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At least 541 records · Page 30

Optical cone beam tomography of Cherenkov-mediated signals for fast 3D dosimetry of x-ray photon beams in water

Purpose: To test the use of a three-dimensional (3D) optical cone beam computed tomography reconstruction algorithm, for estimation of the imparted 3D dose distribution from megavoltage photon beams in a water tank for quality assurance, by imaging the induced Cherenkov-excited fluorescence (CEF). Methods: An intensified charge-coupled device coupled to a standard nontelecentric camera lens was used to tomographically acquire two-dimensional (2D) projection images of CEF from a complex multileaf collimator (MLC) shaped 6 MV linear accelerator x-ray photon beam operating at a dose rate of 600 MU/min. The resulting projections were used to reconstruct the 3D CEF light distribution, a potential surrogate of imparted dose, using a Feldkamp–Davis–Kress cone beam back reconstruction algorithm. Finally, the reconstructed light distributions were compared to the expected dose values from one-dimensional diode scans, 2D film measurements, and the 3D distribution generated from the clinical Varian ECLIPSE treatment planning system using a gamma index analysis. A Monte Carlo derived correction was applied to the Cherenkov reconstructions to account for beam hardening artifacts. Results: 3D light volumes were successfully reconstructed over a 400 × 400 × 350 mm{sup 3} volume at a resolution of 1 mm. The Cherenkov reconstructions showed agreement with all comparative methods and were also able to recover both inter- and intra-MLC leaf leakage. Based upon a 3%/3 mm criterion, the experimental Cherenkov light measurements showed an 83%–99% pass fraction depending on the chosen threshold dose. Conclusions: The results from this study demonstrate the use of optical cone beam computed tomography using CEF for the profiling of the imparted dose distribution from large area megavoltage photon beams in water.

07 ISOTOPE AND RADIATION SOURCES↗

Electromagnetic Transient Simulation Algorithms for Evaluation of Large-Scale Extreme Fast Charging Systems (Distribution Grid Models)

The distribution and transmission grids are observing an increased penetration of power electronics in loads and generations. For example, there is increasing interest in integrating in extreme fast charging (XFC) systems for fast charging of electrical vehicles. As these systems are integrated, developing high-fidelity electromagnetic transient model of XFC systems in distribution grids and evaluating their interactions with the power grid would be of significant interest. This model will be utilized for design of XFC systems, to identify upgrades in distribution and/or transmission grids, for planning purposes by transmission planners or operators or owners, among others. It can also be utilized in operations for improved reliable performance of the grid and/or XFC station. The challenge with simulating these models is the high computational complexity introduced by the large number of states present in the system and the time-step needed to simulate the system. In this paper, advanced simulations algorithms are applied to reduce the computational complexity of simulating large-scale XFC systems. The algorithms include numerical stiffness-based segregation, time constant-based segregation, clustering and aggregation on differential algebraic equations (DAEs), and multi-order integration approaches. While the first three algorithms split the matrix that needs to be inverted from a large matrix to much smaller matrices, the final algorithm reduces the computational burden of applying higher-order integration approaches in the complete system. The comparison made in the previous sentence is with respect to use of homogeneous integration approaches used in conventional electromagnetic transient simulators like power systems computer aided design (PSCAD). The approaches mentioned here have resulted in speed-up of 36x in the simulation of a single distribution system with 15 XFCs.

Debnath, Suman↗

The impact of low-Z and high-Z metal implants in IMRT: A Monte Carlo study of dose inaccuracies in commercial dose algorithms

Purpose: The aim of the study was to evaluate the dosimetric impact of low-Z and high-Z metallic implants on IMRT plans. Methods: Computed tomography (CT) scans of three patients were analyzed to study effects due to the presence of Titanium (low-Z), Platinum and Gold (high-Z) inserts. To eliminate artifacts in CT images, a sinogram-based metal artifact reduction algorithm was applied. IMRT dose calculations were performed on both the uncorrected and corrected images using a commercial planning system (convolution/superposition algorithm) and an in-house Monte Carlo platform. Dose differences between uncorrected and corrected datasets were computed and analyzed using gamma index (Pγ{sub <1}) and setting 2 mm and 2% as distance to agreement and dose difference criteria, respectively. Beam specific depth dose profiles across the metal were also examined. Results: Dose discrepancies between corrected and uncorrected datasets were not significant for low-Z material. High-Z materials caused under-dosage of 20%–25% in the region surrounding the metal and over dosage of 10%–15% downstream of the hardware. Gamma index test yielded Pγ{sub <1}>99% for all low-Z cases; while for high-Z cases it returned 91% < Pγ{sub <1}< 99%. Analysis of the depth dose curve of a single beam for low-Z cases revealed that, although the dose attenuation is altered inside the metal, it does not differ downstream of the insert. However, for high-Z metal implants the dose is increased up to 10%–12% around the insert. In addition, Monte Carlo method was more sensitive to the presence of metal inserts than superposition/convolution algorithm. Conclusions: The reduction in terms of dose of metal artifacts in CT images is relevant for high-Z implants. In this case, dose distribution should be calculated using Monte Carlo algorithms, given their superior accuracy in dose modeling in and around the metal. In addition, the knowledge of the composition of metal inserts improves the accuracy of the Monte Carlo dose calculation significantly.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Bayesian calibration of terrestrial ecosystem models: a study of advanced Markov chain Monte Carlo methods

Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results in a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. Here, the result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.

54 ENVIRONMENTAL SCIENCES↗

SU-F-SPS-11: The Dosimetric Comparison of Truebeam 2.0 and Cyberknife M6 Treatment Plans for Brain SRS Treatment

Purpose: Brain stereotactic radiosurgery involves the use of precisely directed, single session radiation to create a desired radiobiologic response within the brain target with acceptable minimal effects on surrounding structures or tissues. In this study, the dosimetric comparison of Truebeam 2.0 and Cyberknife M6 treatment plans were made. Methods: For Truebeam 2.0 machine, treatment planning were done using 2 full arc VMAT technique with 6 FFF beam on the CT scan of Randophantom simulating the treatment of sterotactic treatments for one brain metastasis. The dose distribution were calculated using Eclipse treatment planning system with Acuros XB algorithm. The treatment planning of the same target were also done for Cyberknife M6 machine with Multiplan treatment planning system using Monte Carlo algorithm. Using the same film batch, the net OD to dose calibration curve was obtained using both machine by delivering 0- 800 cGy. Films were scanned 48 hours after irradiation using an Epson 1000XL flatbed scanner. Dose distribution were measured using EBT3 film dosimeter. The measured and calculated doses were compared. Results: The dose distribution in the target and 2 cm beyond the target edge were calculated on TPSs and measured using EBT3 film. For cyberknife plans, the gamma analysis passing rates between measured and calculated dose distributions were 99.2% and 96.7% for target and peripheral region of target respectively. For Truebeam plans, the gamma analysis passing rates were 99.1% and 95.5% for target and peripheral region of target respectively. Conclusion: Although, target dose distribution calculated accurately by Acuros XB and Monte Carlo algorithms, Monte carlo calculation algorithm predicts dose distribution around the peripheral region of target more accurately than Acuros algorithm.

60 APPLIED LIFE SCIENCES↗

Distributed-Memory Fast Maximal Independent Set

The Maximal Independent Set (MIS) graph problem arises in many applications such as computer vision, information theory, molecular biology, and process scheduling. The growing scale of MIS problems suggests the use of distributed-memory hardware as a cost-effective approach to providing necessary compute and memory resources. Luby proposed four randomized algorithms to solve the MIS problem. All those algorithms are designed focusing on shared-memory machines and are analyzed using the PRAM model. These algorithms do not have direct efficient distributed-memory implementations. In this paper, we extend two of Luby’s seminal MIS algorithms, “Luby(A)” and “Luby(B),” to distributed-memory execution, and we evaluate their performance. We compare our results with the “Filtered MIS” implementation in the Combinatorial BLAS library for two types of synthetic graph inputs.

distributed memory parallel↗

ConKer: An algorithm for evaluating correlations of arbitrary order

Context. High order correlations in the cosmic matter density have become increasingly valuable in cosmological analyses. However, computing these correlation functions is computationally expensive. Aims. We aim to circumvent these challenges by developing a new algorithm called ConKer for estimating correlation functions. Methods. This algorithm performs convolutions of matter distributions with spherical kernels using FFT. Since matter distributions and kernels are defined on a grid, it results in some loss of accuracy in the distance and angle definitions. We study the algorithm setting at which these limitations become critical and suggest ways to minimize them. Results. ConKer is applied to the CMASS sample of the SDSS DR12 galaxy survey and corresponding mock catalogs, and is used to compute the correlation functions up to correlation order n = 5. We compare the n = 2 and n = 3 cases to traditional algorithms to verify the accuracy of the new algorithm. We perform a timing study of the algorithm and find that three of the four distinct processes within the algorithm are nearly independent of the catalog size N , while one subdominant component scales as O ( N ). The dominant portion of the calculation has complexity of O ( N c 4/3 log N c ), where N c is the of cells in a three-dimensional grid corresponding to the matter density. Conclusions. We find ConKer to be a fast and accurate method of probing high order correlations in the cosmic matter density, then discuss its application to upcoming surveys of large-scale structure.

79 ASTRONOMY AND ASTROPHYSICS↗

Economic Dispatch With Distributed Energy Resources: Co-Optimization of Transmission and Distribution Systems

The increasing penetration of distributed energy resources (DERs) in the distribution networks has turned the conventionally passive load buses into active buses that can provide grid services for the transmission system. To take advantage of the DERs in the distribution networks, this letter formulates a transmission-and-distribution (T&D) systems co-optimization problem that achieves economic dispatch at the transmission level and optimal voltage regulation at the distribution level by leveraging large generators and DERs. A primal-dual gradient algorithm is proposed to solve this optimization problem jointly for T&D systems, and a distributed market-based equivalent of the gradient algorithm is used for practical implementation. Finally, the results are corroborated by numerical examples with the IEEE 39-Bus system connected with 7 different distribution networks.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Large Scale Frequent Pattern Mining using MPI One-Sided Model

In this paper, we propose a work-stealing runtime --- Library for Work Stealing LibWS --- using MPI one-sided model for designing scalable FP-Growth --- {\em de facto} frequent pattern mining algorithm --- on large scale systems. LibWS provides locality efficient and highly scalable work-stealing techniques for load balancing on a variety of data distributions. We also propose a novel communication algorithm for FP-growth data exchange phase, which reduces the communication complexity from state-of-the-art O(p) to O(f + p/f) for p processes and f frequent attributed-ids. FP-Growth is implemented using LibWS and evaluated on several work distributions and support counts. An experimental evaluation of the FP-Growth on LibWS using 4096 processes on an InfiniBand Cluster demonstrates excellent efficiency for several work distributions (87\% efficiency for Power-law and 91% for Poisson). The proposed distributed FP-Tree merging algorithm provides 38x communication speedup on 4096 cores.

Vishnu, Abhinav↗

State Estimation in Low-Observable Distribution Systems Using Matrix Completion: Preprint

The need for distribution system state estimation is on the rise because of the increased penetration of distributed energy resources and flexible load. To manage the distribution systems in real time, operators need to first overcome the challenge of low observability in distribution systems. Also, because of the amount of data present from smart meters, distributed generation measurements, switches, etc., the ideal distribution state estimation methods need to be able to process heterogeneous data. In this paper, an algorithm is developed for voltage phasor estimation in low-observability distribution systems. The algorithm is based on the matrix completion approach from signal processing. The traditional matrix completion formulation is augmented with power-flow constraints to improve results while requiring less data. This method can also use all types of measurements (voltage magnitude, voltage angle, real power, reactive power) to complete the state matrix.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Collaborative operational fault tolerant control for stochastic distribution control system

Based on a class of industry processes, a distributed fault diagnosis and a collaborative operational fault tolerant control algorithms are presented for an irreversible interconnected stochastic distribution control system with boundary conditions. Different from the existed collaborative fault tolerant controllers, the controller does not need to change after fault occurs, the system tracking performance can be maintained by adjusting the setpoint of the whole system. Simulations are also included to show the effectiveness of the proposed algorithm and encouraging results have been obtained.

Stochastic distribution control, Fault diagnosis, ↗

Foundations of Feature Selection and Classification for Non-Gaussian Distributed Targets

This report describes the author’s research toward creating algorithms for selecting useful statistical features in pattern/target classification problems in which the features are non-Gaussian distributed. In engineering practice, it is common to either (1) Not perform any feature selection procedure, or (2) Use a feature selection algorithm that assumes the features are Gaussian distributed. This process can be far from optimal if the data are actually non-Gaussian, as they frequently are in practice. This research has the goal of mitigating that problem by creating a useful algorithm that can be used in practice. The approach is to focus on the performance indices used in common feature selection algorithms, such as Branch and Bound algorithms and the Sequential Forward Selection Algorithm. Ordinarily, the performance index used to measure the class separation in feature space involves assuming the data are Gaussian and deriving tractable performance indices that use closed form equations that represent the probability density functions of the class data. The advantage of this approach is that it produces feature selection algorithms that have low computational complexity and do not require knowledge of the actual data densities. The disadvantage is that these algorithms may not perform reasonably when the data are non-Gaussian, as they commonly are in practice. This research examines the use of information-theoretic class separability measures that can deal with the non-Gaussian case. In particular, this work shows that the Hellinger Distance (a divergence measure), has very desirable mathematical properties and can be useful for feature selection. The work in this paper employs a multivariate kernel density estimator along with the Hellinger Distance and an optimal subset selection algorithm to do feature selection. This report (1) Defines the classification and feature selection problems, (2) Describes the continuous variable Hellinger distance in one dimension and discusses its mathematical properties in comparison with other distance measures, (3) Develops the discrete variable Hellinger distance expression for one and two dimensions, and shows that the discrete Hellinger distance for multiple dimensions is a straightforward extension, and (4) Presents experimental density estimation results using a new MATLAB implementation of a multivariate kernel density estimator. The draft of this report served as a starting point for Ensign Matthew Wilder’s MSEE thesis work at the Naval Postgraduate School (NPS) in 2010 and 2011. Ensign Wilder completed his thesis and graduated from NPS in June 2011 (M. J. Wilder, “Automatic Target Recognition: Statistical Feature Selection of Non-Gaussian Distributed Target Classes,” MSEE Thesis, Naval Postgraduate School, Thesis Advisor: Grace A. Clark, Second Reader: Monique P. Fargues, June 2011). In the thesis, Ensign Wilder created implementations of the Branch and Bound and Sequential Feature Selection algorithms, extended the multivariate kernel density estimator code, and evaluated the performance of Hellinger Distance-based feature selection algorithms using both simulated data and data from a real-world benchmark data set. The new algorithm was shown to be very effective for both Gaussian and non-Gaussian data sets. The advantages gained for non-Gaussian data come at the cost of increased computational complexity. Using a laptop computer for practical problems, we generally use initial feature vectors containing no more than about ten or twelve features. Proposed future research lies in creating faster kernel density estimator algorithms that would allow for the use of higher dimensional data.

42 ENGINEERING↗

Resilient Information Architecture Platform for the Smart Grid (RIAPS): A Novel Open-Source Platform for Microgrid Control

Microgrids are seen as an effective way to achieve reliable, resilient, and efficient operation of the power distribution system. Core functions of the microgrid control system are defined by the IEEE standard 2030.7; however, the algorithms that realize these functions are not standardized, and are a topic of research. Furthermore, the corresponding controller hardware, operating system, and communication system to implement these functions vary significantly from one implementation to the next. In this paper, we introduce an open-source platform, Resilient Information Architecture Platform for the Smart Grid (RIAPS), ideally suited for implementing and deploying distributed microgrid control algorithms. RIAPS provides a design-time tool suite for development and deployment of distributed microgrid control algorithms. With support from a number of run-time platform services, developed algorithms can be easily implemented and deployed into real microgrids. To demonstrate the unique features of RIAPS, we propose and implement a distributed microgrid secondary control algorithm capable of synchronized and proportional compensation of voltage unbalance using distributed generators. In conclusion, test results show the effectiveness of the proposed control and the salient features of the RIAPS platform.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of the problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.

97 MATHEMATICS AND COMPUTING↗

TH-E-BRE-08: GPU-Monte Carlo Based Fast IMRT Plan Optimization

Purpose: Intensity-modulated radiation treatment (IMRT) plan optimization needs pre-calculated beamlet dose distribution. Pencil-beam or superposition/convolution type algorithms are typically used because of high computation speed. However, inaccurate beamlet dose distributions, particularly in cases with high levels of inhomogeneity, may mislead optimization, hindering the resulting plan quality. It is desire to use Monte Carlo (MC) methods for beamlet dose calculations. Yet, the long computational time from repeated dose calculations for a number of beamlets prevents this application. It is our objective to integrate a GPU-based MC dose engine in lung IMRT optimization using a novel two-steps workflow. Methods: A GPU-based MC code gDPM is used. Each particle is tagged with an index of a beamlet where the source particle is from. Deposit dose are stored separately for beamlets based on the index. Due to limited GPU memory size, a pyramid space is allocated for each beamlet, and dose outside the space is neglected. A two-steps optimization workflow is proposed for fast MC-based optimization. At first step, rough beamlet dose calculations is conducted with only a small number of particles per beamlet. Plan optimization is followed to get an approximated fluence map. In the second step, more accurate beamlet doses are calculated, where sampled number of particles for a beamlet is proportional to the intensity determined previously. A second-round optimization is conducted, yielding the final Result. Results: For a lung case with 5317 beamlets, 10{sup 5} particles per beamlet in the first round, and 10{sup 8} particles per beam in the second round are enough to get a good plan quality. The total simulation time is 96.4 sec. Conclusion: A fast GPU-based MC dose calculation method along with a novel two-step optimization workflow are developed. The high efficiency allows the use of MC for IMRT optimizations.

60 APPLIED LIFE SCIENCES↗

Spatio-Temporal Deep Graph Network for Event Detection, Localization, and Classification in Cyber-Physical Electric Distribution System

This work proposes a deep graph learning framework to identify, locate, and classify power, cyber, and cyber power events at the distribution system level. The proposed algorithm jointly exploits spatial, temporal, and node-level cyber and physical data features. The developed graph neural network, together with a deep autoencoder, utilizes physical measurements from distribution level phasor measurement units and cyber data from communication network logs. The spatial structure of the synchrophasor measurements and network is incorporated through a weighted adjacency matrix. The temporal structure is incorporated by defining a spatial operation in the gated recurrent unit. This spatio-temporal learning element resides inside a power event detection, localization, and classification module that provides the degree of confidence for an event label. To accurately pinpoint the location of an event to the nearest bus equipped with a measurement unit, a combination of squared error and proximity score is utilized. Also included is a cyber event detection module that employs heteroskedasticity to analyze the significance of various cyber features during different types of attacks. Finally, a dual-bit cyber-power decision table determines the nature of the event. The proposed method is validated on two distribution systems modeled in OPAL-RT/Hypersim with limited phasor measurement units for different possible physical and cyber events. Further analyses include comparison with other state-of-the-art methods and validation in the presence of measurement noise. As a result, our method outperforms existing approaches and achieves an average detection accuracy of 97.97%, F1-score of 96.88%, precision of 96.53%, and recall of 98.57%.

24 POWER TRANSMISSION AND DISTRIBUTION↗

TU-EF-304-12: Proton Radiation Therapy for Left-Sided Breast Cancer: LET and RBE Considerations for Cardiac Toxicity

Purpose: Increased risk of coronary artery disease has been documented for patients treated with radiation for left-sided breast cancer. Proton therapy (PRT) has been shown to significantly decrease cardiac irradiation, however variations in relative biological effectiveness (RBE) have been ignored so far. In this study we evaluate the impact of accounting for RBE variations on sensitive structures located within high linear energy transfer (LET) areas (distal end) of the proton treatment fields, for this treatment site. Methods: Three patients treated in our institution with PRT for left-sided breast cancer were selected. All patients underwent reconstructive surgery after mastectomy and treated to a total dose of 50.4Gy with beam(s) vertical to the chest wall. Dose and LET distributions were calculated using Monte Carlo (MC-TOPAS - TOol for PArticle Simulation). The LET-based, variable-RBE-weighted dose was compared to the analytical calculation algorithm (ACA) and MC dose distributions for a constant RBE of 1.1, based on volume histograms and mean values for the target, heart and left anterior descending coronary artery (LAD). Results: Assuming a constant RBE and compared to the ACA dose, MC predicted lower mean target and heart doses by 0.5% to 2.7% of the prescription dose. For variable RBE, plan evaluation showed increased mean target dose by up to 5%. Mean variable-RBE-weighted doses for the LAD ranged from 2.7 to 5.9Gy(RBE) among patients increased by 41%–64.2% compared to constant RBE ACA calculation (absolute dose: 1.7–3.9Gy(RBE)). Smaller increase in mean heart doses was noticed. Conclusion: ACA overestimates the target mean dose by up to 2.7%. However, disregarding variations in RBE may lead to significant underestimation of the dose to sensitive structures at the distal end of the proton treatment field and could thus impact outcome modeling for cardiac toxicities after proton therapy. These results are subject to RBE model and parameter uncertainties.

60 APPLIED LIFE SCIENCES↗

NEW SUNS IN THE COSMOS. III. MULTIFRACTAL SIGNATURE ANALYSIS

In the present paper, we investigate the multifractality signatures in hourly time series extracted from the CoRoT spacecraft database. Our analysis is intended to highlight the possibility that astrophysical time series can be members of a particular class of complex and dynamic processes, which require several photometric variability diagnostics to characterize their structural and topological properties. To achieve this goal, we search for contributions due to a nonlinear temporal correlation and effects caused by heavier tails than the Gaussian distribution, using a detrending moving average algorithm for one-dimensional multifractal signals (MFDMA). We observe that the correlation structure is the main source of multifractality, while heavy-tailed distribution plays a minor role in generating the multifractal effects. Our work also reveals that the rotation period of stars is inherently scaled by the degree of multifractality. As a result, analyzing the multifractal degree of the referred series, we uncover an evolution of multifractality from shorter to larger periods.

79 ASTRONOMY AND ASTROPHYSICS↗