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Mechanized tunneling in harsh environments faces many hazards, which can stop tunneling operations for a long time. Due to the high investment volume in tunneling projects, it is imperative to predict and assess the geotechnical hazards. This research has tried to evaluate and introduce the most dangerous section of the Kerman water conveyance tunnel (KWCT) using multi-index decision-making techniques including PROMETHEE II, WASPAS, and CoCoSo models. For this purpose, at first, the most important hazards in the tunnel route including dealing with fault zones, water inflow into the tunnel, rock abrasivity, and squeezing potential were identified. Then, the most dangerous sections of the tunnel were determined using empirical and analytical methods. In the next step, the weight of each criterion at most dangerous sections was determined using Shannon's entropy method. The results showed that using PROMETHEE II, WASPAS, and CoCoSo models, section Hz11 of the tunnel is the most dangerous section among all sections from a geotechnical point of view. Finally, this study suggests the PROMETHEE II-entropy, WASPAS-entropy, and CoCoSo-entropy models as the suitable methods with more accuracy among MCDM techniques for evaluating the geotechnical and geological hazards in a real situation of tunneling projects. [ABSTRACT FROM AUTHOR]

Urbanization is a widespread phenomenon worldwide, especially in developing countries, and it has an irreversible effect on the environment and land use. Therefore, it is necessary to identify and understand urban growth patterns to guide future urban growth patterns toward sustainable development through appropriate spatial policies. According to this need, the present study aims to calculate the urban growth rate and identify the growth patterns and the resulting changes in the urban landscape pattern in Shiraz metropolitan in the period from 2001 to 2023. Using Landsat satellite images, satellite image classification maps were obtained in 2001, 2013, and 2023. After that, to increase the accuracy of measuring the growth patterns of Shiraz metropolitan, from the combination of 4 spatial criteria of urban expansion intensity index, Shannon entropy, landscape indices, and landscape expansion index, in general, and sub-scales (in 8 geographical directions and 2 km distances from the center) was used. The results showed that the growth pattern of Shiraz metropolitan is scattered and has intensified over time. It was also found that the growth rate and pattern of Shiraz metropolitan areas are different in each direction and distance. The urban expansion intensity index showed that the highest speed of expansion in these 22 years was related to the south, southwest, and northwest regions. Shannon's entropy and landscape indices showed that the northwest and south regions have the highest amount of dispersion. Finally, the landscape expansion index identified the dominant pattern of urban growth in Shiraz metropolitan as the edge expansion pattern. It was found that the highest percentage of outlying expansion also occurred in the south and northwest regions. [ABSTRACT FROM AUTHOR]

The accurate and timely detection of cyber threats is critical to keeping our online economy and data safe. A key technique in early detection is the classification of unusual patterns of network behaviour, often hidden as low-frequency events within complex time-series packet flows. One of the ways in which such anomalies can be detected is to analyse the information entropy of the payload within individual packets, since changes in entropy can often indicate suspicious activity—such as whether session encryption has been compromised, or whether a plaintext channel has been co-opted as a covert channel. To decide whether activity is anomalous, we need to compare real-time entropy values with baseline values, and while the analysis of entropy in packet data is not particularly new, to the best of our knowledge, there are no published baselines for payload entropy across commonly used network services. We offer two contributions: (1) we analyse several large packet datasets to establish baseline payload information entropy values for standard network services, and (2) we present an efficient method for engineering entropy metrics from packet flows from real-time and offline packet data. Such entropy metrics can be included within feature subsets, thus making the feature set richer for subsequent analysis and machine learning applications. [ABSTRACT FROM AUTHOR]

Human resources are undoubtedly the most crucial resources of organizations. A significant part of the human resources includes retirees of the organization. Organizations must provide adequate support to acknowledge their years of service to facilitate retirees' adaptation to new circumstances. This study investigates retirement adjustment among personnel of the Yazd Electricity Distribution Company (YEDC). For this purpose, the challenges and problems that discourage people from retiring are identified first. Based on these challenges, retirement adjustment solutions are proposed. The retirement adaptation solutions have been ranked based on three criteria: financial promotion, identity improvement, and interaction improvement, using Shannon’s Entropy and TOPSIS techniques. The extraction of factors in two categories of challenges and solutions represents a contribution of this research. Furthermore, this research examines the different views of personnel with varying job levels, work experience, and genders through statistical analysis, which is another contribution of this research. Finally, the results of this research show the ranking of solutions using combined Shannon’s Entropy and TOPSIS techniques, which emphasize the novelty of this research.

Humans affect the biosphere by producing entropy as living beings –as explained by Schröedinger [What is Life? The physical aspect of the living cell (Cambridge University Press, New York, 1992)] – but mostly as a consequence of our ever increasing economic interventions. However, humans also create new forms and arrangements of matter. Is it possible that they carry less entropy than equivalent object subject to natural forces? Art and tech works tell us something, thus carry information. The connection between probability and information was introduced by Shannon 75 years ago [Bell Syst. Tech. J. 27, 379–423 (1948)]. In this work we calculate the probability that a stone tool could have been constructed by random, natural causes. We do so by considering the earliest tools created by our hominin ancestors, the stone tools of the Paleolithic. By analysing a sample of tools, we show that they are highly unlikely constructs by random means, and that therefore carry a great deal of information, as generations of archaeologists and anthropologists have eloquently exhibited. Further, we quantify this information, and following Shannon, we ascribe an entropy to the stone tools. We thus find that the stone tool carries less entropy than a stone hit by dispersed blows. This work presents a first simplified approach to these important issues. [ABSTRACT FROM AUTHOR]

This study aims to investigate the impact of spatio-temporal dynamics of urban sprawl on habitats in Istanbul, using the CORINE 1990 and 2018 land cover datasets. In this context, by means of geographic information system (GIS) tools and techniques, land cover maps are created for land cover change analysis and visualization, the Shannon's entropy method is performed for measuring urban growth and sprawl, and the landscape metrics method is applied for assessing habitat loss and fragmentation. Results indicate that the rate of urban sprawl in the area increased by 0.1230 as per the Shannon's entropy index over the 28-year period. Similarly, the Shannon Diversity Index and the Shannon Evenness Index rose from 1.74 to 1.85 and from 0.68 to 0.70, respectively, indicating an increase in urbanization within the area. Moreover, an analysis of patch numbers reveals that habitat fragmentation increased in shrub and/or herbaceous vegetation associations (72.55%), heterogeneous agricultural areas (45.11%), arable lands (42.5%), forests (36.13%) and pastures (15.05%), due to urbanization. Habitat fragmentation has had a detrimental effect on the local biodiversity. While 15 flora species were identified as vulnerable, 13 as endangered and 9 as critically endangered, 19 fauna species were identified as vulnerable and 5 as endangered. This study highlights that the natural habitats and biodiversity of Istanbul will suffer further decline due to urbanization unless sustainable urban planning and management policies are put into practice. It is essential to have controlled urban development to preserve the ecosystem's carrying capacity, and urbanization decisions must consider this requirement. [ABSTRACT FROM AUTHOR]

The general connectivity indices (including the general Randić index, the general sum-connectivity index, the general ABC index and the general ABS index) are an important degree-based topological index in chemical informatics. In this paper, the general connectivity entropies of a graph are defined as the Shannon's entropy based on the information functional that associates the general connectivity indices. We compute the general connectivity entropies for certain interconnection networks like butterfly networks, Benes networks, and mesh derived networks, which can be helpful to understand their underlying topologies and structural complexity. [ABSTRACT FROM AUTHOR]

N-carbophenes are two-dimensional covalent organic frameworks (2D-COF) that incorporate low-mobility bands and band gaps. These are promising materials that have applications in nanotechnology. We have obtained the topological indices and graph entropies of hexagonal and rectangular phases of N-carbophene covalent organic frameworks by incorporating vertex degree parameters. The computed topological indices are employed to develop QSPR models for Young's modulus of one-dimensional wires. Additionally, we compare the structural complexity of the two phases of N-carbophenes which reveals that the hexagonal 2D-COF exhibits a greater entropy compared to the rectangular 2D-COF of N-carbophenes. [ABSTRACT FROM AUTHOR]

The development of growth poles, urban activity centers, and service centers in Banda Aceh City has impacted the spread, a complex urban phenomenon challenging to measure due to urban sprawl. The increasing need for space in urban areas drives the development of suburban and random areas (urban sprawl). This is evident from the BPS Banda Aceh City data for 2024, where the population increased by 25.61% post-tsunami, affecting the density of each sub-district in Banda Aceh City. Research using Shannon's Entropy Method and the Gravitational Model is necessary to prevent uneven growth in the city of Banda Aceh. The application of Shannon's Entropy method in Banda Aceh City from 2010 to 2020 can be seen in the Relative Entropy Matrix, which shows that the linear spread pattern (Quadrant C) is more dominant in the districts of Banda Raya, Baiturrahman, Kuta Raja, Kuta Alam, Lueng Bata, and Syiah Kuala. The urban spread pattern of Banda Aceh tends to move towards the East, largely due to the landform factors that are very suitable for being developed into built-up areas. Meanwhile, the results of the gravity analysis show that the area of interaction with the most substantial interaction value as the growth pole is the interaction between Kuta Alam District and Baiturrahman District, with a value of 190,617,812.346 interactions. The results of identifying the factors influencing the development of urban sprawl, such as the distance to the CBD, the GRDP of Banda Aceh City, changes in land use, housing demand, and the availability of infrastructure facilities in the districts of Banda Aceh City, can be concluded that there is an influence of urban sprawl on the spatial structure and regional patterns in Banda Aceh City. [ABSTRACT FROM AUTHOR]

The article assesses the extent and pattern of urban area expansion in the Jorhat municipality in Assam, India using geographic information system and remote sensing techniques. The study quantifies urban sprawl through parameters including land cover changes. It analyzes the impact of urban sprawl on environment, such as habitat loss and biodiversity, and infrastructure and shares insights for informed decision-making in urban planning and management and sustainability efforts.

Recognised as the phenomena of worldwide occurrence, urban sprawl and accompanied chaotic built-up growth in and around existing urban clusters, have been found to have irreversible environmental, social and economic externalities, many of which are negative in nature. Though urban sprawl has emerged as a significant dimension of urbanisation throughout the world, it is imperative to be cognizant of the ways in which urban areas spatially grow since they differ in accordance with specific norms and regulations. To understand the spatio-temporal trajectory of urban sprawl of a city, therefore, it is essential to first understand the existing nature of land utilisation and its dynamics. Accordingly, the present study endeavours to understand and detect the territorial transformations encompassing Siliguri, the third largest city of West Bengal, India, over a period of two decades (2001–2021), through an integrated remote sensing-GIS approach. The research is grounded on quantitative methods like 'Urban Expansion Intensity Index' (UEII), 'Landscape Expansion Index' (LEI) and 'Shannon's entropy' to quantify and address the non-linear pattern of urban spatial growth in and around Siliguri city. The results of UEII indicate that the growth intensity of built-up areas in Siliguri urban agglomeration has increased over the time, whereas Shannon's entropy portrays a picture of increasing magnitude of built-up expansion in the study area. Finally, the LEI depicts an extraordinary dominance of edge-expansion as the principal mode of urban sprawl around Siliguri, as well as a growing number of new urban patches coming out over the agricultural tracts without any direct spatial association with pre-existing urban patches. The results of this study are expected to furnish empirical insights into the spatial pattern of urban growth, encompassing Siliguri, which may assist policymakers in planning for a sustainable pattern of urbanisation for the city and its surrounding region. [ABSTRACT FROM AUTHOR]

Portfolio management typically aims to achieve better returns per unit of risk by building efficient portfolios. The Markowitz framework is the classic approach used when decision-makers know the expected returns and covariance matrix of assets. However, the theory does not always apply when the time horizon of investments is short; the realized return and covariance of different assets are usually far from the expected values, and considering additional factors, such as diversification and information ambiguity, can lead to better portfolios. This study proposes models for constructing efficient portfolios using fuzzy parameters like entropy, return, variance, and entropy membership functions in multi-criteria optimization models. Our approach leverages aspects related to multi-criteria optimization and Shannon entropy to deal with diversification, and fuzzy and fuzzy entropy variants provide a better representation of the ambiguity of the information according to the investors' deadline. We compare 418 optimal portfolios for different objectives (return, variance, and entropy), using data from 2003 to 2023 of indexes from the USA, EU, China, and Japan. We use the Sharpe index as a decision variable, in addition to the multi-criteria decision analysis method TOPSIS. Our models provided high-efficiency portfolios, particularly those considering fuzzy entropy membership functions for return and variance. [ABSTRACT FROM AUTHOR]

Purpose: The present research aimed to provide content analysis of emotional intelligence dimensions in Farsi textbook stories of elementary schools using Shannon's entropy approach. Methodology: The research method was descriptive ad had a content analysis type using "Shannon's entropy" method. The statistical population consisted of 108 stories in Farsi textbooks of the elementary school in 2022. The statistical sample was also equal to the statistical population according to the census approach. The research tool included the emotional intelligence checklist with five components (interpersonal skills, intrapersonal skills, adaptability, general mood, and stress management) based on the Bar-On model. The reliability of the data was desirable using the paired t-test. Findings: The research findings indicated that there were significant differences in the representation of dimensions of emotional intelligence in stories of Farsi textbooks. Therefore, topics of intrapersonal and interpersonal skills were taken into consideration in a relatively favorable way, but stress management skill was neglected in the textbooks. Furthermore, a comparison of the sixth-grade elementary schools indicated that most of their stories had a general pattern of the importance of interpersonal and intrapersonal skill dimensions, and the adaptability dimension was relatively favorable only in the fifth-grade of elementary schools. Conclusion: According to the role of emotional intelligence in learners' lives, authors of Farsi textbooks need to provide a necessary revision of emotional intelligence components in the stories of the textbooks. [ABSTRACT FROM AUTHOR]

Urban agglomerations across the world have witnessed haphazard and unprecedented growth in the recent past, giving rise to urban sprawling. This study analyses the spatio-temporal growth dynamics of 16 major Indian cities (population above one million) using remote sensing approaches. Land Use and Land Cover (LULC) thematic datasets are considered for the years 2005, 2010, 2015, and 2021. The variability of the five LULC classes, viz., urban built-up, vegetation, water body, agriculture, and barren land, implied that urban expansion mostly took place at the cost of barren lands. The urbanised landscape mainly portrayed dispersive outward growth since the beginning of the 21st century, with significant compaction (infill urban growth) near the urban core in recent years. The results derived through Shannon's Entropy, spatial metrics, and urban density gradient analysis (in eight directions) indicated the same. Population density variation with respect to the horizontal urban growth and dynamics in each considered direction, further supported the concept of overcrowded city centres and sprawled outskirts. Besides population density, other factors that could be associated with urbanisation include the local environment, meteorology, and some geophysical characteristics. [ABSTRACT FROM AUTHOR]

The rapid urban growth and anthropogenic activities have posed a threat to the local environment and ecosystem around the world. This situation has become a hindrance to planners and policy makers for sustainable urban development. Therefore, this study mainly focuses on the assessment of urban growth patterns in relation to urban sprawl in Jalpaiguri urban agglomeration. Multi-temporal Landsat data have been used for land use change detection and urban sprawl quantification. The maximum likelihood classifier technique has been performed to create land use land cover maps for each study year (2001, 2011 and 2021). Urban expansion intensity index has been applied to determine the magnitude of urban expansion. Landscape metrics and Shannon's entropy have been employed to assess the urban sprawl to a spatial extent. Spatiotemporal land use changes reveal that the non-urban class (vegetation, agriculture, water bodies, and fallow) have been decreasing consistently with an increase in built-up areas over time. Built-up area has increased by almost seven times in the span of the last 20 years (2001-2021). In the first decade, the growth rate of urban areas was 145.42% with a medium speed of expansion and in the next decade, it was 180.83% with a very high speed. Landscape metrics show that the fragmentation of the entire urban landscape into small patches happened from 2001 to 2011 in a higher magnitude indicating the occurrence of sprawling characteristics. But in recent times, the entire landscape is aggregating into large single urban patches which indicate a clumpy situation and would affect the local ecological environment. Shannon's entropy model also verifies the compact urban sprawl in different directions and distances from the city centre. The understanding of urban growth dynamics and land use changes is essential for addressing the rapid urbanization within this urban region. There is an immediate need for an appropriate strategy for effective utilization of land use and monitoring of uncontrolled and haphazard urban growth. This research study would help the urban planner to take a specific scope of action for future urban growth and development. [ABSTRACT FROM AUTHOR]

This work presents a novel optimization strategy for maximum coupling results in optical coupler design. It was performed by the association between Evolutionary Strategy based metaheuristic with Fuzzy Logic and Shannon’s Entropy estimation for fitness bias support and control population diversity, respectively. This solution provided convergence for better results with fewer iterations and, consequently, reduced processing time. The results of some of the performance tests are presented, in which the best configuration obtained using the ES+Fuzzy with Shannon’s Entropy leads to an optical coupling around 86% by a device operating at a wavelength of 1.55μm to support the telecommunication services.

Introduction Preservation and proper management of water resources are one of the essential fields of study in the world. In arid and semi-arid regions like Iran, quantitative and qualitative management of underground water resources is particularly important. In most hydrological issues and groundwater resources studies, groundwater statistics and information availability are critical. To collect information without side effects, comprehensive and sufficient data collection with the help of a groundwater monitoring network is very important. In line with the sustainable management of renewable water resources, the need for a network of underground water observation (monitoring) wells to accurately measure the water level is necessary and necessary. Considering the complexities of the underground water environment and the high costs of conventional monitoring methods, inventing new technologies and using advanced methods in this matter will significantly help improve the underground water systems. One of the parameters of particular importance in monitoring groundwater quantity is the groundwater level. Therefore, this parameter should be measured or estimated as accurately as possible. In recent decades, the use of computer and calculation models to monitor the level of underground water has developed significantly. Considering the importance of underground water resources and network monitoring, to save time and money, in this research, principal component analysis and Shannon's entropy theory were used to monitor the underground water network of the Dezful-Andimeshk Plain. Materials and Methods This research used monthly groundwater level information from 77 observation wells in the Dezful-Andimeshk Plain during 2018-2019. Groundwater level information is collected twice a month. Principal component analysis and Shannon entropy methods were used for monitoring. In the current research, the number of statistical periods for each well is 24, less than the total number of observation wells. Twenty-four observation wells around it were used to monitor each well. In groundwater level monitoring, the relative importance of each well is defined by the ratio of the number of times that well is recognized as a compelling well to the number of times that well is included in the analysis of the main components. This ratio shows the importance of each well compared to other wells. Therefore, to save time and costs, less important wells can be removed in the monitoring of the underground water level. In 1948, Shannon showed that events with a high probability of occurrence show less information, and on the contrary, the lower the probability of an event, the more information it provides. In this method, the weight of each well was obtained using Shannon's entropy theory. Any well that has a higher Shannon entropy weight contains more important and unpredictable information and should be preserved. On the contrary, a well that has a lower Shannon entropy weight can be removed from the network. Principal component analysis and Shannon's entropy method in the current research were done with the help of coding in Matlab software due to the high volume of calculations. Results and Discussion To rank the wells, the threshold limits are equal to zero, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and one considered. At threshold one, only wells that have a rank of one remain (wells that are recognized as effective wells in all analyses) and threshold zero includes all wells (effective and ineffective). According to the obtained results, increasing the error in the threshold zero to 0.7 is gradual, but in the thresholds 0.8, 0.9, and one, the error value increases with a high slope. So, the amount of error in the thresholds of 0.7, 0.8, 0.9, and 1 has been calculated as 12.2, 17.7, 25.3 and 34.2 respectively. Therefore, the threshold limit in the current research is considered to be 0.7. However, the number of wells effective in monitoring the underground water level is reduced from 77 to 32. Shannon's entropy weight values were also calculated for all wells. 11 wells have the highest value of Shannon's entropy weight, which shows that they contain the most information. Conclusion The general comparison of the results of the two methods showed that all 11 wells with the highest weight in the Shannon entropy method were also observed as effective wells in the principal component analysis method. By knowing the effective wells in the region, firstly, in the face of lack of time and money, it is possible to use known effective wells for monitoring secondly, by removing ineffective wells, there will be little change in the average level of underground water. It is not possible, or in other words, the tracking error does not increase significantly. Comparing the results of the two methods showed that the remaining wells in Shannon's entropy theory are among the wells identified in the principal component analysis method. Also, considering that the wells in the region were built by the Khuzestan Water and Electricity Organization considering the types of uses, removing the ineffective wells will not affect the process of using the information of the wells. It is recommended to use principal component analysis and Shannon entropy for groundwater quality monitoring in the study area. Additionally, it is suggested to monitor the quality of the underground water network in the study area using the methods used in future research.

The accurate and timely detection of cyber threats is critical to keeping our online economy and data safe. A key technique in early detection is the classification of unusual patterns of network behaviour, often hidden as low-frequency events within complex time-series packet flows. One of the ways in which such anomalies can be detected is to analyse the information entropy of the payload within individual packets, since changes in entropy can often indicate suspicious activity—such as whether session encryption has been compromised, or whether a plaintext channel has been co-opted as a covert channel. To decide whether activity is anomalous, we need to compare real-time entropy values with baseline values, and while the analysis of entropy in packet data is not particularly new, to the best of our knowledge, there are no published baselines for payload entropy across commonly used network services. We offer two contributions: (1) we analyse several large packet datasets to establish baseline payload information entropy values for standard network services, and (2) we present an efficient method for engineering entropy metrics from packet flows from real-time and offline packet data. Such entropy metrics can be included within feature subsets, thus making the feature set richer for subsequent analysis and machine learning applications.

Summary: The right to privacy refers to an individual's decision about how personal information can be gathered, utilized, and disseminated. Individual consent and openness are the most important foundations for gaining consumers' confidence, and this pushes businesses to use privacy‐enhancing techniques while developing systems. The purpose of a privacy‐aware design is to safeguard data in such a manner that it does not expand an adversary's current understanding of an individual beyond what would be permitted. When these data pieces are coupled with the plethora of source data accessible outside the system to identify a user, this becomes crucial. Individual privacy is protected by privacy rules all around the globe, but they are often complicated and ambiguous, making their translation into practical and technologically privacy‐friendly structures difficult. The main contribution of this article is that we use Shannon's entropy (SE) to construct an objective measure that may guide our major technical design choices. And for privacy‐aware architecture, simplifying the state‐of‐the‐art security approaches given in the literature. [ABSTRACT FROM AUTHOR]

Over the past few decades, flood disasters have emerged as the predominant natural hazard in Cyprus, primarily driven by the escalating influence of climate change in the Mediterranean region. In view of this, the objective of this study is to develop a geospatial flood risk map for the island of Cyprus by considering 14 flood hazard factors and five flood vulnerability factors, utilizing geographic information systems (GIS) and remotely sensed datasets. A comparative assessment was conducted for hazard mapping, employing statistical methods of frequency ratio (FR) and FR Shannon's entropy (FR-SE), and multi-criteria decision analysis method of fuzzy analytic hierarchy process (F-AHP). The main findings indicated that the FR method exhibited the highest predictive capability, establishing it as the most suitable approach for flood hazard mapping. Additionally, vulnerability factors were aggregated using F-AHP to generate the vulnerability map. The resulting flood risk map, which is the product of flood hazard and flood vulnerability, revealed that 9% of the island was located within highly risky regions, while 13.2% was classified as moderate risk zones. Spatial analysis of these high-risk areas indicated their concentration in the primary city districts of the island. Therefore, to mitigate future risks within these cities, an analysis of potential expansion zones was conducted, identifying the best-suited zone exhibiting the lowest risk. The generated flood risk map can serve as a valuable resource for decision-makers on the island, facilitating the integration of flood risk analysis into urban management plans. [ABSTRACT FROM AUTHOR]

The upsurge in economic activities and urban dwellers has spurred sprawl-like growth in the Sekondi-Takoradi metropolis. This study used Landsat imageries and Shannon entropy to assess sprawl in the Sekondi-Takoradi metropolis. Analysis of the study revealed an increase in built-up by 63.07 km2 while Shannon entropy result (which ranged from 2.17 to 2.47), revealed that the metropolis has been sprawling from 1991 to 2023. Hence, causing significant changes in the land cover composition of the metropolis. This study provides valuable insights into the spatial dynamics of the metropolis, which will guide policymakers in addressing the environmental challenges associated with urban expansion. [ABSTRACT FROM AUTHOR]

The transport industry is one of the main contributors to environmental pollutions. Sustainability evaluation of the transport industry helps companies to increase their awareness and leads to the right decisions. This study addresses the subject of sustainability for the transportation supply chain. Data envelopment analysis (DEA is a popular approach for efficiency evaluation. This work develops a common set of weights (CSW) model using two-stage network DEA and Shannon's entropy. The proposed CSW model evaluates the sustainability of transportation supply chains in DEA context. The objective of this paper is to propose an integrated slack-based two-stage network DEA model with zero inputs and CSW analysis using Shannon's entropy technique. To calculate the optimal weights, the Shannon entropy technique is used. To the best of the authors' knowledge, there is no two-stage network DEA model based on Shannon's entropy for evaluating the sustainability of transport companies when there are zero inputs. The proposed model can fully rank DMUs. In this study, optimal scores by different weights are obtained and can be applied in real-world problems. To demonstrate the applicability of the proposed approach, the sustainability of transportation supply chains is assessed. [ABSTRACT FROM AUTHOR]

Shannon's entropy is a fundamental concept in information theory that quantifies the uncertainty or information in a random variable or data set. This article addresses the estimation of Shannon's entropy for the Maxwell lifetime model based on progressively first-failure-censored data from both classical and Bayesian points of view. In the classical perspective, the entropy is estimated using maximum likelihood estimation and bootstrap methods. For Bayesian estimation, two approximation techniques, including the Tierney-Kadane (T-K) approximation and the Markov Chain Monte Carlo (MCMC) method, are used to compute the Bayes estimate of Shannon's entropy under the linear exponential (LINEX) loss function. We also obtained the highest posterior density (HPD) credible interval of Shannon's entropy using the MCMC technique. A Monte Carlo simulation study is performed to investigate the performance of the estimation procedures and methodologies studied in this manuscript. A numerical example is used to illustrate the methodologies. This paper aims to provide practical values in applied statistics, especially in the areas of reliability and lifetime data analysis. [ABSTRACT FROM AUTHOR]

With the development of environmental reporting, the concern about the greenwashing behavior of companies has increased, so the aim of the current research is presenting a pattern of greenwashing phenomenon in corporate reporting. This research is practical in terms of purpose and it is a meta-synthesis research in terms of the nature of data analysis. For this purpose, by referring to english and persian studies published in reliable databases, in all geographical areas and during the years 1381 to November 1402 (2002 to November 2023), 53 articles were identified with the prisma method, also Shannon's entropy was used to rank the concepts. The validation of the output of the meta-synthesis method has been done using 11 experts who were selected using the snowball sampling method. In the current research, greenwashing pattern is presented using the seven-stage method of Sandelowski and Barroso, this pattern includes 5 main categories (including causal factors, contextual factors, interventing factors, prevention strategies and consequences of greenwashing), 22 concepts and 124 codes. The results also show that in each of the main categories, the motivation to gain legitimacy, the lack of related laws, the existence of institutional shareholders, environmental scandal and promotion of legal mechanisms are the most important. The presented pattern of the current research can be useful for managers and researchers interested in the field of environmental reporting, in order to gain a comprehensive understanding of the concept of greenwashing, to evaluate the importance and weight of each of the components in the greenwashing. [ABSTRACT FROM AUTHOR]

Shannon’s entropy is a fundamental concept in information theory that quantifies the uncertainty or information in a random variable or data set. This article addresses the estimation of Shannon’s entropy for the Maxwell lifetime model based on progressively first-failure-censored data from both classical and Bayesian points of view. In the classical perspective, the entropy is estimated using maximum likelihood estimation and bootstrap methods. For Bayesian estimation, two approximation techniques, including the Tierney-Kadane (T-K) approximation and the Markov Chain Monte Carlo (MCMC) method, are used to compute the Bayes estimate of Shannon’s entropy under the linear exponential (LINEX) loss function. We also obtained the highest posterior density (HPD) credible interval of Shannon’s entropy using the MCMC technique. A Monte Carlo simulation study is performed to investigate the performance of the estimation procedures and methodologies studied in this manuscript. A numerical example is used to illustrate the methodologies. This paper aims to provide practical values in applied statistics, especially in the areas of reliability and lifetime data analysis.

The risk of unintentional islanding creation in distributed energy systems poses a significant security concern since unintentional islanding formation could lead to a supply of energy outside of the optimal quality limits. This constitutes a risk for users, maintenance personnel, infrastructure, and devices. To mitigate this problem, anti-islanding protections are widely used to prevent the distributed generator from feeding a portion of the radial distribution grid when a protection device trips upstream. However, the effectiveness of these protections heavily relies on properly tuning protection setting thresholds (such as time delay and pickup). This work proposes a novel approach that utilizes entropy as a model and metric of the uncertainty associated with a particular protection setting. By minimizing entropy, the proposed method aims to improve stability and sensitivity, consequently improving the overall performance of anti-islanding protection. Simulation results demonstrate that the Bayesian entropy methodology (BEM) approach achieves enhanced stability in various scenarios, including frequency transients, and demonstrates a notable reduction in the size of the dataset and computational burden, ranging between 91% and 98%, when compared to related works, with an improvement of the uncertainty achieved. The findings of this study contribute to the development of more robust and reliable anti-islanding protections. [ABSTRACT FROM AUTHOR]

Flooding is a common and catastrophic natural event that has serious consequences for both human and nature. The assessment of flood susceptibility within watersheds and the implementation of measures to mitigate flood-related impacts and damages are integral aspects of environmental, water resources and disaster management. Assam is significantly impacted by recurring flood events consisting of multiple waves. Consequently, it is imperative to precisely identify the areas susceptible to flooding. Therefore, this research aims to assess the capability of the Frequency Ratio (FR) and Shannon's Entropy (SE) model for mapping flood susceptibility; and to identify extremely flood prone locations in Assam, India. The study was conducted in four main stages. Firstly, a flood inventory map was developed by using historic records (1998 to 2017) from the Assam Water Resources Department (AWRD), Assam State Disaster Management Authority (ASDMA), and extensive field surveys. A total of 1630 flood occurrence points were extracted; and of these 75% were randomly selected for model training and 25% for validation. Secondly, nine flood conditioning factors were considered, including elevation, aspect, distance from river, drainage density, Land-use and Land-cover (LULC), rainfall, geomorphology, Topographic Wetness Index (TWI), and Normalised Difference Vegetative Index (NDVI). The thematic layers were prepared in a Geographic Information System (GIS). Thirdly, flood susceptibility maps (FSMs) were generated by applying FR and SE models, using the flood conditioning factors and the occurrence locations. The FSMs were classified into five classes. Finally, the predictive capability of FR and SE models and the validation was done by using Receiver Operating Characteristic (ROC) curves and computing the Area Under Curves (AUC). The AUC for the FR model was 0.748, and the SE model, it was 0.761. The validation results suggests that the SE model is more suitable for predicting flood susceptibility in the study area. The study makes a unique contribution by identifying the flood susceptible zones in Assam, a state afflicted by recurrent floods. The derived FSMs of the region can be used for effective decision making in flood management, as well as for strategic planning and mitigation measures toward flood events in the future. [ABSTRACT FROM AUTHOR]

Introduction: Multiple analysis techniques evaluate electrograms during atrial fibrillation (AF), but none have been established to guide catheter ablation. This study compares electrogram properties recorded from multiple right (RA) and left atrial (LA) sites. Methods: Multisite LA/RA mapping (281 ± 176/239 ± 166 sites/patient) was performed in 42 patients (30 males, age 63 ± 9 years) undergoing first (n = 32) or redo‐AF ablation (n = 10). All electrogram recordings were visually reviewed and artifactual signals were excluded leaving a total of 21 846 for analysis. Electrogram characteristics evaluated were cycle length (CL), amplitude, Shannon's entropy (ShEn), fractionation interval, dominant frequency, organizational index, and cycle length of most recurrent morphology (CLR) from morphology recurrence plot analysis. Results: Electrogram characteristics were correlated to each other. All pairwise comparisons were significant (p <.001) except for dominant frequency and CLR (p =.59), and amplitude and dominant frequency (p =.38). Only ShEn and fractionation interval demonstrated a strong negative correlation (r = −.94). All other pairwise comparisons were poor to moderately correlated. The relationships are highly conserved among patients, in the RA versus LA, and in those undergoing initial versus redo ablations. Antiarrhythmic drug therapy did not have a significant effect on electrogram characteristics, except minimum ShEn. Electrogram characteristics associated with ablation outcome were shorter minimum CLR, lower minimum ShEn, and longer mimimum CL. There was minimal overlap between the top 10 sites identified by one electrogram characteristic and the top 10 sites identified by the other 10 characteristics. Conclusion: Multiple techniques can be employed for electrogram analysis in AF. In this analysis of eight different electrogram characteristics, seven were poorly to moderately correlated and do not identify similar locations. Only some characteristics were predictive of ablation outcome. Further studies to consider electrogram properties, perhaps in combination, for categorizing and/or mapping AF are warranted. [ABSTRACT FROM AUTHOR]

Introduction Preservation and proper management of water resources are one of the essential fields of study in the world. In arid and semi-arid regions like Iran, quantitative and qualitative management of underground water resources is particularly important. In most hydrological issues and groundwater resources studies, groundwater statistics and information availability are critical. To collect information without side effects, comprehensive and sufficient data collection with the help of a groundwater monitoring network is very important. In line with the sustainable management of renewable water resources, the need for a network of underground water observation (monitoring) wells to accurately measure the water level is necessary and necessary. Considering the complexities of the underground water environment and the high costs of conventional monitoring methods, inventing new technologies and using advanced methods in this matter will significantly help improve the underground water systems. One of the parameters of particular importance in monitoring groundwater quantity is the groundwater level. Therefore, this parameter should be measured or estimated as accurately as possible. In recent decades, the use of computer and calculation models to monitor the level of underground water has developed significantly. Considering the importance of underground water resources and network monitoring, to save time and money, in this research, principal component analysis and Shannon's entropy theory were used to monitor the underground water network of the Dezful-Andimeshk Plain. Materials and Methods This research used monthly groundwater level information from 77 observation wells in the Dezful-Andimeshk Plain during 2018-2019. Groundwater level information is collected twice a month. Principal component analysis and Shannon entropy methods were used for monitoring. In the current research, the number of statistical periods for each well is 24, less than the total number of observation wells. Twenty-four observation wells around it were used to monitor each well. In groundwater level monitoring, the relative importance of each well is defined by the ratio of the number of times that well is recognized as a compelling well to the number of times that well is included in the analysis of the main components. This ratio shows the importance of each well compared to other wells. Therefore, to save time and costs, less important wells can be removed in the monitoring of the underground water level. In 1948, Shannon showed that events with a high probability of occurrence show less information, and on the contrary, the lower the probability of an event, the more information it provides. In this method, the weight of each well was obtained using Shannon's entropy theory. Any well that has a higher Shannon entropy weight contains more important and unpredictable information and should be preserved. On the contrary, a well that has a lower Shannon entropy weight can be removed from the network. Principal component analysis and Shannon's entropy method in the current research were done with the help of coding in Matlab software due to the high volume of calculations. Results and Discussion To rank the wells, the threshold limits are equal to zero, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and one considered. At threshold one, only wells that have a rank of one remain (wells that are recognized as effective wells in all analyses) and threshold zero includes all wells (effective and ineffective). According to the obtained results, increasing the error in the threshold zero to 0.7 is gradual, but in the thresholds 0.8, 0.9, and one, the error value increases with a high slope. So, the amount of error in the thresholds of 0.7, 0.8, 0.9, and 1 has been calculated as 12.2, 17.7, 25.3 and 34.2 respectively. Therefore, the threshold limit in the current research is considered to be 0.7. However, the number of wells effective in monitoring the underground water level is reduced from 77 to 32. Shannon's entropy weight values were also calculated for all wells. 11 wells have the highest value of Shannon's entropy weight, which shows that they contain the most information. Conclusion The general comparison of the results of the two methods showed that all 11 wells with the highest weight in the Shannon entropy method were also observed as effective wells in the principal component analysis method. By knowing the effective wells in the region, firstly, in the face of lack of time and money, it is possible to use known effective wells for monitoring secondly, by removing ineffective wells, there will be little change in the average level of underground water. It is not possible, or in other words, the tracking error does not increase significantly. Comparing the results of the two methods showed that the remaining wells in Shannon's entropy theory are among the wells identified in the principal component analysis method. Also, considering that the wells in the region were built by the Khuzestan Water and Electricity Organization considering the types of uses, removing the ineffective wells will not affect the process of using the information of the wells. It is recommended to use principal component analysis and Shannon entropy for groundwater quality monitoring in the study area. Additionally, it is suggested to monitor the quality of the underground water network in the study area using the methods used in future research. [ABSTRACT FROM AUTHOR]

In 1997, Sierpinski graphs, S (n , k) , were obtained by Klavzar and Milutinovic. The graph S (1 , k) represents the complete graph K k and S (n , 3) is known as the graph of the Tower of Hanoi. Through generalizing the notion of a Sierpinski graph, a graph named a generalized Sierpinski graph, denoted by S i e (Λ , t) , already exists in the literature. For every graph, numerous polynomials are being studied, such as chromatic polynomials, matching polynomials, independence polynomials, and the M-polynomial. For every polynomial there is an underlying geometrical object which extracts everything that is hidden in a polynomial of a common framework. Now, we describe the steps by which we complete our task. In the first step, we generate an M-polynomial for a generalized Sierpinski graph S i e (Λ , t) . In the second step, we extract some degree-based indices of a generalized Sierpinski graph S i e (Λ , t) using the M-polynomial generated in step 1. In step 3, we generate the entropy of a generalized Sierpinski graph S i e (Λ , t) by using the Randić index. [ABSTRACT FROM AUTHOR]

Several information measures have been proposed and studied in the literature. One such measure is extropy, a complementary dual function of entropy. Its meaning and related aging notions have not yet been studied in great detail. In this paper, we first illustrate that extropy information ranks the uniformity of a wide array of absolutely continuous families. We then discuss several theoretical merits of extropy. We also provide a closed-form expression of it for finite mixture distributions. Finally, the dynamic versions of extropy are also discussed, specifically the residual extropy and past extropy measures. [ABSTRACT FROM AUTHOR]

In this paper, we establish a new refinement of Jensen-type inequality for uniformly convex functios. Furthermore, we apply those results in information theory and we obtain strong and more precise bounds for Shannon's entropy. [ABSTRACT FROM AUTHOR]

Urban sprawl, characterized by unorganized, irregular built-up development encircling cities, poses a grave peril to natural resources and disrupts the delicate ecological equilibrium. Hence, comprehending and dissecting the spatial dynamics of urban expansion assumes critical significance for fostering effective and sustainable urban planning practices. Employing fractal dimension, Shannon's entropy, and classified built-up maps for the years 2000, 2011, and 2021, this study is dedicated to scrutinizing the fractal attributes of urban structures and the sprawling nature prevalent in Thiruvananthapuram city, situated in the state of Kerala, India. The findings of the study reveal that dispersed settlement growth is notably concentrated towards the northern and northwestern fringes of the city, exerting substantial stress on the existing natural environment. The progressively widening gap between the textural and structural fractal dimensions serves as a stark indicator of impending threats to the sustainability of urban development. Among different urban forms, the central urban core, secondary urban core, and ribbon settlements display a more complex interplay in their textural and structural associations over time, while the fringe zones consistently uphold optimal settings conducive to thoughtful settlement development. The study also establishes that the year 2011 stands as a pivotal milestone, distinguished by an optimal urban composition within the evolutionary trajectory of the city. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an universal definition (fgh-convex) that results in several types of convexity. Particular cases of the fgh-convex are for instance the harmonically convex, geometrically convex, GA-convex, log-convex, and several others. Also, we obtain some useful inequalities such as Jensen, generalization of Jensen Hermite-Hadamard, Mercer inequalities. Moreover, with the use of these inequalities, we obtained bounds for Shannon's entropy and Kapur's entropy. Finally, we found an application of the obtained inequalities in means. [ABSTRACT FROM AUTHOR]

The evaluation of irrigation suitability plays a crucial role for the socio-economic development of the society, especially in the region of Sundarban. For sustainable agricultural practices, groundwater quality must be suitable for irrigation; otherwise, it can degrade soil and diminish crop yield. The entropy information theory, several irrigational indices, multivariate statistics, GIS, and geostatistics are used in this work to evaluate the geographical distribution and quality of groundwater in the Indian Sundarban region. In total, 33 groundwater samples were collected in 2018 (April and May), and they were evaluated for major cations, anions, as well as other parameters like electrical conductivity (EC), soluble sodium percentage (SSP), potential salinity (PS), total dissolved solids (TDS), Kelly ratio (KR), sodium absorption ratio (SAR), permeability index (PI), residual sodium carbonate (RSC), magnesium hazard (MH), and residual sodium bicarbonate (RSBC). The overall trend of the principal cations and anions is in the sequence of Na+ ≥ Mg2+ ≥ Ca2+ ≥ K2+ and HCO3− ≥ Cl− ≥ NO3− ≥ SO42− ≥ F−, respectively, whereas the spatial variation of %Na, SAR, RSBC, and MH demonstrate very poor irrigation water quality, and spatial variation of KR, RSC, SSP, PI, and PS signifies that the irrigation water quality is excellent to good. In order to identify the specific association and potential source of the dissolved chemical in the groundwater, statistical techniques like correlation and principal component analysis were also employed. The hydrochemical facies indicates that mixed type makes up the bulk (51.51%) of the water samples. Following the Wilcox plot, more than 75% of the water samples are good to doubtful; however, by the US salinity hazard map, roughly 60.60% of the samples had high salinity (C3-S1 zone). The EWQII reports that no samples fall into the very good (no restriction) category, whereas 30.30%, 30.30%, and 39.40% of the sample wells record good (low restriction), average (moderate restriction), and poor (severe restriction) irrigation water quality, respectively. Based on this study, the bulk of the groundwater samples taken from the study area are unsuitable for cultivation. The findings of this study will also help decision-makers develop adequate future plans for irrigation and groundwater resource management. [ABSTRACT FROM AUTHOR]

Shannon's entropy is a concept used in the field of theoretical chemistry since the early 70s. The versatility of the concept makes possible its association with the chemical reactivity theory. In this work, we present a development that relates Shannon's entropy to chemical hardness. The obtained equations were applied to the set of 1641 molecules. Based on our computational results, we reveal a relationship between Shannon's entropy and chemical hardness. [ABSTRACT FROM AUTHOR]

Social organisms benefit from division of labour and collective behaviours. However, if individuals overlap widely in their efforts, these benefits may not be proportional to the number of individuals that take part in an activity. We examined foraging behaviour and route fidelity in colonies of the ant Dinoponera grandis (formerly Dinoponera australis), a large species with relatively few active foragers that lack nestmate recruitment and chemical trailing behaviour. For 12 colonies, we marked individual foragers and mapped their foraging routes to test the hypothesis that each ant specializes in a particular area around the nest and that this route fidelity increases the overall area covered by the colony. For each individual, we recorded the mean direction and duration of each foraging trip, foraging success and maximal distance from the nest. For each colony, we measured the number of workers and the total foraging area. Additionally, we measured Shannon's entropy to describe foraging behaviour structure of the colonies. Overall, we mapped 272 foraging routes from 95 different foragers. The total area used by each colony averaged 66.2 m2. Within colonies, over 68% of foragers exhibited a high degree of route fidelity, with most foragers following different foraging directions. Most colonies had a high Shannon's entropy, suggesting an even exploration of the foraging territory. Our results suggest that D. grandis exhibit route fidelity and high entropy. This strategy likely increases foraging efficiency and search area and may be particularly important for species with relatively few foragers. • The giant ant Dinoponera grandis exhibits route fidelity when foraging. • Different areas within each territory were explored with similar probability. • By departing in different directions, foragers may increase their search area. • Shannon's entropy is a useful measure to quantify foraging behaviour patterns. • The number of foragers determines the size of the foraging territory. [ABSTRACT FROM AUTHOR]