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Entropy originated in thermodynamics and has since become a central tool for quantifying uncertainty in probabilistic and information-theoretic systems. This study provides a unified mathematical synthesis of the Shannon, Rényi, Tsallis, and Sharma–Mittal entropies, focusing on their axiomatic foundations, functional structures, and limiting relationships. We show that Rényi entropy reduces to Shannon entropy as α → 1, Tsallis entropy reduces to Shannon entropy as q → 1, and the two-parameter Sharma–Mittal entropy encompasses both Rényi (as β → 1) and Tsallis (when β = α), converging to Shannon entropy in the joint limit (α, β) → (1, 1). Additivity, pseudo-additivity, concavity, and stability are compared across the four families, consolidating the unifying role of Sharma–Mittal entropy noted in earlier work rather than treating it merely as a more flexible formulation. Building on this synthesis, we connect it to a previously developed parameter-integrated framework that addresses the practical difficulty introduced by the Sharma–Mittal entropy’s two-parameter structure: fixing (α, β) at a single, arbitrary pair makes any derived quantity—and, in feature selection, the resulting variable ranking—dependent on that choice. The framework integrates the conditional Sharma–Mittal entropy and information-gain surfaces volumetrically over a bounded region of the α-β plane, yielding three parameter-integrated indices—PICSME, PIGSME, and NIGSME—that are exact monotone transformations of one another and therefore induce an identical variable ranking for a fixed dataset and integration region. This illustrates how the unifying position of Sharma–Mittal entropy can be operationalized into a practical feature-ranking tool that does not require the selection of a single predefined (α, β) pair.

Feature selection is a critical step in regression problems where a large number of continuous explanatory variables explain the same target through different dependency structures. Classical filters may remain sensitive to a single form of dependence, a single scale, or a specific discretization scheme; generalized entropy measures, on the other hand, typically require the parameters to be fixed at a single point. This study proposes a framework that evaluates the Sharma–Mittal entropy volumetrically across a two-dimensional parameter region rather than for a single parameter pair. For the continuous target and explanatory variables, the marginal, joint, and conditional densities are obtained using a Gaussian kernel density estimation; the conditional entropy and information gain surfaces are integrated across the region Ω = [0.05, 0.95]² in the α-β plane to define three indices: PICSME, which measures the conditional uncertainty volume; PIGSME, which measures the gain volume; and NIGSME, which is the ratio of this gain to the total entropy volume of the target. The method is supported by bandwidth consistency and the renormalization of conditional densities; thus, the issue of negative gain that can occur in the continuous variables is resolved, yielding positive and interpretable scores across all six datasets. It is formally demonstrated that the fact that the three indices produce the same ranking is not an empirical observation but rather the result of a monotonicity relationship valid under a fixed target entropy volume. The method is compared with Pearson and Spearman correlations, the Shannon information gain, mutual information, and random forest variable importance across six regression datasets (Airfoil Self-Noise, AirQualityUCI, BodyFat, Meteorology, Concrete, and WineQualityWhite) that differ in their sample size, dimensions, and application domain. The evaluation is not limited to ranking consistency; the out-of-sample prediction performance is measured using least-squares models on the top-k subsets, with rankings calculated from the training partition. The findings show that NIGSME exhibits a performance comparable to that of built-in filters, outperforms them on the Concrete and Meteorology datasets, and never ranks as the weakest method on any dataset. The results demonstrate that volumetric entropy metrics defined across the entire parameter space provide a feature-ranking tool that is independent of parameter selection for continuous variables.

In this study, changes in the surface area of Lake Burdur during the 2015–2025 period and the spatial direction of the associated shrinkage were examined using Sentinel-2 Level-2A satellite images. A total of 111 satellite images, each representing a monthly period, were analyzed using a fixed study window and a lake vicinity mask; a three-cluster unsupervised K-means segmentation method was applied to separate the water surface from bare/drained areas and vegetation classes. The resulting binary water masks were used to convert the lake surface area to km² on a pixel-by-pixel basis, and the geometric center of the lake mass was calculated for each observation date. The unique aspect of this study is that it evaluates lake shrinkage not only through a decrease in surface area but also as a directional spatial process via the movement of the centroid center. In this context, the cumulative displacement was decomposed into X/West and Y/South components using the initial centroid point as a reference; OLS-based linear and logarithmic trend models were established for both directions. Model performances were compared using a 15-fold Monte Carlo cross-validation approach with R², adjusted R², NSE, KGE, MAE, MAPE, MSE, and RMSE metrics; additionally, the statistical significance of model differences was assessed using the Wilcoxon signed-rank test. The findings indicate that the logarithmic model yields more balanced and reliable results in the X/West direction, while the linear model does so in the Y/South direction. Based on this model structure, spatial projections were generated for the 2026–2035 period, and it was observed that the projection bands remained stable despite Monte Carlo-based coefficient uncertainty. In conclusion, the study demonstrates that lake drawdowns in semi-arid closed basins can be monitored in a more interpretable and statistically robust manner using Sentinel-2-based segmentation, centroid kinematics, and cross-validated trend modeling.

Feature selection is one of the fundamental steps in producing simpler, more interpretable, and computationally efficient models while maintaining predictive power. In this study, rather than fixing the uncertainty relationship between the target variable and each candidate feature to a single entropy parameter, three volume-based indices are proposed that integrate the two-parameter structure of the Sharma-Mittal entropy over a defined parameter region. The indices, named Parameter-Integrated Conditional Sharma-Mittal Entropy, Parameter-Integrated Sharma-Mittal Entropy Information Gain, and Normalized Parameter-Integrated Sharma-Mittal Entropy Information Gain, represent, respectively, the conditional entropy volume, the information gain volume, and the form of this volume normalized relative to the total entropy volume of the target, respectively. Densities were estimated using Gaussian kernel density estimation; the alpha and beta parameters were numerically integrated over the range [0.05; 0.95] × [0.05; 0.95]. The methods were compared across six different regression datasets-Airfoil Self-Noise, AirQualityUCI, BodyFat, meteorology-based reference evapotranspiration, Concrete, and WineQualityWhite-using absolute Pearson correlation, absolute Spearman rank correlation, Shannon information gain, mutual information, and random forest variable importance. The comparison was conducted using raw importance scores, derived feature rankings, Spearman’s rho and Kendall’s tau rank correlations, bivariate rank scatter plots, and Mann–Whitney U test results. The results show that the proposed indices produced high or very high rank agreement with correlation- and information-based reference methods in the Airfoil Self-Noise, AirQualityUCI, BodyFat, and meteorological datasets. Specifically, the absolute Pearson correlation, absolute Spearman rank correlation, Shannon information gain, and mutual information, along with the average Spearman rho values across all datasets, were obtained as 0.884, 0.874, 0.883, and 0.903, respectively; the average agreement with random forest importance scores remained at 0.538. The findings reveal that the parameter-integrated Sharma–Mittal framework offers a density-based and discretization-independent filtering perspective for continuous data; however, they also highlight the need for additional sensitivity and out-of-sample prediction performance evaluations regarding absolute score scales, negative information-gain values, and the rank equivalence of the three proposed indices.

In this study, changes in the surface area of Lake Burdur during the 2015-2025 period and the spatial direction of the associated shrinkage were examined using Sentinel-2 Level-2A satellite images. A total of 111 satellite images, each representing a monthly period, were analyzed using a fixed study window and a lake perimeter mask; a three-cluster unsuper-vised K-means segmentation method was applied to separate the water surface from bare/drained areas and vegetation classes. The resulting binary water masks were used to convert the lake surface area to km2 on a pixel-by-pixel basis, and the geometric center of the lake mass was calculated for each observation date. The unique aspect of this study is that it evaluates lake shrinkage not only through a decrease in surface area but also as a directional spatial process via the movement of the centroid center. In this context, the cumulative displacement was decomposed into X/West and Y/South components using the initial centroid point as a reference; OLS-based linear and logarithmic trend models were established for both directions. Model performances were compared using a 15-fold Monte Carlo cross-validation approach with R2, adjusted R2, NSE, KGE, MAE, MAPE, MSE, and RMSE metrics; additionally, the statistical significance of model differences was assessed using the Wilcoxon signed-rank test. The findings indicate that the logarithmic model yields more balanced and reliable results in the X/West direction, while the linear model does so in the Y/South direction. Based on this model structure, spatial projections were generated for the 2026-2035 period, and it was observed that the projection bands remained stable despite Monte Carlo-based coefficient uncertainty. In conclusion, the study demonstrates that lake drawdowns in semi-arid closed basins can be monitored in a more interpretable and statistically robust manner using Sentinel-2-based segmentation, centroid kinematics, and cross-validated trend modeling.

This study aims to analyze text data obtained from Turkish phone calls to manage credit risk in the banking sector and predict whether customers will fulfill their payment promises. Data cleaning was identified as a critical step to improve the quality of the texts, and various natural language processing (NLP) techniques were used. The model was built using a two-layer LSTM architecture, starting with a Self-Embedding layer, and achieved approximately 80% accuracy on the test data. The findings indicate that customers who break their payment promises often cite personal life issues such as health problems, family issues, financial difficulties, and religious beliefs to ensure reliability. These results demonstrate the importance of text data in the banking sector, the applicability of different embedding methods to Turkish datasets, and their advantages and disadvantages. Furthermore, the model built using data obtained from customer conversations can help predict credit risk more accurately and contribute to improving call center processes. Automating data cleaning processes and developing speech-to-text translation tools are recommended for future studies.

Using Python-based face recognition technology, this work aims to forecast characteristics including age, gender, and moods of individuals shown in video uploaded on the YouTube platform from 2017 to 2021. This study particularly makes use of this method on individuals engaged in YouTube street interviews, focusing on issues related to the unemployment and economy. The concordance and distribution of emotional variables alongside demographic variables such as age and gender were investigated using the "correspondence" analysis method, a multivariate technique that visualizes relationships among variables and categorical cross-relationships through graphical mapping. Data concerning the emotional variance from every year between 2017 and 2021 were gathered. Data were especially separated, and unhappiness rates were computed as percentages from the gathered data. The study looked at the relationship between the unemployment rate for the particular years and the computed degree of discontent. Non-parametric statistical methods were seen more suitable in this phase of the research as the low data volume made normalcy testing impossible. The value of facial recognition systems in demographic prediction and emotional evaluation is underlined by this work. Furthermore, it emphasizes the possible value of matching emotional forecasts with unemployment data in order to assess how economic changes affect personal emotional responses. This study emphasizes how improvements in artificial intelligence and data analysis could improve the understanding and answers for society issues. Therefore, it could motivate similar future study with great benefits in marketing, economics, and social sciences as well as highlight developments in data analysis and artificial intelligence.

Faktör analizi, belirli bir olguyla ilgili ve birbirleriyle ilişkili çok sayıda değişkenin birbirleriyle olan ilişkisini inceleyerek, değişkenlerin sayısını azaltmak ve ilişkisiz yeni değişkenler yaratmak için kullanılan çok değişkenli istatistiksel bir analizdir. Bu çalışmada farklı bir yaklaşım olarak, faktör çıkarmada birleşik entropiden yararlanılmıştır. Buradan elde edilen “Faktörleşme” ile “Açıklayıcı Faktör Analizi” sonuçları karşılaştırılarak benzerlik ve farklılıkları tartışılmıştır. İstatistik ile entropiyi birleştiren bir model kullanılmıştır. Uygulama kısmında ilk olarak istatistikte yaygın olarak kullanılan faktör analizi sonuçları elde edilmiştir. Ardından, kovaryans matrisi yerine birleşik entropi matrisi kullanılan entropi tabanlı yaklaşımla elde edilen matrisle bir karşılaştırma yapılmıştır. Bu bağlamda birleşik entropi matrisi ile elde ettiğimiz sonuçlar ile faktör analizi ile elde ettiğimiz sonuçlar karşılaştırılmıştır. Son durumda ise birleşik entropi matrisi ile elde edilen sonuçlar gösterilmiştir. Ek olarak, bu çalışma ile entropiye teorik destek ile aslında varyans-kovaryans ölçülerinin kullanım alanlarına uygulanabileceği ve desteklenebileceğini göstermek hedeflenmiş ve çözülmesi gereken bazı sorunlara rağmen, alternatif olarak bilinen yöntemlerin yerine önerilmektedir.

Amaç –Bu makalenin temel amacı iki yönlüdür.Öncelikle,bağımsız çalışan Serbest Muhasebeci Mali Müşavirlerin (SMMM) meslek etiğine, meslek odalarına, diğer meslektaşlarına ve hizmet verdikleri müşterilerine ilişkin etik konusundaki genel algılarını ve görüşlerini incelemektir. İkinci olarak, katılımcıların etik algılarındaki potansiyel farklılıkların cinsiyete ve mesleki tecrübeye bağlı olup olmadığını araştırmaktır.Yöntem –Makalenin amacı doğrultusunda İstanbul ilinde mesleklerini icra eden ve bağımsız çalışan SMMM’lerle ilgili olarak yapılan araştırmanın saha çalışması, yüz yüze anket yöntemi kullanılarak gerçekleştirilmiştir. Örnek seçiminde basit rassal örnekleme yöntemi kullanılmıştır. İstatistik analizlerde kullanılan yöntemler ise, Ki-Kare testi ve uyum (Correspondence) analizidir. Bu araştırma için etik onay, İstanbul Gelişim Üniversitesi’nin Etik Kurul Başkanlığı’ndan 18.01.2023tarihve 2023-02-55 no’lu karar ile alınmıştır.Bulgular –İstanbul ilinde 385 bağımsız çalışan SMMM’lere yapılan anket sonucunda, meslek odalarının etik konusunda daha çok eğitim vermeleri ve etik konusunda vereceği cezaların artırılarak uygulanması konusu ön plana çıkmıştır. Ayrıca, yetkili kurumlarca mali denetimlerinin sıklaştırılmasının yanı sıra ücret tarifesinin belirlenenden daha yüksek olması durumunda meslek mensuplarının etik ilkelere olan bağlılıklarının ve muhasebe mesleğine olan saygınlığın daha da artacağını konusunda görüş bildirmişlerdir.Tartışma –Günümüzde yaşanan ekonomik zorluklardan dolayı meslek mensuplarının ücret tarifelerinin yeniden yapılandırılmalıdır. SMMM’lerin, müşterileri ile olan uzun dönemli ilişkilerinden ötürü veya müşteri kaybetme korkusundan dolayı müşterilerinin kendi çıkarları adına yapacakları teklifler karşısında etik ilkelere olan bağlılıklarından uzaklaşmamaları gerekir. Etik ilkelerin hem SMMM’ler hem de onların müşterileri tarafından daha iyi anlaşılabilmesi adına konuyla ilgili yetkili kurumların yapacakları ortak bir çalışma ile verilecek eğitimlerle hem kamu yararı hem de mesleğin geleceği açısından önemlidir.