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Ten-Year Survival Results of a Randomized Trial of Irradiation of Internal Mammary Nodes After Mastectomy
Purpose: To evaluate the efficacy of irradiation of internal mammary nodes (IMN) on 10-year overall survival in breast cancer patients after mastectomy. Methods and Patients: This multicenter phase 3 study enrolled patients with positive axillary nodes (pN+) or central/medial tumors with or without pN+. Other inclusion criteria were age <75 and a Karnofsky index ≥70. All patients received postoperative irradiation of the chest wall and supraclavicular nodes and were randomly assigned to receive IMN irradiation or not. Randomization was stratified by tumor location (medial/central or lateral), axillary lymph node status, and adjuvant therapy (chemotherapy vs no chemotherapy). The prescribed dose of irradiation to the target volumes was 50 Gy or equivalent. The first 5 intercostal spaces were included in the IMN target volume, and two-thirds of the dose (31.5 Gy) was given by electrons. The primary outcome was overall survival at 10 years. Disease-free survival and toxicity were secondary outcomes. Results: T total of 1334 patients were analyzed after a median follow-up of 11.3 years among the survivors. No benefit of IMN irradiation on the overall survival could be demonstrated: the 10-year overall survival was 59.3% in the IMN-nonirradiated group versus 62.6% in the IMN-irradiated group (P=.8). According to stratification factors, we defined 6 subgroups (medial/central or lateral tumor, pN0 [only for medial/central] or pN+, and chemotherapy or not). In all these subgroups, IMN irradiation did not significantly improve overall survival. Conclusions: In patients treated with 2-dimensional techniques, we failed to demonstrate a survival benefit for IMN irradiation. This study cannot rule out a moderate benefit, especially with more modern, conformal techniques applied to a higher risk population.
Loop current fluctuations and quantum critical transport
We study electrical transport at quantum critical points (QCPs) associated with loop current ordering in a metal, focusing specifically on models of the “Hertz-Millis” type. At the infrared (IR) fixed point and in the absence of disorder, the simplest such models have infinite DC conductivity and zero incoherent conductivity at nonzero frequencies. However, we find that a particular deformation, involving N N species of bosons and fermions with random couplings in flavor space, admits a finite incoherent, frequency-dependent conductivity at the IR fixed point, \sigma(\omega>0)\sim\omega^{-2/z} σ ( ω > 0 ) ∼ ω − 2 / z , where z z is the boson dynamical exponent. Leveraging the non-perturbative structure of quantum anomalies, we develop a powerful calculational method for transport. The resulting "anomaly-assisted large N N expansion" allows us to extract the conductivity systematically. Although our results imply that such random-flavor models are problematic as a description of the physical N = 1 N = 1 system, they serve to illustrate some general conditions for quantum critical transport as well as the anomaly-assisted calculational methods. In addition, we revisit an old result that irrelevant operators generate a frequency-dependent conductivity, \sigma(\omega>0) \sim \omega^{-2(z-2)/z} σ ( ω > 0 ) ∼ ω − 2 ( z − 2 ) / z , in problems of this kind. We show explicitly, within the scope of the original calculation, that this result does not hold for any order parameter.
Validation on Aggregate Flexibility from Residential Air Conditioning Systems for Building-to-Grid Integration
To facilitate the integration of buildings to the power grid, battery-equivalent models have been proposed to characterize and quantify aggregate flexibility from building loads. An analytical method has been proposed to construct such a flexibility model for thermostatically controlled loads. Since this analytical method is derived from a simplified representation of building thermal dynamics, it is necessary to evaluate the resulting flexibility model in a more realistic context. This paper focuses on the validation of this analytical method for estimating aggregate flexibility from residential air conditioning (ACs) systems. A high-fidelity model is first developed to mimic thermal behaviors of a residential AC system through a co-simulation between Modelica and EnergyPlus. A population of virtual residential AC systems is then generated by randomizing parameters of the high-fidelity model. Finally, an aggregate flexibility model is constructed for the residential AC population using the analytical method and validated using results from simulation of the high-fidelity model. It is found that the flexibility estimated using the analytical method is with reasonable accuracy, but can be improved by explicitly incorporating heat gains into the method.
Extracting E Versus K Effective Band Structure from Supercell Calculations on Alloys and Impurities
The supercell approach to defects and alloys has circumvented the limitations of those methods that insist on using artificially high symmetry, yet this step usually comes at the cost of abandoning the language of E versus k band dispersion. Here we describe a computational method that maps the energy eigenvalues obtained from large supercell calculations into an effective band structure (EBS) and recovers an approximate E(k) for alloys. Making use of supercells allows one to model a random alloy A{sub 1-x}B{sub x}C by occupying the sites A and B via a coin-toss procedure, affording many different local environments (polymorphic description) to occur. We present the formalism and implementation details of the method and apply it to study the evolution of the impurity band appearing in the dilute GaN:P alloy. We go beyond the perfectly random case, realizing that many alloys may have nonrandom microstructures, and investigate how their formation is reflected in the EBS. It turns out that the EBS is extremely sensitive in determining the critical disorder level for which delocalized states start to appear in the intermediate band. In addition, the EBS allows us to identify the role played by atomic relaxation in the positioning of the impurity levels.
Cryo-STEM Tomography with Inpainting
Traditionally, microscopists have worked with the Nyquist-Shannon theory of sampling, which states that to be able to reconstruct the image fully it needs to be sampled at a rate of at least twice the highest spatial frequency in the image. This sampling rate assumes that the image is sampled at regular intervals and that every pixel contains information that is crucial for the image (it even assumes that noise is important). Images in general, and especially low dose S/TEM images, contain significantly less information than can be encoded by a grid of pixels (which is why image compression works). Mathematically speaking, the image data has a low dimensional or sparse representation. Through the application of compressive sensing methods [1,2,3] this representation can be found using pre-designed measurements that are usually random for implementation simplicity. These measurements and the compressive sensing reconstruction algorithms have the added benefit of reducing noise. This reconstruction approach can be extended into higher dimensions, whereby the random sampling in each 2-D image can be extended into: a sequence of tomographic projections (i.e. tilt images); a sequence of video frames (i.e. incorporating temporal resolution and dynamics); spectral resolution (i.e. energy filtering an image to see the distribution of elements); and ptychography (i.e. sampling a full diffraction image at each location in a 2-D grid across the sample). This approach has been employed experimentally for materials science samples requiring low-dose imaging [2], and can be readily applied to biological samples. Figure 1 shows the resolution possible in a complex biological system, mouse pancreatic islet beta cells [4], when tomogram slices are reconstructed using subsampling. Reducing the number of pixels (1/6 pix and 1/3*1/3) shows minimal degradation compared to the reconstructions using all pixels (all data and 1/3 tilt). Although subsampling 1/6 of the tilts (1/6 of overall dose) degrades the reconstruction to the point that the cellular structures cannot be identified. Using 1/3 of both the pixels and the tilts provides a high quality image at 1/9 the overall dose even for this most basic and rapid demonstration of the CS methods. Figure 2 demonstrates the theoretical tomogram reconstruction quality (vertical axis) as undersampling (horizontal axis) is increased; we examined subsampling pixels and tilt-angles individually and a combined approach in which both pixels and tilts are sub-sampled. Note that subsampling pixels maintains high quality reconstructions (solid lines). Using the inpainting algorithm to obtain tomograms can automatically reduce the dose applied to the system by an order of magnitude. Perhaps the best way to understand the impact is to consider that by using inpainting (and with minimal hardware changes), a sample that can normally withstand a dose of ~10 e/Å2 can potentially be imaged with an “equivalent quality” to a dose level of 103 e/Å2. To put this in perspective, this is approaching the dose level used for the most advanced images, in terms of spatial resolution, for inorganic systems. While there are issues for biological specimens beyond dose (structural complexity being the most important one), this sampling approach allows the methods that are traditionally used for materials science to be applied to biological systems [5]. References: [1] A Stevens, H Yang, L Carin et al. Microscopy 63(1), (2014), pp. 41. [2] L Kovarik, A Stevens, A Liyu et al. Appl. Phys. Lett. 109, 164102 (2016) [3] A Stevens, L Kovarik, P Abellan et al. Adv. Structural and Chemical Imaging 1(10), (2015), pp. 1. [4] MD Guay, W Czaja, MA Aronova et al. Scientific Reports 6, 27614 (2016) [5] Supported by the Chemical Imaging, Signature Discovery, and Analytics in Motion Initiatives at PNNL. PNNL is operated by Battelle Memorial Inst. for the US DOE; contract DE-AC05-76RL01830.
Analysis of Long-Term Quality Control Data for a 137 Cs Dosimetry Calibration Source
Strict quality assurance programs are required for many radiological applications, but these seldom exist for verifying dosimetry calibration sources. After initial characterization of a dosimetry calibration facility, quality control procedures are recommended to ensure the early detection of any changes or malfunctions. These also result in refined knowledge about average dose rate and experimental variations in dose delivery. This paper describes the implementation of a phase I quality control protocol for a 137 Cs dosimetry calibration source and includes an analysis of the resulting data collected over a 24-mo period. During this time, substantial data was collected to establish trial control limits. Air kerma rate measurements were obtained using an ion chamber and were adjusted for decay, corrected for ambient temperature, pressure and humidity, and then analyzed using quality control charts. Three variations of rational subgrouping methods were used in order to find assignable causes of error, and Nelson's Rules were followed to detect any non-random statistical variations. Measurements were subgrouped according to same-day measurements in order to detect positional errors as well as atmospheric correction errors. Additionally, measurements were subgrouped according to analogous experimental setups in order to detect failure in equipment or incorrect settings. Both were analyzed using the X-bar and R chart method. Similarly, individuals and moving ranges charts were used to carefully examine each position in order to observe any situational errors that may occur which include timing, positional, or interference errors. Each method was successful in identifying unique out-of-control data points that occurred during the phase I application of forming control limits. Furthermore, over the 24-mo period, enough data points were deemed in-control to establish reliable trial limits. Future experiments will include the phase II application of gaining more reliable measurements in order to fine-tune the limits, as well as performing a designed experiment, where variables are purposefully changed in order to test the variation of the data.
Sepsis reconsidered: Identifying novel metrics for behavioral landscape characterization with a high-performance computing implementation of an agent-based model
Objectives: Sepsis affects nearly 1 million people in the United States per year, has a mortality rate of 28–50% and requires more than $20 billion a year in hospital costs. Over a quarter century of research has not yielded a single reliable diagnostic test or a directed therapeutic agent for sepsis. Central to this insufficiency is the fact that sepsis remains a clinical/physiological diagnosis representing a multitude of molecularly heterogeneous pathological trajectories. Advances in computational capabilities offered by High Peformance Computing (HPC) platforms call for an evolution in the investigation of sepsis to attempt to define the boundaries of traditional research (bench, clinical and computational) through the use of computational proxy models. We present a novel investigatory and analytical approach, derived from how HPC resources and simulation are used in the physical sciences, to identify the epistemic boundary con- ditions of the study of clinical sepsis via the use of a proxy agent-based model of systemic inflammation. Design: Current predictive models for sepsis use correlative methods that are limited by patient heterogeneity and data sparseness. We address this issue by using an HPC version of a system-level validated agent-based model of sepsis, the Innate Immune Response ABM (IIRBM), as a proxy system in order to identify boundary conditions for the possible behavioral space for sepsis. We then apply advanced analysis derived from the study of Random Dynamical Systems (RDS) to identify novel means for characterizing system behavior and providing insight into the tractability of traditional investigatory methods. Results: The behavior space of the IIRABM was examined by simulating over 70 million sepsis patients for up to 90 days in a sweep across the following parameters: cardio-respiratory-metabolic resilience; microbial invasiveness; microbial toxigenesis; and degree of nosocomial exposure. In addition to using established methods for describing parameter space, we developed two novel methods for characterizing the behavior of a RDS: Probabilistic Basins of Attraction (PBoA) and Stochastic Trajectory Analysis (STA). Computationally generated behavioral landscapes demonstrated attractor structures around stochastic re- gions of behavior that could be described in a complementary fashion through use of PBoA and STA. The stochasticity of the boundaries of the attractors highlights the challenge for correlative attempts to characterize and classify clinical sepsis. Conclusions: HPC simulations of models like the IIRABM can be used to generate approximations of the behavior space of sepsis to both establish “boundaries of futility” with respect to existing investi- gatory approaches and apply system engineering principles to investigate the general dynamic properties of sepsis to provide a pathway for developing control strategies. Here, the issues that bedevil the study and treatment of sepsis, namely clinical data sparseness and inadequate experimental sampling of system behavior space, are fundamental to nearly all biomedical research, manifesting in the “Crisis of Reproducibility” at all levels. HPC-augmented simulation-based research offers an investigatory strategy more consistent with that seen in the physical sciences (which combine experiment, theory and simulation), and an opportunity to utilize the leading advances in HPC, namely deep machine learning and evolutionary computing, to form the basis of an iterative scientific process to meet the full promise of Precision Medicine (right drug, right patient, right time).
On-the-fly generation of differential resonance scattering probability distribution functions for Monte Carlo codes
Current Monte Carlo codes use one of three models to model neutron scattering in the epithermal energy range: (1) the asymptotic scattering model, (2) the free gas scattering model, or (3) the S({alpha},{beta}) model, depending on the neutron energy and the specific Monte Carlo code. The free gas scattering model assumes the scattering cross section is constant over the neutron energy range, which is usually a good approximation for light nuclei, but not for heavy nuclei where the scattering cross section may have several resonances in the epithermal region. Several researchers in the field have shown that using the free gas scattering model in the vicinity of the resonances in the lower epithermal range can under-predict resonance absorption due to the up-scattering phenomenon. Existing methods all involve performing the collision analysis in the center-of-mass frame, followed by a conversion back to the laboratory frame. In this paper, we will present a new sampling methodology that (1) accounts for the energy-dependent scattering cross sections in the collision analysis and (2) acts in the laboratory frame, avoiding the conversion to the center-of-mass frame. The energy dependence of the scattering cross section was modeled with even-ordered polynomials to approximate the scattering cross section in Blackshaw's equations for the moments of the differential scattering PDFs. These moments were used to sample the outgoing neutron speed and angle in the laboratory frame on-the-fly during the random walk of the neutron. Results for criticality studies on fuel pin and fuel assembly calculations using these methods showed very close comparison to results using the reference Doppler-broadened rejection correction (DBRC) scheme. (authors)
Generalized Optimized Effective Potential for Orbital Functionals and Self-Consistent Calculation of Random Phase Approximations
A new self-consistent procedure for calculating the total energy with an orbital-dependent density functional approximation (DFA), the generalized optimized effective potential (GOEP), is developed in the present work. The GOEP is a nonlocal Hermitian potential that delivers the sets of occupied and virtual orbitals and minimizes the total energy. The GOEP optimization leads to the same minimum as does the orbital optimization. The GOEP method is promising as an effective optimization approach for orbital-dependent functionals, as demonstrated for the self-consistent calculations of the random phase approximation (RPA) to the correlation functionals in the particle–hole (ph) and particle–particle (pp) channels. The results show that the accuracy in describing the weakly interacting van der Waals systems is significantly improved in the self-consistent calculations. In particular, the important single excitations contribution in non-self-consistent RPA calculations can be captured self-consistently through the GOEP optimization, leading to orbital renormalization, without using the single excitations in the energy functional.
Hybrid detection of lung nodules on CT scan images
Purpose: The diversity of lung nodules poses difficulty for the current computer-aided diagnostic (CAD) schemes for lung nodule detection on computed tomography (CT) scan images, especially in large-scale CT screening studies. We proposed a novel CAD scheme based on a hybrid method to address the challenges of detection in diverse lung nodules. Methods: The hybrid method proposed in this paper integrates several existing and widely used algorithms in the field of nodule detection, including morphological operation, dot-enhancement based on Hessian matrix, fuzzy connectedness segmentation, local density maximum algorithm, geodesic distance map, and regression tree classification. All of the adopted algorithms were organized into tree structures with multi-nodes. Each node in the tree structure aimed to deal with one type of lung nodule. Results: The method has been evaluated on 294 CT scans from the Lung Image Database Consortium (LIDC) dataset. The CT scans were randomly divided into two independent subsets: a training set (196 scans) and a test set (98 scans). In total, the 294 CT scans contained 631 lung nodules, which were annotated by at least two radiologists participating in the LIDC project. The sensitivity and false positive per scan for the training set were 87% and 2.61%. The sensitivity and false positive per scan for the testing set were 85.2% and 3.13%. Conclusions: The proposed hybrid method yielded high performance on the evaluation dataset and exhibits advantages over existing CAD schemes. We believe that the present method would be useful for a wide variety of CT imaging protocols used in both routine diagnosis and screening studies.
Quality of Life in Women Undergoing Breast Irradiation in a Randomized, Controlled Clinical Trial Evaluating Different Tumor Bed Boost Fractionations
Purpose: To identify differences in breast cancer patient-reported quality of life (QOL) between 2 radiation tumor bed boost dose regimens. Methods and Materials: Four hundred patients with stage 0, I, or II breast cancer who underwent segmental mastectomy with sentinel node biopsy and/or axillary node dissection were treated with either a daily or weekly boost. Patients were treated prone to 40.5 Gy/15 fractions to the whole breast, 5 days per week. Patients were randomized to a concomitant daily boost to the tumor bed of 0.5 Gy, or a weekly boost of 2 Gy on Friday. Patients completed 6 validated QOL survey instruments at baseline, last week of treatment (3 weeks), 45-60 days from the completion of radiation treatment, and at 2-year follow-up. Results: There were no statistically significance differences in responses to the 6 QOL instruments between the daily and weekly radiation boost regimens, even after adjustment for important covariates. However, several changes in responses over time occurred in both arms, including worsening functional status, cosmetic status, and breast-specific pain at the end of treatment as compared with before and 45 to 60 days after the conclusion of treatment. Conclusions: Whole-breast, prone intensity modulated radiation has similar outcomes in QOL measures whether given with a daily or weekly boost. This trial has generated the foundation for a current study of weekly versus daily radiation boost in women with early breast cancer in which 3-dimensional conformal radiation is allowed as a prospective stratification factor.
Diffraction Methods for Qualitative and Quantitative Texture Analysis of Ferroelectric Ceramics
Crystallographic textures are pervasive in ferroelectrics and underpin the functional properties of devices utilizing these materials because many macroscopic properties (e.g., piezoelectricity) require a non-random distribution of dipoles. Inducing a preferred grain texture has become a viable route to improve these functional properties. X-ray and neutron diffraction have become valuable tools to probe crystallographic textures. This paper presents an overview of qualitative and quantitative methods for assessing crystallographic textures in electroceramics (domain and grain textures) and discusses their strengths and weaknesses.
Statistical Modeling and Analysis of k -Layer Coverage of Two-Dimensional Materials in Inkjet Printing Processes
Two-dimensional layered materials/flakes, also known as crystalline atom-thick layer nanosheets, have recently been receiving great attention in electronics fabrication due to their unique and intriguing properties. The k-layer coverage area (i.e., the area covered by k number of overlapping layers) of the printed flake pattern significantly impacts on the properties of the printed electronics. In this work, we constructed a statistical model to describe the k-layer coverage of randomly distributed two-dimensional materials. A series of results are obtained to provide not only the expectation but also the variance of the coverage area. The boundary effects on the random flakes coverage are also studied. In addition, an approximated statistical testing approach is also developed in this work to detect abnormal coverage patterns. Furthermore, the case studies based on simulated data and real flakes images obtained from the inkjet printing process demonstrate the accuracy and effectiveness of the proposed model and analysis methods.
Kinetics of State Switching in Quasi-One-Dimensional Nanosystems. Statistical Model of the Influence of Defects
The role of native and radiation-induced defects in the state switching kinetics for one-dimensional systems (nanowires, molecular single-chain magnets, biological macromolecules, and many others) has been studied. An analytical approach to the description of the influence of randomly located defects on the dynamics of new-phase domains is developed using an analogy with stochastic processes in queueing theory. This method makes it possible to calculate threshold phenomena and the dependence of switching fields on material parameters.
SU-F-T-202: An Evaluation Method of Lifetime Attributable Risk for Comparing Between Proton Beam Therapy and Intensity Modulated X-Ray Therapy for Pediatric Cancer Patients by Averaging Four Dose-Response Models for Carcinoma Induction
Purpose: To examine how much lifetime attributable risk (LAR) as an in silico surrogate marker of radiation-induced secondary cancer would be lowered by using proton beam therapy (PBT) in place of intensity modulated x-ray therapy (IMXT) in pediatric patients. Methods: From 242 pediatric patients with cancers who were treated with PBT, 26 patients were selected by random sampling after stratification into four categories: a) brain, head, and neck, b) thoracic, c) abdominal, and d) whole craniospinal (WCNS) irradiation. IMXT was re-planned using the same computed tomography and region of interest. Using dose volume histogram (DVH) of PBT and IMXT, the LAR of Schneider et al. was calculated for the same patient. The published four dose-response models for carcinoma induction: i) full model, ii) bell-shaped model, iii) plateau model, and ix) linear model were tested for organs at risk. In the case that more than one dose-response model was available, the LAR for this patient was calculated by averaging LAR for each dose-response model. Results: Calculation of the LARs of PBT and IMXT based on DVH was feasible for all patients. The mean±standard deviation of the cumulative LAR difference between PBT and IMXT for the four categories was a) 0.77±0.44% (n=7, p=0.0037), b) 23.1±17.2%,(n=8, p=0.0067), c) 16.4±19.8% (n=8, p=0.0525), and d) 49.9±21.2% (n=3, p=0.0275, one tailed t-test), respectively. The LAR was significantly lower by PBT than IMXT for the the brain, head, and neck region, thoracic region, and whole craniospinal irradiation. Conclusion: In pediatric patients who had undergone PBT, the LAR of PBT was significantly lower than the LAR of IMXT estimated by in silico modeling. This method was suggested to be useful as an in silico surrogate marker of secondary cancer induced by different radiotherapy techniques. This research was supported by the Translational Research Network Program, JSPS KAKENHI Grant No. 15H04768 and the Global Institution for Collaborative Research and Education (GI-CoRE), Hokkaido University, founded by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.
SU-F-BRD-07: Empirical Derivation of Site-Specific Margin Formulas
Purpose: To empirically derive margin formulas from existing clinical radiotherapy plans accounting for respiratory motion and setup uncertainties. Methods: We simulated realistic treatment scenarios, including respiratory motion and setup errors. Individual probability density functions (PDF) from respiratory data were used to simulate respiratory motion. Random (σ) and systematic (Σ) setup errors were modeled as Gaussian distributions. One-dimensional dose profiles were extracted from existing radiotherapy plans and convolved with respiratory PDFs and random error distributions to produce blurred dose profiles. Each blurred dose profile was then shifted 1000 times by randomly sampling the simulated systematic error distribution. Margins were determined from the distance between the simulated treatment and the original 95% isodose level. An equation was fit for each (σ, Σ) combination to derive margin formulas for 90% of the population receiving 95% dose. This methodology can be applied to different tumor sites. Here, dose profiles were extracted from partial breast 3DCRT plans in the anterior-posterior (AP) and superior-inferior (SI) directions. Respiratory motion data was from healthy volunteers, and a clinically relevant range of random and systematic setup errors (standard deviations 1 – 4 mm) was determined from the literature. Results: The PBI margin formulas in the AP and SI directions for 95% dose coverage for 90% of the population were very similar: M= 0.68σ + 1.54Σ and M= 0.72σ + 1.50Σ, respectively. Systematic setup errors had the largest influence on required margin size, whereas realistic respiratory amplitude had minimal impact. The derived formulas resulted in a smaller systematic component than commonly-used theoretical margin recipes. Conclusion: We have demonstrated a method to derive empirical margin formulas from existing patient radiotherapy plans, incorporating realistic respiratory motion and appropriate ranges of random and systematic error. Site-specific margin formulas may be better suited to patient populations than theoretically derived, ideal geometry general margin formulas.
Automatic treatment of the variance estimation bias in TRIPOLI-4 criticality calculations
The central limit (CLT) theorem States conditions under which the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed. The use of Monte Carlo transport codes, such as Tripoli4, relies on those conditions. While these are verified in protection applications (the cycles provide independent measurements of fluxes and related quantities), the hypothesis of independent estimates/cycles is broken in criticality mode. Indeed the power iteration technique used in this mode couples a generation to its progeny. Often, after what is called 'source convergence' this coupling almost disappears (the solution is closed to equilibrium) but for loosely coupled systems, such as for PWR or large nuclear cores, the equilibrium is never found, or at least may take time to reach, and the variance estimation such as allowed by the CLT is under-evaluated. In this paper we first propose, by the mean of two different methods, to evaluate the typical correlation length, as measured in cycles number, and then use this information to diagnose correlation problems and to provide an improved variance estimation. Those two methods are based on Fourier spectral decomposition and on the lag k autocorrelation calculation. A theoretical modeling of the autocorrelation function, based on Gauss-Markov stochastic processes, will also be presented. Tests will be performed with Tripoli4 on a PWR pin cell. (authors)