence-diffusion. • Increased land consumption (1535m2/person) led to decline in green spaces (−168.6 km2). • Shahdara, Ghaziabad, Panipat, Rewari, Gurgaon are the hotspot zones for accelerated UGS loss. • UGSs recovery in Delhi-urban (25–50m2/person) compared to peri-urban (2014–2020). [ABSTRACT FROM AUTHOR]