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ABSTRACT Aim Location Taxon Methods Results Main Conclusions An ecological community consists of species of various abundances that reflect their responses to the environmental conditions. A classic macroecological pattern, the species abundance distribution (SAD), has been studied for diverse taxa and communities and integrated into numerous modelling tools. Despite its widespread use, a mathematical model that can capture variations in the empirical SAD and describe its response to environmental changes is still lacking. By integrating the Maximum Entropy Theory of Ecology (METE) with a generalised entropy called Rényi's entropy, we aim to develop a new ecoinformatic model that can predict the variation of empirical SAD along multiple environmental gradients.Panama.Angiosperms.We extend the METE using the Rényi's entropy as an uncertainty measure. We apply this extended METE, called Rényi model, to the tree abundance data from 49 plots in Panama and predict the SAD within each plot. We estimate Rényi's parameter q by fitting the predicted SAD to the empirical SAD in each plot. We further compile climate and soil data from the Panama plots and analyse their relationships with the estimated q using multiple regressions.Rényi model provides adequate description of the empirical SADs and outperforms lognormal or log‐series models in 40 of the 49 tree plots, according to the Akaike information criterion. Variations in Renyi's q estimates (from 1/2 to 1) reflect shifts in the empirical SADs. Multiple regressions reveal that P, Al and NH4, three soil chemicals that are important for tree growth and species distribution, significantly affect Renyi's q across plots.These findings suggest that the Rényi model and Rényi's q can characterise the SAD of communities under environmental changes. They also indicate the potential of using generalised entropies to predict macroecological patterns in stressed ecosystems. [ABSTRACT FROM AUTHOR]

Determination of distribution range with the suitability of available habitat is one of the important facets for conservation planning on any threatened species. The slender-billed vulture (SBV) Gyps tenuirostris is one of the three critically endangered Gyps vultures found in Arunachal Pradesh, North East India. Maximum Entropy (MaxEnt) software was used to predict potential distribution range, habitat suitability and influence of environmental variables on the distribution of SBV. Analysis showed that out of the total area of 81658.85 km2, 95.88 km2 (0.12%) fell in the 'extremely suitable area' category. The prediction from MaxEnt was highly accurate, with a statistical AUC value of 0.994. The predicted preferred habitat of SBV includes areas with low elevation, high temperature, high precipitation, and open land with less vegetation cover. Elevation (63%) was found to have the most significant influence on the distribution of SBV. The findings of the present study will help in the implementation of any conservation initiatives required in the future with respect to SBV population protection or habitat conservation in Arunachal Pradesh. [ABSTRACT FROM AUTHOR]

Global climate change is one of the most critical challenges facing natural ecosystems. As sedentary organisms, plant communities are especially vulnerable, with climate change significantly impacting their development, productivity, and distribution. This study focuses on modelling and mapping the potential distribution of black pine (Pinus nigra) within the Antalya Regional Forest Directorate under the SSP1 2.6 climate scenario for the years 2040, 2060, 2080, and 2100. The MaxEnt modelling method, combined with the HadGEM3-GC31-LL climate model from WorldClim, was used to assess the impact of climate change on black pine. The current distribution model results showed "good" predictive performance, with AUC values of 0.855 for training data and 0.851 for testing data. Key variables influencing the model included precipitation during the wettest quarter, annual precipitation, maximum temperature of the warmest month, and elevation. Projections indicate that the black pine's distribution will shrink by 2040, become increasingly fragmented by 2060, and decline further by 2080, with near-total disappearance by 2100. In conclusion, this study highlights the urgent need for adaptive management strategies to address the effects of climate change on black pine forests. [ABSTRACT FROM AUTHOR]

BACKGROUND: The range of Glires is influenced by human activities and climate change. However, the extent to which human activities and environmental changes have contributed to this relationship remains unclear. We examined alterations in the distribution changes and driving factors of the Himalayan marmot, plateau pika, and plateau zokor on the Qinghai–Tibet Plateau (QTP) using the maximum entropy (MaxEnt) model and a geographical detector (Geodetector). RESULTS: The MaxEnt model showed that the contribution rates of the human footprint index (HFI) to the distribution patterns of the three types of Glires were 46.70%, 58.70%, and 59.50%, respectively. The Geodetector results showed that the distribution pattern of the Himalayan marmot on the QTP was influenced by altitude and the normalized difference vegetation index (NDVI). The distribution patterns for plateau pikas and plateau zokors were driven by HFI and NDVI. Climate has played a substantial role in shaping suitable habitats for these three Glires on the QTP. Their suitable area is expected to decrease over the next 30–50 years, along with their niche breadth and overlap. Future suitable habitats for the three Glires tended to shift toward higher latitudes on the QTP. CONCLUSION: These findings underscore the impacts of environmental and human factors on the distribution of the three Glires on the QTP. They have enhanced our understanding of the intricate relationships between Glires niches and environments. This can aid in identifying necessary interventions for developing effective early warning systems and prevention strategies to mitigate Glires infestations and plague epidemics on the QTP. © 2024 Society of Chemical Industry. [ABSTRACT FROM AUTHOR]

Peatlands play a key role in the circulation of the main greenhouse gases (GHG) – methane (CH4), carbon dioxide (CO2), and nitrous oxide (N2O). Therefore, detecting the spatial pattern of GHG sinks and sources in peatlands is pivotal for guiding effective climate change mitigation in the land use sector. While geospatial environmental data, which provide detailed spatial information on ecosystems and land use, offer valuable insights into GHG sinks and sources, the potential of directly using remote sensing data from satellites remains largely unexplored. We predicted the spatial distribution of three major GHGs (CH4, CO2, and N2O) sinks and sources across Finland. Utilizing 143 field measurements, we compared the predictive capacity of three different data sets with MaxEnt machine-learning modeling: (1) geospatial environmental data including climate, topography and habitat variables, (2) remote sensing data (Sentinel-1 and Sentinel-2), and (3) a combination of both. The combined dataset yielded the highest accuracy with an average test area under the receiver operating characteristic curve (AUC) of 0.845 and AUC stability of 0.928. A slightly lower accuracy was achieved using only geospatial environmental data (test AUC 0.810, stability AUC 0.924). In contrast, using only remote sensing data resulted in reduced predictive accuracy (test AUC 0.763, stability AUC 0.927). Our results suggest that (1) reliable estimates of GHG sinks and sources cannot be produced with remote sensing data only and (2) integrating multiple data sources is recommended to achieve accurate and realistic predictions of GHG spatial patterns. Highlights: We compared remote sensing and geospatial data to predict peatland greenhouse gas sinks and sources across Finland. Remote sensing data perform less effectively than habitat and climate-related variables. We recommend integrating various data sources for modeling greenhouse gas sinks and sources. [ABSTRACT FROM AUTHOR]

Network or matrix reconstruction is a general problem that occurs if the row‐ and column sums of a matrix are given, and the matrix entries need to be predicted conditional on the aggregated information. In this paper, we show that the predictions obtained from the iterative proportional fitting procedure (IPFP) or equivalently maximum entropy (ME) can be obtained by restricted maximum likelihood estimation relying on augmented Lagrangian optimization. Based on this equivalence, we extend the framework of network reconstruction, conditional on row and column sums, toward regression, which allows the inclusion of exogenous covariates and bootstrap‐based uncertainty quantification. More specifically, the mean of the regression model leads to the observed row and column margins. To exemplify the approach, we provide a simulation study and investigate interbank lending data, provided by the Bank for International Settlement. This dataset provides full knowledge of the real network and is, therefore, suitable to evaluate the predictions of our approach. It is shown that the inclusion of exogenous information leads to superior predictions in terms of L1 and L2 errors. [ABSTRACT FROM AUTHOR]

Landslide mapping inventories are crucial for disaster prevention and risk mitigation. Remote sensing uses remote sensors that record data from the Earth's surface encoded in digital images distributed in electromagnetic spectrum ranges, allowing us access to various types of information. This, in conjunction with appropriate spatial analysis and modeling techniques, allows us to monitor the phenomena, such as landslides, that put man-nature coupled systems at risk. This paper presents a practical alternative for integrating landslide inventories in the central area of the state of Guerrero in Mexico by using the maximum entropy model (MaxEnt), a machine learning algorithm oriented to the potential prediction of patterns using continuous change (CC) maps as input. These maps were obtained using the unsupervised change detection methods linear regression and difference applied to transformed images, the normalized difference vegetation index (NDVI), and principal component analysis (PCA). The selection of supplementary input data was made by using the jackknife test to assess the contribution of the main determinant factors of slope stability: lithology (L), angular slopes (AS), and terrain orientation (TO). Ground truth landslide samples were used for the algorithm training (2/3) and the accuracy assessment of the final inventory map (1/3). The landslide inventory map derived by combining the MaxEnt model, the thresholding by the secant method, and the discrimination of pixels with slope values less than 5° reveals a high accuracy and visual concordance with reality, reaching 3.0% and 3.5% in commission and omission errors, a Kappa concordance index of 93.37%, and an AUC of 0.75, indicating MaxEnt is a practical and efficient tool that allows for the rapid and accurate generation of reliable maps for the detection of landslides. [ABSTRACT FROM AUTHOR]

The entropy-based goodness-of-fit tests have gained prominence due to their easiness and accuracy. In this paper, the goodness of fit test problem is developed for widely used Exponential distribution under imprecise conditions. To this aim, a novel concept called fuzzy differential entropy is introduced to measure the degree of uncertainty for fuzzy random variables. Then, the fuzzy empirical differential entropy proposed to estimate the new fuzzy information measure. We consider the Vasicek estimator of entropy and use the α-pessimistic approach to propose an entropy-based goodness of fit test for the fuzzy Exponential distribution. The practical applicability and superiority of the proposed test over other fuzzy goodness-of-fit tests were demonstrated through Monte Carlo simulation using a numerical example and two real-life applications. [ABSTRACT FROM AUTHOR]

An iterative evaluation method for testability of avionics electronic system in field is proposed to improve the accuracy of testability evaluation and solve the problems of few testability evaluation samples and low evaluation accuracy of avionics electronic system after aircraft service. Firstly, the idea of field testability evaluation based on Bayesian framework is expounded. Secondly, according to the prior information, the maximum entropy method, combined with PSO algorithm, is used to find hyper-parameters in the prior distribution of fault detection rate, and hyper-parameters consistency check is carried out. Then, the posterior distribution is obtained by Bayes formula, and the iterative estimation results of fault detection rate are obtained. Combined with the example, the comparison and analyses between this method and existing method further proved the correctness and advantages of the proposed method.

Abstract Background Understanding the distribution pattern of species and their suitable habitat is key to focus conservation efforts. Climate change has had notable impact on the distribution and extent of suitable habitats, and the long-term survival of various species. We aim to determine the distribution and extent of suitable habitats for Tauraco ruspolii and T. leucotis in Ethiopia and predict their range in the 2050s and 2070s using MaxEnt algorithm. We used 25 and 29 rarified occurrence points for T. ruspolii and T. leucotis, respectively, and 13 environmental variables. Three regularization multipliers and two cut-off thresholds were used to map the potential suitable habitats for each species under current and future climates. Maps were assembled from these techniques to produce final composite tertiary maps and investigated the habitat suitability overlap between the two species using the UNION tool in the geographical information system. Result All model run performances were highly accurate for both species. Precipitation of the driest month and vegetation cover are the most influential variables for the habitat suitability of T. ruspolii. The habitat suitability of T. leucotis is also mainly influenced by mean temperature of the driest quarter and vegetation cover. Under the current climate, the suitable habitat predicted for T. ruspolii covered about 24,639.19 km2, but its range size change shows a gain and increase by 156.00% and 142.68% in 2050 and 2070, respectively. The T. leucotis‘s current suitable habitat ranges about 204,397.62 km², but this is reduced by 40.84% and 68.67% in 2050 and 2070, respectively. Our modeling also showed that there was suitable habitat overlap between them at the margin of their respective habitat types in time series. Conclusion We concluded that there is a direct or indirect impact of climate change on the suitable habitat range expansion for T. ruspolii and contraction for T. leucotis as well as overlapping of these turaco species in different regions of Ethiopia. Therefore, understanding the distribution of current and future suitable habitats of the two turaco species can provide valuable information to implement conservation practices for the species and the regions as well.

Species' ranges are shifting rapidly with climate change, altering the composition of biological communities and interactions within and among species. Hybridization is among the species interactions that may change markedly with climate change, yet it is understudied relative to others. We used non‐invasive genetic detections to build a maximum entropy species distribution model and investigate the factors that delimit the present and future ranges of American marten (Martes americana) and Pacific marten (Martes caurina) in a contact zone in the Northern Rockies. We found that climate change will decrease the suitable habitat predicted for both species, as well as the amount of overlap in predicted suitable habitat between the species. Interestingly, predicted suitable habitat for Pacific marten extended further north in the study region than our genetic detections for the species, suggesting that biotic factors, such as interactions with American marten, may affect the realized range of this species. Our results suggest that future work investigating the interactions among biotic and abiotic factors that influence hybrid zone dynamics is important for predicting the futures of these two species in this area under climate change. Climate change is altering the distributions of species worldwide, including those of hybridizing species. We use species distribution models, built from non‐invasive genetic detections of marten species, to show that the distributions of American marten and Pacific marten in the Northern Rockies of the United States will be differentially affected by climate change. [ABSTRACT FROM AUTHOR]

This study proposes the foremost application of the entropy concept to investigate the streamwise S-type mean velocity distribution with infection-phenomenon in turbulent open-channel flows and turbulent Couette flows. Probability based fractional entropy is used for this study. Using the concept of entropy maximization the velocity distribution models are derived. Proposed models are fully analytical and applicable to the whole flow depth in both for open-channel flows and the turbulent Couette flows. All the proposed models are validated with different experimental data sets, field data and DNS data available in the literature. The validation results show good performance for both of the velocity distribution models. Apart form validation, the present velocity distribution models are compared with deterministic (non-entropy based) models since there exists no entropy based velocity distributions to describe the infection-phenomenon in turbulent open-channel flows and turbulent Couette flows. To understand the performance of these models, the relative error and the coefficient of determination ( R 2 ) are computed. Results of the error analysis show the good efficiency of the proposed models for several experimental and field data sets. [ABSTRACT FROM AUTHOR]

Robust geometric fitting is one of the crucial and fundamental problems in computer vision and pattern recognition. While random sampling and consensus maximization have been popular strategies for robust fitting, finding a balance between optimization quality and computational efficiency remains a persistent obstacle. In this paper, we adopt an optimization perspective and introduce a novel maximum consensus robust fitting algorithm that incorporates the maximum entropy framework into the consensus maximization problem. Specifically, we incorporate the probability distribution of inliers calculated using maximum entropy with consensus constraints. Furthermore, we introduce an improved relaxed and accelerated alternating direction method of multipliers (R-A-ADMMs) strategy tailored to our framework, facilitating an efficient solution to the optimization problem. Our proposed algorithm demonstrates superior performance compared to state-of-the-art methods on both synthetic and contaminated real datasets, particularly when dealing with contaminated datasets containing a high proportion of outliers. [ABSTRACT FROM AUTHOR]

Copyright of Artvin Çoruh Üniversitesi Orman Fakültesi Dergisi is the property of Artvin Coruh University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Forestry Society of Croatia / Sumarski List Hrvatskoga Sumarskoga Drustva is the property of Forestry Society of Croatia and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Successional patterns in lacustrine sand dunes along Lake Superior begin with grass-dominated plant communities leading to the establishment of Pinus banksiana Lamb. as initial forests. Using maximum entropy models, we predicted P. banksiana seedling and sapling patterns within the Grand Sable Dunes, Pictured Rocks National Lakeshore, USA, based on slope, aspect, forest basal area, and vegetation types. Across the different vegetation types, there were variable probabilities of seedling and sapling occurrence. For both seedlings and saplings, the higher likelihoods of occurrence were observed in coastal pine barrens vegetation types. P. banksiana regeneration is occurring in the Grand Sable Dunes in the absence of fire, with seedlings establishing and saplings being recruited in a variety of vegetation types. With the greatest probabilities in barrens, there is likely a relationship with seed source and canopy density. Understanding regeneration patterns in dune ecosystems is necessary to predict the future forest arrangement and colonization of P. banksiana into the dunes. These results contribute insights into the dynamics of plant communities in lacustrine dune systems, specifically the establishment of P. banksiana seedlings in various vegetation types. Continued forest establishment and increasing P. banksiana density will influence endangered species and non-native species management strategies for Pictured Rocks National Lakeshore. [ABSTRACT FROM AUTHOR]

The maximum information entropy production model (MaxEnt), the relative humidity at equilibrium approach (ETRHEQ), and the Surface Flux Equilibrium model (SFE) are three recently developed models to estimate evapotranspiration. Although the connection between ETRHEQ and SFE is evident, no attempts have been made to investigate the congruence, distinctions, or potential complementarity between the two models and MaxEnt. Our mathematical analysis demonstrates that minimizing the vertical variance of RH in ETRHEQ is equivalent to minimizing the dissipation function of energy fluxes in MaxEnt, under the assumption of the same eddy diffusivity of heat and water vapor and with a specific expression for the ratio between the thermal inertia terms for H and LE. The connection between ETRHEQ, SFE, and MaxEnt is independent of Monin‐Obukhov similarity theory (MOST)'s extremum solution, and MOST's extreme solution can be viewed as equivalent to introducing a constant correction factor to account for atmospheric stability. While ETRHEQ and MaxEnt can be united within a single hydrometeorological framework, they diverge in their approaches to modeling evapotranspiration, particularly in how they address the roles of vegetation and land surface heterogeneity. More importantly, the unified framework suggests that turbulence fluxes within the atmospheric boundary layer adhere to the principles of maximum information entropy production. The way in which dissipation, along with its associated entropy production, is established using information entropy theory deviates from traditional thermodynamic entropy formulations. Exploring the connection between thermodynamic and information entropy and developing proper formulations of dissipation for energy fluxes presents an appealing avenue for prospective research. Plain Language Summary: This paper seeks to establish a common theory for explaining the effectiveness of the maximum information entropy production model (MaxEnt), the relative humidity at equilibrium approach (ETRHEQ), and the Surface Flux Equilibrium model (SFE) in estimating evapotranspiration over a wide range of conditions. It uncovers that under reasonable assumptions, ETRHEQ's method in terms of minimizing the vertical variance in relative humidity is equivalent to MaxEnt's approach to minimizing dissipation. The united theory suggests that the movement of air and energy in the lower atmosphere follows the principles of maximum information entropy production, a concept that is a bit different from traditional ideas of entropy in thermodynamics. Looking into how thermodynamic entropy and information entropy are connected and figuring out the right way to calculate dissipation and entropy production for energy flux could lead to new insights in atmospheric science and land‐atmosphere interactions. Key Points: The study presented a pure theorical analysis to unifying MaxEnt, ETRHEQ, and SFE within the same hydrometeorological frameworkMinimizing the vertical variance of RH in ETRHEQ is equivalent to minimizing the dissipation function of energy fluxes in MaxEntThe connection between MaxEnt, ETRHEQ, and SFE is independent of Monin‐Obukhov similarity theory (MOST)'s extremum solution [ABSTRACT FROM AUTHOR]

Climate change significantly impacted on the survival, development, distribution, and abundance of living organisms. The Chinese serow Capricornis milneedwardsii, known as the "four unlike," is a Class II nationally protected species in China. In this study, we predicted the geographical suitability of C. milneedwardsii under current and future climatic conditions using MaxEnt. The model simulations resulted in area under the receiver operating characteristic curve (AUC) values above 0.9 for both current and future climate scenarios, indicating the excellent performance, high accuracy, and credibility of the MaxEnt model. The results also showed that annual precipitation (Bio12), slope, elevation, and mean temperature of wettest quarter (Bio8) were the key environmental variables affecting the distribution of C. milneedwardsii, with contributions of 31.2%, 26.4%, 11%, and 10.3%, respectively. The moderately and highly suitable habitats were mainly located in the moist area of China, with a total area of 34.56 × 104 and 16.61 × 104 km2, respectively. Under future climate change scenarios, the areas of suitability of C. milneedwardsii showed an increasing trend. The geometric center of the total suitable habitats of C. milneedwardsii would show the trend of northwest expansion and southeast contraction. These findings could provide a theoretical reference for the protection of C. milneedwardsii in the future. This study used the MaxEnt model to predict the current and future potential geographical distribution of Capricornis milneedwardsii, a vulnerable species endemic to China, under different climate change scenarios. Results suggest that the distribution of C. milneedwardsii is likely to expand in the future, with highly suitable areas increasing under both RCP 4.5 and RCP 8.5 scenarios. These findings could provide a theoretical reference for the protection of C. milneedwardsii in the future. [ABSTRACT FROM AUTHOR]

The exposure of dairy cows to Coxiella burnetii using molecular and serological techniques was investigated in this study. Bulk tank milk and serum samples were collected from various farms in Greece (mainly northern Greece). DNA extraction was performed on milk samples, and qPCR targeting the IS1111 insertion sequence was performed to detect bacterial pathogens. An ELISA was used to detect specific antibodies in bulk milk and individual serum samples. Data on farms were collected in the field using handheld Global Positioning System Garmin units. The collected data were analyzed using an Ecological Niche Model within the framework of a geographic information system. The results indicated that in more than half of the dairy farms (35/60, 58.3%), C. burnetii is present in milk. Specific antibodies were also detected in almost all milk samples (57/60, 95.0%). At least one seropositive animal was identified using ELISA in the majority of the examined farms (25/28, 89.3%). C. burnetii PCR-positive farms were located in the low-altitude zone with a mean value of 97 m above sea level (range: 2–681). The environmental variable with the highest gain when used in isolation is precipitation in the wettest quarter (28.3% contribution), which therefore appears to have the most useful information by itself. The environmental variable that decreases the gain the most when omitted is the minimal temperature of the coldest month (6.9% contribution). The analysis demonstrated that a mild climate with low precipitation favors a positive status. The exposure of dairy cattle farms to C. burnetii is massive, raising significant concerns regarding livestock production and public health implications. [ABSTRACT FROM AUTHOR]

Copyright of Aero Weaponry is the property of Aero Weaponry Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Railway Science & Engineering is the property of Journal of Railway Science & Engineering Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract COVID-19 has been massively transmitted for almost 3 years, and its multiple variants have caused serious health problems and an economic crisis. Our goal was to identify the influencing factors that reduce the threshold of disease transmission and to analyze the epidemiological patterns of COVID-19. This study served as an early assessment of the epidemiological characteristics of COVID-19 using the MaxEnt species distribution algorithm using the maximum entropy model. The transmission of COVID-19 was evaluated based on human factors and environmental variables, including climate, terrain and vegetation, along with COVID-19 daily confirmed case location data. The results of the SDM model indicate that population density was the major factor influencing the spread of COVID-19. Altitude, land cover and climatic factor showed low impact. We identified a set of practical, high-resolution, multi-factor-based maximum entropy ecological niche risk prediction systems to assess the transmission risk of the COVID-19 epidemic globally. This study provided a comprehensive analysis of various factors influencing the transmission of COVID-19, incorporating both human and environmental variables. These findings emphasize the role of different types of influencing variables in disease transmission, which could have implications for global health regulations and preparedness strategies for future outbreaks.

Global climate change is a process with dramatic consequences for ecosystems, and changes that may occur in the potential distribution of plant communities especially draw attention. This study aimed to reveal the potential distribution modeling and mapping of the Oriental spruce (Picea orientalis L.), distributed in a limited area, using current and future (year 2100) climate scenarios in Turkey. The maximum entropy method for potential distribution and Chelsa V2.1 technical specification IPSL-CM6A-LR scenarios (SSP126-SSP370-SSP585) were preferred to reveal the effect of climate change. Results for the current were in the “excellent” category with training and test data AUC 0.981 and 0.977, respectively. The variables contributing to the model were the precipitation amount of the driest month, mean diurnal air temperature range, annual precipitation amount, and mean annual air temperature. Variables contributing to the current model were analysed using the SSP126, SSP370, and SSP585 scenarios of the year 2100. It was assessed that the potential distribution for 2100 decreases according to SSP126, was fragmented according to SSP370, and decreased according to the SSP585 scenario. As a result, the authors determined that the high potential distribution is reduced 61% when the current mapping of Oriental spruce is compared with the SSP585 mapping.

Introduction and GoalFloods cause loss of life and financial losses every year, and their management is one of the essential elements of watershed management. In this research, an attempt is made to determine the flood susceptibility of the Sirwan watershed and finally the importance of various environmental factors in flood susceptibility based on historical flood events.Materials and MethodsIn this research, the maximum entropy model along with 13 topographical, hydrological, morpho-hydrological, geological, and environmental flood-affecting factors were used to model the flood susceptibility of the Sirwan watershed and determine the importance and percentage of participation of various factors in the state of flooding potential. A cellular computing unit (pixel) was chosen as the criterion for preparing the predictive factors and flood susceptibility maps. A total of 123 historical flood inundation events detected in the last decade were used as target variables in the model, of which 70% were considered for learning and the remaining 30% for validating the model results. To evaluate the performance of the model, the criterion of the area under the receiver operating characteristic curve was also used.Results The results indicate that the accuracy of learning and validation were 98.2% and 97.3%, respectively, indicating the excellent performance of the model. Based on the visual interpretation of the flood susceptibility map, streams with a higher order near the watershed outlet, which are the conduits for the passage of the flow with a larger volume and are located in lower areas, often have a higher proneness to flood inundation. Based on the results of the relative importance test, the four factors of distance from the stream, topographic wetness index, drainage density, and land use were introduced as the most important factors in the modeling flood susceptibility, with of 17, 13, 12 and 10% participation, respectively. These results show that natural hydrological, morpho-hydrological and environmental factors (both natural and man-made) have a mutual effect in increasing flooding susceptibility. Based on the quantitative analysis of modeling, about 0.76% (5600 hectares) of the studied area is in the high and very high flood susceptibility class, which requires planning and flood management.Conclusion and SuggestionsThe high classification of flood susceptibility classes in the Sirwan watershed of Kurdistan province and the determination of the importance of environmental factors in the event of flooding make it possible for managers to take an effective preventive approach by planning relief facilities and infrastructure. To reduce the risk of flooding, flood crisis management in the Sirwan watershed should be defined based on the four main factors identified in this study. Application of the maximum entropy model in flood susceptibility analysis is suggested for flood management of watersheds.

Background and Aim: Lumpy skin disease (LSD) is a transboundary viral disease of cattle that causes serious economic losses due to a significant decrease in meat and milk productivity. This study analyzed the influence of natural and anthropogenic environmental factors on LSD spread seasonality and assessed the risk of LSD outbreaks in the Saratovskaya oblast of the Russian Federation. Materials and Methods: Data on LSD outbreaks and environmental factors during different seasons were collected for the period 2011-2020 in the Balkan Peninsula, Middle East, and Russia. Risk assessment was performed using mathematical modeling with generalized linear regression and maximum entropy. Results: Fourteen statistically significant environmental factors influencing LSD spread were identified. The analysis of MaxEnt models built using the selected factors showed that the presence of the pathogen is mostly exerted by: the density of susceptible cattle (an increased risk is observed at a density above 10 and 20 heads/10 km2 in winter and autumn, with a permanent risk in spring and summer), the density of water bodies (the risk is increased at any density in winter and autumn, in the range of 13-23.5 m2/km2 in spring, in the ranges of 0-8 and over 14.5 m2/km2 in summer), and average monthly precipitation rate (the most risky are 105-185 mm/month in winter, 35 mm in spring, 15-105 mm in summer, and above 50 mm in autumn). Conclusion: LSD tends to spread during the warm season. Compared with other test zones, the Saratovskaya oblast has a negligible risk of disease spread (in winter), low risk (in spring), or medium risk (in summer and autumn). The annual risk is low to medium.

We derive asymptotic formulas for the number of integer partitions with given sums of \(j\)th powers of the parts for \(j\) belonging to a finite, non-empty set \(J \subset \mathbb N\). The method we use is based on the `principle of maximum entropy' of Jaynes. This principle leads to an intuitive variational formula for the asymptotics of the logarithm of the number of constrained partitions as the solution to a convex optimization problem over real-valued functions. Finding the polynomial corrections and leading constant involves two steps: quantifying the error in approximating a discrete optimization problem by a continuous one and proving a multivariate local central limit theorem.Mathematics Subject Classifications: 05A17, 05A16, 60F05Keywords: Integer partitions, maximum entropy, asymptotic enumeration, local central limit theorem, limit shape

Bearing failure occurs when the dynamic contact stress exceeds the yield strength of the bearing material during operation. To minimise the risk of bearing failure, a new reliability theory method is proposed based on the stress-strength model of bearings, incorporating random input variables to analyse the reliability of angular contact ball bearings (ACBBs) and quantify their dynamic performance. The maximum entropy quadratic fourth moment method is used to calculate the probability distribution of maximum orthogonal shear stress-strength of bearing, and the maximum entropy principle is used to obtain the approximation of the minimum human error factors. Additionally, reliability-based sensitivity indices are derived to investigate the parametric significance of random input variables. Using B218 bearing as an example, the engineering application of this method in dynamic reliability and reliability-based sensitivity analysis is illustrated. Monte Carlo simulation is performed to verify the accuracy and effectiveness of the method to provide benchmark results. The results show that the Poisson’s ratio have a greater influence on the dynamic reliability of ACBBs than other parameters. Improving parameters such as ball diameter, raceway groove curvature radius and contact angle can also improve the reliability of bearings to some extent. [ABSTRACT FROM AUTHOR]

Climate change majorly impacts biodiversity in diverse regions across the world, including South Asia, a megadiverse area with heterogeneous climatic and vegetation regions. However, climate impacts on bats in this region are not well‐studied, and it is unclear whether climate effects will follow patterns predicted in other regions. We address this by assessing projected near‐future changes in climatically suitable areas for 110 bat species from South Asia. We used ensemble ecological niche modelling with four algorithms (random forests, artificial neural networks, multivariate adaptive regression splines and maximum entropy) to define climatically suitable areas under current conditions (1970–2000). We then extrapolated near future (2041–2060) suitable areas under four projected scenarios (combining two global climate models and two shared socioeconomic pathways, SSP2: middle‐of‐the‐road and SSP5: fossil‐fuelled development). Projected future changes in suitable areas varied across species, with most species predicted to retain most of the current area or lose small amounts. When shifts occurred due to projected climate change, new areas were generally northward of current suitable areas. Suitability hotspots, defined as regions suitable for >30% of species, were generally predicted to become smaller and more fragmented. Overall, climate change in the near future may not lead to dramatic shifts in the distribution of bat species in South Asia, but local hotspots of biodiversity may be lost. Our results offer insight into climate change effects in less studied areas and can inform conservation planning, motivating reappraisals of conservation priorities and strategies for bats in South Asia. [ABSTRACT FROM AUTHOR]

The entropy concept has been applied for one-dimensional (1D) velocity modeling in partially and fully filled pipe flows. The 1D velocity distribution models for partially and fully filled pipes are derived using fractional entropy by employing the entropy maximization concept and dividing the whole flow depth into two regions. For a partially filled pipe flow, two regions are distinguished using the dip-position whereas, for the fully filled pipe flow, it is decided using the pipe centerline. The entropy approaches have been applied individually in each region to derive the velocity distributions. Finally, using the asymptotic matching method, single velocity distribution laws are proposed which apply to the entire flow depth. Both the proposed velocity models for partially and fully filled pipes are validated with different sets of experimental data and satisfactory results are achieved. Proposed fractional entropy-based velocity models in partially filled and fully filled pipes are compared with the Tsallis wavelet entropy-based velocity distribution model (for partially filled pipes), and Guo and Julien's modified log-wake law and Guo's second log-wake law respectively. Comparison results show that the proposed models are comparable with existing models and give better results when quantitatively analyzed. First entropy-based eddy viscosity model is proposed for fully filled pipe flows and compared with experimental data. Results show that the eddy viscosity model produces good agreement with the data (near pipe invert and obvert) except in the core region of the pipe comprising 40 % of the radius. [ABSTRACT FROM AUTHOR]

Simple Summary: Exploring species' potential suitable habitats is crucial for endangered species conservation, in particular under future global climate change conditions. The Wushan salamander (Liua shihi) is an endangered salamander in China, which is a national protected species (level II). Based on the distribution records of L. shihi, the main objective of this study was to predict the distribution of suitable habitats under current and future climate conditions for L. shihi. Our results showed that precipitation, cloud density, vegetation type, and ultraviolet radiation were the main environmental factors affecting the distribution of suitable habitat for L. shihi. At present, the suitable habitats are mainly distributed in the Daba Mountain area. Under the future climate conditions, the area of suitable habitats increased, which mainly occurred in central Guizhou Province. These findings provided important information for the conservation of L. shihi. Climate change has been considered to pose critical threats for wildlife. During the past decade, species distribution models were widely used to assess the effects of climate change on the distribution of species' suitable habitats. Among all the vertebrates, amphibians are most vulnerable to climate change. This is especially true for salamanders, which possess some specific traits such as cutaneous respiration and low vagility. The Wushan salamander (Liua shihi) is a threatened and protected salamander in China, with its wild population decreasing continuously. The main objective of this study was to predict the distribution of suitable habitat for L. shihi using the ENMeval parameter-optimized MaxEnt model under current and future climate conditions. Our results showed that precipitation, cloud density, vegetation type, and ultraviolet radiation were the main environmental factors affecting the distribution of L. shihi. Currently, the suitable habitats for L. shihi are mainly concentrated in the Daba Mountains, including northeastern Chongqing and western Hubei Provinces. Under the future climate conditions, the area of suitable habitats increased, which mainly occurred in central Guizhou Province. This study provided important information for the conservation of L. shihi. Future studies can incorporate more species distribution models to better understand the effects of climate change on the distribution of L. shihi. [ABSTRACT FROM AUTHOR]

Magnolia biondii Pampan., a traditional Chinese medicinal plant, holds significant ornamental and medicinal value. We used the MaxEnt model and ArcGIS software to study the potential habitats of M. biondii in China. The results showed that the model exhibited outstanding accuracy, boasting an average area under the receiver-operator curve (AUC) of 0.955. The distribution of M. biondii was primarily influenced by three key environmental factors: min temperature of coldest month (Bio06), precipitation of warmest quarter (Bio18), and precipitation of coldest quarter (Bio19). Currently, M. biondii habitats are concentrated in East, Central, and Southwest China, covering 107.95 × 104 km2. Notably, Hubei, Henan, and Shandong host the majority of highly suitable areas. Future global warming will have a positive impact on the potential distribution area of M. biondii, and its distribution center has a tendency to migrate to higher latitudes. These findings contribute to the theoretical understanding of plant resources and provide insights into the habitat conservation of M. biondii. [ABSTRACT FROM AUTHOR]

Maleo and knobbed hornbill are bird species that are endemic on the island of Sulawesi, which is highly threatened by forest fires. Fires tend to destroy any affected species; however, it is not possible to survey the entire range of the original distribution of the two endemic bird species that are affected by forest fires due to practical constraints. Species distribution modeling using maximum entropy is considered to be an alternative to understanding the potential distribution area of species against the threat of forest fires. The prediction model from MaxEnt all have AUC values of greater than 0.70, which means that the model is good enough to classify the records of the presence of M. maleo and R. cassidix along with the past forest fires. The environmental variables that affect the distribution of M. maleo are its distance from hot water, rivers, and roads, while the distribution of R. cassidix is strongly influenced by its distance from roads, settlements, and rivers. Forest fire distribution is mostly influenced by soil type, land-use land cover, and rainfall. It is predicted that around 238,690 and 677,070 ha of the potential distribution of M. maleo and R. cassidix, respectively, are potentially disturbed and affected by forest fires. However, this number much greater outside conservation areas. The results of this study can be used by the government of the Republic of Indonesia (especially the Ministry of Environment and Forestry) for determining conservation actions for both species in the future. [ABSTRACT FROM AUTHOR]

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Full understanding of proteostasis and energy utilization in cells will require knowledge of the fraction of cell proteins being degraded with different half- lives and their rates of synthesis. We therefore developed a method to determine such information that combines mathematical analysis of protein degradation kinetics obtained in pulse--chase experiments with Bayesian data fitting using the maximum entropy principle. This approach will enable rapid analyses of whole- cell protein dynamics in different cell types, physiological states, and neurodegenerative disease. Using it, we obtained surprising insights about protein stabilities in cultured cells normally and upon activation of proteolysis by mTOR inhibition and increasing cAMP or cGMP. It revealed that >90% of protein content in dividing mammalian cell lines is long- lived, with half- lives of 24 to 200 h, and therefore comprises much of the proteins in daughter cells. The well- studied short- lived proteins (half- lives < 10 h) together comprise <2% of cell protein mass, but surprisingly account for 10 to 20% of measurable newly synthesized protein mass. Evolution thus appears to have minimized intracellular proteolysis except to rapidly eliminate misfolded and regulatory proteins. [ABSTRACT FROM AUTHOR]

The collective statistics of voting on judicial courts present hints about their inner workings. Many approaches for studying these statistics, however, assume that judges' decisions are conditionally independent: a judge reaches a decision based on the case at hand and his or her personal views. In reality, judges interact. We develop a minimal model that accounts for judge bias, depending on the context of the case, and peer interaction. We apply the model to voting data from the US Supreme Court. We find strong evidence that interaction is an important factor across natural courts from 1946 to 2021. We also find that, after accounting for interaction, the recovered biases differ from highly cited ideological scores. Our method exemplifies how physics and complexity-inspired modelling can drive the development of theoretical models and improved measures for political voting. This article is part of the theme issue 'A complexity science approach to law and governance'. [ABSTRACT FROM AUTHOR]

In our exploration, we aimed at identifying seismic anomalies using limited ionospheric data for earthquake forecasting and we meticulously compiled datasets under conditions of minimal geomagnetic disturbance. Our systematic evaluation affirmed the ITransformer as a potent tool for the feature extraction of ionospheric data, standing out within the domain of transformer-based time series prediction models. We integrated the maximum entropy principle to fully leverage the available information, while minimizing the influence of presuppositions on our predictions. This led to the creation of the MaxEnt SeismoSense Model, a novel composite model that combines the strengths of the transformer architecture with the maximum entropy principle to improve prediction accuracy. The application of this model demonstrated a proficient capability to detect seismic disturbances in the ionosphere, showcasing an improvement in both recall rate and accuracy to 71% and 69%, respectively, when compared to conventional baseline models. This indicates that the combined use of transformer technology and the maximum entropy principle could allow pre-seismic anomalies in the ionosphere to be sensed more efficiently and could offer a more reliable and precise approach to earthquake prediction. [ABSTRACT FROM AUTHOR]

This article aims to understand mobility within income distribution in cases where there is incomplete information about how individuals transit between income distribution brackets. Understanding these transitions is crucial for evaluating and designing economic policies that affect the population in the long run. For this reason, we propose a methodology that may assist decision-makers to improve policies related to poverty reduction. We start by assuming that the income distribution bracket a person holds exclusively depends on the previous generation's income bracket, i.e. it has the memoryless property. Therefore, our model resembles a Markov chain model with a steady state distribution that describes the distribution of the income brackets in the long run, and a transition matrix that describes the transitions between income distribution brackets from generation to generation. In contrast to a Markov chain, we assume a given steady state, in order to analyze the space of consistent transition matrices that could generate the steady state proposed. Additionally, we used the joint distribution simulation algorithm developed by Montiel and Bickel (Decis Anal 9:329–347, https://doi.org/10.1287/deca.1120.0252, 2012) to analyze the transition matrix, which allows us to understand the effects of partial information. We test the model with official data from the National Institute of Statistics and Geography and the Social Mobility Survey in Mexico. [ABSTRACT FROM AUTHOR]

This paper shows that the empirical distribution of cross-sectional analyst coverage in China's stock markets follows an exponential law in a given month from 2011 to 2020. The findings hold in both the emerging (Shanghai) and the developed market (Hong Kong). Moreover, the unique distribution parameter (i.e., mean) is directly related to the amount of market-wide information. Average analyst coverage exhibits a significant negative predictive power for stock-market uncertainty, highlighting the role of security analysts in diminishing the total uncertainty. The exponential law can be derived from the maximum entropy principle (MEP). When analysts, who are constrained by average ability in generating information (i.e., the first-order moment), strive to maximize the amount of market-wide information, this objective yields the exponential distribution. Contrary to the conventional wisdom that security analysts specialize in the generation of firm-specific information, empirical findings suggest that analysts primarily produce market-wide information for 25 countries. Nevertheless, it remains unclear why cross-sectional analyst coverage reflects market-wide information, this paper provides an entropy-based explanation. [ABSTRACT FROM AUTHOR]

This paper presents a rich class of information theoretical measures designed to enhance the accuracy of portfolio risk assessments. The Mean-Variance model, pioneered by Harry Markowitz, revolutionized the financial sector as the first formal mathematical method to risk-averse investing in portfolio optimization theory. We analyze the effectiveness of this with the models that replace expected portfolio variance with measures of information (uncertainty of the portfolio allocations to the different assets) and five major practical issues. The empirical analysis is carried out on the historical data of Indian financial stock indices by application of portfolio optimization problem with information measures as the objective function and constraints derived from the return and the risk. Our findings indicate that the information measures with parameters can be used as an adequate supplement to traditional portfolio optimization models such as the mean-variance model. [ABSTRACT FROM AUTHOR]

Crop condition reports are an important source of information for producers, grain traders, businesses, and policymakers to assess and manage the price and yield risk inherent in a given crop. A Markov chain model is proposed for describing the weekly dynamic behavior of reported crop conditions. Empirical transition probabilities are estimated for corn grown in Nebraska, and forecasted crop conditions from the Markov chain are used as inputs to forecast final crop yields prior to harvest time. The results suggest that the modeling and forecasting approach has value for estimating crop yields as intrayear information about crop conditions materializes. [ABSTRACT FROM AUTHOR]

This research focuses on the slopes of an active volcano, seeing its importance in studying disaster mitigation, especially evacuation routes, to minimize fatality during a volcanic eruption. Determining evacuation routes using local wisdom is used as a guide for communities around the mountain slopes to safeguard themselves in the event of a mountain eruption. This research aims to model an eruption disaster evaluation pathway using a local wisdom approach. This research employs a mixed-method approach, combining quantitative and qualitative methods to process and analyze relevant variables. The ultimate output is a map illustrating volcanic disaster evacuation routes. For vulnerability analysis related to volcanic disasters, this research uses quantitative methods with the Maximum Entropy algorithm. The research identifies slope as the environmental variable with the highest gain when used in isolation, suggesting its significant informational value. The modeling used was in the 12th iteration of 25 model test replications, with AUC training data reaching a value of 0.877 and AUC test data of 0.932, indicating highly effective modeling results. In addition, the local wisdom from the community plays a crucial role in recognizing impending eruption signs, with an emphasis on observing natural symptoms in the surrounding environment. The people of Nagari Batu Palano do not have specific social traditions related to volcanic eruptions. Instead, their primary response involves surrendering to God and seeking a safe place if an eruption occurs. In relation to saltwater pools, there is a need for further studies to establish the reliability of the information produced. [ABSTRACT FROM AUTHOR]

Background and Aim: Lumpy skin disease (LSD) is a transboundary viral disease of cattle that causes serious economic losses due to a significant decrease in meat and milk productivity. This study analyzed the influence of natural and anthropogenic environmental factors on LSD spread seasonality and assessed the risk of LSD outbreaks in the Saratovskaya oblast of the Russian Federation. Materials and Methods: Data on LSD outbreaks and environmental factors during different seasons were collected for the period 2011-2020 in the Balkan Peninsula, Middle East, and Russia. Risk assessment was performed using mathematical modeling with generalized linear regression and maximum entropy. Results: Fourteen statistically significant environmental factors influencing LSD spread were identified. The analysis of MaxEnt models built using the selected factors showed that the presence of the pathogen is mostly exerted by: the density of susceptible cattle (an increased risk is observed at a density above 10 and 20 heads/10 km² in winter and autumn, with a permanent risk in spring and summer), the density of water bodies (the risk is increased at any density in winter and autumn, in the range of 13-23.5 m² /km² in spring, in the ranges of 0-8 and over 14.5 m²/km² in summer), and average monthly precipitation rate (the most risky are 105-185 mm/month in winter, 35 mm in spring, 15-105 mm in summer, and above 50 mm in autumn). Conclusion: LSD tends to spread during the warm season. Compared with other test zones, the Saratovskaya oblast has a negligible risk of disease spread (in winter), low risk (in spring), or medium risk (in summer and autumn). The annual risk is low to medium. [ABSTRACT FROM AUTHOR]

The aim of this paper is to consider the indeterminate Stieltjes moment problem together with all its probability density functions that have the positive real or the entire real axis as support. As a consequence of the concavity of the entropy function in both cases, there is one such density that has the largest entropy: we call it f hmax , the largest entropy density. We will prove that the Jaynes maximum entropy density (MaxEnt), constrained by an increasing number of integer moments, converges in entropy to the largest entropy density f hmax . Note that this kind of convergence implies convergence almost everywhere, with remarkable consequences in real applications in terms of the reliability of the results obtained by the MaxEnt approximation of the underlying unknown distribution, both for the determinate and the indeterminate case. [ABSTRACT FROM AUTHOR]

The 2nd law of thermodynamics yields an irreversible increase in entropy until thermal equilibrium is achieved. This irreversible increase is often assumed to require large and complex systems to emerge from the reversible microscopic laws of physics. We test this assumption using simulations and theory of a 1D ring of N Ising spins coupled to an explicit heat bath of N Einstein oscillators. The simplicity of this system allows the exact entropy to be calculated for the spins and the heat bath for any N , with dynamics that is readily altered from reversible to irreversible. We find thermal-equilibrium behavior in the thermodynamic limit, and in systems as small as N = 2 , but both results require microscopic dynamics that is intrinsically irreversible. [ABSTRACT FROM AUTHOR]

Cloud computing and its derivatives, such as fog and edge computing, have propelled the IoT era, integrating AI and deep learning for process automation. Despite transformative growth in healthcare, education, and automation domains, challenges persist, particularly in addressing the impact of multi-hopping public networks on data upload time, affecting response time, failure rates, and security. Existing scheduling algorithms, designed for multiple parameters like deadline, priority, rate of arrival, and arrival pattern, can minimize execution time for high-priority applications. However, the difficulty lies in simultaneously minimizing overall application execution time while mitigating resource depletion issues for low-priority applications. This paper introduces a cloud-fog-based computing architecture to tackle fog node resource starvation, incorporating joint probability, loss probability, and maximum entropy concepts. The proposed model utilizes a probabilistic application scheduling algorithm, considering priority and deadline and employing expected loss probability for task offloading. Additionally, a second algorithm focuses on resource starvation, optimizing task sequence for minimal response time and improved quality of service in a multi-Queueing fog system. The paper demonstrates that the proposed model outperforms state-of-the-art models, achieving a 3.43-5.71% quality of service improvement and a 99.75-267.68 msec reduction in response time through efficient resource allocation. [ABSTRACT FROM AUTHOR]

Abstract Species' ranges are shifting rapidly with climate change, altering the composition of biological communities and interactions within and among species. Hybridization is among the species interactions that may change markedly with climate change, yet it is understudied relative to others. We used non‐invasive genetic detections to build a maximum entropy species distribution model and investigate the factors that delimit the present and future ranges of American marten (Martes americana) and Pacific marten (Martes caurina) in a contact zone in the Northern Rockies. We found that climate change will decrease the suitable habitat predicted for both species, as well as the amount of overlap in predicted suitable habitat between the species. Interestingly, predicted suitable habitat for Pacific marten extended further north in the study region than our genetic detections for the species, suggesting that biotic factors, such as interactions with American marten, may affect the realized range of this species. Our results suggest that future work investigating the interactions among biotic and abiotic factors that influence hybrid zone dynamics is important for predicting the futures of these two species in this area under climate change.

Here we propose a model-free, non-parametric method to solve an ill-posed inverse problem arising in several fields. It consists of determining a probability density of the lifetime, or the probability of survival of an individual, from the knowledge of the fractional moments of its probability distribution. The two problems are related, but they are different because of the natural normalization condition in each case. We provide a maximum entropy based approach to solve both problems. This problem provides a concrete framework to analyze an interesting problem in the theory of exponential models for probability densities. The central issue that comes up concerns the choice of the fractional moments and their number. We find that there are many possible choices that lead to solutions compatible with the data but in all of them, no more than four moments are necessary. The fact that a given data set can be accurately described by different exponential families poses a challenging problem for the model builder when attaching theoretical meaning to the resulting exponential density.