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DOE OSTI2023

Efficient fully-coherent quantum signal processing algorithms for real-time dynamics simulation

Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the simulation of electronic dynamics, which plays an essential role in chemical reactions, non-equilibrium dynamics, and material design. These systems are time-dependent, which requires that the corresponding simulation algorithm can be successfully concatenated with itself over different time intervals to reproduce the overall coherent quantum dynamics of the system. In this paper, we quantify such simulation algorithms by the property of being fully-coherent: the algorithm succeeds with arbitrarily high success probability 1 − δ while only requiring a single copy of the initial state. Here we subsequently develop fully-coherent simulation algorithms based on quantum signal processing (QSP), including a novel algorithm that circumvents the use of amplitude amplification while also achieving a query complexity additive in time t, ln(1/δ), and ln(1/ϵ) for error tolerance ϵ: $Θ‖\mathscr{H}‖|t|+ln(1/ϵ)+ln(1/δ)$. Furthermore, we numerically analyze these algorithms by applying them to the simulation of the spin dynamics of the Heisenberg model and the correlated electronic dynamics of an H2 molecule. Since any electronic Hamiltonian can be mapped to a spin Hamiltonian, our algorithm can efficiently simulate time-dependent ab initio electronic dynamics in the circuit model of quantum computation. Accordingly, it is also our hope that the present work serves as a bridge between QSP-based quantum algorithms and chemical dynamics, stimulating a cross-fertilization between these exciting fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Elastic cross section is entanglement entropy

We present universal relations between entanglement entropy, which quantifies the quantum correlation between subsystems, and the cross section, which is the primary observable for high-energy particle scattering, by employing a careful formulation of wave packets for the incoming particles. For 2-to-2 elastic scattering with no initial entanglement and subdividing the system along particle labels, we show that both the Rényi and Tsallis entropies in the final states are directly proportional to the elastic cross section in units of the transverse size for the initial wave packets, which is then interpreted as the elastic scattering probability. The relations do not depend on the underlying dynamics of the quantum field theory and are valid to all orders in coupling strengths. Furthermore, computing quantum correlations between momentum and nonkinematic data leads to entanglement entropies expressed as various semi-inclusive elastic cross sections. Our result gives rise to a novel “area law” for entanglement entropy in a two-body system. Published by the American Physical Society 2025

Low, Ian (ORCID:0000000275709597)↗

DOE OSTI2024

Formation of transfermium elements in reactions with Pb 208

Within the Langevin framework, we investigate the dynamics of the fusion process for production of transfermium elements in reactions of Ca 48 , Ti 50 , Cr 54 , and Fe 58 with Pb 208 . After the reacting nuclei have made contact, the early dynamical stage is dominated by the dissipation of the initial radial kinetic energy, while the subsequent shape evolution is diffusive. The probability for surmounting the inner barrier and forming a compound system is obtained by simulating the evolution as a Metropolis random walk in a five-dimensional potential-energy landscape. Good agreement with the available data is obtained, especially for the maximal formation probability. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Risk-Informed MultiPphysics BestEestimate Plus Uncertainties (BEPU) Application Development of RELAP5-3D Perturbation Model

The United States nuclear industry is facing a strong challenge to ensure maximum safety while enhancing economic benefit. Safety is a key parameter to all aspects related to light water reactor (LWR) nuclear power plants (NPPs), especially cost savings. Since the goal is to extend the lifetimes of these NPPs, the traditional deterministic safety concept may not guarantee a current economic asset. The Light Water Reactor Sustainability (LWRS) Program has been promoting a wide range of research and development (R&D) in this field to maximize the safety, economics, and performance of these NPPs through improved scientific understanding. One of the best practices to achieve this goal is to identify and optimize safety margins, which can lead to cost reduction. To do this, under the LWRS framework, the Risk-Informed Systems Analysis (RISA) Pathway will focus on the optimization of safety margin and minimization of uncertainties to ensure both safety and economics at the highest level. The RISA Pathway will provide enhanced capabilities for analyzing and characterizing LWR systems performance by developing and demonstrating methods, tools, and data to enable risk-informed margins management (RIMM). The goals of the RISA Pathway are twofold: (1) deploy the risk-informed tools and methods that enable better representation of safety margins and factors that contribute to cost and safety; and (2) conduct advanced risk assessment applications with industry to support margin management strategies that enable more cost-effective plant operation. The tools and methods provided by the RISA Pathway will support effective margin management for both active and passive safety systems, structures, and components (SSC) of an NPP. The tools and methods used in the RISA Pathway should have high confidence and highest technical maturity for and implementation to industry at its current setting. They should also have a capability to support risk-informed decision making for both probabilistic and deterministic elements of safety. The RISA Pathway will, therefore, perform a comprehensive assessment of verification and validation (V&V) status of RISA Toolkit to enhance credibility RISA Toolkit which be used by industry. This report summarizes RELAP5-3D development activities for best estimated and uncertainty (BEPU) capability to support ongoing RISA Pathway pilot projects for risk informed uncertainty quantification applications. Work scope includes (1) development of initial perturbation model for selected closure laws and (2) testing of suitable probability distribution functions (PDF) for the selected correlations. Developed BEPU modules are tested with selected separate effect cases and compared with conventional thermal-hydraulics model.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Effect of void positioning on the detonation sensitivity of a heterogeneous energetic material

We show although it is well-established that voids profoundly influence the initiation and reaction behaviors of heterogeneous energetic materials such as polymer-bonded explosives (PBX) and propellants, there has been little study of how void location in different constituents in the microstructures of such materials affect the macroscale behavior. Here, we use three-dimensional (3D) mesoscale simulations to study how void placement within the reactive grains versus the polymer binder influences the shock-to-detonation transition (SDT) in a polymer-bonded explosive. The material studied here has a microstructure comprised of 75% PETN (pentaerythritol tetranitrate) grains and 25% HTPB (hydroxyl-terminated polybutadiene) polymer binder by volume. Porosities up to 10% in the form of spherical voids distributed in both the grains and polymer are considered. An Arrhenius reactive burn relation is used to model the chemical kinetics of the PETN grains under shock loading, thereby resolving the heterogeneous detonation behavior of the PBX. The influence of void location on the shock initiation sensitivity of the material is quantitatively ranked by comparing the predicted run distance to detonation (RDD) for each sample. The analysis includes inherent quantification of uncertainties arising from the stochastic variations in the microstructure morphologies and void distributions by using statistically equivalent microstructure sample sets (SEMSS), leading to probabilistic formulations for the RDD as a function of shock pressure. The calculations reveal that the location of voids in the composite microstructure significantly affects the RDD. Specifically, voids exclusively within the grains cause the PBX to be more sensitive (having shorter RDD) than voids in the polymer binder. Unique probabilistic relationships are derived to map the probability of observing RDD for each void location material case, allowing for prediction of initiation behavior anywhere in the shock pressure – RDD space. These findings agree with trends reported in the literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

A probabilistic creep model incorporating test condition, initial damage, and material property uncertainty

Uncertainty is prevalent in the creep resistance of alloys, where at elevated temperature and low pressure, rupture can range across logarithmic decades. In this study, a probabilistic continuum-damage-mechanics (CDM)-based model is derived to capture the uncertainty of creep resistance. To meet this objective, creep data for alloy 304 Stainless Steel is gathered. A constitutive model, “Sinh”, is calibrated deterministically to determine the statistical variability of the material properties. Three sources of uncertainty are injected into the model: test condition (stress and temperature), initial damage, and material properties. Probabilistic simulations are carried out by (a) calibrating probability distribution functions (pdfs) for each source of uncertainty (b) randomly sampling the pdfs using Monte Carlo methods and (c) executing simulations to replicate the uncertain creep behavior. A sensitivity analysis is performed to evaluate the relative effect of each source of uncertainty. In full probabilistic simulations, the cumulative uncertainty of creep behavior is evaluated. The probabilistic model accurately predicts the creep deformation and rupture of the available experiments. The probabilistic model is validated for interpolation but lacks extrapolation ability. Several future works are proposed to further improve the model.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Chemomechanical weakening of muscovite quantified with in situ liquid nanoindentation

Abstract Chemomechanical weakening of layered phyllosilicate muscovite mica was studied as a function of chemical environment via in situ liquid-nanoindentation under four conditions (dry, deionized water, and two NaCl solutions of different pH). While traditional indentation analyses of layered materials with extreme mechanical anisotropy have been limited due to displacement bursts (pop-ins), here the bursts were used as proxies for delamination, fracture, and spalling events. Since displacement bursts during an indent represent a stochastic process, 120 indents were conducted for each condition to generate statistically significant amounts of data. In total, over 9000 bursts were assessed using a load–displacement threshold criterion, classifying this as a high-throughput nanoscale fracture technique. For each burst, initiation load, initiation displacement, plastic zone volume at initiation, and energy dissipation were analyzed. A power-law relationship between the burst load and burst energy was noted which separated the bursts into two continuous distributions: (1) bursts due only to the mechanics of the indent and (2) bursts due to both the mechanics of the indent and the environment. By using a cumulative probability distribution, it was found that the NaCl solutions decreased the minimum plastic zone volume necessary to initiate a displacement burst by an order of magnitude relative to the dry condition. Finally, the underlying mechanisms explaining the trends in initiation volume as a function of environment were discussed, with a focus on the chemomechanical degradation processes via chemical attack and cation exchange.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Learning Forecasts of Rare Stratospheric Transitions from Short Simulations

Abstract Rare events arising in nonlinear atmospheric dynamics remain hard to predict and attribute. We address the problem of forecasting rare events in a prototypical example, sudden stratospheric warmings (SSWs). Approximately once every other winter, the boreal stratospheric polar vortex rapidly breaks down, shifting midlatitude surface weather patterns for months. We focus on two key quantities of interest: the probability of an SSW occurring, and the expected lead time if it does occur, as functions of initial condition. These optimal forecasts concretely measure the event’s progress. Direct numerical simulation can estimate them in principle but is prohibitively expensive in practice: each rare event requires a long integration to observe, and the cost of each integration grows with model complexity. We describe an alternative approach using integrations that are short compared to the time scale of the warming event. We compute the probability and lead time efficiently by solving equations involving the transition operator, which encodes all information about the dynamics. We relate these optimal forecasts to a small number of interpretable physical variables, suggesting optimal measurements for forecasting. We illustrate the methodology on a prototype SSW model developed by Holton and Mass and modified by stochastic forcing. While highly idealized, this model captures the essential nonlinear dynamics of SSWs and exhibits the key forecasting challenge: the dramatic separation in time scales between a single event and the return time between successive events. Our methodology is designed to fully exploit high-dimensional data from models and observations, and has the potential to identify detailed predictors of many complex rare events in meteorology.

Finkel, Justin↗

DOE OSTI2020

Multi-Mechanism Flood Hazard Assessment: Critical Review of Current Practice and Approaches

This report documents the initial findings from the Nuclear Regulatory commission (NRC)-sponsored research project Methods for Estimating Joint Probabilities of Coincident and Correlated Flooding Mechanisms for Nuclear Power Plant Flood Hazard Assessments.1 This research project is a part of NRC’s Probabilistic Flood Hazard Assessment (PFHA) Research Program and will aid the development of guidance on the use of PFHA methods to evaluate infrastructure safety for existing and proposed US nuclear power plants (NPPs). More specifically, this project intends to provide technical background for the development of flood hazard curves for multi-mechanism floods (MMFs). MMFs are flood events caused by more than one flooding mechanism (e.g., flood events due to the simultaneous occurrence of precipitation-induced river flooding and storm surge). Project activities include three main tasks: Task 1—Survey of current concepts and methods in assessing MMF hazards; Task 2—Critical assessment of selected methods and approaches for quantifying probabilistic MMF hazard risk; Task 3—Development of example case studies to illustrate best practices for quantifying probabilistic MMF hazard risk The initial findings from Tasks 1 and 2 are documented in this report. Task 1 comprised a survey of approaches and methods that have been applied to understand and assess flood hazards due to MMFs. Task 2 involved a critical review of the selected approaches and methods. To that end, the scope of this report includes documentation of (1) a reconnaissance-level survey of the current state of concepts and practice for MMF hazard assessment; (2) a generalized MMF assessment framework to address the distinctions among various types of flood-forcing phenomena, flood mechanisms (grouped into three mechanism types), and flood severity metrics; (3) a wide-ranging survey of approaches and methods that have been applied to various flooding phenomena and settings; and (4) a critical assessment of MMF hazard assessment methods. Studies were identified involving MMFs related to coastal flooding mechanisms, fluvial (rivers/streams) flooding mechanisms, and associated combinations of coastal and fluvial flooding mechanisms. Studies were also identified that address MMFs involving coastal and fluvial flooding mechanisms as well as coastal flooding mechanisms along with extreme precipitation (without specific attribution to fluvial or pluvial mechanisms). The studies identified for review in this report included assessments at varying spatial scales (from local to global) with differing geographic regions of focus using both observed and synthetic data. The majority of studies identified and reviewed were site-specific assessments focusing on relatively short return periods. Studies considered a range of flood severity metrics, made differing assumptions regarding the occurrence of extrema, and used multiple statistical techniques; the use of copulas for the development of joint distributions was a particularly popular analysis technique. The literature review highlighted the differences among existing studies relative to terminology used, means of presenting results, framework and techniques employed, and level of sophistication regarding the number and types of variables considered. Despite the significant diversity in existing studies, the review identified several promising techniques that will be considered in future work under this project, including the development of joint distributions for MMFs using copula and Bayesian-motivated approaches.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2023

INVESTIGATION OF HUMAN RELIABILITY ANALYSIS METHODS FOR ANALYZING PRE-INITIATORS

As a type of human actions defined in human reliability analysis (HRA), pre-initiator refers to the human actions that may lead to the unavailability of systems, typically committed during maintenance, test, or calibration. This paper investigates representative HRA methods used for analyzing pre-initiators. The HRA methods are Technique for Human Error Rate Prediction (THERP), Korean Standard HRA (K-HRA) and Standard Plant Risk HRA (SPAR-H). In this paper, characteristics of each HRA method are compared for qualitative and quantification aspects. Two pre-initiators, i.e., a calibration task and a valve restoration task, are analyzed using the HRA methods to compare human error probabilities. Then, insights from the analysis and additional research requirements are discussed in this paper.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2021

Monte Carlo simulation of the passage of $\gamma$-rays and $\alpha$-particles in CsI

In this work, theoretical and computational methods for simulating the creation of ionization tracks by fast ions in solids were applied to the passage of a-particles in CsI, an inorganic scintillator commonly used for radiation detection. The methods were implemented in a Monte Carlo program to simulate the interaction of $\alpha$-particles, with incident energies of up to 1 MeV, with CsI. The simulations followed the fate of individual electron-hole pairs and thus allowed for a detailed description of the microscopic structure of ionization tracks created by incident radiation. Simulations were also performed with $\gamma$-rays of the same energy to compare and contrast the ionization tracks obtained with both types of particle. Intrinsic properties such as the mean energy per electron-hole pair, Fano factor, maximum theoretical light yield, and spatial distributions of electron-hole pairs were computed for both $\alpha$-particles and $\gamma$-rays. $\alpha$-particles created cylindrical tracks that were initially aligned with the incident direction and with initial radii of a few nanometers, whereas $\gamma$-rays showed significant scattering, resulting in probability distributions with lower intensities and much greater radial extents.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Blending Pipeline Analysis Tool for Hydrogen (BlendPATH) Documentation and User Manual

The Blending Pipeline Analysis Tool for Hydrogen (BlendPATH) is a flexible, open-source Python tool designed to provide users with case-by-case analysis capabilities to identify the necessary modifications to repurpose existing natural gas transmission pipeline networks to transport hydrogen as a blend of a user-specified volume fraction of hydrogen or as a pure stream and to estimate the associated capital and operating expenditures resulting from those modifications. This tool is intended to be applied during the initial screening stage of a prospective project when pipeline developers compile transmission pipeline technical documentation and history but prior to performing detailed pipeline inspections. Performing analysis with BlendPATH during this initial screening stage can provide the user with an understanding of promising opportunities and probable economic outcomes of repurposing their pipeline network for hydrogen before proceeding with detailed pipeline materials testing and pipeline inspections. BlendPATH consists of multiple modules to simulate, assess, and modify existing natural gas transmission pipeline network designs to be compatible with hydrogen as a blend or pure stream. The tool employs an open-source gas network hydraulic model to simulate existing, user-specified transmission pipeline networks, and it applies ASME B31.12 to assess the pipe segments within these networks for compatibility with hydrogen and to modify the networks to achieve compatibility where the existing infrastructure is inadequate. Users can specify ASME B31.12 design options for pipeline assessment and can select from multiple methods for pipeline modification. This report details the functionalities of BlendPATH Version 2.0.2 and demonstrates an example of applying BlendPATH to a case study. Potential and intended users of this framework include natural gas pipeline developers and operators and researchers at both public and private institutions. BlendPATH is publicly available at https://github.com/NREL/BlendPATH.

08 HYDROGEN↗

DOE OSTI2025

Probabilistic Predictions for Fastener Failure in the Sandia Mechanics Challenge Using the Discrete-Direct Uncertainty Quantification Approach

This paper documents the blind and post-blind analysis predictions for the 2023 Sandia Mechanics Challenge (SMC), which involved predicting the behavior of a threaded fastener joint structure subjected to shock loading. Utilizing repeat sets of fastener calibration data from various experimental configurations including tension, double shear, and joint tension, we developed a library of calibrated models which were propagated through the application model using the Discrete-Direct (DD) uncertainty quantification (UQ) approach. Although the initial blind predictions did not incorporate spare-sample processing to quantify fastener failure probabilities, the analyses yielded reasonable conclusions aligned with experimental results. In the post-blind analysis phase, we focused on enhancing the fidelity of the aluminum constitutive model and innovating the DD approach to obtain probabilistic predictions for fastener failure, particularly when quantities of interest (QoIs) approach their bounds. The improved aluminum model captures the behavior of the cantilever under shock loading more accurately, predicting both partial and complete cracks, although it tends to underpredict failure propagation. The enhanced DD approach facilitates probabilistic predictions that reflect the interdependent failure mechanisms of the fasteners and the cantilever, revealing that while certain fasteners are more likely to fail, the failure does not necessarily follow a progressive pattern. Overall, the post-blind analyses significantly improved the predictive capabilities of the model, providing valuable insights into the SMC application and establishing a robust foundation for informed engineering decisions. The methodology demonstrates a cost-effective and extensible approach suitable for a wide range of applications, highlighting the importance of uncertainty quantification to provide context for engineering decision making.

42 ENGINEERING↗

DOE OSTI2024

Estimating the influence of field inventory sampling intensity on forest landscape model performance for determining high-severity wildfire risk

Abstract Historically, fire has been essential in Southwestern US forests. However, a century of fire-exclusion and changing climate created forests which are more susceptible to uncharacteristically severe wildfires. Forest managers use a combination of thinning and prescribed burning to reduce forest density to help mitigate the risk of high-severity fires. These treatments are laborious and expensive, therefore optimizing their impact is crucial. Landscape simulation models can be useful in identifying high risk areas and assessing treatment effects, but uncertainties in these models can limit their utility in decision making. In this study we examined underlying uncertainties in the initial vegetation layer by leveraging a previous study from the Santa Fe fireshed and using new inventory plots from 111 stands to interpolate the initial forest conditions. We found that more inventory plots resulted in a different geographic distribution and wider range of the modelled biomass. This changed the location of areas with high probability of high-severity fires, shifting the optimal location for management. The increased range of biomass variability from using a larger number of plots to interpolate the initial vegetation layer also influenced ecosystem carbon dynamics, resulting in simulated forest conditions that had higher rates of carbon uptake. We conclude that the initial forest layer significantly affects fire and carbon dynamics and is dependent on both number of plots, and sufficient representation of the range of forest types and biomass density.

Science & Technology - Other Topics↗

DOE OSTI2024

Diagnosis of Alzheimer’s disease using plasma biomarkers adjusted to clinical probability

Abstract Recently approved anti-amyloid immunotherapies for Alzheimer’s disease (AD) require evidence of amyloid-β pathology from positron emission tomography (PET) or cerebrospinal fluid (CSF) before initiating treatment. Blood-based biomarkers promise to reduce the need for PET or CSF testing; however, their interpretation at the individual level and the circumstances requiring confirmatory testing are poorly understood. Individual-level interpretation of diagnostic test results requires knowledge of disease prevalence in relation to clinical presentation (clinical pretest probability). Here, in a study of 6,896 individuals evaluated from 11 cohort studies from six countries, we determined the positive and negative predictive value of five plasma biomarkers for amyloid-β pathology in cognitively impaired individuals in relation to clinical pretest probability. We observed that p-tau217 could rule in amyloid-β pathology in individuals with probable AD dementia (positive predictive value above 95%). In mild cognitive impairment, p-tau217 interpretation depended on patient age. Negative p-tau217 results could rule out amyloid-β pathology in individuals with non-AD dementia syndromes (negative predictive value between 90% and 99%). Our findings provide a framework for the individual-level interpretation of plasma biomarkers, suggesting that p-tau217 combined with clinical phenotyping can identify patients where amyloid-β pathology can be ruled in or out without the need for PET or CSF confirmatory testing.

Cell Biology↗

DOE OSTI2021

Leading jets and energy loss

The formation and evolution of leading jets can be described by jet functions which satisfy non-linear DGLAP-type evolution equations. Different than for inclusive jets, the leading jet functions constitute normalized probability densities for the leading jet to carry a longitudinal momentum fraction relative to the initial fragmenting parton. We present a parton shower algorithm which allows for the calculation of leading-jet cross sections where logarithms of the jet radius and threshold logarithms are resummed to next-to-leading logarithmic (NLL') accuracy. By calculating the mean of the leading jet distribution, we are able to quantify the average out-of-jet radiation, the so-called jet energy loss. When an additional reference scale is measured, we are able to determine the energy loss of leading jets at the cross section level which is identical to parton energy loss at leading-logarithmic accuracy. We identify several suitable cross sections for an extraction of the jet energy loss and we present numerical results for leading subjets at the LHC. In addition, we consider hemisphere and event-wide leading jets in electron-positron annihilation similar to measurements performed at LEP. Besides the average energy loss, we also consider its variance and other statistical quantities such as the KL divergence which quantifies the difference between quark and gluon jet energy loss. We expect that our results will be particularly relevant for quantifying the energy loss of quark and gluon jets that propagate through hot or cold nuclear matter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Multi-Mechanism Flood Hazard Assessment: Critical Review of Current Practice and Approaches

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

MAPPER – A NOVEL CAPABILITY TO SUPPORT NUCLEAR MODEL VALIDATION AND MAPPING OF BIASES AND UNCERTAINTIES

This paper overviews the initial results of a new project at the Oak Ridge National Laboratory -- supported via an internal seed funding program -- focused on the development of a novel computational capability, called MAPPER, to support model validation. The MAPPER development aims to eliminate the need for empirical criteria, such as similarity indices, often employed to identify applicable experiments for given application conditions. To achieve that, MAPPER employs an information-theoretic-based approach, based on the Kullback-Leibler (KL) divergence principle, to combine responses of available or to-be-built experiments with application responses of interest using a training set of samples generated using randomized execution of the experiments and the application high fidelity analysis models. These samples are condensed using reduced order modeling techniques in the form of a joint probability distribution function (PDF) connecting each application response of interest with a new effective experimental response. The initial focus of the MAPPER capability will be to support the confirmatory analysis required for criticality safety analysis of storage facilities which require k-eff biases to be known for safe operation. This paper reports some of the initial results obtained with MAPPER as applied to a set of critical experiments for which existing similarity-based methods have been shown to provide inaccurate estimates of the biases.

Mertyurek, Ugur↗