Entropy Analysis Research Articles

Use of GLCM Entropy Parameter in the Analysis of Urban Function Spaces; Antalya City Example

Urban spaces are concentrated in certain functions to meet the needs and desires of the urbanites. However, for each city, different functions and the value of the space to meet these functions are different. In this study, spatial entropy analysis of Antalya, the most important tourism city of our country, was carried out through GLCM Entropy analysis, one of the texture parameter methods. In the study, firstly, function areas and function spaces were determined. A 5-meter resolution satellite image for 2022 was obtained to perform texture parameter analyses. The satellite image was scaled to include the whole city and urban spaces with QGIS software, and then the general entropy values of the city were calculated with Definies software. Then, selected urban spaces with different functions were extracted from the satellite image and subjected to entropy analyses. According to the results obtained, the areas with the highest entropy difference for Antalya city were determined as airport and harbour, which are transportation and trade places. For Antalya, which has poor road access to the world due to geographical reasons, it is seen as an important determination in terms of analysis that the places representing air and sea connection come to the fore.

Effect of trapezoidal louvered winglets on increased heat transfer and exergy in tubular heat exchanger

The effect of inserting a trapezoidal louvered winglet tape (TLWT) into a uniformly heat-fluxed tube on its thermal effectiveness was studied experimentally. The exergy and entropy analyses for turbulent flows, as well as frictional loss and thermal features, were highlighted as key aspects of the experimental finding for the Reynolds number which measured between about 4700 and 30,000. Because fixing baffles to the curved shape of tube wall presented a challenge, the baffles were consequently positioned on double surfaces of a flat tape. Six values of the louver angle (θ1 = 0°, 25°, 30°, 45°, 60°, and 90°) and three values of the relative pitch of winglet (PR = 1.0, 1.5, and 2.0) were employed in the arrangement of TLWTs, with the V-apex oriented upstream (V-up). Each of these had only a fixed height (BR = 0.25) and angle of attack (α = 30°). The winglets were utilized to induce streamwise vortices which can hinder the boundary layer formation, while the louvered openings were adopted to lessen pressure drop without significantly impacting the primary vortices. The experiment results disclosed that the smallest θ1 and PR produced the largest relative friction factor (fR) and NuR, which were about 13.57 and 4.04 times higher, while PR = 1 and θ1 = 45° provide the greatest TEF of about 2.27. The greatest exergy efficiency (ηEx) resulting from the TLWT was reached at θ1 = 0°, but the generation of entropy (S˙g′) dropped with lowering θ1 and Re. A further examination, however, showed that the best scenario with α = 60° and staggered arrays is more desirable since it yields the largest TEF of 2.45 at θ1 = 45° and PR = 1. For the range of parameters under consideration, the Nu and f correlations were additionally established.

Multimodal machine learning approach for emotion recognition using physiological signals

This study explores a novel approach to emotion recognition through machine learning, addressing the limitations of previous methods. While deep learning has shown promise in this field, it often requires significant computational resources and time. In response, we propose a multimodal approach utilizing Feature-level Fusion (FLF) and Decision-level Fusion (DLF) to enhance performance while reducing complexity. The study focuses on integrating electroencephalogram (EEG), electromyography (EMG), and electrooculogram (EOG) signals. Signal preprocessing involves extracting statistical features, power spectral density (PSD), and incremental entropy analysis. Recursive Feature Elimination (RFE) is employed as a feature selector, facilitating the fusion of different signal features. Three fusion strategies are explored: EEG with EOG, EEG with EMG, and a combination of EEG with EOG and EMG. For classification, the Bagging Classifier and K-Nearest Neighbors Algorithm are chosen. Results demonstrate promising accuracy rates, with 95.7% for arousal, 96.41% for valence in subject-dependent classification, 93.68% for arousal, and 93.23% for valence in subject-independent classification. This approach presents a viable alternative to deep learning methods, offering improved performance with reduced computational burden.

Exploring the interplay of intrinsic fluctuation and complexity in intracellular calcium dynamics

The concentration of intracellular calcium ion (Ca2＋) exhibits complex oscillations, including bursting and chaos, as observed experimentally. These dynamics are influenced by inherent fluctuations within cells, which serve as crucial determinants in cellular decision-making processes and fate determination. In this study, we systematically explore the interplay between intrinsic fluctuation and the complexity of various dynamic states of intracellular cytosolic Ca2＋. To investigate this interplay, we employ complexity measures such as permutation entropy and statistical complexity. Using a stochastic chemical Langevin equation, we simulate the dynamics of cytosolic Ca2＋. Our findings reveal that permutation entropy and statistical complexity effectively characterize the diverse, dynamic states of cytosolic Ca2＋ and illustrate their interactions with intrinsic fluctuation. Permutation entropy analysis elucidates that the chaotic state is more sensitive to intrinsic fluctuation than the other periodic states. Furthermore, we identify distinct states of cytosolic Ca2＋ occupying specific locations within the theoretical bounds of the complexity–entropy causality plane. These locations indicate varying complexity and information content as intrinsic fluctuation varies. When adjusting the permutation order, the statistical complexity measure for the different periodic and chaotic states exhibits peaks in an intermediate range of intrinsic fluctuation values. Additionally, we identify scale-free or fractal patterns in this intermediate range, which are further corroborated by multifractal detrended fluctuation analysis. These high-complexity states likely correspond to optimal Ca2＋ dynamics with biological significance, revealing rich and complex dynamics shaped by the interplay of intrinsic fluctuation and complexity. Our investigation enhances our understanding of the intricate regulatory mechanisms governing intracellular Ca2＋ dynamics and how intrinsic fluctuation modulates the complexity of the various dynamics that play crucial roles in biological cells.

Generalized weighted permutation entropy analysis of SPEI index in Serbia as a proxy of corn production

AbstractIn this work we analyse yearly standardized precipitation evapotranspiration index for accumulation timescale of 6 months (SPEI‐6) for August which has been identified as a strong proxy for corn production in Serbia. By applying recently proposed method generalized weighted permutation entropy (GWPE), which provides the information about predictability of large/small fluctuations in nonstationary time series, on SPEI index calculated from high‐resolution gridded dataset for the period 1951–2022, we found that the small fluctuation sequences of consecutive 4‐year SPEI values are the most predictable (indicated by lowest entropy values). The order of large fluctuation sequences is less predictable, while the order of sequences considering all magnitudes of fluctuations are the least predictable (indicated by highest entropy values). We also analysed 4‐month SPEI‐6 sequences for May, June, July and August (during the growing season of corn) along the years under study and found that they display lower GWPE values and thus are more predictable than yearly SPEI‐6 August sequences (small fluctuations displaying lower entropy values than large fluctuations). Regarding spatial distributions, in both cases SPEI‐6 sequences show similar pattern for large fluctuations: higher predictability (lower entropy values) in northern and eastern part of Serbia and lower predictability (higher entropy values) in southern and western part. For small fluctuations spatial distribution of GWPE values indicates that yearly SPEI‐6 August series are more predictable in the western part of the country while May to August monthly SPEI‐6 sequences are more predictable in the eastern part.

Entropy analysis on chaos excited through destabilization of semiconductor lasers at period-one nonlinear dynamics for physical random number generation

This study analyzes entropy of broadband chaos excited in a semiconductor laser subject to intensity-modulated optical injection for random number generation with guaranteed unpredictability. It is identified that the flattening of spectral profile around the laser relaxation resonance blurs the periodicity it brings, and thus leads to a high entropy value and a high random number generation rate. The effect of measurement device noise on entropy suggests that both the power of chaos needs to be kept at a level to achieve an adequate signal-to-noise ratio, 24 dB or more, and the entropy contribution of the measurement device noise is excluded in order to assert entropy that can be extracted solely from the intrinsic property of chaos. The effect of data sampling rate on entropy shows that entropy reaches its maximum at the Nyquist rate, which is two times the standard bandwidth of chaos, and the rate of change in entropy is much slower than that in sampling rate as the sampling rate varies, which leads to the dominance of the sampling rate, not entropy, in determining the random number generation rate. It is highly likely that modest oversampling (i.e., a sampling rate modestly higher than the Nyquist rate) gives rise to a higher random number generation rate while entropy slightly decreases.

The impact of the colonial architecture on the urban sustainability of Laghouat city in Algeria: ksar of Laghouat as a case

Among the risks that cities are exposed to, colonization emerges as a multifaceted concern representing historical and modern dimensions that can significantly impact a city’s urban sustainability. This study explores the diverse implications of colonization on the urban sustainability with a focus on the Ksar of Laghouat in Laghouat city, Algeria. It examines the urban adaptation cycle and the imprint left by the colonial era on the fabric of the city. Utilizing the method of adaptive cycle approach and transfer entropy analysis, our goal is to quantify interaction on the historical and urban development of potential, connectedness, and resilience of Laghouat city. This study enhances the understanding of the Architectural heritage of Algeria and highlights dynamics between traditional and colonial architectural dimensions of Ksar of Laghouat. By assimilating the impact of colonization on the urban development of the city, we aim to improve the resilience and sustainability of Laghouat, through empowering its local community, and providing decision-makers with valuable sustainable strategies and adaptation mechanisms for future urban visions of the city.

Entropy analysis of a non-Darcian mixed convective flow of Cu-Al2O3-based hybrid nanofluid with thermal dispersioneffect

Entropy measures the disorderness or randomness of the systems. It may affect the effectiveness and performance of the thermal systems. That is why entropy analysis is one of the trending research topic in modern era of society. The motive of this article is to present a comprehensive analysis of entropy generation and thermal dispersion effect on mixed convective flow of (Cu-Al2O3)/(H2O) based hybrid nanofluid along a plate submerged in a non-Darcy porous medium. The mathematical model describing the flow problem encompasses a system of partial differential equation, resulting from the single-phase flow model of the nanofluid combined with the Darcy-Forchheimer expression for porous medium flow. The dimensional system of partial differential equation is transformed into a non-dimensional nonlinear ordinary differential system through a similarity transformations and subsequently, the system is solved using the BVP4C module in MATLAB. The study analyzes the flow variables and entropy generation with respect to the parameters inherent in the problem. The findings suggests that, the increasing thermal dispersion effects enhances the Heat transfer rate of the hybrid nanofluid. Further, it is reported that the entropy generation in hybrid nanofluid is lower than the mono nanofluid which makes the hybrid nanofluid a better choice for entropy management in the thermal systems. The outcome of the research has practical implications in various real-life applications, such as crude oil production, oil flow filtration, electronic cooling equipment, etc.

Entropy-based syntactic tree analysis for text classification: a novel approach to distinguishing between original and translated Chinese texts

Abstract This research focuses on classifying translated and non-translated Chinese texts by analyzing syntactic rule features, using an integrated approach of machine learning and entropy analysis. The methodology employs information entropy to gauge the complexity of syntactic rules in both text types. The methodology is based on the concept of information entropy, which serves as a quantitative measure for the complexity inherent in syntactic rules as manifested from tree-based annotations. The goal of the study is to explore whether translated Chinese texts demonstrate syntactic characteristics that are significantly different from those of non-translated texts, thereby permitting a reliable classification between the two. To do this, the research calculates information entropy values for syntactic rules in two comparable corpora, one of translated and the other of non-translated Chinese texts. Then, various machine learning models are applied to these entropy metrics to identify any significant differences between the two groups. The results show significant differences in the syntactic structures. Translated texts have a higher degree of entropy, indicating more complex syntactic constructs compared to non-translated texts. These findings contribute to our understanding of the effect of translation on language syntax, with implications for text classification and translation studies.

Melting heat transfer and entropy analysis of ternary Casson nanofluids flow with second slip conditions: Application on rocket engine cooling

Heat transfer analysis of Casson nanofluid flow with single and multi-walled carbon nanotubes and Al2O3 or GO nanoparticles, which are suspended in kerosene oil, is elucidated. The impact of second slip conditions on the flow system’s velocity, temperature, and solutal is considered, along with the effect of melting heat transfer and nanoparticle shape factor. The appraisal’s novelty is the incorporation of second slip conditions on kerosene oil flow containing with new three distinct nanoparticles. Similar variables are used to convert the governing equations into ordinary equations which are then solved using homotopy perturbation method (HPM). The profiles of velocity, temperature, concentration, and Bejan number are estimated for various values of relevant parameters. Results demonstrate that the Bejan number declines due to enhance the first thermal parameter and second velocity parameter, while the contrary tendency is examined by raising the Casson fluid parameter and first velocity parameter. Al2O3-SWCNT-MWCNT TNF responds more strongly than GO-SWCNT-MWCNT TNF when the temperature is coupled with (nanoparticles volume fraction, first thermal parameter), axial velocity with (nanoparticles volume fraction, first velocity parameter, first thermal parameter), and Bejan number with melting parameter. This study is to help rocket engine designers identify the optimal nanofluids for cooling and fuel.

Numerical energy and entropy analyses of a tube with wavy tape insert including CoFe2O4/water nanofluid under laminar regime

The primary objective of this investigation is to assess the impact of vortex generator geometry and nanofluid on thermohydraulic and irreversibility characteristics within a laminar flow regime. The study introduces an original CoFe2O4/H2O (1 % vol.) nanofluid and employs a wave tape insert to induce forced convection in a tube, accompanied by first and second-law thermodynamic analysis. The novelty of this research lies in the numerical exploration of heat transfer and flow profiles for a nanofluid in a tube, varying the wave rate (y = 4-5-6). The investigation considers the laminar model and single-phase approach in all analyses under constant heat flux (q” = 2000 W/m2). The study observed that the nanofluid flowing in the tube with a wave ratio of 4, 5, and 6 resulted in an average enhancement in the Nusselt number of 93.25 %, 86.26 %, and 80.06 %, respectively. The optimal performance evaluation criterion (PEC) for water flowing in the tube with a wave ratio of 6 at Re = 500 exhibited an increase of 11.0 %, whereas the CoFe2O4/H2O flow showed a 9.14 % increment in the average PEC along the Reynolds number. Moreover, the total entropy generation values for water flowing in tubes with wave ratios of 5, 6, and 4 exhibited increases of 101.88 %, 94.66 %, and 51.34 %, respectively, in comparison to the smooth tube.

Analysis of application of entropy methods of vibration diagnostic signal processing to assess technical condition of pipelines

The purpose of this article is to review the existing reliability problems of pipeline systems of power complexes. The article considers the existing statistical and logistics systems, which allow to process diagnostic information when assessing the technical condition of pipelines. Modern diagnostic methods are mainly based on the use of vibration, sound, and ultrasonic sensors. The presence of a defect in a pipeline is determined by analysis of the amplitude of a diagnostic signal. Higher efficiency in detecting defects was shown by probability-statistical methods of signal analysis, which are based on chaos theory. One such method is entropy analysis. Analysis of modern signal processing methods has shown that methods based on chaos theory are the most effective. The possibility of using entropy indices as sensitive diagnostic signs is considered. Comparative analysis of signal processing was carried out using entropy methods (Shannon entropy, Kolmogorov entropy) and using known statistical and logistic methods (Fourier Transform, Wavelet Transform, Hilbert-Huang Transform). The analysis results showed that entropy indicators respond to a change in signal structure caused by the presence of a defect in the pipeline or Entropy analysis is a promising method of processing diagnostic signals when assessing the technical condition of pipelines.

Numerical simulation of sudden expansion tubes with Ag-MgO nanofluid and innovative fin structure: A thermo-fluidic analysis

This study introduces an innovative approach to employing mono/hybrid nanofluids in tubes with sudden expansion, structured at various expansion angles and equipped with novel capsule-type dimpled fins. Pumping of hybrid nanofluids into sudden expansion tube combined with capsule-type dimpled fins and different expansion angles (ranging from 30° to 90°) has not been investigated so far in terms of energy, exergy, and entropy analyses. Recognizing the attention currently devoted to the climate effect of a system exposed to high thermal loads, this study sheds light on the literature how a system preferred by engineers and professionals can be cooled down efficiently to increase the performance of the system. The objective is to analyze a detailed 3E-study (energy, exergy, and entropy production) on water-based mono and hybrid nanofluids, exploring various volume fractions and combinations (including 2.0% Ag, 2.0% MgO, and blends of Ag-MgO). The study finds that a 45° expansion angle, combined with capsule-type dimpled fins and 0.5% Ag-1.5% MgO nanofluid, offers the most efficient tube design, enhancing the average Nusselt number by 20.0%. This configuration, also, reduces total entropy generation by approximately 23.0 % and shows exergy output by 26.0%, though it does lead to a 26.0% decrease in second law efficiency due to increased pumping power. Interestingly, the first law efficiency remains unchanged mainly across different nanofluid types. These findings provide valuable insights into optimizing heat transfer and fluid dynamics in engineering applications.

Comparative analysis of resting-state EEG-based multiscale entropy between schizophrenia and bipolar disorder

BackgroundStudies that use nonlinear methods to identify abnormal brain dynamics in patients with psychiatric disorders are limited. This study investigated brain dynamics based on EEG using multiscale entropy (MSE) analysis in patients with schizophrenia (SZ) and bipolar disorder (BD). MethodsThe eyes-closed resting-state EEG data were collected from 51 patients with SZ, 51 patients with BD, and 51 healthy controls (HCs). Patients with BD were further categorized into type I (n = 23) and type II (n = 16), and then compared with patients with SZ. A sample entropy-based MSE was evaluated from the bilateral frontal, central, and parieto-occipital regions using 30-s artifact-free EEG data for each individual. Correlation analyses of MSE values and psychiatric symptoms were performed. ResultsFor patients with SZ, higher MSE values were observed at higher-scale factors (i.e., 41–70) across all regions compared with both HCs and patients with BD. Furthermore, there were positive correlations between the MSE values in the left frontal and parieto-occipital regions and PANSS scores. For patients with BD, higher MSE values were observed at middle-scale factors (i.e., 13–40) in the bilateral frontal and central regions compared with HCs. Patients with BD type I exhibited higher MSE values at higher-scale factors across all regions compared with those with BD type II. In BD type I, positive correlations were found between MSE values in all left regions and YMRS scores. ConclusionsPatients with psychiatric disorders exhibited group-dependent MSE characteristics. These results suggest that MSE features may be useful biomarkers that reflect pathophysiological characteristics.

A two-dimensional chaotic model and its application in image encryption

In this paper, we propose a rule that follows a time-varying delay construction method and construct a time-varying delay scheme based on it. This construction scheme is also combined with a polynomial to obtain a novel two-dimensional chaotic model. Both mathematical analysis and experimental results show that the model satisfies the chaos condition. Good experimental results have been achieved in complexity analysis, information entropy analysis, and Auto-correlation analysis, and have certain competitiveness. The obtained chaotic model is also applied to the image encryption algorithm. The experimental results show that the encryption algorithm has high security and can effectively resist noise attacks, shear attacks, differential attacks.

Application in environmental art design practice based on a fuzzy evaluation system

Environmental art design (EAD) has recently encouraged creative thinking by investigating novel materials, technologies, and techniques for designing environmental art that advances sustainability. EAD faces challenges in integrating novel materials and technologies while promoting sustainability. Environmental art design is targeted at human living areas; here, adequate and excessive utilization of resources is minimized, and the social and natural environments are utilized aesthetically. Aesthetic excellence in environmental art design, along with growing technological accomplishments and cultural heritage, is concentrated on meeting the demands of human aesthetic pursuits in the new era, which lacks earlier techniques. Hence, an algorithm named environmental art design using fuzzy (EADF) to evaluate the environmental criteria for better decision-making is introduced. Initially, a fuzzy-based technique for order preference similar to the ideal solution (FTOPSIS), which considers multiple variables such as visual appeal, environmental impact, sustainability, and audience involvement in the community, was employed in the design process. Environmental art designers utilize fuzzy TOPSIS to assess works of art using several criteria. It seeks to make accurate decisions and accomplish desirable creative effects by considering ambiguity and subjectivity. The approach utilizes fuzzy variable entropy analysis to determine questionable attribute weightings and employs triangular fuzzy numbers to represent criteria and analyze preference values. Artworks are evaluated for deviation from ideal results using the Euclidean distance measure, enabling logical ranking evaluation and comparison. The EADF model outperforms the other models when considering different input factors. EADF excels in color (83.74), composition (82.37), emotion (85.61), contrast (97.52), clarity (98.16), harmony (95.49), and sensitivity (96.44) when evaluated in environmental art design, showcasing its usefulness. This work has implications for directing artists, designers, and decision-makers toward environmentally sustainable and artistically impactful art practices. Hence, the performance of this EADF model is validated using audience involvement, environmental impact, sustainability, and a visual appeal score.

Permutation entropy and complexity analysis of large-scale solar wind structures and streams

Abstract. In this work, we perform a statistical study of magnetic field fluctuations in the solar wind at 1 au using permutation entropy and complexity analysis and the investigation of the temporal variations of the Hurst exponents. Slow and fast wind, magnetic clouds, interplanetary coronal mass ejection (ICME)-driven sheath regions, and slow–fast stream interaction regions (SIRs) have been investigated separately. Our key finding is that there are significant differences in permutation entropy and complexity values between the solar wind types at larger timescales and little difference at small timescales. Differences become more distinct with increasing timescales, suggesting that smaller-scale turbulent features are more universal. At larger timescales, the analysis method can be used to identify localised spatial structures. We found that, except in magnetic clouds, fluctuations are largely anti-persistent and that the Hurst exponents, in particular in compressive structures (sheaths and SIRs), exhibit a clear locality. Our results shows that, in all cases apart from magnetic clouds at the largest scales, solar wind fluctuations are stochastic, with the fast wind having the highest entropies and low complexities. Magnetic clouds, in turn, exhibit the lowest entropy and highest complexity, consistent with them being coherent structures in which the magnetic field components vary in an ordered manner. SIRs, slow wind and ICME sheaths are intermediate in relation to magnetic clouds and fast wind, reflecting the increasingly ordered structure. Our results also indicate that permutation entropy–complexity analysis is a useful tool for characterising the solar wind and investigating the nature of its fluctuations.

Numerical study on natural convection in a saturated non Darcian porous medium under radiation and entropy generation effects

This work focuses on analyzing fluid flow, generation of entropy, and heat transfer during natural convection in a cavity enclosed with a non-Darcian saturated porous medium. The influence of viscous dissipation and thermal radiation are considered. The Lattice Boltzmann method is adopted to simulate the governing equations. The study discusses the general effect of dimensionless parameters on the fluid structure interaction properties, entropy generation and the thermal field. The parameters investigated include the Grashof number, Eckert number, Rayleigh number, Forchheimer Resistance, inverse Darcy, radiation parameter, and Prandtl number. The combination of studying dimensionless parameters on non-Darcian porous medium, along with the consideration of thermal radiation, viscous dissipation, and entropy analysis, has made this research valuable and worth pursuing. The findings reveal that the areas of high entropy generation are primarily located along the walls (vertical) of the cavity. Moreover, it is observed that as the inverse Darcy and Forchheimer resistance increase, their effect on the average Nusselt number diminishes for varying parameters of radiation. As the Prandtl number increases, the isotherms cluster along the walls (vertical) of the porous cavity. With high Grashof values, convection becomes turbulent, and the temperature distribution becomes non-uniform. Additionally, the entropy caused by heat and fluid friction decreases as the Forchheimer resistance increases.

An efficient image encryption model based on 6D hyperchaotic system and symmetric matrix for color and gray images

The security of images is one of the predominant pivotal aspects in the mammoth and still expanding digital domain. Due to chaotic system properties i.e. randomness and unpredictability is very appropriate to encrypt the images. In this research article, we construct an encryption model via 6D hyperchaotic map and a symmetric matrix for both color and grayscale images. We utilize the 6D hyperchaotic map in the confusion stage to change the pixel location and the symmetric matrix is used for changing the pixel value in the diffusion step for each RGB channel extraction from plain or original image. The image encryption model is checked over differential attacks (NPCR and UACI). Histogram analysis, correlation coefficients, and entropy analysis are also performed as statistical attacks. In conclusion, the image pixels are uniformly distributed, and the average entropy value are 7.9992 and 7.9973 for color and grayscale images, subsequently. The average NPCR and UACI for color images are 99.5956 and 33.4061, correspondingly, while the values for grayscale images are 99.5934 and 33.3054, respectively. These values are in the vicinity of optimal ranges. The suggested scheme's great efficiency and the proposed algorithm's resilience to a wide range of cryptanalytic attacks are implied by experimental results, statistical analysis, and differential attacks.

Bioinformatic Analysis of Topoisomerase IIα Reveals Interdomain Interdependencies and Critical C-Terminal Domain Residues.

DNA Topoisomerase IIα (Top2A) is a nuclear enzyme that is a cancer drug target, and there is interest in identifying novel sites on the enzyme to inhibit cancer cells more selectively and to reduce off-target toxicity. The C-terminal domain (CTD) is one potential target, but it is an intrinsically disordered domain, which prevents structural analysis. Therefore, we set out to analyze the sequence of Top2A from 105 species using bioinformatic analysis, including the PSICalc algorithm, Shannon entropy analysis, and other approaches. Our results demonstrate that large (10th-order) interdependent clusters are found including non-proximal positions across the major domains of Top2A. Further, CTD-specific clusters of the third, fourth, and fifth order, including positions that had been previously analyzed via mutation and biochemical assays, were identified. Some of these clusters coincided with positions that, when mutated, either increased or decreased relaxation activity. Finally, sites of low Shannon entropy (i.e., low variation in amino acids at a given site) were identified and mapped as key positions in the CTD. Included in the low-entropy sites are phosphorylation sites and charged positions. Together, these results help to build a clearer picture of the critical positions in the CTD and provide potential sites/regions for further analysis.